SET007 Axioms: SET007+73.ax


%------------------------------------------------------------------------------
% File     : SET007+73 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Replacing of Variables in Formulas of ZF Theory
% 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_lang1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  215 (   9 unit)
%            Number of atoms       : 1575 ( 234 equality)
%            Maximal formula depth :   22 (   9 average)
%            Number of connectives : 1505 ( 145 ~  ;   5  |; 588  &)
%                                         (  41 <=>; 726 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-3 arity)
%            Number of functors    :   60 (   9 constant; 0-7 arity)
%            Number of variables   :  669 (   0 singleton; 661 !;   8 ?)
%            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(fc1_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => v1_finset_1(k1_zf_model(A)) ) )).

fof(t1_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ( k18_zf_lang(k4_zf_lang(A,B)) = A
            & k19_zf_lang(k4_zf_lang(A,B)) = B ) ) ) )).

fof(t2_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ( k18_zf_lang(k5_zf_lang(A,B)) = A
            & k19_zf_lang(k5_zf_lang(A,B)) = B ) ) ) )).

fof(t3_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k20_zf_lang(k6_zf_lang(A)) = A ) )).

fof(t4_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( k21_zf_lang(k7_zf_lang(A,B)) = A
            & k22_zf_lang(k7_zf_lang(A,B)) = B ) ) ) )).

fof(t5_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( k21_zf_lang(k10_zf_lang(A,B)) = A
            & k22_zf_lang(k10_zf_lang(A,B)) = B ) ) ) )).

fof(t6_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( k25_zf_lang(k11_zf_lang(A,B)) = A
            & k26_zf_lang(k11_zf_lang(A,B)) = B ) ) ) )).

fof(t7_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( k27_zf_lang(k12_zf_lang(A,B)) = A
            & k28_zf_lang(k12_zf_lang(A,B)) = B ) ) ) )).

fof(t8_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ( k23_zf_lang(k8_zf_lang(B,A)) = B
            & k24_zf_lang(k8_zf_lang(B,A)) = A ) ) ) )).

fof(t9_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ( k23_zf_lang(k13_zf_lang(B,A)) = B
            & k24_zf_lang(k13_zf_lang(B,A)) = A ) ) ) )).

fof(t10_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k10_zf_lang(A,B) = k11_zf_lang(k6_zf_lang(A),B) ) ) )).

fof(t11_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ( k14_zf_lang(C,D,A) = k8_zf_lang(E,B)
                       => ( C = E
                          & k8_zf_lang(D,A) = B ) ) ) ) ) ) ) )).

fof(t12_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ( k15_zf_lang(C,D,A) = k13_zf_lang(E,B)
                       => ( C = E
                          & k13_zf_lang(D,A) = B ) ) ) ) ) ) ) )).

fof(t13_zf_lang1,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)
             => ( v6_zf_lang(k14_zf_lang(B,C,A))
                & k23_zf_lang(k14_zf_lang(B,C,A)) = B
                & k24_zf_lang(k14_zf_lang(B,C,A)) = k8_zf_lang(C,A) ) ) ) ) )).

fof(t14_zf_lang1,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)
             => ( v11_zf_lang(k15_zf_lang(B,C,A))
                & k23_zf_lang(k15_zf_lang(B,C,A)) = B
                & k24_zf_lang(k15_zf_lang(B,C,A)) = k13_zf_lang(C,A) ) ) ) ) )).

fof(t15_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k16_zf_lang(B,C,D,A) = k8_zf_lang(B,k8_zf_lang(C,k8_zf_lang(D,A)))
                    & k16_zf_lang(B,C,D,A) = k14_zf_lang(B,C,k8_zf_lang(D,A)) ) ) ) ) ) )).

fof(t16_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k14_zf_lang(C,D,A) = k14_zf_lang(E,F,B)
                           => ( C = E
                              & D = F
                              & A = B ) ) ) ) ) ) ) ) )).

fof(t17_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ! [G] :
                              ( m2_subset_1(G,k5_numbers,k1_zf_lang)
                             => ! [H] :
                                  ( m2_subset_1(H,k5_numbers,k1_zf_lang)
                                 => ( k16_zf_lang(C,D,E,A) = k16_zf_lang(F,G,H,B)
                                   => ( C = F
                                      & D = G
                                      & E = H
                                      & A = B ) ) ) ) ) ) ) ) ) ) )).

fof(t18_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k16_zf_lang(C,D,E,A) = k8_zf_lang(F,B)
                           => ( C = F
                              & k14_zf_lang(D,E,A) = B ) ) ) ) ) ) ) ) )).

fof(t19_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ! [G] :
                              ( m2_subset_1(G,k5_numbers,k1_zf_lang)
                             => ( k16_zf_lang(C,D,E,A) = k14_zf_lang(F,G,B)
                               => ( C = F
                                  & D = G
                                  & k8_zf_lang(E,A) = B ) ) ) ) ) ) ) ) ) )).

fof(t20_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k15_zf_lang(C,D,A) = k15_zf_lang(E,F,B)
                           => ( C = E
                              & D = F
                              & A = B ) ) ) ) ) ) ) ) )).

fof(t21_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k17_zf_lang(B,C,D,A) = k13_zf_lang(B,k13_zf_lang(C,k13_zf_lang(D,A)))
                    & k17_zf_lang(B,C,D,A) = k15_zf_lang(B,C,k13_zf_lang(D,A)) ) ) ) ) ) )).

