SET007 Axioms: SET007+57.ax


%------------------------------------------------------------------------------
% File     : SET007+57 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Models and Satisfiability
% 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    : zf_model [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   60 (   9 unit)
%            Number of atoms       :  598 (  96 equality)
%            Maximal formula depth :   25 (  10 average)
%            Number of connectives :  634 (  96 ~  ;   1  |; 284  &)
%                                         (  37 <=>; 216 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :   80 (  18 constant; 0-4 arity)
%            Number of variables   :  234 (   0 singleton; 218 !;  16 ?)
%            Maximal term depth    :   11 (   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(fc1_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k3_zf_model(A)) ) )).

fof(d1_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( B = k1_zf_model(A)
        <=> ? [C] :
              ( ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ( r2_hidden(k4_tarski(k4_zf_lang(D,E),k2_tarski(D,E)),C)
                        & r2_hidden(k4_tarski(k5_zf_lang(D,E),k2_tarski(D,E)),C) ) ) )
              & r2_hidden(k4_tarski(A,B),C)
              & ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] :
                      ( r2_hidden(k4_tarski(D,E),C)
                     => ( ( v2_zf_lang(D)
                         => E = k2_tarski(k18_zf_lang(D),k19_zf_lang(D)) )
                        & ( v3_zf_lang(D)
                         => E = k2_tarski(k18_zf_lang(D),k19_zf_lang(D)) )
                        & ~ ( v4_zf_lang(D)
                            & ! [F] :
                                ~ ( E = F
                                  & r2_hidden(k4_tarski(k20_zf_lang(D),F),C) ) )
                        & ~ ( v5_zf_lang(D)
                            & ! [F,G] :
                                ~ ( E = k3_tarski(k2_tarski(F,G))
                                  & r2_hidden(k4_tarski(k21_zf_lang(D),F),C)
                                  & r2_hidden(k4_tarski(k22_zf_lang(D),G),C) ) )
                        & ~ ( v6_zf_lang(D)
                            & ! [F] :
                                ~ ( E = k4_xboole_0(k3_tarski(k1_tarski(F)),k1_tarski(k23_zf_lang(D)))
                                  & r2_hidden(k4_tarski(k24_zf_lang(D),F),C) ) ) ) ) ) ) ) ) )).

fof(t1_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ( v2_zf_lang(A)
         => k2_zf_model(A) = k2_tarski(k18_zf_lang(A),k19_zf_lang(A)) )
        & ( v3_zf_lang(A)
         => k2_zf_model(A) = k2_tarski(k18_zf_lang(A),k19_zf_lang(A)) )
        & ( v4_zf_lang(A)
         => k2_zf_model(A) = k2_zf_model(k20_zf_lang(A)) )
        & ( v5_zf_lang(A)
         => k2_zf_model(A) = k4_subset_1(k1_zf_lang,k2_zf_model(k21_zf_lang(A)),k2_zf_model(k22_zf_lang(A))) )
        & ( v6_zf_lang(A)
         => k2_zf_model(A) = k4_xboole_0(k2_zf_model(k24_zf_lang(A)),k1_tarski(k23_zf_lang(A))) ) ) ) )).

fof(d2_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( B = k3_zf_model(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,A)
                & m2_relset_1(C,k1_zf_lang,A) ) ) ) ) )).

fof(t2_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,A)
                    & m2_relset_1(D,k1_zf_lang,A) )
                 => ( k8_funct_2(k1_zf_lang,A,D,B) = k8_funct_2(k1_zf_lang,A,D,C)
                  <=> r2_hidden(D,k5_zf_model(k4_zf_lang(B,C),A)) ) ) ) ) ) )).

fof(t3_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,A)
                    & m2_relset_1(D,k1_zf_lang,A) )
                 => ( r2_hidden(k8_funct_2(k1_zf_lang,A,D,B),k8_funct_2(k1_zf_lang,A,D,C))
                  <=> r2_hidden(D,k5_zf_model(k5_zf_lang(B,C),A)) ) ) ) ) ) )).

