SET007 Axioms: SET007+115.ax


%------------------------------------------------------------------------------
% File     : SET007+115 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Definable Functions
% 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    : zfmodel2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   25 (   0 unit)
%            Number of atoms       :  298 (  38 equality)
%            Maximal formula depth :   31 (  14 average)
%            Number of connectives :  330 (  57 ~  ;  11  |; 113  &)
%                                         (   8 <=>; 141 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   19 (   0 propositional; 1-3 arity)
%            Number of functors    :   31 (   8 constant; 0-4 arity)
%            Number of variables   :  120 (   0 singleton; 118 !;   2 ?)
%            Maximal term depth    :    7 (   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(t1_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B))) ) ) ) )).

fof(t2_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( ~ r2_hidden(A,k4_zf_lang1(C))
               => ( ( r2_hidden(B,k2_zf_model(C))
                   => k2_zf_model(k6_zf_lang1(C,B,A)) = k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(B)),k1_tarski(A)) )
                  & ( ~ r2_hidden(B,k2_zf_model(C))
                   => k2_zf_model(k6_zf_lang1(C,B,A)) = k2_zf_model(C) ) ) ) ) ) ) )).

fof(t3_zfmodel2,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => v1_finset_1(k4_zf_lang1(A)) ) )).

fof(t4_zfmodel2,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ? [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( r2_hidden(k2_zf_lang(C),k4_zf_lang1(A))
                    & r1_xreal_0(B,C) ) ) )
        & ~ ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => r2_hidden(B,k4_zf_lang1(A)) ) ) ) )).

fof(t5_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,B)
                    & m2_relset_1(D,k1_zf_lang,B) )
                 => ( ~ r2_hidden(A,k4_zf_lang1(C))
                   => ( r1_zf_model(B,D,C)
                    <=> r1_zf_model(B,D,k8_zf_lang(A,C)) ) ) ) ) ) ) )).

fof(t6_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,B)
                        & m2_relset_1(E,k1_zf_lang,B) )
                     => ( ~ r2_hidden(A,k4_zf_lang1(D))
                       => ( r1_zf_model(B,E,D)
                        <=> r1_zf_model(B,k1_zf_lang1(B,E,A,C),D) ) ) ) ) ) ) ) )).

fof(t7_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [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] :
                      ( m1_subset_1(E,D)
                     => ! [F] :
                          ( m1_subset_1(F,D)
                         => ! [G] :
                              ( m1_subset_1(G,D)
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k1_zf_lang,D)
                                    & m2_relset_1(H,k1_zf_lang,D) )
                                 => ~ ( A != B
                                      & B != C
                                      & C != A
                                      & ~ ( k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,A,E),B,F),C,G) = k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,C,G),B,F),A,E)
                                          & k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,A,E),B,F),C,G) = k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,B,F),C,G),A,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t8_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( ~ v1_xboole_0(E)
                     => ! [F] :
                          ( m1_subset_1(F,E)
                         => ! [G] :
                              ( m1_subset_1(G,E)
                             => ! [H] :
                                  ( m1_subset_1(H,E)
                                 => ! [I] :
                                      ( m1_subset_1(I,E)
                                     => ! [J] :
                                          ( ( v1_funct_1(J)
                                            & v1_funct_2(J,k1_zf_lang,E)
                                            & m2_relset_1(J,k1_zf_lang,E) )
                                         => ~ ( A != B
                                              & A != C
                                              & A != D
                                              & B != C
                                              & B != D
                                              & C != D
                                              & ~ ( k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,A,F),B,G),C,H),D,I) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,B,G),C,H),D,I),A,F)
                                                  & k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,A,F),B,G),C,H),D,I) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,C,H),D,I),A,F),B,G)
                                                  & k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,A,F),B,G),C,H),D,I) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,D,I),B,G),C,H),A,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t9_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( ~ v1_xboole_0(E)
                     => ! [F] :
                          ( m1_subset_1(F,E)
                         => ! [G] :
                              ( m1_subset_1(G,E)
                             => ! [H] :
                                  ( m1_subset_1(H,E)
                                 => ! [I] :
                                      ( m1_subset_1(I,E)
                                     => ! [J] :
                                          ( m1_subset_1(J,E)
                                         => ! [K] :
                                              ( ( v1_funct_1(K)
                                                & v1_funct_2(K,k1_zf_lang,E)
                                                & m2_relset_1(K,k1_zf_lang,E) )
                                             => ( k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),A,H)
                                                & k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),C,I),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),C,I),A,H)
                                                & k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),C,I),D,J),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),C,I),D,J),A,H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t10_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,B)
                        & m2_relset_1(E,k1_zf_lang,B) )
                     => ( ~ r2_hidden(A,k2_zf_model(D))
                       => ( r1_zf_model(B,E,D)
                        <=> r1_zf_model(B,k1_zf_lang1(B,E,A,C),D) ) ) ) ) ) ) ) )).