fof(t22_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ! [G] :
                              ( m2_subset_1(G,k5_numbers,k1_zf_lang)
                             => ! [H] :
                                  ( m2_subset_1(H,k5_numbers,k1_zf_lang)
                                 => ( k17_zf_lang(C,D,E,A) = k17_zf_lang(F,G,H,B)
                                   => ( C = F
                                      & D = G
                                      & E = H
                                      & A = B ) ) ) ) ) ) ) ) ) ) )).

fof(t23_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k17_zf_lang(C,D,E,A) = k13_zf_lang(F,B)
                           => ( C = F
                              & k15_zf_lang(D,E,A) = B ) ) ) ) ) ) ) ) )).

fof(t24_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ! [G] :
                              ( m2_subset_1(G,k5_numbers,k1_zf_lang)
                             => ( k17_zf_lang(C,D,E,A) = k15_zf_lang(F,G,B)
                               => ( C = F
                                  & D = G
                                  & k13_zf_lang(E,A) = B ) ) ) ) ) ) ) ) ) )).

fof(t25_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( v6_zf_lang(k16_zf_lang(B,C,D,A))
                    & k23_zf_lang(k16_zf_lang(B,C,D,A)) = B
                    & k24_zf_lang(k16_zf_lang(B,C,D,A)) = k14_zf_lang(C,D,A) ) ) ) ) ) )).

fof(t26_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( v11_zf_lang(k17_zf_lang(B,C,D,A))
                    & k23_zf_lang(k17_zf_lang(B,C,D,A)) = B
                    & k24_zf_lang(k17_zf_lang(B,C,D,A)) = k15_zf_lang(C,D,A) ) ) ) ) ) )).

fof(t27_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v8_zf_lang(A)
       => k21_zf_lang(A) = k20_zf_lang(k21_zf_lang(k20_zf_lang(A))) ) ) )).

fof(t28_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v8_zf_lang(A)
       => k22_zf_lang(A) = k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) )).

fof(t29_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v9_zf_lang(A)
       => k25_zf_lang(A) = k21_zf_lang(k20_zf_lang(A)) ) ) )).

fof(t30_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v9_zf_lang(A)
       => k26_zf_lang(A) = k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) )).

fof(t31_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v10_zf_lang(A)
       => ( k27_zf_lang(A) = k25_zf_lang(k21_zf_lang(A))
          & k27_zf_lang(A) = k26_zf_lang(k22_zf_lang(A)) ) ) ) )).

fof(t32_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v10_zf_lang(A)
       => ( k28_zf_lang(A) = k26_zf_lang(k21_zf_lang(A))
          & k28_zf_lang(A) = k25_zf_lang(k22_zf_lang(A)) ) ) ) )).

fof(t33_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v11_zf_lang(A)
       => ( k23_zf_lang(A) = k23_zf_lang(k20_zf_lang(A))
          & k24_zf_lang(A) = k20_zf_lang(k24_zf_lang(k20_zf_lang(A))) ) ) ) )).

fof(t34_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( k20_zf_lang(k10_zf_lang(A,B)) = k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))
            & k25_zf_lang(k10_zf_lang(A,B)) = k6_zf_lang(A)
            & k26_zf_lang(k10_zf_lang(A,B)) = B ) ) ) )).

fof(t35_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k20_zf_lang(k11_zf_lang(A,B)) = k7_zf_lang(A,k6_zf_lang(B)) ) ) )).

fof(t36_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( k21_zf_lang(k12_zf_lang(A,B)) = k11_zf_lang(A,B)
            & k22_zf_lang(k12_zf_lang(A,B)) = k11_zf_lang(B,A) ) ) ) )).

fof(t37_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k20_zf_lang(k13_zf_lang(B,A)) = k8_zf_lang(B,k6_zf_lang(A)) ) ) )).

fof(t38_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v8_zf_lang(A)
       => ( v9_zf_lang(A)
          & v4_zf_lang(A)
          & v5_zf_lang(k20_zf_lang(A))
          & v4_zf_lang(k21_zf_lang(k20_zf_lang(A)))
          & v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) ) )).

fof(t39_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v9_zf_lang(A)
       => ( v4_zf_lang(A)
          & v5_zf_lang(k20_zf_lang(A))
          & v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) ) )).

fof(t40_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v10_zf_lang(A)
       => ( v5_zf_lang(A)
          & v9_zf_lang(k21_zf_lang(A))
          & v9_zf_lang(k22_zf_lang(A)) ) ) ) )).

fof(t41_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v11_zf_lang(A)
       => ( v4_zf_lang(A)
          & v6_zf_lang(k20_zf_lang(A))
          & v4_zf_lang(k24_zf_lang(k20_zf_lang(A))) ) ) ) )).

fof(t42_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ~ ( v2_zf_lang(A)
            & ~ ( ~ v3_zf_lang(A)
                & ~ v4_zf_lang(A)
                & ~ v5_zf_lang(A)
                & ~ v6_zf_lang(A) ) )
        & ~ ( v3_zf_lang(A)
            & ~ ( ~ v4_zf_lang(A)
                & ~ v5_zf_lang(A)
                & ~ v6_zf_lang(A) ) )
        & ~ ( v4_zf_lang(A)
            & ( v5_zf_lang(A)
              | v6_zf_lang(A) ) )
        & ~ ( v5_zf_lang(A)
            & v6_zf_lang(A) ) ) ) )).

