SET007 Axioms: SET007+56.ax


%------------------------------------------------------------------------------
% File     : SET007+56 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Model of ZF Set Theory Language
% 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_lang [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  193 (  25 unit)
%            Number of atoms       : 1239 ( 217 equality)
%            Maximal formula depth :   28 (   7 average)
%            Number of connectives : 1141 (  95 ~  ;   8  |; 546  &)
%                                         (  41 <=>; 451 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   30 (   1 propositional; 0-3 arity)
%            Number of functors    :   48 (  11 constant; 0-4 arity)
%            Number of variables   :  430 (   0 singleton; 367 !;  63 ?)
%            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_lang,axiom,(
    ~ v1_xboole_0(k1_zf_lang) )).

fof(rc1_zf_lang,axiom,(
    ? [A] :
      ( m1_finseq_1(A,k5_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_zf_lang(A) ) )).

fof(fc2_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => ( v1_relat_1(k4_zf_lang(A,B))
        & v1_funct_1(k4_zf_lang(A,B))
        & v1_finset_1(k4_zf_lang(A,B))
        & v1_finseq_1(k4_zf_lang(A,B))
        & v1_zf_lang(k4_zf_lang(A,B)) ) ) )).

fof(fc3_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => ( v1_relat_1(k5_zf_lang(A,B))
        & v1_funct_1(k5_zf_lang(A,B))
        & v1_finset_1(k5_zf_lang(A,B))
        & v1_finseq_1(k5_zf_lang(A,B))
        & v1_zf_lang(k5_zf_lang(A,B)) ) ) )).

fof(fc4_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_relat_1(k6_zf_lang(A))
        & v1_funct_1(k6_zf_lang(A))
        & v1_finset_1(k6_zf_lang(A))
        & v1_finseq_1(k6_zf_lang(A))
        & v1_zf_lang(k6_zf_lang(A)) ) ) )).

fof(fc5_zf_lang,axiom,(
    ! [A,B] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_relat_1(k7_zf_lang(A,B))
        & v1_funct_1(k7_zf_lang(A,B))
        & v1_finset_1(k7_zf_lang(A,B))
        & v1_finseq_1(k7_zf_lang(A,B))
        & v1_zf_lang(k7_zf_lang(A,B)) ) ) )).

fof(fc6_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_relat_1(k8_zf_lang(A,B))
        & v1_funct_1(k8_zf_lang(A,B))
        & v1_finset_1(k8_zf_lang(A,B))
        & v1_finseq_1(k8_zf_lang(A,B))
        & v1_zf_lang(k8_zf_lang(A,B)) ) ) )).

fof(d2_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_zf_lang(A) = k1_nat_1(np__5,A) ) )).

fof(d3_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k4_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__0),k3_zf_lang(A)),k3_zf_lang(B)) ) ) )).

fof(d4_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k5_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__1),k3_zf_lang(A)),k3_zf_lang(B)) ) ) )).

fof(t1_zf_lang,axiom,(
    $true )).

fof(t2_zf_lang,axiom,(
    $true )).

fof(t3_zf_lang,axiom,(
    $true )).

fof(t4_zf_lang,axiom,(
    $true )).

fof(t5_zf_lang,axiom,(
    $true )).

fof(t6_zf_lang,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)
                 => ( k4_zf_lang(A,B) = k4_zf_lang(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t7_zf_lang,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)
                 => ( k5_zf_lang(A,B) = k5_zf_lang(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(d5_zf_lang,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => k6_zf_lang(A) = k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__2),A) ) )).

fof(d6_zf_lang,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k5_numbers)
         => k7_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__3),A),B) ) ) )).

fof(t8_zf_lang,axiom,(
    $true )).

fof(t9_zf_lang,axiom,(
    $true )).

fof(t10_zf_lang,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k5_numbers)
         => ( k6_zf_lang(A) = k6_zf_lang(B)
           => A = B ) ) ) )).

fof(d7_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_finseq_1(B,k5_numbers)
         => k8_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__4),k3_zf_lang(A)),B) ) ) )).

fof(t11_zf_lang,axiom,(
    $true )).

fof(t12_zf_lang,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [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) = k8_zf_lang(D,B)
                   => ( C = D
                      & A = B ) ) ) ) ) ) )).