fof(t4_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,A)
                & m2_relset_1(C,k1_zf_lang,A) )
             => ( ~ r2_hidden(C,k5_zf_model(B,A))
              <=> r2_hidden(C,k5_zf_model(k6_zf_lang(B),A)) ) ) ) ) )).

fof(t5_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,A)
                    & m2_relset_1(D,k1_zf_lang,A) )
                 => ( ( r2_hidden(D,k5_zf_model(B,A))
                      & r2_hidden(D,k5_zf_model(C,A)) )
                  <=> r2_hidden(D,k5_zf_model(k7_zf_lang(B,C),A)) ) ) ) ) ) )).

fof(t6_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,A)
                    & m2_relset_1(D,k1_zf_lang,A) )
                 => ( ( r2_hidden(D,k5_zf_model(C,A))
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k1_zf_lang,A)
                            & m2_relset_1(E,k1_zf_lang,A) )
                         => ( ! [F] :
                                ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                               => ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,D,F)
                                 => B = F ) )
                           => r2_hidden(E,k5_zf_model(C,A)) ) ) )
                  <=> r2_hidden(D,k5_zf_model(k8_zf_lang(B,C),A)) ) ) ) ) ) )).

fof(t7_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( v2_zf_lang(A)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,B)
                  & m2_relset_1(C,k1_zf_lang,B) )
               => ( k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)) = k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A))
                <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).

fof(t8_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( v3_zf_lang(A)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,B)
                  & m2_relset_1(C,k1_zf_lang,B) )
               => ( r2_hidden(k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)),k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)))
                <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).

fof(t9_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( v4_zf_lang(A)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,B)
                  & m2_relset_1(C,k1_zf_lang,B) )
               => ( ~ r2_hidden(C,k5_zf_model(k20_zf_lang(A),B))
                <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).

fof(t10_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( v5_zf_lang(A)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,B)
                  & m2_relset_1(C,k1_zf_lang,B) )
               => ( ( r2_hidden(C,k5_zf_model(k21_zf_lang(A),B))
                    & r2_hidden(C,k5_zf_model(k22_zf_lang(A),B)) )
                <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).

fof(t11_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( v6_zf_lang(A)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,B)
                  & m2_relset_1(C,k1_zf_lang,B) )
               => ( ( r2_hidden(C,k5_zf_model(k24_zf_lang(A),B))
                    & ! [D] :
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,k1_zf_lang,B)
                          & m2_relset_1(D,k1_zf_lang,B) )
                       => ( ! [E] :
                              ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                             => ( k8_funct_2(k1_zf_lang,B,D,E) != k8_funct_2(k1_zf_lang,B,C,E)
                               => k23_zf_lang(A) = E ) )
                         => r2_hidden(D,k5_zf_model(k24_zf_lang(A),B)) ) ) )
                <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).

fof(d4_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r1_zf_model(A,B,C)
              <=> r2_hidden(B,k5_zf_model(C,A)) ) ) ) ) )).

fof(t12_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k4_zf_lang(C,D))
                  <=> k8_funct_2(k1_zf_lang,A,B,C) = k8_funct_2(k1_zf_lang,A,B,D) ) ) ) ) ) )).

fof(t13_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k5_zf_lang(C,D))
                  <=> r2_hidden(k8_funct_2(k1_zf_lang,A,B,C),k8_funct_2(k1_zf_lang,A,B,D)) ) ) ) ) ) )).

fof(t14_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r1_zf_model(A,B,C)
              <=> ~ r1_zf_model(A,B,k6_zf_lang(C)) ) ) ) ) )).

fof(t15_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k7_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                      & r1_zf_model(A,B,D) ) ) ) ) ) ) )).

fof(t16_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k8_zf_lang(D,C))
                  <=> ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k1_zf_lang,A)
                          & m2_relset_1(E,k1_zf_lang,A) )
                       => ( ! [F] :
                              ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                             => ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F)
                               => D = F ) )
                         => r1_zf_model(A,E,C) ) ) ) ) ) ) ) )).

fof(t17_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k10_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                      | r1_zf_model(A,B,D) ) ) ) ) ) ) )).

fof(t18_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k11_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                     => r1_zf_model(A,B,D) ) ) ) ) ) ) )).