fof(t43_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r2_zf_lang(A,B)
           => r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) )).

fof(t44_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( ~ ( ~ ( r3_zf_lang(A,B)
                        & r2_zf_lang(B,C) )
                    & ~ ( r2_zf_lang(A,B)
                        & r3_zf_lang(B,C) )
                    & ~ ( r2_zf_lang(A,B)
                        & r1_zf_lang(B,C) )
                    & ~ ( r1_zf_lang(A,B)
                        & r2_zf_lang(B,C) )
                    & ~ ( r3_zf_lang(A,B)
                        & r1_zf_lang(B,C) )
                    & ~ ( r1_zf_lang(A,B)
                        & r3_zf_lang(B,C) ) )
               => r3_zf_lang(A,C) ) ) ) ) )).

fof(t45_zf_lang1,axiom,(
    $true )).

fof(t46_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ~ r1_zf_lang(A,A) ) )).

fof(t47_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ~ ( r3_zf_lang(A,B)
              & r2_zf_lang(B,A) ) ) ) )).

fof(t48_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ~ ( r3_zf_lang(A,B)
              & r3_zf_lang(B,A) ) ) ) )).

fof(t49_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ~ ( r2_zf_lang(A,B)
              & r1_zf_lang(B,A) ) ) ) )).

fof(t50_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ~ ( r3_zf_lang(A,B)
              & r1_zf_lang(B,A) ) ) ) )).

fof(t51_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r2_zf_lang(k6_zf_lang(A),B)
           => r3_zf_lang(A,B) ) ) ) )).

fof(t52_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r2_zf_lang(k7_zf_lang(A,B),C)
               => ( r3_zf_lang(A,C)
                  & r3_zf_lang(B,C) ) ) ) ) ) )).

fof(t53_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ( r2_zf_lang(k8_zf_lang(C,A),B)
               => r3_zf_lang(A,B) ) ) ) ) )).

fof(t54_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r3_zf_lang(k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B))
            & r3_zf_lang(A,k11_zf_lang(A,B))
            & r3_zf_lang(k6_zf_lang(B),k11_zf_lang(A,B))
            & r3_zf_lang(B,k11_zf_lang(A,B)) ) ) ) )).

fof(t55_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r3_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k10_zf_lang(A,B))
            & r3_zf_lang(k6_zf_lang(A),k10_zf_lang(A,B))
            & r3_zf_lang(k6_zf_lang(B),k10_zf_lang(A,B))
            & r3_zf_lang(A,k10_zf_lang(A,B))
            & r3_zf_lang(B,k10_zf_lang(A,B)) ) ) ) )).

fof(t56_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ( r3_zf_lang(k8_zf_lang(B,k6_zf_lang(A)),k13_zf_lang(B,A))
            & r3_zf_lang(k6_zf_lang(A),k13_zf_lang(B,A)) ) ) ) )).

fof(t57_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r2_zf_lang(A,B)
          <=> r2_hidden(A,k29_zf_lang(B)) ) ) ) )).

fof(t58_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r2_hidden(A,k29_zf_lang(B))
           => r1_tarski(k29_zf_lang(A),k29_zf_lang(B)) ) ) ) )).

fof(t59_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => r2_hidden(A,k29_zf_lang(A)) ) )).

fof(t60_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k29_zf_lang(k11_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k1_enumset1(k6_zf_lang(B),k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B))) ) ) )).

fof(t61_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k29_zf_lang(k10_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k2_enumset1(k6_zf_lang(B),k6_zf_lang(A),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k10_zf_lang(A,B))) ) ) )).

fof(t62_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k29_zf_lang(k12_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k5_enumset1(k6_zf_lang(B),k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B),k6_zf_lang(A),k7_zf_lang(B,k6_zf_lang(A)),k11_zf_lang(B,A),k12_zf_lang(A,B))) ) ) )).

fof(t63_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k4_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).

fof(t64_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k5_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).

fof(t65_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k2_zf_model(k6_zf_lang(A)) = k2_zf_model(A) ) )).

fof(t66_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k2_zf_model(k7_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).

fof(t67_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k8_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)) ) ) )).

fof(t68_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k2_zf_model(k10_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).

fof(t69_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k2_zf_model(k11_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).

fof(t70_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k2_zf_model(k12_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).

fof(t71_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k13_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)) ) ) )).

fof(t72_zf_lang1,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)
             => k2_zf_model(k14_zf_lang(B,C,A)) = k4_xboole_0(k2_zf_model(A),k2_tarski(B,C)) ) ) ) )).

fof(t73_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => k2_zf_model(k16_zf_lang(B,C,D,A)) = k4_xboole_0(k2_zf_model(A),k1_enumset1(B,C,D)) ) ) ) ) )).

fof(t74_zf_lang1,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)
             => k2_zf_model(k15_zf_lang(B,C,A)) = k4_xboole_0(k2_zf_model(A),k2_tarski(B,C)) ) ) ) )).

fof(t75_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => k2_zf_model(k17_zf_lang(B,C,D,A)) = k4_xboole_0(k2_zf_model(A),k1_enumset1(B,C,D)) ) ) ) ) )).

fof(d1_zf_lang1,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) )
                     => ( E = k1_zf_lang1(A,B,C,D)
                      <=> ( k8_funct_2(k1_zf_lang,A,E,C) = D
                          & ! [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)
                               => C = F ) ) ) ) ) ) ) ) ) )).

