SET007 Axioms: SET007+865.ax


%------------------------------------------------------------------------------
% File     : SET007+865 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Godel's Completeness Theorem
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : goedelcp [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   53 (   3 unit)
%            Number of atoms       :  298 (  22 equality)
%            Maximal formula depth :   16 (   8 average)
%            Number of connectives :  263 (  18 ~  ;   5  |;  67  &)
%                                         (  27 <=>; 146 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   25 (   0 propositional; 1-4 arity)
%            Number of functors    :   43 (  12 constant; 0-4 arity)
%            Number of variables   :  136 (   0 singleton; 127 !;   9 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( v1_goedelcp(A)
      <=> ! [B] :
            ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
           => ( r1_henmodel(A,B)
              | r1_henmodel(A,k10_cqc_lang(B)) ) ) ) ) )).

fof(d2_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( v2_goedelcp(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
           => ! [C] :
                ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
               => ? [D] :
                    ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                    & r1_henmodel(A,k13_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,C)),k4_substut2(C,B,D))) ) ) ) ) ) )).

fof(t1_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( ( v1_henmodel(B)
            & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
         => ( v1_goedelcp(B)
           => ( r1_henmodel(B,A)
            <=> ~ r1_henmodel(B,k10_cqc_lang(A)) ) ) ) ) )).

fof(t2_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k13_cqc_lang(k10_cqc_lang(A),B))))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) )).

fof(t3_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( v2_goedelcp(A)
               => ( r1_henmodel(A,k16_cqc_lang(C,B))
                <=> ? [D] :
                      ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                      & r1_henmodel(A,k4_substut2(B,C,D)) ) ) ) ) ) ) )).

fof(t4_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( ( v1_henmodel(B)
            & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
         => ! [C] :
              ( m1_henmodel(C,B)
             => ( ( v1_goedelcp(B)
                  & v2_goedelcp(B) )
               => ( ( v1_goedelcp(B)
                    & v2_goedelcp(B)
                    & ~ ( r1_valuat_1(k2_henmodel,A,C,k4_henmodel)
                      <=> r1_henmodel(B,A) ) )
                  | ( r1_valuat_1(k2_henmodel,k10_cqc_lang(A),C,k4_henmodel)
                  <=> r1_henmodel(B,k10_cqc_lang(A)) ) ) ) ) ) ) )).

fof(t5_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k11_cqc_lang(A,B)))) ) ) ) ) )).

fof(t6_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( r1_henmodel(A,B)
                  & r1_henmodel(A,C) )
              <=> r1_henmodel(A,k11_cqc_lang(B,C)) ) ) ) ) )).

fof(t7_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( ( v1_henmodel(C)
                & m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang)) )
             => ! [D] :
                  ( m1_henmodel(D,C)
                 => ( ( v1_goedelcp(C)
                      & v2_goedelcp(C) )
                   => ( ( v1_goedelcp(C)
                        & v2_goedelcp(C)
                        & ~ ( r1_valuat_1(k2_henmodel,A,D,k4_henmodel)
                          <=> r1_henmodel(C,A) ) )
                      | ( v1_goedelcp(C)
                        & v2_goedelcp(C)
                        & ~ ( r1_valuat_1(k2_henmodel,B,D,k4_henmodel)
                          <=> r1_henmodel(C,B) ) )
                      | ( r1_valuat_1(k2_henmodel,k11_cqc_lang(A,B),D,k4_henmodel)
                      <=> r1_henmodel(C,k11_cqc_lang(A,B)) ) ) ) ) ) ) ) )).

fof(t8_goedelcp,axiom,(
    ! [A] :
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] :
          ( m1_henmodel(B,A)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( r1_xreal_0(k6_cqc_sim1(C),np__0)
                  & v1_goedelcp(A)
                  & v2_goedelcp(A) )
               => ( r1_valuat_1(k2_henmodel,C,B,k4_henmodel)
                <=> r1_henmodel(A,C) ) ) ) ) ) )).

fof(t9_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ! [E] :
                      ( m1_subset_1(E,k2_valuat_1(C))
                     => ( r1_valuat_1(C,k16_cqc_lang(B,A),D,E)
                      <=> ? [F] :
                            ( m1_subset_1(F,C)
                            & r1_valuat_1(C,A,D,k1_sublemma(C,E,k13_sublemma(C,F,B))) ) ) ) ) ) ) ) )).

fof(t10_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ( v1_henmodel(C)
                & m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang)) )
             => ! [D] :
                  ( m1_henmodel(D,C)
                 => ( r1_valuat_1(k2_henmodel,k16_cqc_lang(B,A),D,k4_henmodel)
                  <=> ? [E] :
                        ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                        & r1_valuat_1(k2_henmodel,k4_substut2(A,B,E),D,k4_henmodel) ) ) ) ) ) ) )).

