SET007 Axioms: SET007+61.ax


%------------------------------------------------------------------------------
% File     : SET007+61 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Curried and Uncurried Functions
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : funct_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   86 (  12 unit)
%            Number of atoms       :  403 ( 126 equality)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :  332 (  15 ~  ;  10  |; 183  &)
%                                         (   8 <=>; 116 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   1 propositional; 0-2 arity)
%            Number of functors    :   28 (   2 constant; 0-2 arity)
%            Number of variables   :  213 (   0 singleton; 207 !;   6 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_funct_5,axiom,(
    k2_funct_4(k1_xboole_0) = k1_xboole_0 )).

fof(d1_funct_5,axiom,(
    ! [A,B] :
      ( B = k1_funct_5(A)
    <=> ! [C] :
          ( r2_hidden(C,B)
        <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) )).

fof(d2_funct_5,axiom,(
    ! [A,B] :
      ( B = k2_funct_5(A)
    <=> ! [C] :
          ( r2_hidden(C,B)
        <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) )).

fof(t2_funct_5,axiom,(
    $true )).

fof(t3_funct_5,axiom,(
    $true )).

fof(t4_funct_5,axiom,(
    ! [A,B,C] :
      ( r2_hidden(k4_tarski(A,B),C)
     => ( r2_hidden(A,k1_funct_5(C))
        & r2_hidden(B,k2_funct_5(C)) ) ) )).

fof(t5_funct_5,axiom,(
    ! [A,B] :
      ( r1_tarski(A,B)
     => ( r1_tarski(k1_funct_5(A),k1_funct_5(B))
        & r1_tarski(k2_funct_5(A),k2_funct_5(B)) ) ) )).

fof(t6_funct_5,axiom,(
    ! [A,B] :
      ( k1_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k1_funct_5(A),k1_funct_5(B))
      & k2_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) ) )).

fof(t7_funct_5,axiom,(
    ! [A,B] :
      ( r1_tarski(k1_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k1_funct_5(A),k1_funct_5(B)))
      & r1_tarski(k2_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k2_funct_5(A),k2_funct_5(B))) ) )).

fof(t8_funct_5,axiom,(
    ! [A,B] :
      ( r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B)))
      & r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))) ) )).

fof(t9_funct_5,axiom,(
    ! [A,B] :
      ( r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B)))
      & r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))) ) )).

fof(t10_funct_5,axiom,
    ( k1_funct_5(k1_xboole_0) = k1_xboole_0
    & k2_funct_5(k1_xboole_0) = k1_xboole_0 )).

fof(t11_funct_5,axiom,(
    ! [A,B] :
      ( ~ ( A = k1_xboole_0
          & k2_zfmisc_1(B,A) = k1_xboole_0
          & k2_zfmisc_1(A,B) = k1_xboole_0 )
     => ( k1_funct_5(k2_zfmisc_1(B,A)) = B
        & k2_funct_5(k2_zfmisc_1(A,B)) = B ) ) )).

fof(t12_funct_5,axiom,(
    ! [A,B] :
      ( r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A)
      & r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B) ) )).

fof(t13_funct_5,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,k2_zfmisc_1(B,C))
     => ( r1_tarski(k1_funct_5(A),B)
        & r1_tarski(k2_funct_5(A),C) ) ) )).

fof(t14_funct_5,axiom,(
    $true )).

fof(t15_funct_5,axiom,(
    ! [A,B] :
      ( k1_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(A)
      & k2_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(B) ) )).

fof(t16_funct_5,axiom,(
    ! [A,B,C,D] :
      ( k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(A,C)
      & k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(B,D) ) )).

fof(t17_funct_5,axiom,(
    ! [A] :
      ( ! [B,C] : ~ r2_hidden(k4_tarski(B,C),A)
     => ( k1_funct_5(A) = k1_xboole_0
        & k2_funct_5(A) = k1_xboole_0 ) ) )).

fof(t18_funct_5,axiom,(
    ! [A] :
      ( ( k1_funct_5(A) = k1_xboole_0
        | k2_funct_5(A) = k1_xboole_0 )
     => ! [B,C] : ~ r2_hidden(k4_tarski(B,C),A) ) )).

fof(t19_funct_5,axiom,(
    ! [A] :
      ( k1_funct_5(A) = k1_xboole_0
    <=> k2_funct_5(A) = k1_xboole_0 ) )).

fof(t20_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A)))
        & k2_funct_5(k1_relat_1(A)) = k1_funct_5(k1_relat_1(k2_funct_4(A))) ) ) )).