fof(d2_zf_lang1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ( r1_tarski(B,C)
                   => k2_zf_lang1(A,B,C,D) = D ) ) ) ) ) )).

fof(t76_zf_lang1,axiom,(
    $true )).

fof(t77_zf_lang1,axiom,(
    $true )).

fof(t78_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,B)
                        & m2_relset_1(E,k1_zf_lang,B) )
                     => ( k1_zf_lang1(B,k1_zf_lang1(B,E,A,C),A,D) = k1_zf_lang1(B,E,A,D)
                        & k1_zf_lang1(B,E,A,k8_funct_2(k1_zf_lang,B,E,A)) = E ) ) ) ) ) ) )).

fof(t79_zf_lang1,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] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( m1_subset_1(E,C)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k1_zf_lang,C)
                            & m2_relset_1(F,k1_zf_lang,C) )
                         => ( A != B
                           => k1_zf_lang1(C,k1_zf_lang1(C,F,A,D),B,E) = k1_zf_lang1(C,k1_zf_lang1(C,F,B,E),A,D) ) ) ) ) ) ) ) )).

fof(t80_zf_lang1,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)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k8_zf_lang(B,A))
                  <=> ! [E] :
                        ( m1_subset_1(E,C)
                       => r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) )).

fof(t81_zf_lang1,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)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [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(B,A))
                      <=> r1_zf_model(C,k1_zf_lang1(C,E,B,D),k8_zf_lang(B,A)) ) ) ) ) ) ) )).

fof(t82_zf_lang1,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)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k13_zf_lang(B,A))
                  <=> ? [E] :
                        ( m1_subset_1(E,C)
                        & r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) )).

fof(t83_zf_lang1,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)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [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,k13_zf_lang(B,A))
                      <=> r1_zf_model(C,k1_zf_lang1(C,E,B,D),k13_zf_lang(B,A)) ) ) ) ) ) ) )).

fof(t84_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,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)
                         => ( r2_hidden(E,k2_zf_model(A))
                           => k8_funct_2(k1_zf_lang,B,D,E) = k8_funct_2(k1_zf_lang,B,C,E) ) )
                      & r1_zf_model(B,C,A) )
                   => r1_zf_model(B,D,A) ) ) ) ) ) )).

fof(t85_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => v1_finset_1(k2_zf_model(A)) ) )).

fof(t86_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k2_zf_lang(A) = k2_zf_lang(B)
           => A = B ) ) ) )).

fof(t87_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k2_zf_lang(B) ) ) )).

fof(t88_zf_lang1,axiom,(
    $true )).

fof(t89_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => r1_zf_model(B,C,k4_zf_lang(A,A)) ) ) ) )).

fof(t90_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => r2_zf_model(B,k4_zf_lang(A,A)) ) ) )).

fof(t91_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ~ r1_zf_model(B,C,k5_zf_lang(A,A)) ) ) ) )).

fof(t92_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( ~ r2_zf_model(B,k5_zf_lang(A,A))
            & r2_zf_model(B,k6_zf_lang(k5_zf_lang(A,A))) ) ) ) )).

fof(t93_zf_lang1,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)
             => ( r2_zf_model(C,k4_zf_lang(A,B))
              <=> ~ ( A != B
                    & ! [D] : k1_tarski(D) != C ) ) ) ) ) )).

fof(t94_zf_lang1,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)
             => ( r2_zf_model(C,k6_zf_lang(k5_zf_lang(A,B)))
              <=> ( A = B
                  | ! [D] :
                      ( r2_hidden(D,C)
                     => r1_xboole_0(D,C) ) ) ) ) ) ) )).

fof(t95_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v2_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)) = k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)) ) ) ) ) ) )).

fof(t96_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v3_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> 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))) ) ) ) ) ) )).

fof(t97_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v4_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> ~ r1_zf_model(B,C,k20_zf_lang(A)) ) ) ) ) ) )).

fof(t98_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v5_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> ( r1_zf_model(B,C,k21_zf_lang(A))
                    & r1_zf_model(B,C,k22_zf_lang(A)) ) ) ) ) ) ) )).

fof(t99_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v6_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> ! [D] :
                      ( m1_subset_1(D,B)
                     => r1_zf_model(B,k1_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)) ) ) ) ) ) ) )).

fof(t100_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v8_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> ( r1_zf_model(B,C,k21_zf_lang(A))
                    | r1_zf_model(B,C,k22_zf_lang(A)) ) ) ) ) ) ) )).

fof(t101_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v9_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> ( r1_zf_model(B,C,k25_zf_lang(A))
                   => r1_zf_model(B,C,k26_zf_lang(A)) ) ) ) ) ) ) )).

fof(t102_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v10_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> ( r1_zf_model(B,C,k27_zf_lang(A))
                  <=> r1_zf_model(B,C,k28_zf_lang(A)) ) ) ) ) ) ) )).

fof(t103_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( v11_zf_lang(A)
               => ( r1_zf_model(B,C,A)
                <=> ? [D] :
                      ( m1_subset_1(D,B)
                      & r1_zf_model(B,k1_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)) ) ) ) ) ) ) )).

fof(t104_zf_lang1,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,k13_zf_lang(B,A))
              <=> ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,k1_zf_lang,C)
                      & m2_relset_1(D,k1_zf_lang,C) )
                   => ? [E] :
                        ( m1_subset_1(E,C)
                        & r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) )).