fof(t11_zfmodel2,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) )
             => ( r1_zf_model(A,C,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(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
               => ( r2_hidden(k2_zf_lang(np__0),k2_zf_model(B))
                  | ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => ( k8_funct_2(A,A,k1_zfmodel1(B,A,C),D) = E
                          <=> r1_zf_model(A,k1_zf_lang1(A,k1_zf_lang1(A,C,k2_zf_lang(np__3),D),k2_zf_lang(np__4),E),B) ) ) ) ) ) ) ) ) )).

fof(t12_zfmodel2,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) )
             => ( ( r1_tarski(k2_zf_model(B),k2_tarski(k2_zf_lang(np__3),k2_zf_lang(np__4)))
                  & r2_zf_model(A,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(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) )
               => k1_zfmodel1(B,A,C) = k2_zfmodel1(B,A) ) ) ) ) )).

fof(t13_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,C)
                        & m2_relset_1(E,k1_zf_lang,C) )
                     => ( ~ r2_hidden(A,k4_zf_lang1(D))
                       => ( r1_zf_model(C,E,k6_zf_lang1(D,B,A))
                        <=> r1_zf_model(C,k1_zf_lang1(C,E,B,k8_funct_2(k1_zf_lang,C,E,A)),D) ) ) ) ) ) ) ) )).

fof(t14_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,C)
                        & m2_relset_1(E,k1_zf_lang,C) )
                     => ( r1_zf_model(C,E,D)
                       => ( r2_hidden(A,k4_zf_lang1(D))
                          | r1_zf_model(C,k1_zf_lang1(C,E,A,k8_funct_2(k1_zf_lang,C,E,B)),k6_zf_lang1(D,B,A)) ) ) ) ) ) ) ) )).

fof(t15_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,C)
                        & m2_relset_1(E,k1_zf_lang,C) )
                     => ( r1_zf_model(C,E,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(D,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                       => ( r2_hidden(k2_zf_lang(np__0),k2_zf_model(D))
                          | r2_hidden(A,k4_zf_lang1(D))
                          | B = k2_zf_lang(np__3)
                          | B = k2_zf_lang(np__4)
                          | r2_hidden(B,k2_zf_model(D))
                          | A = k2_zf_lang(np__0)
                          | A = k2_zf_lang(np__3)
                          | A = k2_zf_lang(np__4)
                          | ( ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(k6_zf_lang1(D,B,A)))
                            & r1_zf_model(C,k1_zf_lang1(C,E,A,k8_funct_2(k1_zf_lang,C,E,B)),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(k6_zf_lang1(D,B,A),k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                            & k1_zfmodel1(D,C,E) = k1_zfmodel1(k6_zf_lang1(D,B,A),C,k1_zf_lang1(C,E,A,k8_funct_2(k1_zf_lang,C,E,B))) ) ) ) ) ) ) ) ) )).

fof(t16_zfmodel2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( ~ r2_hidden(A,k4_zf_lang1(D))
                   => ( r2_zf_model(C,k6_zf_lang1(D,B,A))
                    <=> r2_zf_model(C,D) ) ) ) ) ) ) )).

fof(t17_zfmodel2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,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(k2_zf_lang(np__0),k2_zf_model(C))
                      & r1_zf_model(A,D,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(C,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                      & ! [E] :
                          ( ( v1_zf_lang(E)
                            & m2_finseq_1(E,k5_numbers) )
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,k1_zf_lang,A)
                                & m2_relset_1(F,k1_zf_lang,A) )
                             => ~ ( ! [G] :
                                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                                     => ~ ( ~ r1_xreal_0(B,G)
                                          & r2_hidden(k2_zf_lang(G),k4_zf_lang1(E))
                                          & G != np__3
                                          & G != np__4 ) )
                                  & ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(E))
                                  & r1_zf_model(A,F,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(E,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                                  & k1_zfmodel1(C,A,D) = k1_zfmodel1(E,A,F) ) ) ) ) ) ) ) ) )).