fof(d8_zf_lang,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( A = k9_zf_lang
      <=> ( ! [B] :
              ( r2_hidden(B,A)
             => m2_finseq_1(B,k5_numbers) )
          & ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => ! [C] :
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                 => ( r2_hidden(k4_zf_lang(B,C),A)
                    & r2_hidden(k5_zf_lang(B,C),A) ) ) )
          & ! [B] :
              ( m2_finseq_1(B,k5_numbers)
             => ( r2_hidden(B,A)
               => r2_hidden(k6_zf_lang(B),A) ) )
          & ! [B] :
              ( m2_finseq_1(B,k5_numbers)
             => ! [C] :
                  ( m2_finseq_1(C,k5_numbers)
                 => ( ( r2_hidden(B,A)
                      & r2_hidden(C,A) )
                   => r2_hidden(k7_zf_lang(B,C),A) ) ) )
          & ! [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
             => ! [C] :
                  ( m2_finseq_1(C,k5_numbers)
                 => ( r2_hidden(C,A)
                   => r2_hidden(k8_zf_lang(B,C),A) ) ) )
          & ! [B] :
              ( ~ v1_xboole_0(B)
             => ( ( ! [C] :
                      ( r2_hidden(C,B)
                     => m2_finseq_1(C,k5_numbers) )
                  & ! [C] :
                      ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                     => ! [D] :
                          ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                         => ( r2_hidden(k4_zf_lang(C,D),B)
                            & r2_hidden(k5_zf_lang(C,D),B) ) ) )
                  & ! [C] :
                      ( m2_finseq_1(C,k5_numbers)
                     => ( r2_hidden(C,B)
                       => r2_hidden(k6_zf_lang(C),B) ) )
                  & ! [C] :
                      ( m2_finseq_1(C,k5_numbers)
                     => ! [D] :
                          ( m2_finseq_1(D,k5_numbers)
                         => ( ( r2_hidden(C,B)
                              & r2_hidden(D,B) )
                           => r2_hidden(k7_zf_lang(C,D),B) ) ) )
                  & ! [C] :
                      ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                     => ! [D] :
                          ( m2_finseq_1(D,k5_numbers)
                         => ( r2_hidden(D,B)
                           => r2_hidden(k8_zf_lang(C,D),B) ) ) ) )
               => r1_tarski(A,B) ) ) ) ) ) )).

fof(d9_zf_lang,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ( v1_zf_lang(A)
      <=> m1_subset_1(A,k9_zf_lang) ) ) )).

fof(t13_zf_lang,axiom,(
    $true )).

fof(t14_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
    <=> r2_hidden(A,k9_zf_lang) ) )).

fof(d10_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v2_zf_lang(A)
      <=> ? [B] :
            ( m2_subset_1(B,k5_numbers,k1_zf_lang)
            & ? [C] :
                ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                & A = k4_zf_lang(B,C) ) ) ) ) )).

fof(d11_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v3_zf_lang(A)
      <=> ? [B] :
            ( m2_subset_1(B,k5_numbers,k1_zf_lang)
            & ? [C] :
                ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                & A = k5_zf_lang(B,C) ) ) ) ) )).

fof(d12_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v4_zf_lang(A)
      <=> ? [B] :
            ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers)
            & A = k6_zf_lang(B) ) ) ) )).

fof(d13_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v5_zf_lang(A)
      <=> ? [B] :
            ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers)
            & ? [C] :
                ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers)
                & A = k7_zf_lang(B,C) ) ) ) ) )).

fof(d14_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v6_zf_lang(A)
      <=> ? [B] :
            ( m2_subset_1(B,k5_numbers,k1_zf_lang)
            & ? [C] :
                ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers)
                & A = k8_zf_lang(B,C) ) ) ) ) )).

fof(t15_zf_lang,axiom,(
    $true )).

fof(t16_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ~ ( v2_zf_lang(A)
            & ! [B] :
                ( m2_subset_1(B,k5_numbers,k1_zf_lang)
               => ! [C] :
                    ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                   => A != k4_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
              & ? [C] :
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                  & A = k4_zf_lang(B,C) ) )
         => v2_zf_lang(A) )
        & ~ ( v3_zf_lang(A)
            & ! [B] :
                ( m2_subset_1(B,k5_numbers,k1_zf_lang)
               => ! [C] :
                    ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                   => A != k5_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
              & ? [C] :
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                  & A = k5_zf_lang(B,C) ) )
         => v3_zf_lang(A) )
        & ~ ( v4_zf_lang(A)
            & ! [B] :
                ( ( v1_zf_lang(B)
                  & m2_finseq_1(B,k5_numbers) )
               => A != k6_zf_lang(B) ) )
        & ( ? [B] :
              ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers)
              & A = k6_zf_lang(B) )
         => v4_zf_lang(A) )
        & ~ ( v5_zf_lang(A)
            & ! [B] :
                ( ( v1_zf_lang(B)
                  & m2_finseq_1(B,k5_numbers) )
               => ! [C] :
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k7_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers)
              & ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k7_zf_lang(B,C) ) )
         => v5_zf_lang(A) )
        & ~ ( v6_zf_lang(A)
            & ! [B] :
                ( m2_subset_1(B,k5_numbers,k1_zf_lang)
               => ! [C] :
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k8_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
              & ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k8_zf_lang(B,C) ) )
         => v6_zf_lang(A) ) ) ) )).

fof(d15_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v7_zf_lang(A)
      <=> ( v2_zf_lang(A)
          | v3_zf_lang(A) ) ) ) )).

fof(d16_zf_lang,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) = k6_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))) ) ) )).

fof(d17_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k11_zf_lang(A,B) = k6_zf_lang(k7_zf_lang(A,k6_zf_lang(B))) ) ) )).

fof(d18_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k12_zf_lang(A,B) = k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,A)) ) ) )).