fof(t11_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ! [E] :
                      ( m1_subset_1(E,k2_valuat_1(C))
                     => ( r1_valuat_1(C,k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))),D,E)
                      <=> r1_valuat_1(C,k15_cqc_lang(B,A),D,E) ) ) ) ) ) ) )).

fof(t12_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r1_henmodel(A,k10_cqc_lang(k16_cqc_lang(C,k10_cqc_lang(B))))
              <=> r1_henmodel(A,k15_cqc_lang(C,B)) ) ) ) ) )).

fof(t13_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => k6_cqc_sim1(k16_cqc_lang(B,A)) = k1_nat_1(k6_cqc_sim1(A),np__1) ) ) )).

fof(t14_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => k6_cqc_sim1(A) = k6_cqc_sim1(k4_substut2(A,B,C)) ) ) ) )).

fof(t15_goedelcp,axiom,(
    ! [A] :
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] :
          ( m1_henmodel(B,A)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( k6_cqc_sim1(C) = np__1
                  & v1_goedelcp(A)
                  & v2_goedelcp(A) )
               => ( r1_valuat_1(k2_henmodel,C,B,k4_henmodel)
                <=> r1_henmodel(A,C) ) ) ) ) ) )).

fof(t16_goedelcp,axiom,(
    ! [A] :
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] :
          ( m1_henmodel(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ! [D] :
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => ( ( r1_xreal_0(k6_cqc_sim1(D),C)
                        & v1_goedelcp(A)
                        & v2_goedelcp(A) )
                     => ( r1_valuat_1(k2_henmodel,D,B,k4_henmodel)
                      <=> r1_henmodel(A,D) ) ) )
               => ! [D] :
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => ( ( r1_xreal_0(k6_cqc_sim1(D),k1_nat_1(C,np__1))
                        & v1_goedelcp(A)
                        & v2_goedelcp(A) )
                     => ( r1_valuat_1(k2_henmodel,D,B,k4_henmodel)
                      <=> r1_henmodel(A,D) ) ) ) ) ) ) ) )).

fof(t17_goedelcp,axiom,(
    ! [A] :
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] :
          ( m1_henmodel(B,A)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( v1_goedelcp(A)
                  & v2_goedelcp(A) )
               => ( r1_valuat_1(k2_henmodel,C,B,k4_henmodel)
                <=> r1_henmodel(A,C) ) ) ) ) ) )).

fof(t18_goedelcp,axiom,(
    v1_card_4(k8_qc_lang1) )).

fof(d3_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( A = k1_goedelcp
      <=> ! [B] :
            ( r2_hidden(B,A)
          <=> ? [C] :
                ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
                & ? [D] :
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                    & B = k16_cqc_lang(C,D) ) ) ) ) ) )).

fof(t19_goedelcp,axiom,(
    v1_card_4(k7_cqc_lang) )).

fof(t20_goedelcp,axiom,
    ( ~ v1_xboole_0(k1_goedelcp)
    & v1_card_4(k1_goedelcp) )).

fof(d4_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang2(A)
       => ! [B] :
            ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
           => ( B = k2_goedelcp(A)
            <=> ? [C] :
                  ( m1_subset_1(C,k8_qc_lang1)
                  & A = k5_qc_lang2(B,C) ) ) ) ) ) )).

fof(d5_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ( v4_qc_lang2(A)
       => ! [B] :
            ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
           => ( B = k3_goedelcp(A)
            <=> ? [C] :
                  ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
                  & A = k16_cqc_lang(C,B) ) ) ) ) ) )).

fof(d6_goedelcp,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m2_relset_1(A,k5_numbers,k7_cqc_lang) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( C = k4_goedelcp(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => ( D = k8_funct_2(k5_numbers,k7_cqc_lang,A,B)
                     => C = k2_goedelcp(D) ) ) ) ) ) ) )).

fof(d7_goedelcp,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m2_relset_1(A,k5_numbers,k7_cqc_lang) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( C = k5_goedelcp(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => ( D = k8_funct_2(k5_numbers,k7_cqc_lang,A,B)
                     => C = k3_goedelcp(D) ) ) ) ) ) ) )).

fof(t21_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(B,A)
           => r1_henmodel(A,B) ) ) ) )).

fof(t22_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( k2_goedelcp(k16_cqc_lang(B,A)) = B
            & k3_goedelcp(k16_cqc_lang(B,A)) = A ) ) ) )).

fof(t23_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => r1_henmodel(A,k9_cqc_lang) ) )).

fof(t24_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( r1_henmodel(A,k10_cqc_lang(k9_cqc_lang))
      <=> ~ v1_henmodel(A) ) ) )).