fof(t19_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k12_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                    <=> r1_zf_model(A,B,D) ) ) ) ) ) ) )).

fof(t20_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k13_zf_lang(D,C))
                  <=> ? [E] :
                        ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,A)
                        & m2_relset_1(E,k1_zf_lang,A)
                        & ! [F] :
                            ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                           => ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F)
                             => D = F ) )
                        & r1_zf_model(A,E,C) ) ) ) ) ) ) )).

fof(t21_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,k1_zf_lang,A)
                      & m2_relset_1(E,k1_zf_lang,A)
                      & k8_funct_2(k1_zf_lang,A,E,C) = D
                      & ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( F != C
                           => k8_funct_2(k1_zf_lang,A,E,F) = k8_funct_2(k1_zf_lang,A,B,F) ) ) ) ) ) ) ) )).

fof(t22_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,D)
                        & m2_relset_1(E,k1_zf_lang,D) )
                     => ( r1_zf_model(D,E,k14_zf_lang(B,C,A))
                      <=> ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,k1_zf_lang,D)
                              & m2_relset_1(F,k1_zf_lang,D) )
                           => ( ! [G] :
                                  ( m2_subset_1(G,k5_numbers,k1_zf_lang)
                                 => ~ ( k8_funct_2(k1_zf_lang,D,F,G) != k8_funct_2(k1_zf_lang,D,E,G)
                                      & B != G
                                      & C != G ) )
                             => r1_zf_model(D,F,A) ) ) ) ) ) ) ) ) )).

fof(t23_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,D)
                        & m2_relset_1(E,k1_zf_lang,D) )
                     => ( r1_zf_model(D,E,k15_zf_lang(B,C,A))
                      <=> ? [F] :
                            ( v1_funct_1(F)
                            & v1_funct_2(F,k1_zf_lang,D)
                            & m2_relset_1(F,k1_zf_lang,D)
                            & ! [G] :
                                ( m2_subset_1(G,k5_numbers,k1_zf_lang)
                               => ~ ( k8_funct_2(k1_zf_lang,D,F,G) != k8_funct_2(k1_zf_lang,D,E,G)
                                    & B != G
                                    & C != G ) )
                            & r1_zf_model(D,F,A) ) ) ) ) ) ) ) )).

fof(d5_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r2_zf_model(A,B)
          <=> ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,A)
                  & m2_relset_1(C,k1_zf_lang,A) )
               => r1_zf_model(A,C,B) ) ) ) ) )).

fof(t24_zf_model,axiom,(
    $true )).

fof(t25_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( r2_zf_model(C,k8_zf_lang(B,A))
              <=> r2_zf_model(C,A) ) ) ) ) )).

fof(d6_zf_model,axiom,(
    k6_zf_model = k14_zf_lang(k2_zf_lang(np__0),k2_zf_lang(np__1),k11_zf_lang(k8_zf_lang(k2_zf_lang(np__2),k12_zf_lang(k5_zf_lang(k2_zf_lang(np__2),k2_zf_lang(np__0)),k5_zf_lang(k2_zf_lang(np__2),k2_zf_lang(np__1)))),k4_zf_lang(k2_zf_lang(np__0),k2_zf_lang(np__1)))) )).

fof(d7_zf_model,axiom,(
    k7_zf_model = k14_zf_lang(k2_zf_lang(np__0),k2_zf_lang(np__1),k13_zf_lang(k2_zf_lang(np__2),k8_zf_lang(k2_zf_lang(np__3),k12_zf_lang(k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__2)),k10_zf_lang(k4_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__0)),k4_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__1))))))) )).

fof(d8_zf_model,axiom,(
    k8_zf_model = k8_zf_lang(k2_zf_lang(np__0),k13_zf_lang(k2_zf_lang(np__1),k8_zf_lang(k2_zf_lang(np__2),k12_zf_lang(k5_zf_lang(k2_zf_lang(np__2),k2_zf_lang(np__1)),k13_zf_lang(k2_zf_lang(np__3),k7_zf_lang(k5_zf_lang(k2_zf_lang(np__2),k2_zf_lang(np__3)),k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__0)))))))) )).