fof(d19_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k13_zf_lang(A,B) = k6_zf_lang(k8_zf_lang(A,k6_zf_lang(B))) ) ) )).

fof(d20_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v8_zf_lang(A)
      <=> ? [B] :
            ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers)
            & ? [C] :
                ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers)
                & A = k10_zf_lang(B,C) ) ) ) ) )).

fof(d21_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v9_zf_lang(A)
      <=> ? [B] :
            ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers)
            & ? [C] :
                ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers)
                & A = k11_zf_lang(B,C) ) ) ) ) )).

fof(d22_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v10_zf_lang(A)
      <=> ? [B] :
            ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers)
            & ? [C] :
                ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers)
                & A = k12_zf_lang(B,C) ) ) ) ) )).

fof(d23_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v11_zf_lang(A)
      <=> ? [B] :
            ( m2_subset_1(B,k5_numbers,k1_zf_lang)
            & ? [C] :
                ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers)
                & A = k13_zf_lang(B,C) ) ) ) ) )).

fof(t17_zf_lang,axiom,(
    $true )).

fof(t18_zf_lang,axiom,(
    $true )).

fof(t19_zf_lang,axiom,(
    $true )).

fof(t20_zf_lang,axiom,(
    $true )).

fof(t21_zf_lang,axiom,(
    $true )).

fof(t22_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ~ ( v8_zf_lang(A)
            & ! [B] :
                ( ( v1_zf_lang(B)
                  & m2_finseq_1(B,k5_numbers) )
               => ! [C] :
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k10_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers)
              & ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k10_zf_lang(B,C) ) )
         => v8_zf_lang(A) )
        & ~ ( v9_zf_lang(A)
            & ! [B] :
                ( ( v1_zf_lang(B)
                  & m2_finseq_1(B,k5_numbers) )
               => ! [C] :
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k11_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers)
              & ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k11_zf_lang(B,C) ) )
         => v9_zf_lang(A) )
        & ~ ( v10_zf_lang(A)
            & ! [B] :
                ( ( v1_zf_lang(B)
                  & m2_finseq_1(B,k5_numbers) )
               => ! [C] :
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k12_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers)
              & ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k12_zf_lang(B,C) ) )
         => v10_zf_lang(A) )
        & ~ ( v11_zf_lang(A)
            & ! [B] :
                ( m2_subset_1(B,k5_numbers,k1_zf_lang)
               => ! [C] :
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k13_zf_lang(B,C) ) ) )
        & ( ? [B] :
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
              & ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k13_zf_lang(B,C) ) )
         => v11_zf_lang(A) ) ) ) )).

fof(d24_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => k14_zf_lang(A,B,C) = k8_zf_lang(A,k8_zf_lang(B,C)) ) ) ) )).

fof(d25_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => k15_zf_lang(A,B,C) = k13_zf_lang(A,k13_zf_lang(B,C)) ) ) ) )).

fof(t23_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( k14_zf_lang(A,B,C) = k8_zf_lang(A,k8_zf_lang(B,C))
                & k15_zf_lang(A,B,C) = k13_zf_lang(A,k13_zf_lang(B,C)) ) ) ) ) )).

fof(d26_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => k16_zf_lang(A,B,C,D) = k8_zf_lang(A,k14_zf_lang(B,C,D)) ) ) ) ) )).

fof(d27_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => k17_zf_lang(A,B,C,D) = k13_zf_lang(A,k15_zf_lang(B,C,D)) ) ) ) ) )).

fof(t24_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( k16_zf_lang(A,B,C,D) = k8_zf_lang(A,k14_zf_lang(B,C,D))
                    & k17_zf_lang(A,B,C,D) = k13_zf_lang(A,k15_zf_lang(B,C,D)) ) ) ) ) ) )).

fof(t25_zf_lang,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) ) ) )).

fof(t26_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ~ ( ~ v7_zf_lang(A)
          & ~ v4_zf_lang(A)
          & ~ v5_zf_lang(A)
          & ~ v6_zf_lang(A) ) ) )).

fof(t27_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v7_zf_lang(A)
       => k3_finseq_1(A) = np__3 ) ) )).

fof(t28_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ~ ( ~ v7_zf_lang(A)
          & ! [B] :
              ( ( v1_zf_lang(B)
                & m2_finseq_1(B,k5_numbers) )
             => ~ r1_xreal_0(k1_nat_1(k3_finseq_1(B),np__1),k3_finseq_1(A)) ) ) ) )).

fof(t29_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => r1_xreal_0(np__3,k3_finseq_1(A)) ) )).

fof(t30_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( k3_finseq_1(A) = np__3
       => v7_zf_lang(A) ) ) )).

fof(t31_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ( k1_funct_1(k4_zf_lang(A,B),np__1) = np__0
            & k1_funct_1(k5_zf_lang(A,B),np__1) = np__1 ) ) ) )).

fof(t32_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k1_funct_1(k6_zf_lang(A),np__1) = np__2 ) )).