fof(t105_zf_lang1,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,A)
               => r2_zf_model(C,k13_zf_lang(B,A)) ) ) ) ) )).

fof(t106_zf_lang1,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)
                 => ( r2_zf_model(D,A)
                  <=> r2_zf_model(D,k14_zf_lang(B,C,A)) ) ) ) ) ) )).

fof(t107_zf_lang1,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)
                 => ( r2_zf_model(D,A)
                   => r2_zf_model(D,k15_zf_lang(B,C,A)) ) ) ) ) ) )).

fof(t108_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( ~ v1_xboole_0(E)
                     => ( r2_zf_model(E,A)
                      <=> r2_zf_model(E,k16_zf_lang(B,C,D,A)) ) ) ) ) ) ) )).

fof(t109_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( ~ v1_xboole_0(E)
                     => ( r2_zf_model(E,A)
                       => r2_zf_model(E,k17_zf_lang(B,C,D,A)) ) ) ) ) ) ) )).

fof(t110_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B)))
                    & r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B))) ) ) ) ) ) )).

fof(t111_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(B,A)))
                    & r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(B,A))) ) ) ) ) ) )).

fof(t112_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(B,C),k11_zf_lang(A,C)))) ) ) ) ) )).

fof(t113_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [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,k11_zf_lang(A,B))
                          & r1_zf_model(D,E,k11_zf_lang(B,C)) )
                       => r1_zf_model(D,E,k11_zf_lang(A,C)) ) ) ) ) ) ) )).

fof(t114_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ( ( r2_zf_model(D,k11_zf_lang(A,B))
                      & r2_zf_model(D,k11_zf_lang(B,C)) )
                   => r2_zf_model(D,k11_zf_lang(A,C)) ) ) ) ) ) )).

fof(t115_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [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,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,C)),k11_zf_lang(A,C)))
                        & r2_zf_model(D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,C)),k11_zf_lang(A,C))) ) ) ) ) ) ) )).

fof(t116_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(A,k11_zf_lang(B,A)))
                    & r2_zf_model(C,k11_zf_lang(A,k11_zf_lang(B,A))) ) ) ) ) ) )).

fof(t117_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [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,k11_zf_lang(k11_zf_lang(A,k11_zf_lang(B,C)),k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,C))))
                        & r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,k11_zf_lang(B,C)),k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,C)))) ) ) ) ) ) ) )).

fof(t118_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),A))
                    & r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),A)) ) ) ) ) ) )).

fof(t119_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),B))
                    & r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),B)) ) ) ) ) ) )).

fof(t120_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),k7_zf_lang(B,A)))
                    & r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),k7_zf_lang(B,A))) ) ) ) ) ) )).

fof(t121_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( r1_zf_model(B,C,k11_zf_lang(A,k7_zf_lang(A,A)))
                & r2_zf_model(B,k11_zf_lang(A,k7_zf_lang(A,A))) ) ) ) ) )).

fof(t122_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [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,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(A,C),k11_zf_lang(A,k7_zf_lang(B,C)))))
                        & r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(A,C),k11_zf_lang(A,k7_zf_lang(B,C))))) ) ) ) ) ) ) )).

fof(t123_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(A,k10_zf_lang(A,B)))
                    & r2_zf_model(C,k11_zf_lang(A,k10_zf_lang(A,B))) ) ) ) ) ) )).

fof(t124_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(A,k10_zf_lang(B,A)))
                    & r2_zf_model(C,k11_zf_lang(A,k10_zf_lang(B,A))) ) ) ) ) ) )).

fof(t125_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k10_zf_lang(A,B),k10_zf_lang(B,A)))
                    & r2_zf_model(C,k11_zf_lang(k10_zf_lang(A,B),k10_zf_lang(B,A))) ) ) ) ) ) )).

fof(t126_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( r1_zf_model(B,C,k11_zf_lang(A,k10_zf_lang(A,A)))
                & r2_zf_model(B,k11_zf_lang(A,k10_zf_lang(A,A))) ) ) ) ) )).

fof(t127_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [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,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(C,B),k11_zf_lang(k10_zf_lang(A,C),B))))
                        & r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(C,B),k11_zf_lang(k10_zf_lang(A,C),B)))) ) ) ) ) ) ) )).

fof(t128_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [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,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(C,B)),k11_zf_lang(k10_zf_lang(A,C),B)))
                        & r2_zf_model(D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(C,B)),k11_zf_lang(k10_zf_lang(A,C),B))) ) ) ) ) ) ) )).

fof(t129_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k11_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(B,k6_zf_lang(A))))
                    & r2_zf_model(C,k11_zf_lang(k11_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(B,k6_zf_lang(A)))) ) ) ) ) ) )).

fof(t130_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(A),k11_zf_lang(A,B)))
                    & r2_zf_model(C,k11_zf_lang(k6_zf_lang(A),k11_zf_lang(A,B))) ) ) ) ) ) )).

fof(t131_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,k6_zf_lang(B))),k6_zf_lang(A)))
                    & r2_zf_model(C,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,k6_zf_lang(B))),k6_zf_lang(A))) ) ) ) ) ) )).

fof(t132_zf_lang1,axiom,(
    $true )).

fof(t133_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( ( r2_zf_model(C,k11_zf_lang(A,B))
                  & r2_zf_model(C,A) )
               => r2_zf_model(C,B) ) ) ) ) )).