fof(d9_zf_model,axiom,(
    k9_zf_model = k15_zf_lang(k2_zf_lang(np__0),k2_zf_lang(np__1),k7_zf_lang(k5_zf_lang(k2_zf_lang(np__1),k2_zf_lang(np__0)),k8_zf_lang(k2_zf_lang(np__2),k11_zf_lang(k5_zf_lang(k2_zf_lang(np__2),k2_zf_lang(np__0)),k13_zf_lang(k2_zf_lang(np__3),k7_zf_lang(k7_zf_lang(k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__0)),k6_zf_lang(k4_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__2)))),k8_zf_lang(k2_zf_lang(np__4),k11_zf_lang(k5_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__2)),k5_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__3)))))))))) )).

fof(d10_zf_model,axiom,(
    k10_zf_model = k8_zf_lang(k2_zf_lang(np__0),k13_zf_lang(k2_zf_lang(np__1),k8_zf_lang(k2_zf_lang(np__2),k12_zf_lang(k5_zf_lang(k2_zf_lang(np__2),k2_zf_lang(np__1)),k8_zf_lang(k2_zf_lang(np__3),k11_zf_lang(k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__2)),k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__0)))))))) )).

fof(d11_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k11_zf_model(A) = k11_zf_lang(k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))),k8_zf_lang(k2_zf_lang(np__1),k13_zf_lang(k2_zf_lang(np__2),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(k5_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__2)),k13_zf_lang(k2_zf_lang(np__3),k7_zf_lang(k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__1)),A))))))) ) )).

fof(d12_zf_model,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_zf_model(A)
      <=> ( v1_ordinal1(A)
          & r2_zf_model(A,k7_zf_model)
          & r2_zf_model(A,k8_zf_model)
          & r2_zf_model(A,k9_zf_model)
          & r2_zf_model(A,k10_zf_model)
          & ! [B] :
              ( ( v1_zf_lang(B)
                & m2_finseq_1(B,k5_numbers) )
             => ( r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B))
               => r2_zf_model(A,k11_zf_model(B)) ) ) ) ) ) )).

fof(s1_zf_model,axiom,(
    ? [A,B] :
      ( ! [C] :
          ( m2_subset_1(C,k5_numbers,k1_zf_lang)
         => ! [D] :
              ( m2_subset_1(D,k5_numbers,k1_zf_lang)
             => ( r2_hidden(k4_tarski(k4_zf_lang(C,D),f1_s1_zf_model(C,D)),B)
                & r2_hidden(k4_tarski(k5_zf_lang(C,D),f2_s1_zf_model(C,D)),B) ) ) )
      & r2_hidden(k4_tarski(f6_s1_zf_model,A),B)
      & ! [C] :
          ( ( v1_zf_lang(C)
            & m2_finseq_1(C,k5_numbers) )
         => ! [D] :
              ( r2_hidden(k4_tarski(C,D),B)
             => ( ( v2_zf_lang(C)
                 => D = f1_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C)) )
                & ( v3_zf_lang(C)
                 => D = f2_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C)) )
                & ~ ( v4_zf_lang(C)
                    & ! [E] :
                        ~ ( D = f3_s1_zf_model(E)
                          & r2_hidden(k4_tarski(k20_zf_lang(C),E),B) ) )
                & ~ ( v5_zf_lang(C)
                    & ! [E,F] :
                        ~ ( D = f4_s1_zf_model(E,F)
                          & r2_hidden(k4_tarski(k21_zf_lang(C),E),B)
                          & r2_hidden(k4_tarski(k22_zf_lang(C),F),B) ) )
                & ~ ( v6_zf_lang(C)
                    & ! [E] :
                        ~ ( D = f5_s1_zf_model(k23_zf_lang(C),E)
                          & r2_hidden(k4_tarski(k24_zf_lang(C),E),B) ) ) ) ) ) ) )).