fof(t33_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k1_funct_1(k7_zf_lang(A,B),np__1) = np__3 ) ) )).

fof(t34_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k1_funct_1(k8_zf_lang(A,B),np__1) = np__4 ) ) )).

fof(t35_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v2_zf_lang(A)
       => k1_funct_1(A,np__1) = np__0 ) ) )).

fof(t36_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v3_zf_lang(A)
       => k1_funct_1(A,np__1) = np__1 ) ) )).

fof(t37_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v4_zf_lang(A)
       => k1_funct_1(A,np__1) = np__2 ) ) )).

fof(t38_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v5_zf_lang(A)
       => k1_funct_1(A,np__1) = np__3 ) ) )).

fof(t39_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v6_zf_lang(A)
       => k1_funct_1(A,np__1) = np__4 ) ) )).

fof(t40_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ~ ( ~ ( v2_zf_lang(A)
              & k1_funct_1(A,np__1) = np__0 )
          & ~ ( v3_zf_lang(A)
              & k1_funct_1(A,np__1) = np__1 )
          & ~ ( v4_zf_lang(A)
              & k1_funct_1(A,np__1) = np__2 )
          & ~ ( v5_zf_lang(A)
              & k1_funct_1(A,np__1) = np__3 )
          & ~ ( v6_zf_lang(A)
              & k1_funct_1(A,np__1) = np__4 ) ) ) )).

fof(t41_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( k1_funct_1(A,np__1) = np__0
       => v2_zf_lang(A) ) ) )).

fof(t42_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( k1_funct_1(A,np__1) = np__1
       => v3_zf_lang(A) ) ) )).

fof(t43_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( k1_funct_1(A,np__1) = np__2
       => v4_zf_lang(A) ) ) )).

fof(t44_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( k1_funct_1(A,np__1) = np__3
       => v5_zf_lang(A) ) ) )).

fof(t45_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( k1_funct_1(A,np__1) = np__4
       => v6_zf_lang(A) ) ) )).

fof(t46_zf_lang,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_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( A = k7_finseq_1(B,C)
               => A = B ) ) ) ) )).

fof(t47_zf_lang,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) )
                 => ( k7_zf_lang(A,B) = k7_zf_lang(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t48_zf_lang,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) )
                 => ( k10_zf_lang(A,B) = k10_zf_lang(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t49_zf_lang,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) )
                 => ( k11_zf_lang(A,B) = k11_zf_lang(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t50_zf_lang,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) )
                 => ( k12_zf_lang(A,B) = k12_zf_lang(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t51_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] :
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( k13_zf_lang(A,C) = k13_zf_lang(B,D)
                   => ( A = B
                      & C = D ) ) ) ) ) ) )).

fof(d28_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v7_zf_lang(A)
       => k18_zf_lang(A) = k1_funct_1(A,np__2) ) ) )).

fof(d29_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v7_zf_lang(A)
       => k19_zf_lang(A) = k1_funct_1(A,np__3) ) ) )).

fof(t52_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v7_zf_lang(A)
       => ( k18_zf_lang(A) = k1_funct_1(A,np__2)
          & k19_zf_lang(A) = k1_funct_1(A,np__3) ) ) ) )).

fof(t53_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v2_zf_lang(A)
       => A = k4_zf_lang(k18_zf_lang(A),k19_zf_lang(A)) ) ) )).

fof(t54_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v3_zf_lang(A)
       => A = k5_zf_lang(k18_zf_lang(A),k19_zf_lang(A)) ) ) )).

fof(d30_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v4_zf_lang(A)
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( B = k20_zf_lang(A)
            <=> k6_zf_lang(B) = A ) ) ) ) )).

fof(d31_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ( v5_zf_lang(A)
          | v8_zf_lang(A) )
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( ( v5_zf_lang(A)
               => ( B = k21_zf_lang(A)
                <=> ? [C] :
                      ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers)
                      & k7_zf_lang(B,C) = A ) ) )
              & ( ~ v5_zf_lang(A)
               => ( B = k21_zf_lang(A)
                <=> ? [C] :
                      ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers)
                      & k10_zf_lang(B,C) = A ) ) ) ) ) ) ) )).

fof(d32_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ( v5_zf_lang(A)
          | v8_zf_lang(A) )
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( ( v5_zf_lang(A)
               => ( B = k22_zf_lang(A)
                <=> ? [C] :
                      ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers)
                      & k7_zf_lang(C,B) = A ) ) )
              & ( ~ v5_zf_lang(A)
               => ( B = k22_zf_lang(A)
                <=> ? [C] :
                      ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers)
                      & k10_zf_lang(C,B) = A ) ) ) ) ) ) ) )).

fof(t55_zf_lang,axiom,(
    $true )).

fof(t56_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( v5_zf_lang(A)
           => ( ~ ( B = k21_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => k7_zf_lang(B,C) != A ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & k7_zf_lang(B,C) = A )
               => B = k21_zf_lang(A) )
              & ~ ( B = k22_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => k7_zf_lang(C,B) != A ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & k7_zf_lang(C,B) = A )
               => B = k22_zf_lang(A) ) ) ) ) ) )).