fof(t134_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(k7_zf_lang(A,B)),k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B))))
                    & r2_zf_model(C,k11_zf_lang(k6_zf_lang(k7_zf_lang(A,B)),k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))) ) ) ) ) ) )).

fof(t135_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k7_zf_lang(A,B))))
                    & r2_zf_model(C,k11_zf_lang(k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k7_zf_lang(A,B)))) ) ) ) ) ) )).

fof(t136_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(k10_zf_lang(A,B)),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))))
                    & r2_zf_model(C,k11_zf_lang(k6_zf_lang(k10_zf_lang(A,B)),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))) ) ) ) ) ) )).

fof(t137_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k10_zf_lang(A,B))))
                    & r2_zf_model(C,k11_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k10_zf_lang(A,B)))) ) ) ) ) ) )).

fof(t138_zf_lang1,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,k11_zf_lang(k8_zf_lang(B,A),A)) ) ) ) )).

fof(t139_zf_lang1,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,k11_zf_lang(A,k13_zf_lang(B,A))) ) ) ) )).

fof(t140_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ( ~ r2_hidden(C,k2_zf_model(A))
                   => r2_zf_model(D,k11_zf_lang(k8_zf_lang(C,k11_zf_lang(A,B)),k11_zf_lang(A,k8_zf_lang(C,B)))) ) ) ) ) ) )).

fof(t141_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ( r2_zf_model(D,k11_zf_lang(A,B))
                   => ( r2_hidden(C,k2_zf_model(A))
                      | r2_zf_model(D,k11_zf_lang(A,k8_zf_lang(C,B))) ) ) ) ) ) ) )).

fof(t142_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ( ~ r2_hidden(C,k2_zf_model(A))
                   => r2_zf_model(D,k11_zf_lang(k8_zf_lang(C,k11_zf_lang(B,A)),k11_zf_lang(k13_zf_lang(C,B),A))) ) ) ) ) ) )).

fof(t143_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ( r2_zf_model(D,k11_zf_lang(B,A))
                   => ( r2_hidden(C,k2_zf_model(A))
                      | r2_zf_model(D,k11_zf_lang(k13_zf_lang(C,B),A)) ) ) ) ) ) ) )).

fof(t144_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ( r2_zf_model(D,k11_zf_lang(A,k8_zf_lang(C,B)))
                   => r2_zf_model(D,k11_zf_lang(A,B)) ) ) ) ) ) )).

fof(t145_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ( r2_zf_model(D,k11_zf_lang(k13_zf_lang(C,A),B))
                   => r2_zf_model(D,k11_zf_lang(A,B)) ) ) ) ) ) )).

fof(t146_zf_lang1,axiom,(
    r1_tarski(k9_zf_lang,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers))) )).

fof(d3_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k3_zf_lang1(A) = k4_xboole_0(k2_relat_1(A),k3_enumset1(np__0,np__1,np__2,np__3,np__4)) ) )).

fof(t147_zf_lang1,axiom,(
    $true )).

fof(t148_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ( A != np__0
        & A != np__1
        & A != np__2
        & A != np__3
        & A != np__4 ) ) )).

fof(t149_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ~ r2_hidden(A,k3_enumset1(np__0,np__1,np__2,np__3,np__4)) ) )).

fof(t150_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( r2_hidden(B,k3_zf_lang1(A))
         => ( B != np__0
            & B != np__1
            & B != np__2
            & B != np__3
            & B != np__4 ) ) ) )).

fof(t151_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k3_zf_lang1(k4_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).

fof(t152_zf_lang1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k3_zf_lang1(k5_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).

fof(t153_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k3_zf_lang1(k6_zf_lang(A)) = k3_zf_lang1(A) ) )).

fof(t154_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k3_zf_lang1(k7_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).

fof(t155_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k3_zf_lang1(k8_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)) ) ) )).

fof(t156_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k3_zf_lang1(k10_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).

fof(t157_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k3_zf_lang1(k11_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).

fof(t158_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k3_zf_lang1(k12_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).

fof(t159_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k3_zf_lang1(k13_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)) ) ) )).

fof(t160_zf_lang1,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)
             => k3_zf_lang1(k14_zf_lang(B,C,A)) = k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) ) ) ) )).

fof(t161_zf_lang1,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)
             => k3_zf_lang1(k15_zf_lang(B,C,A)) = k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) ) ) ) )).

fof(t162_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => k3_zf_lang1(k16_zf_lang(B,C,D,A)) = k2_xboole_0(k3_zf_lang1(A),k1_enumset1(B,C,D)) ) ) ) ) )).

fof(t163_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => k3_zf_lang1(k17_zf_lang(B,C,D,A)) = k2_xboole_0(k3_zf_lang1(A),k1_enumset1(B,C,D)) ) ) ) ) )).

fof(t164_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => r1_tarski(k2_zf_model(A),k3_zf_lang1(A)) ) )).

fof(d4_zf_lang1,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_relat_1(D)
                    & v1_funct_1(D) )
                 => ( D = k5_zf_lang1(A,B,C)
                  <=> ( k1_relat_1(D) = k4_finseq_1(A)
                      & ! [E] :
                          ( r2_hidden(E,k4_finseq_1(A))
                         => ( ( k1_funct_1(A,E) = B
                             => k1_funct_1(D,E) = C )
                            & ( k1_funct_1(A,E) != B
                             => k1_funct_1(D,E) = k1_funct_1(A,E) ) ) ) ) ) ) ) ) ) )).