fof(s2_zf_model,axiom,
    ( ( ? [A] :
          ( ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => ! [C] :
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                 => ( r2_hidden(k4_tarski(k4_zf_lang(B,C),f1_s2_zf_model(B,C)),A)
                    & r2_hidden(k4_tarski(k5_zf_lang(B,C),f2_s2_zf_model(B,C)),A) ) ) )
          & r2_hidden(k4_tarski(f6_s2_zf_model,f7_s2_zf_model),A)
          & ! [B] :
              ( ( v1_zf_lang(B)
                & m2_finseq_1(B,k5_numbers) )
             => ! [C] :
                  ( r2_hidden(k4_tarski(B,C),A)
                 => ( ( v2_zf_lang(B)
                     => C = f1_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) )
                    & ( v3_zf_lang(B)
                     => C = f2_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) )
                    & ~ ( v4_zf_lang(B)
                        & ! [D] :
                            ~ ( C = f3_s2_zf_model(D)
                              & r2_hidden(k4_tarski(k20_zf_lang(B),D),A) ) )
                    & ~ ( v5_zf_lang(B)
                        & ! [D,E] :
                            ~ ( C = f4_s2_zf_model(D,E)
                              & r2_hidden(k4_tarski(k21_zf_lang(B),D),A)
                              & r2_hidden(k4_tarski(k22_zf_lang(B),E),A) ) )
                    & ~ ( v6_zf_lang(B)
                        & ! [D] :
                            ~ ( C = f5_s2_zf_model(k23_zf_lang(B),D)
                              & r2_hidden(k4_tarski(k24_zf_lang(B),D),A) ) ) ) ) ) )
      & ? [A] :
          ( ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => ! [C] :
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                 => ( r2_hidden(k4_tarski(k4_zf_lang(B,C),f1_s2_zf_model(B,C)),A)
                    & r2_hidden(k4_tarski(k5_zf_lang(B,C),f2_s2_zf_model(B,C)),A) ) ) )
          & r2_hidden(k4_tarski(f6_s2_zf_model,f8_s2_zf_model),A)
          & ! [B] :
              ( ( v1_zf_lang(B)
                & m2_finseq_1(B,k5_numbers) )
             => ! [C] :
                  ( r2_hidden(k4_tarski(B,C),A)
                 => ( ( v2_zf_lang(B)
                     => C = f1_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) )
                    & ( v3_zf_lang(B)
                     => C = f2_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) )
                    & ~ ( v4_zf_lang(B)
                        & ! [D] :
                            ~ ( C = f3_s2_zf_model(D)
                              & r2_hidden(k4_tarski(k20_zf_lang(B),D),A) ) )
                    & ~ ( v5_zf_lang(B)
                        & ! [D,E] :
                            ~ ( C = f4_s2_zf_model(D,E)
                              & r2_hidden(k4_tarski(k21_zf_lang(B),D),A)
                              & r2_hidden(k4_tarski(k22_zf_lang(B),E),A) ) )
                    & ~ ( v6_zf_lang(B)
                        & ! [D] :
                            ~ ( C = f5_s2_zf_model(k23_zf_lang(B),D)
                              & r2_hidden(k4_tarski(k24_zf_lang(B),D),A) ) ) ) ) ) ) )
   => f7_s2_zf_model = f8_s2_zf_model )).