fof(t57_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( v8_zf_lang(A)
           => ( ~ ( B = k21_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => k10_zf_lang(B,C) != A ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & k10_zf_lang(B,C) = A )
               => B = k21_zf_lang(A) )
              & ~ ( B = k22_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => k10_zf_lang(C,B) != A ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & k10_zf_lang(C,B) = A )
               => B = k22_zf_lang(A) ) ) ) ) ) )).

fof(t58_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v5_zf_lang(A)
       => A = k7_zf_lang(k21_zf_lang(A),k22_zf_lang(A)) ) ) )).

fof(t59_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v8_zf_lang(A)
       => A = k10_zf_lang(k21_zf_lang(A),k22_zf_lang(A)) ) ) )).

fof(d33_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ( v6_zf_lang(A)
          | v11_zf_lang(A) )
       => ! [B] :
            ( m2_subset_1(B,k5_numbers,k1_zf_lang)
           => ( ( v6_zf_lang(A)
               => ( B = k23_zf_lang(A)
                <=> ? [C] :
                      ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers)
                      & k8_zf_lang(B,C) = A ) ) )
              & ( ~ v6_zf_lang(A)
               => ( B = k23_zf_lang(A)
                <=> ? [C] :
                      ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers)
                      & k13_zf_lang(B,C) = A ) ) ) ) ) ) ) )).

fof(d34_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ( v6_zf_lang(A)
          | v11_zf_lang(A) )
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( ( v6_zf_lang(A)
               => ( B = k24_zf_lang(A)
                <=> ? [C] :
                      ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                      & k8_zf_lang(C,B) = A ) ) )
              & ( ~ v6_zf_lang(A)
               => ( B = k24_zf_lang(A)
                <=> ? [C] :
                      ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                      & k13_zf_lang(C,B) = A ) ) ) ) ) ) ) )).

fof(t60_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( v6_zf_lang(B)
               => ( ~ ( A = k23_zf_lang(B)
                      & ! [D] :
                          ( ( v1_zf_lang(D)
                            & m2_finseq_1(D,k5_numbers) )
                         => k8_zf_lang(A,D) != B ) )
                  & ( ? [D] :
                        ( v1_zf_lang(D)
                        & m2_finseq_1(D,k5_numbers)
                        & k8_zf_lang(A,D) = B )
                   => A = k23_zf_lang(B) )
                  & ~ ( C = k24_zf_lang(B)
                      & ! [D] :
                          ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                         => k8_zf_lang(D,C) != B ) )
                  & ( ? [D] :
                        ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                        & k8_zf_lang(D,C) = B )
                   => C = k24_zf_lang(B) ) ) ) ) ) ) )).

fof(t61_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( v11_zf_lang(B)
               => ( ~ ( A = k23_zf_lang(B)
                      & ! [D] :
                          ( ( v1_zf_lang(D)
                            & m2_finseq_1(D,k5_numbers) )
                         => k13_zf_lang(A,D) != B ) )
                  & ( ? [D] :
                        ( v1_zf_lang(D)
                        & m2_finseq_1(D,k5_numbers)
                        & k13_zf_lang(A,D) = B )
                   => A = k23_zf_lang(B) )
                  & ~ ( C = k24_zf_lang(B)
                      & ! [D] :
                          ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                         => k13_zf_lang(D,C) != B ) )
                  & ( ? [D] :
                        ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                        & k13_zf_lang(D,C) = B )
                   => C = k24_zf_lang(B) ) ) ) ) ) ) )).

fof(t62_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v6_zf_lang(A)
       => A = k8_zf_lang(k23_zf_lang(A),k24_zf_lang(A)) ) ) )).

fof(t63_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v11_zf_lang(A)
       => A = k13_zf_lang(k23_zf_lang(A),k24_zf_lang(A)) ) ) )).

fof(d35_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v9_zf_lang(A)
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( B = k25_zf_lang(A)
            <=> ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k11_zf_lang(B,C) ) ) ) ) ) )).

fof(d36_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v9_zf_lang(A)
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( B = k26_zf_lang(A)
            <=> ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k11_zf_lang(C,B) ) ) ) ) ) )).

fof(t64_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( v9_zf_lang(A)
           => ( ~ ( B = k25_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => A != k11_zf_lang(B,C) ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & A = k11_zf_lang(B,C) )
               => B = k25_zf_lang(A) )
              & ~ ( B = k26_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => A != k11_zf_lang(C,B) ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & A = k11_zf_lang(C,B) )
               => B = k26_zf_lang(A) ) ) ) ) ) )).

fof(t65_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v9_zf_lang(A)
       => A = k11_zf_lang(k25_zf_lang(A),k26_zf_lang(A)) ) ) )).

fof(d37_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v10_zf_lang(A)
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( B = k27_zf_lang(A)
            <=> ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k12_zf_lang(B,C) ) ) ) ) ) )).

fof(d38_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v10_zf_lang(A)
       => ! [B] :
            ( ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers) )
           => ( B = k28_zf_lang(A)
            <=> ? [C] :
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k12_zf_lang(C,B) ) ) ) ) ) )).