fof(t165_zf_lang1,axiom,(
    $true )).

fof(t166_zf_lang1,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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k5_zf_lang1(k4_zf_lang(A,B),C,D) = k4_zf_lang(E,F)
                          <=> ~ ( ~ ( A != C
                                    & B != C
                                    & E = A
                                    & F = B )
                                & ~ ( A = C
                                    & B != C
                                    & E = D
                                    & F = B )
                                & ~ ( A != C
                                    & B = C
                                    & E = A
                                    & F = D )
                                & ~ ( A = C
                                    & B = C
                                    & E = D
                                    & F = D ) ) ) ) ) ) ) ) ) )).

fof(t167_zf_lang1,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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                      & ? [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                          & k5_zf_lang1(k4_zf_lang(A,B),C,D) = k4_zf_lang(E,F) ) ) ) ) ) ) )).

fof(t168_zf_lang1,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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k5_zf_lang1(k5_zf_lang(A,B),C,D) = k5_zf_lang(E,F)
                          <=> ~ ( ~ ( A != C
                                    & B != C
                                    & E = A
                                    & F = B )
                                & ~ ( A = C
                                    & B != C
                                    & E = D
                                    & F = B )
                                & ~ ( A != C
                                    & B = C
                                    & E = A
                                    & F = D )
                                & ~ ( A = C
                                    & B = C
                                    & E = D
                                    & F = D ) ) ) ) ) ) ) ) ) )).

fof(t169_zf_lang1,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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                      & ? [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                          & k5_zf_lang1(k5_zf_lang(A,B),C,D) = k5_zf_lang(E,F) ) ) ) ) ) ) )).

fof(t170_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k6_zf_lang(A) = k5_zf_lang1(k6_zf_lang(B),C,D)
                  <=> A = k5_zf_lang1(B,C,D) ) ) ) ) ) )).

fof(t171_zf_lang1,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)
             => r2_hidden(k5_zf_lang1(A,B,C),k9_zf_lang) ) ) ) )).

fof(t172_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k7_zf_lang(A,B) = k6_zf_lang1(k7_zf_lang(C,D),E,F)
                          <=> ( A = k6_zf_lang1(C,E,F)
                              & B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) )).

fof(t173_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ( C != D
                       => ( k8_zf_lang(C,A) = k6_zf_lang1(k8_zf_lang(C,B),D,E)
                        <=> A = k6_zf_lang1(B,D,E) ) ) ) ) ) ) ) )).

fof(t174_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k8_zf_lang(C,A) = k6_zf_lang1(k8_zf_lang(D,B),D,C)
                  <=> A = k6_zf_lang1(B,D,C) ) ) ) ) ) )).

fof(t175_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k10_zf_lang(A,B) = k6_zf_lang1(k10_zf_lang(C,D),E,F)
                          <=> ( A = k6_zf_lang1(C,E,F)
                              & B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) )).

fof(t176_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k11_zf_lang(A,B) = k6_zf_lang1(k11_zf_lang(C,D),E,F)
                          <=> ( A = k6_zf_lang1(C,E,F)
                              & B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) )).

fof(t177_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [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] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] :
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k12_zf_lang(A,B) = k6_zf_lang1(k12_zf_lang(C,D),E,F)
                          <=> ( A = k6_zf_lang1(C,E,F)
                              & B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) )).

fof(t178_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] :
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ( C != D
                       => ( k13_zf_lang(C,A) = k6_zf_lang1(k13_zf_lang(C,B),D,E)
                        <=> A = k6_zf_lang1(B,D,E) ) ) ) ) ) ) ) )).

fof(t179_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k13_zf_lang(C,A) = k6_zf_lang1(k13_zf_lang(D,B),D,C)
                  <=> A = k6_zf_lang1(B,D,C) ) ) ) ) ) )).

fof(t180_zf_lang1,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)
             => ( v2_zf_lang(A)
              <=> v2_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t181_zf_lang1,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)
             => ( v3_zf_lang(A)
              <=> v3_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t182_zf_lang1,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)
             => ( v4_zf_lang(A)
              <=> v4_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t183_zf_lang1,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)
             => ( v5_zf_lang(A)
              <=> v5_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t184_zf_lang1,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)
             => ( v6_zf_lang(A)
              <=> v6_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t185_zf_lang1,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)
             => ( v4_zf_lang(A)
               => k20_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k20_zf_lang(A),B,C) ) ) ) ) )).

fof(t186_zf_lang1,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)
             => ( v5_zf_lang(A)
               => ( k21_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k21_zf_lang(A),B,C)
                  & k22_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k22_zf_lang(A),B,C) ) ) ) ) ) )).

fof(t187_zf_lang1,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)
             => ( v6_zf_lang(A)
               => ( k24_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k24_zf_lang(A),B,C)
                  & ( k23_zf_lang(A) = B
                   => k23_zf_lang(k6_zf_lang1(A,B,C)) = C )
                  & ( k23_zf_lang(A) != B
                   => k23_zf_lang(k6_zf_lang1(A,B,C)) = k23_zf_lang(A) ) ) ) ) ) ) )).

fof(t188_zf_lang1,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)
             => ( v8_zf_lang(A)
              <=> v8_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t189_zf_lang1,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)
             => ( v9_zf_lang(A)
              <=> v9_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t190_zf_lang1,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)
             => ( v10_zf_lang(A)
               => v10_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t191_zf_lang1,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)
             => ( v11_zf_lang(A)
              <=> v11_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).