fof(s3_zf_model,axiom,
    ( ! [A] :
        ( ( v1_zf_lang(A)
          & m2_finseq_1(A,k5_numbers) )
       => ! [B] :
            ( B = f7_s3_zf_model(A)
          <=> ? [C] :
                ( ! [D] :
                    ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                   => ! [E] :
                        ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                       => ( r2_hidden(k4_tarski(k4_zf_lang(D,E),f1_s3_zf_model(D,E)),C)
                          & r2_hidden(k4_tarski(k5_zf_lang(D,E),f2_s3_zf_model(D,E)),C) ) ) )
                & r2_hidden(k4_tarski(A,B),C)
                & ! [D] :
                    ( ( v1_zf_lang(D)
                      & m2_finseq_1(D,k5_numbers) )
                   => ! [E] :
                        ( r2_hidden(k4_tarski(D,E),C)
                       => ( ( v2_zf_lang(D)
                           => E = f1_s3_zf_model(k18_zf_lang(D),k19_zf_lang(D)) )
                          & ( v3_zf_lang(D)
                           => E = f2_s3_zf_model(k18_zf_lang(D),k19_zf_lang(D)) )
                          & ~ ( v4_zf_lang(D)
                              & ! [F] :
                                  ~ ( E = f3_s3_zf_model(F)
                                    & r2_hidden(k4_tarski(k20_zf_lang(D),F),C) ) )
                          & ~ ( v5_zf_lang(D)
                              & ! [F,G] :
                                  ~ ( E = f4_s3_zf_model(F,G)
                                    & r2_hidden(k4_tarski(k21_zf_lang(D),F),C)
                                    & r2_hidden(k4_tarski(k22_zf_lang(D),G),C) ) )
                          & ~ ( v6_zf_lang(D)
                              & ! [F] :
                                  ~ ( E = f5_s3_zf_model(k23_zf_lang(D),F)
                                    & r2_hidden(k4_tarski(k24_zf_lang(D),F),C) ) ) ) ) ) ) ) )
   => ( ( v2_zf_lang(f6_s3_zf_model)
       => f7_s3_zf_model(f6_s3_zf_model) = f1_s3_zf_model(k18_zf_lang(f6_s3_zf_model),k19_zf_lang(f6_s3_zf_model)) )
      & ( v3_zf_lang(f6_s3_zf_model)
       => f7_s3_zf_model(f6_s3_zf_model) = f2_s3_zf_model(k18_zf_lang(f6_s3_zf_model),k19_zf_lang(f6_s3_zf_model)) )
      & ( v4_zf_lang(f6_s3_zf_model)
       => f7_s3_zf_model(f6_s3_zf_model) = f3_s3_zf_model(f7_s3_zf_model(k20_zf_lang(f6_s3_zf_model))) )
      & ( v5_zf_lang(f6_s3_zf_model)
       => ! [A,B] :
            ( ( A = f7_s3_zf_model(k21_zf_lang(f6_s3_zf_model))
              & B = f7_s3_zf_model(k22_zf_lang(f6_s3_zf_model)) )
           => f7_s3_zf_model(f6_s3_zf_model) = f4_s3_zf_model(A,B) ) )
      & ( v6_zf_lang(f6_s3_zf_model)
       => f7_s3_zf_model(f6_s3_zf_model) = f5_s3_zf_model(k23_zf_lang(f6_s3_zf_model),f7_s3_zf_model(k24_zf_lang(f6_s3_zf_model))) ) ) )).

fof(s4_zf_model,axiom,
    ( ( ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ! [B] :
              ( B = f6_s4_zf_model(A)
            <=> ? [C] :
                  ( ! [D] :
                      ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                     => ! [E] :
                          ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                         => ( r2_hidden(k4_tarski(k4_zf_lang(D,E),f1_s4_zf_model(D,E)),C)
                            & r2_hidden(k4_tarski(k5_zf_lang(D,E),f2_s4_zf_model(D,E)),C) ) ) )
                  & r2_hidden(k4_tarski(A,B),C)
                  & ! [D] :
                      ( ( v1_zf_lang(D)
                        & m2_finseq_1(D,k5_numbers) )
                     => ! [E] :
                          ( r2_hidden(k4_tarski(D,E),C)
                         => ( ( v2_zf_lang(D)
                             => E = f1_s4_zf_model(k18_zf_lang(D),k19_zf_lang(D)) )
                            & ( v3_zf_lang(D)
                             => E = f2_s4_zf_model(k18_zf_lang(D),k19_zf_lang(D)) )
                            & ~ ( v4_zf_lang(D)
                                & ! [F] :
                                    ~ ( E = f3_s4_zf_model(F)
                                      & r2_hidden(k4_tarski(k20_zf_lang(D),F),C) ) )
                            & ~ ( v5_zf_lang(D)
                                & ! [F,G] :
                                    ~ ( E = f4_s4_zf_model(F,G)
                                      & r2_hidden(k4_tarski(k21_zf_lang(D),F),C)
                                      & r2_hidden(k4_tarski(k22_zf_lang(D),G),C) ) )
                            & ~ ( v6_zf_lang(D)
                                & ! [F] :
                                    ~ ( E = f5_s4_zf_model(k23_zf_lang(D),F)
                                      & r2_hidden(k4_tarski(k24_zf_lang(D),F),C) ) ) ) ) ) ) ) )
      & ! [A] :
          ( m2_subset_1(A,k5_numbers,k1_zf_lang)
         => ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => ( p1_s4_zf_model(f1_s4_zf_model(A,B))
                & p1_s4_zf_model(f2_s4_zf_model(A,B)) ) ) )
      & ! [A] :
          ( p1_s4_zf_model(A)
         => p1_s4_zf_model(f3_s4_zf_model(A)) )
      & ! [A,B] :
          ( ( p1_s4_zf_model(A)
            & p1_s4_zf_model(B) )
         => p1_s4_zf_model(f4_s4_zf_model(A,B)) )
      & ! [A,B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ( p1_s4_zf_model(A)
           => p1_s4_zf_model(f5_s4_zf_model(B,A)) ) ) )
   => p1_s4_zf_model(f6_s4_zf_model(f7_s4_zf_model)) )).