fof(t25_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_finseq_1(B,k7_cqc_lang)
         => ! [C] :
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)))
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),C),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,B))),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ) )).

fof(t26_goedelcp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => k6_goedelcp(k6_domain_1(k7_cqc_lang,A)) = k24_qc_lang1(A) ) )).

fof(t27_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => k6_goedelcp(k4_subset_1(k7_cqc_lang,A,B)) = k4_subset_1(k2_qc_lang1,k6_goedelcp(A),k6_goedelcp(B)) ) ) )).

fof(t28_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k2_qc_lang1))
     => ~ ( v1_finset_1(A)
          & ! [B] :
              ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
             => r2_hidden(B,A) ) ) ) )).

fof(t29_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( r1_tarski(A,B)
           => r1_tarski(k6_goedelcp(A),k6_goedelcp(B)) ) ) ) )).

fof(t30_goedelcp,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k7_cqc_lang)
     => k6_goedelcp(k5_relset_1(k5_numbers,k7_cqc_lang,A)) = k3_calcul_1(A) ) )).

fof(t31_goedelcp,axiom,(
    ! [A] :
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ~ ( v1_finset_1(k6_goedelcp(A))
          & ! [B] :
              ( ( v1_henmodel(B)
                & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
             => ~ ( r1_tarski(A,B)
                  & v2_goedelcp(B) ) ) ) ) )).

fof(t32_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( r1_henmodel(A,C)
                  & r1_tarski(A,B) )
               => r1_henmodel(B,C) ) ) ) ) )).

fof(t33_goedelcp,axiom,(
    ! [A] :
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ~ ( v2_goedelcp(A)
          & ! [B] :
              ( ( v1_henmodel(B)
                & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
             => ~ ( r1_tarski(A,B)
                  & v1_goedelcp(B)
                  & v2_goedelcp(B) ) ) ) ) )).

fof(t34_goedelcp,axiom,(
    ! [A] :
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ~ ( v1_finset_1(k6_goedelcp(A))
          & ! [B] :
              ( ( v1_henmodel(B)
                & m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
             => ! [C] :
                  ( m1_henmodel(C,B)
                 => ~ r6_calcul_1(A,k2_henmodel,C,k4_henmodel) ) ) ) ) )).

fof(t35_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ! [E] :
                      ( m1_subset_1(E,k2_valuat_1(C))
                     => ( ( r6_calcul_1(A,C,D,E)
                          & r1_tarski(B,A) )
                       => r6_calcul_1(B,C,D,E) ) ) ) ) ) ) )).

fof(t36_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v1_finset_1(k6_goedelcp(A))
           => v1_finset_1(k6_goedelcp(k4_subset_1(k7_cqc_lang,A,k6_domain_1(k7_cqc_lang,B)))) ) ) ) )).

fof(t37_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ! [E] :
                      ( m1_subset_1(E,k2_valuat_1(C))
                     => ~ ( r7_calcul_1(A,B)
                          & r6_calcul_1(k4_subset_1(k7_cqc_lang,A,k6_domain_1(k7_cqc_lang,k10_cqc_lang(B))),C,D,E) ) ) ) ) ) ) )).

fof(t38_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( ( v1_finset_1(k6_goedelcp(A))
              & r7_calcul_1(A,B) )
           => r1_henmodel(A,B) ) ) ) )).

fof(dt_k1_goedelcp,axiom,(
    m1_subset_1(k1_goedelcp,k1_zfmisc_1(k7_cqc_lang)) )).

fof(dt_k2_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m2_subset_1(k2_goedelcp(A),k1_qc_lang1,k2_qc_lang1) ) )).

fof(dt_k3_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k7_cqc_lang)
     => m2_subset_1(k3_goedelcp(A),k8_qc_lang1,k7_cqc_lang) ) )).

fof(dt_k4_goedelcp,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m1_relset_1(A,k5_numbers,k7_cqc_lang)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k4_goedelcp(A,B),k1_qc_lang1,k2_qc_lang1) ) )).

fof(dt_k5_goedelcp,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k7_cqc_lang)
        & m1_relset_1(A,k5_numbers,k7_cqc_lang)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k5_goedelcp(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(dt_k6_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => m1_subset_1(k6_goedelcp(A),k1_zfmisc_1(k2_qc_lang1)) ) )).

fof(d8_goedelcp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => k6_goedelcp(A) = k3_tarski(a_1_0_goedelcp(A)) ) )).

fof(fraenkel_a_1_0_goedelcp,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
     => ( r2_hidden(A,a_1_0_goedelcp(B))
      <=> ? [C] :
            ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
            & A = k24_qc_lang1(C)
            & r2_hidden(C,B) ) ) ) )).
%------------------------------------------------------------------------------