fof(t192_zf_lang1,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)
             => ( v8_zf_lang(A)
               => ( k21_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k21_zf_lang(A),B,C)
                  & k22_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k22_zf_lang(A),B,C) ) ) ) ) ) )).

fof(t193_zf_lang1,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)
             => ( v9_zf_lang(A)
               => ( k25_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k25_zf_lang(A),B,C)
                  & k26_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k26_zf_lang(A),B,C) ) ) ) ) ) )).

fof(t194_zf_lang1,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)
             => ( v10_zf_lang(A)
               => ( k27_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k27_zf_lang(A),B,C)
                  & k28_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k28_zf_lang(A),B,C) ) ) ) ) ) )).

fof(t195_zf_lang1,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)
             => ( v11_zf_lang(A)
               => ( k24_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k24_zf_lang(A),B,C)
                  & ( k23_zf_lang(A) = B
                   => k23_zf_lang(k6_zf_lang1(A,B,C)) = C )
                  & ( k23_zf_lang(A) != B
                   => k23_zf_lang(k6_zf_lang1(A,B,C)) = k23_zf_lang(A) ) ) ) ) ) ) )).

fof(t196_zf_lang1,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)
             => ( ~ r2_hidden(B,k4_zf_lang1(A))
               => k6_zf_lang1(A,B,C) = A ) ) ) ) )).

fof(t197_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k6_zf_lang1(A,B,B) = A ) ) )).

fof(t198_zf_lang1,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)
             => ~ ( B != C
                  & r2_hidden(B,k4_zf_lang1(k6_zf_lang1(A,B,C))) ) ) ) ) )).

fof(t199_zf_lang1,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)
             => ( r2_hidden(B,k4_zf_lang1(A))
               => r2_hidden(C,k4_zf_lang1(k6_zf_lang1(A,B,C))) ) ) ) ) )).

fof(t200_zf_lang1,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] :
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( B != C
                   => k6_zf_lang1(k6_zf_lang1(A,B,C),B,D) = k6_zf_lang1(A,B,C) ) ) ) ) ) )).

fof(t201_zf_lang1,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)
             => r1_tarski(k4_zf_lang1(k6_zf_lang1(A,B,C)),k2_xboole_0(k4_xboole_0(k4_zf_lang1(A),k1_tarski(B)),k1_tarski(C))) ) ) ) )).

fof(s1_zf_lang1,axiom,
    ( ( ! [A] :
          ( m2_subset_1(A,k5_numbers,k1_zf_lang)
         => ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => ( p1_s1_zf_lang1(k4_zf_lang(A,B))
                & p1_s1_zf_lang1(k5_zf_lang(A,B)) ) ) )
      & ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ( p1_s1_zf_lang1(A)
           => p1_s1_zf_lang1(k6_zf_lang(A)) ) )
      & ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ! [B] :
              ( ( v1_zf_lang(B)
                & m2_finseq_1(B,k5_numbers) )
             => ( ( p1_s1_zf_lang1(A)
                  & p1_s1_zf_lang1(B) )
               => p1_s1_zf_lang1(k7_zf_lang(A,B)) ) ) )
      & ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => ( p1_s1_zf_lang1(A)
               => p1_s1_zf_lang1(k8_zf_lang(B,A)) ) ) ) )
   => ! [A] :
        ( ( v1_zf_lang(A)
          & m2_finseq_1(A,k5_numbers) )
       => p1_s1_zf_lang1(A) ) )).

fof(dt_k1_zf_lang1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k1_zf_lang,A)
        & m1_relset_1(B,k1_zf_lang,A)
        & m1_subset_1(C,k1_zf_lang)
        & m1_subset_1(D,A) )
     => ( v1_funct_1(k1_zf_lang1(A,B,C,D))
        & v1_funct_2(k1_zf_lang1(A,B,C,D),k1_zf_lang,A)
        & m2_relset_1(k1_zf_lang1(A,B,C,D),k1_zf_lang,A) ) ) )).

fof(dt_k2_zf_lang1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => ( v1_funct_1(k2_zf_lang1(A,B,C,D))
        & v1_funct_2(k2_zf_lang1(A,B,C,D),A,C)
        & m2_relset_1(k2_zf_lang1(A,B,C,D),A,C) ) ) )).

fof(dt_k3_zf_lang1,axiom,(
    $true )).

fof(dt_k4_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( ~ v1_xboole_0(k4_zf_lang1(A))
        & m1_subset_1(k4_zf_lang1(A),k1_zfmisc_1(k1_zf_lang)) ) ) )).

fof(redefinition_k4_zf_lang1,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => k4_zf_lang1(A) = k3_zf_lang1(A) ) )).

fof(dt_k5_zf_lang1,axiom,(
    ! [A,B,C] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => ( v1_relat_1(k5_zf_lang1(A,B,C))
        & v1_funct_1(k5_zf_lang1(A,B,C)) ) ) )).

fof(dt_k6_zf_lang1,axiom,(
    ! [A,B,C] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => ( v1_zf_lang(k6_zf_lang1(A,B,C))
        & m2_finseq_1(k6_zf_lang1(A,B,C),k5_numbers) ) ) )).

fof(redefinition_k6_zf_lang1,axiom,(
    ! [A,B,C] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => k6_zf_lang1(A,B,C) = k5_zf_lang1(A,B,C) ) )).
%------------------------------------------------------------------------------