fof(t66_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( v10_zf_lang(A)
           => ( ~ ( B = k27_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => A != k12_zf_lang(B,C) ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & A = k12_zf_lang(B,C) )
               => B = k27_zf_lang(A) )
              & ~ ( B = k28_zf_lang(A)
                  & ! [C] :
                      ( ( v1_zf_lang(C)
                        & m2_finseq_1(C,k5_numbers) )
                     => A != k12_zf_lang(C,B) ) )
              & ( ? [C] :
                    ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers)
                    & A = k12_zf_lang(C,B) )
               => B = k28_zf_lang(A) ) ) ) ) ) )).

fof(t67_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v10_zf_lang(A)
       => A = k12_zf_lang(k27_zf_lang(A),k28_zf_lang(A)) ) ) )).

fof(d39_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r1_zf_lang(A,B)
          <=> ~ ( B != k6_zf_lang(A)
                & ! [C] :
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => ( B != k7_zf_lang(A,C)
                      & B != k7_zf_lang(C,A) ) )
                & ! [C] :
                    ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                   => B != k8_zf_lang(C,A) ) ) ) ) ) )).

fof(t68_zf_lang,axiom,(
    $true )).

fof(t69_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ~ r1_zf_lang(C,k4_zf_lang(A,B)) ) ) ) )).

fof(t70_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ~ r1_zf_lang(C,k5_zf_lang(A,B)) ) ) ) )).

fof(t71_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r1_zf_lang(A,k6_zf_lang(B))
          <=> A = B ) ) ) )).

fof(t72_zf_lang,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) )
             => ( r1_zf_lang(A,k7_zf_lang(B,C))
              <=> ( A = B
                  | A = C ) ) ) ) ) )).

fof(t73_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r1_zf_lang(B,k8_zf_lang(A,C))
              <=> B = C ) ) ) ) )).

fof(t74_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ~ ( v7_zf_lang(A)
              & r1_zf_lang(B,A) ) ) ) )).

fof(t75_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( v4_zf_lang(A)
           => ( r1_zf_lang(B,A)
            <=> B = k20_zf_lang(A) ) ) ) ) )).

fof(t76_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( v5_zf_lang(A)
           => ( r1_zf_lang(B,A)
            <=> ( B = k21_zf_lang(A)
                | B = k22_zf_lang(A) ) ) ) ) ) )).

fof(t77_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( v6_zf_lang(A)
           => ( r1_zf_lang(B,A)
            <=> B = k24_zf_lang(A) ) ) ) ) )).

fof(d40_zf_lang,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)
          <=> ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ? [D] :
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D)
                    & r1_xreal_0(np__1,C)
                    & k3_finseq_1(D) = C
                    & k1_funct_1(D,np__1) = A
                    & k1_funct_1(D,C) = B
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r1_xreal_0(np__1,E)
                            & ~ r1_xreal_0(C,E)
                            & ! [F] :
                                ( ( v1_zf_lang(F)
                                  & m2_finseq_1(F,k5_numbers) )
                               => ! [G] :
                                    ( ( v1_zf_lang(G)
                                      & m2_finseq_1(G,k5_numbers) )
                                   => ~ ( k1_funct_1(D,E) = F
                                        & k1_funct_1(D,k1_nat_1(E,np__1)) = G
                                        & r1_zf_lang(F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t78_zf_lang,axiom,(
    $true )).

fof(t79_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => r2_zf_lang(A,A) ) )).

fof(d41_zf_lang,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(A,B)
              & A != B ) ) ) ) )).

fof(t80_zf_lang,axiom,(
    $true )).

fof(t81_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ~ ( r1_zf_lang(A,B)
              & r1_xreal_0(k3_finseq_1(B),k3_finseq_1(A)) ) ) ) )).

fof(t82_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r1_zf_lang(A,B)
           => r3_zf_lang(A,B) ) ) ) )).

fof(t83_zf_lang,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_xreal_0(k3_finseq_1(B),k3_finseq_1(A)) ) ) ) )).

fof(t84_zf_lang,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)
              & ! [C] :
                  ( ( v1_zf_lang(C)
                    & m2_finseq_1(C,k5_numbers) )
                 => ~ r1_zf_lang(C,B) ) ) ) ) )).

fof(t85_zf_lang,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)
                  & r3_zf_lang(B,C) )
               => r3_zf_lang(A,C) ) ) ) ) )).

fof(t86_zf_lang,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(A,B)
                  & r2_zf_lang(B,C) )
               => r2_zf_lang(A,C) ) ) ) ) )).

fof(t87_zf_lang,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_zf_lang(B,A) )
           => A = B ) ) ) )).

fof(t88_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ~ r3_zf_lang(C,k4_zf_lang(A,B)) ) ) ) )).

fof(t89_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ~ r3_zf_lang(C,k5_zf_lang(A,B)) ) ) ) )).

fof(t90_zf_lang,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,k6_zf_lang(B))
           => r2_zf_lang(A,B) ) ) ) )).