fof(dt_k1_zf_model,axiom,(
    $true )).

fof(dt_k2_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m1_subset_1(k2_zf_model(A),k1_zfmisc_1(k1_zf_lang)) ) )).

fof(redefinition_k2_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => k2_zf_model(A) = k1_zf_model(A) ) )).

fof(dt_k3_zf_model,axiom,(
    $true )).

fof(dt_k4_zf_model,axiom,(
    $true )).

fof(dt_k5_zf_model,axiom,(
    ! [A,B] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B) )
     => m1_subset_1(k5_zf_model(A,B),k1_zfmisc_1(k3_zf_model(B))) ) )).

fof(redefinition_k5_zf_model,axiom,(
    ! [A,B] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B) )
     => k5_zf_model(A,B) = k4_zf_model(A,B) ) )).

fof(dt_k6_zf_model,axiom,
    ( v1_zf_lang(k6_zf_model)
    & m2_finseq_1(k6_zf_model,k5_numbers) )).

fof(dt_k7_zf_model,axiom,
    ( v1_zf_lang(k7_zf_model)
    & m2_finseq_1(k7_zf_model,k5_numbers) )).

fof(dt_k8_zf_model,axiom,
    ( v1_zf_lang(k8_zf_model)
    & m2_finseq_1(k8_zf_model,k5_numbers) )).

fof(dt_k9_zf_model,axiom,
    ( v1_zf_lang(k9_zf_model)
    & m2_finseq_1(k9_zf_model,k5_numbers) )).

fof(dt_k10_zf_model,axiom,
    ( v1_zf_lang(k10_zf_model)
    & m2_finseq_1(k10_zf_model,k5_numbers) )).

fof(dt_k11_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k11_zf_model(A))
        & m2_finseq_1(k11_zf_model(A),k5_numbers) ) ) )).

fof(d3_zf_model,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( C = k4_zf_model(A,B)
            <=> ? [D] :
                  ( ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( r2_hidden(k4_tarski(k4_zf_lang(E,F),a_3_0_zf_model(B,E,F)),D)
                            & r2_hidden(k4_tarski(k5_zf_lang(E,F),a_3_1_zf_model(B,E,F)),D) ) ) )
                  & r2_hidden(k4_tarski(A,C),D)
                  & ! [E] :
                      ( ( v1_zf_lang(E)
                        & m2_finseq_1(E,k5_numbers) )
                     => ! [F] :
                          ( r2_hidden(k4_tarski(E,F),D)
                         => ( ( v2_zf_lang(E)
                             => F = a_2_0_zf_model(B,E) )
                            & ( v3_zf_lang(E)
                             => F = a_2_1_zf_model(B,E) )
                            & ~ ( v4_zf_lang(E)
                                & ! [G] :
                                    ~ ( F = k4_xboole_0(k3_zf_model(B),k3_tarski(k1_tarski(G)))
                                      & r2_hidden(k4_tarski(k20_zf_lang(E),G),D) ) )
                            & ~ ( v5_zf_lang(E)
                                & ! [G,H] :
                                    ~ ( F = k3_xboole_0(k3_tarski(k1_tarski(G)),k3_tarski(k1_tarski(H)))
                                      & r2_hidden(k4_tarski(k21_zf_lang(E),G),D)
                                      & r2_hidden(k4_tarski(k22_zf_lang(E),H),D) ) )
                            & ~ ( v6_zf_lang(E)
                                & ! [G] :
                                    ~ ( F = a_3_2_zf_model(B,E,G)
                                      & r2_hidden(k4_tarski(k24_zf_lang(E),G),D) ) ) ) ) ) ) ) ) ) )).