fof(t18_zfmodel2,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(k2_zf_lang(np__0),k2_zf_model(B))
                  & r1_zf_model(A,C,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(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                  & ! [D] :
                      ( ( v1_zf_lang(D)
                        & m2_finseq_1(D,k5_numbers) )
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k1_zf_lang,A)
                            & m2_relset_1(E,k1_zf_lang,A) )
                         => ~ ( r1_tarski(k5_subset_1(k1_zf_lang,k2_zf_model(B),k2_zf_model(D)),k2_tarski(k2_zf_lang(np__3),k2_zf_lang(np__4)))
                              & ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(D))
                              & r1_zf_model(A,E,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(D,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                              & k1_zfmodel1(B,A,C) = k1_zfmodel1(D,A,E) ) ) ) ) ) ) ) )).

fof(t19_zfmodel2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_zfmodel1(B,A)
                  & r1_zfmodel1(C,A) )
               => r1_zfmodel1(k5_relat_1(C,B),A) ) ) ) ) )).

fof(t20_zfmodel2,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(k2_zf_lang(np__0),k2_zf_model(B))
               => ( r1_zf_model(A,C,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(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                <=> ! [D] :
                      ( m1_subset_1(D,A)
                     => ? [E] :
                          ( m1_subset_1(E,A)
                          & ! [F] :
                              ( m1_subset_1(F,A)
                             => ( r1_zf_model(A,k1_zf_lang1(A,k1_zf_lang1(A,C,k2_zf_lang(np__3),D),k2_zf_lang(np__4),F),B)
                              <=> F = E ) ) ) ) ) ) ) ) ) )).

fof(t21_zfmodel2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_zfmodel1(C,A)
                      & r1_zfmodel1(D,A)
                      & r1_tarski(k2_zf_model(B),k1_tarski(k2_zf_lang(np__3))) )
                   => ! [E] :
                        ( ( v1_relat_1(E)
                          & v1_funct_1(E) )
                       => ( ( k1_relat_1(E) = A
                            & ! [F] :
                                ( ( v1_funct_1(F)
                                  & v1_funct_2(F,k1_zf_lang,A)
                                  & m2_relset_1(F,k1_zf_lang,A) )
                               => ( ( r1_zf_model(A,F,B)
                                   => k1_funct_1(E,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) = k1_funct_1(C,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) )
                                  & ( r1_zf_model(A,F,k6_zf_lang(B))
                                   => k1_funct_1(E,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) = k1_funct_1(D,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) ) ) ) )
                         => r1_zfmodel1(E,A) ) ) ) ) ) ) ) )).

fof(t22_zfmodel2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r2_zfmodel1(B,A)
                  & r2_zfmodel1(C,A) )
               => r2_zfmodel1(k5_relat_1(B,C),A) ) ) ) ) )).

fof(t23_zfmodel2,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_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,A)
                        & m2_relset_1(E,k1_zf_lang,A) )
                     => ( ( r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B))
                          & r1_zf_model(A,E,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(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                          & r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C))
                          & r1_zf_model(A,E,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(C,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
                          & r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(D)) )
                       => ( r2_hidden(k2_zf_lang(np__4),k2_zf_model(D))
                          | ! [F] :
                              ( ( v1_relat_1(F)
                                & v1_funct_1(F) )
                             => ( ( k1_relat_1(F) = A
                                  & ! [G] :
                                      ( m1_subset_1(G,A)
                                     => ( ( r1_zf_model(A,k1_zf_lang1(A,E,k2_zf_lang(np__3),G),D)
                                         => k1_funct_1(F,G) = k8_funct_2(A,A,k1_zfmodel1(B,A,E),G) )
                                        & ( r1_zf_model(A,k1_zf_lang1(A,E,k2_zf_lang(np__3),G),k6_zf_lang(D))
                                         => k1_funct_1(F,G) = k8_funct_2(A,A,k1_zfmodel1(C,A,E),G) ) ) ) )
                               => r2_zfmodel1(F,A) ) ) ) ) ) ) ) ) ) )).

fof(t24_zfmodel2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => r1_zfmodel1(k6_partfun1(A),A) ) )).

fof(t25_zfmodel2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => r2_zfmodel1(k6_partfun1(A),A) ) )).
%------------------------------------------------------------------------------