fof(t91_zf_lang,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,k7_zf_lang(B,C))
                  & ~ r2_zf_lang(A,B)
                  & ~ r2_zf_lang(A,C) ) ) ) ) )).

fof(t92_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [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(B,k8_zf_lang(A,C))
               => r2_zf_lang(B,C) ) ) ) ) )).

fof(t93_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ~ ( v7_zf_lang(A)
              & r3_zf_lang(B,A) ) ) ) )).

fof(t94_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v4_zf_lang(A)
       => r3_zf_lang(k20_zf_lang(A),A) ) ) )).

fof(t95_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v5_zf_lang(A)
       => ( r3_zf_lang(k21_zf_lang(A),A)
          & r3_zf_lang(k22_zf_lang(A),A) ) ) ) )).

fof(t96_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v6_zf_lang(A)
       => r3_zf_lang(k24_zf_lang(A),A) ) ) )).

fof(t97_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r2_zf_lang(C,k4_zf_lang(A,B))
              <=> C = k4_zf_lang(A,B) ) ) ) ) )).

fof(t98_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] :
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r2_zf_lang(C,k5_zf_lang(A,B))
              <=> C = k5_zf_lang(A,B) ) ) ) ) )).

fof(d42_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] :
          ( B = k29_zf_lang(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] :
                  ( v1_zf_lang(D)
                  & m2_finseq_1(D,k5_numbers)
                  & D = C
                  & r2_zf_lang(D,A) ) ) ) ) )).

fof(t99_zf_lang,axiom,(
    $true )).

fof(t100_zf_lang,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))
           => r2_zf_lang(A,B) ) ) ) )).

fof(t101_zf_lang,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_tarski(k29_zf_lang(A),k29_zf_lang(B)) ) ) ) )).

fof(t102_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k29_zf_lang(k4_zf_lang(A,B)) = k1_tarski(k4_zf_lang(A,B)) ) ) )).

fof(t103_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k29_zf_lang(k5_zf_lang(A,B)) = k1_tarski(k5_zf_lang(A,B)) ) ) )).

fof(t104_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k29_zf_lang(k6_zf_lang(A)) = k2_xboole_0(k29_zf_lang(A),k1_tarski(k6_zf_lang(A))) ) )).

fof(t105_zf_lang,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(k7_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k1_tarski(k7_zf_lang(A,B))) ) ) )).

fof(t106_zf_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] :
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k29_zf_lang(k8_zf_lang(A,B)) = k2_xboole_0(k29_zf_lang(B),k1_tarski(k8_zf_lang(A,B))) ) ) )).

fof(t107_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v7_zf_lang(A)
      <=> k29_zf_lang(A) = k1_tarski(A) ) ) )).

fof(t108_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v4_zf_lang(A)
       => k29_zf_lang(A) = k2_xboole_0(k29_zf_lang(k20_zf_lang(A)),k1_tarski(A)) ) ) )).

fof(t109_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v5_zf_lang(A)
       => k29_zf_lang(A) = k2_xboole_0(k2_xboole_0(k29_zf_lang(k21_zf_lang(A)),k29_zf_lang(k22_zf_lang(A))),k1_tarski(A)) ) ) )).

fof(t110_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v6_zf_lang(A)
       => k29_zf_lang(A) = k2_xboole_0(k29_zf_lang(k24_zf_lang(A)),k1_tarski(A)) ) ) )).

fof(t111_zf_lang,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_hidden(B,k29_zf_lang(C))
               => ( ( ~ r1_zf_lang(A,B)
                    & ~ r3_zf_lang(A,B)
                    & ~ r2_zf_lang(A,B) )
                  | r2_hidden(A,k29_zf_lang(C)) ) ) ) ) ) )).

fof(s1_zf_lang,axiom,
    ( ( ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ( v7_zf_lang(A)
           => p1_s1_zf_lang(A) ) )
      & ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ( ( v4_zf_lang(A)
              & p1_s1_zf_lang(k20_zf_lang(A)) )
           => p1_s1_zf_lang(A) ) )
      & ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ( ( v5_zf_lang(A)
              & p1_s1_zf_lang(k21_zf_lang(A))
              & p1_s1_zf_lang(k22_zf_lang(A)) )
           => p1_s1_zf_lang(A) ) )
      & ! [A] :
          ( ( v1_zf_lang(A)
            & m2_finseq_1(A,k5_numbers) )
         => ( ( v6_zf_lang(A)
              & p1_s1_zf_lang(k24_zf_lang(A)) )
           => p1_s1_zf_lang(A) ) ) )
   => ! [A] :
        ( ( v1_zf_lang(A)
          & m2_finseq_1(A,k5_numbers) )
       => p1_s1_zf_lang(A) ) )).

fof(s2_zf_lang,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(B,A)
               => p1_s2_zf_lang(B) ) )
         => p1_s2_zf_lang(A) ) )
   => ! [A] :
        ( ( v1_zf_lang(A)
          & m2_finseq_1(A,k5_numbers) )
       => p1_s2_zf_lang(A) ) )).