fof(fraenkel_a_3_0_zf_model,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & m2_subset_1(C,k5_numbers,k1_zf_lang)
        & m2_subset_1(D,k5_numbers,k1_zf_lang) )
     => ( r2_hidden(A,a_3_0_zf_model(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k3_zf_model(B))
            & A = E
            & ! [F] :
                ( ( v1_funct_1(F)
                  & v1_funct_2(F,k1_zf_lang,B)
                  & m2_relset_1(F,k1_zf_lang,B) )
               => ( F = E
                 => k8_funct_2(k1_zf_lang,B,F,C) = k8_funct_2(k1_zf_lang,B,F,D) ) ) ) ) ) )).

fof(fraenkel_a_3_1_zf_model,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & m2_subset_1(C,k5_numbers,k1_zf_lang)
        & m2_subset_1(D,k5_numbers,k1_zf_lang) )
     => ( r2_hidden(A,a_3_1_zf_model(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k3_zf_model(B))
            & A = E
            & ! [F] :
                ( ( v1_funct_1(F)
                  & v1_funct_2(F,k1_zf_lang,B)
                  & m2_relset_1(F,k1_zf_lang,B) )
               => ( F = E
                 => r2_hidden(k8_funct_2(k1_zf_lang,B,F,C),k8_funct_2(k1_zf_lang,B,F,D)) ) ) ) ) ) )).

fof(fraenkel_a_2_0_zf_model,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_zf_lang(C)
        & m2_finseq_1(C,k5_numbers) )
     => ( r2_hidden(A,a_2_0_zf_model(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k3_zf_model(B))
            & A = D
            & ! [E] :
                ( ( v1_funct_1(E)
                  & v1_funct_2(E,k1_zf_lang,B)
                  & m2_relset_1(E,k1_zf_lang,B) )
               => ( E = D
                 => k8_funct_2(k1_zf_lang,B,E,k18_zf_lang(C)) = k8_funct_2(k1_zf_lang,B,E,k19_zf_lang(C)) ) ) ) ) ) )).

fof(fraenkel_a_2_1_zf_model,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_zf_lang(C)
        & m2_finseq_1(C,k5_numbers) )
     => ( r2_hidden(A,a_2_1_zf_model(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k3_zf_model(B))
            & A = D
            & ! [E] :
                ( ( v1_funct_1(E)
                  & v1_funct_2(E,k1_zf_lang,B)
                  & m2_relset_1(E,k1_zf_lang,B) )
               => ( E = D
                 => r2_hidden(k8_funct_2(k1_zf_lang,B,E,k18_zf_lang(C)),k8_funct_2(k1_zf_lang,B,E,k19_zf_lang(C))) ) ) ) ) ) )).

fof(fraenkel_a_3_2_zf_model,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_zf_lang(C)
        & m2_finseq_1(C,k5_numbers) )
     => ( r2_hidden(A,a_3_2_zf_model(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k3_zf_model(B))
            & A = E
            & ! [F,G] :
                ( ( v1_funct_1(G)
                  & v1_funct_2(G,k1_zf_lang,B)
                  & m2_relset_1(G,k1_zf_lang,B) )
               => ( ( F = D
                    & G = E )
                 => ( r2_hidden(G,F)
                    & ! [H] :
                        ( ( v1_funct_1(H)
                          & v1_funct_2(H,k1_zf_lang,B)
                          & m2_relset_1(H,k1_zf_lang,B) )
                       => ( ! [I] :
                              ( m2_subset_1(I,k5_numbers,k1_zf_lang)
                             => ( k8_funct_2(k1_zf_lang,B,H,I) != k8_funct_2(k1_zf_lang,B,G,I)
                               => k23_zf_lang(C) = I ) )
                         => r2_hidden(H,F) ) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------