fof(dt_k1_zf_lang,axiom,(
    m1_subset_1(k1_zf_lang,k1_zfmisc_1(k5_numbers)) )).

fof(dt_k2_zf_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k2_zf_lang(A),k5_numbers,k1_zf_lang) ) )).

fof(dt_k3_zf_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zf_lang)
     => m2_finseq_1(k3_zf_lang(A),k5_numbers) ) )).

fof(redefinition_k3_zf_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zf_lang)
     => k3_zf_lang(A) = k5_finseq_1(A) ) )).

fof(dt_k4_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => m2_finseq_1(k4_zf_lang(A,B),k5_numbers) ) )).

fof(dt_k5_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => m2_finseq_1(k5_zf_lang(A,B),k5_numbers) ) )).

fof(dt_k6_zf_lang,axiom,(
    ! [A] :
      ( m1_finseq_1(A,k5_numbers)
     => m2_finseq_1(k6_zf_lang(A),k5_numbers) ) )).

fof(dt_k7_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_finseq_1(A,k5_numbers)
        & m1_finseq_1(B,k5_numbers) )
     => m2_finseq_1(k7_zf_lang(A,B),k5_numbers) ) )).

fof(dt_k8_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_finseq_1(B,k5_numbers) )
     => m2_finseq_1(k8_zf_lang(A,B),k5_numbers) ) )).

fof(dt_k9_zf_lang,axiom,(
    ~ v1_xboole_0(k9_zf_lang) )).

fof(dt_k10_zf_lang,axiom,(
    ! [A,B] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k10_zf_lang(A,B))
        & m2_finseq_1(k10_zf_lang(A,B),k5_numbers) ) ) )).

fof(dt_k11_zf_lang,axiom,(
    ! [A,B] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k11_zf_lang(A,B))
        & m2_finseq_1(k11_zf_lang(A,B),k5_numbers) ) ) )).

fof(dt_k12_zf_lang,axiom,(
    ! [A,B] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k12_zf_lang(A,B))
        & m2_finseq_1(k12_zf_lang(A,B),k5_numbers) ) ) )).

fof(dt_k13_zf_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k13_zf_lang(A,B))
        & m2_finseq_1(k13_zf_lang(A,B),k5_numbers) ) ) )).

fof(dt_k14_zf_lang,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang)
        & v1_zf_lang(C)
        & m1_finseq_1(C,k5_numbers) )
     => ( v1_zf_lang(k14_zf_lang(A,B,C))
        & m2_finseq_1(k14_zf_lang(A,B,C),k5_numbers) ) ) )).

fof(dt_k15_zf_lang,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang)
        & v1_zf_lang(C)
        & m1_finseq_1(C,k5_numbers) )
     => ( v1_zf_lang(k15_zf_lang(A,B,C))
        & m2_finseq_1(k15_zf_lang(A,B,C),k5_numbers) ) ) )).

fof(dt_k16_zf_lang,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang)
        & v1_zf_lang(D)
        & m1_finseq_1(D,k5_numbers) )
     => ( v1_zf_lang(k16_zf_lang(A,B,C,D))
        & m2_finseq_1(k16_zf_lang(A,B,C,D),k5_numbers) ) ) )).

fof(dt_k17_zf_lang,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang)
        & v1_zf_lang(D)
        & m1_finseq_1(D,k5_numbers) )
     => ( v1_zf_lang(k17_zf_lang(A,B,C,D))
        & m2_finseq_1(k17_zf_lang(A,B,C,D),k5_numbers) ) ) )).

fof(dt_k18_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m2_subset_1(k18_zf_lang(A),k5_numbers,k1_zf_lang) ) )).

fof(dt_k19_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m2_subset_1(k19_zf_lang(A),k5_numbers,k1_zf_lang) ) )).

fof(dt_k20_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k20_zf_lang(A))
        & m2_finseq_1(k20_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k21_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k21_zf_lang(A))
        & m2_finseq_1(k21_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k22_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k22_zf_lang(A))
        & m2_finseq_1(k22_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k23_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m2_subset_1(k23_zf_lang(A),k5_numbers,k1_zf_lang) ) )).

fof(dt_k24_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k24_zf_lang(A))
        & m2_finseq_1(k24_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k25_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k25_zf_lang(A))
        & m2_finseq_1(k25_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k26_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k26_zf_lang(A))
        & m2_finseq_1(k26_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k27_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k27_zf_lang(A))
        & m2_finseq_1(k27_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k28_zf_lang,axiom,(
    ! [A] :
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k28_zf_lang(A))
        & m2_finseq_1(k28_zf_lang(A),k5_numbers) ) ) )).

fof(dt_k29_zf_lang,axiom,(
    $true )).

fof(d1_zf_lang,axiom,(
    k1_zf_lang = a_0_0_zf_lang )).

fof(fraenkel_a_0_0_zf_lang,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_zf_lang)
    <=> ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = B
          & r1_xreal_0(np__5,B) ) ) )).
%------------------------------------------------------------------------------