fof(t21_funct_5,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( k1_funct_5(A) = k1_relat_1(A)
        & k2_funct_5(A) = k2_relat_1(A) ) ) )).

fof(d3_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_funct_5(A)
          <=> ( k1_relat_1(B) = k1_funct_5(k1_relat_1(A))
              & ! [C] :
                  ~ ( r2_hidden(C,k1_funct_5(k1_relat_1(A)))
                    & ! [D] :
                        ( ( v1_relat_1(D)
                          & v1_funct_1(D) )
                       => ~ ( k1_funct_1(B,C) = D
                            & k1_relat_1(D) = k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A)))))
                            & ! [E] :
                                ( r2_hidden(E,k1_relat_1(D))
                               => k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E)) ) ) ) ) ) ) ) ) )).

fof(d4_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k4_funct_5(A)
          <=> ( ! [C] :
                  ( r2_hidden(C,k1_relat_1(B))
                <=> ? [D,E] :
                      ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & ? [F] :
                          ( C = k4_tarski(D,F)
                          & r2_hidden(D,k1_relat_1(A))
                          & E = k1_funct_1(A,D)
                          & r2_hidden(F,k1_relat_1(E)) ) ) )
              & ! [C,D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r2_hidden(C,k1_relat_1(B))
                      & D = k1_funct_1(A,k1_mcart_1(C)) )
                   => k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C)) ) ) ) ) ) ) )).

fof(d5_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k5_funct_5(A) = k3_funct_5(k2_funct_4(A)) ) )).

fof(d6_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k6_funct_5(A) = k2_funct_4(k4_funct_5(A)) ) )).

fof(t22_funct_5,axiom,(
    $true )).

fof(t23_funct_5,axiom,(
    $true )).

fof(t24_funct_5,axiom,(
    $true )).

fof(t25_funct_5,axiom,(
    $true )).

fof(t26_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
       => ( r2_hidden(A,k1_relat_1(k3_funct_5(C)))
          & v1_relat_1(k1_funct_1(k3_funct_5(C),A))
          & v1_funct_1(k1_funct_1(k3_funct_5(C),A)) ) ) ) )).

fof(t27_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
              & D = k1_funct_1(k3_funct_5(C),A) )
           => ( r2_hidden(B,k1_relat_1(D))
              & k1_funct_1(D,B) = k1_funct_1(C,k4_tarski(A,B)) ) ) ) ) )).

fof(t28_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
       => ( r2_hidden(B,k1_relat_1(k5_funct_5(C)))
          & v1_relat_1(k1_funct_1(k5_funct_5(C),B))
          & v1_funct_1(k1_funct_1(k5_funct_5(C),B)) ) ) ) )).

fof(t29_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
              & D = k1_funct_1(k5_funct_5(C),B) )
           => ( r2_hidden(A,k1_relat_1(D))
              & k1_funct_1(D,A) = k1_funct_1(C,k4_tarski(A,B)) ) ) ) ) )).

fof(t30_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_relat_1(k5_funct_5(A)) = k2_funct_5(k1_relat_1(A)) ) )).

fof(t31_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( k1_relat_1(C) = k2_zfmisc_1(A,B)
       => ( k2_zfmisc_1(A,B) = k1_xboole_0
          | ( k1_relat_1(k3_funct_5(C)) = A
            & k1_relat_1(k5_funct_5(C)) = B ) ) ) ) )).

fof(t32_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
       => ( r1_tarski(k1_relat_1(k3_funct_5(C)),A)
          & r1_tarski(k1_relat_1(k5_funct_5(C)),B) ) ) ) )).

fof(t33_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
       => ( k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A)
          & k1_relat_1(k6_funct_5(C)) = k2_zfmisc_1(A,k1_relat_1(C)) ) ) ) )).

fof(t34_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ! [B,C] : ~ r2_hidden(k4_tarski(B,C),k1_relat_1(A))
       => ( k3_funct_5(A) = k1_xboole_0
          & k5_funct_5(A) = k1_xboole_0 ) ) ) )).

fof(t35_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ! [B] :
            ~ ( r2_hidden(B,k1_relat_1(A))
              & v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B)) )
       => ( k4_funct_5(A) = k1_xboole_0
          & k6_funct_5(A) = k1_xboole_0 ) ) ) )).

fof(t36_funct_5,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ~ ( k2_zfmisc_1(A,B) != k1_xboole_0
          & k1_relat_1(D) = k2_zfmisc_1(A,B)
          & r2_hidden(C,A)
          & ! [E] :
              ( ( v1_relat_1(E)
                & v1_funct_1(E) )
             => ~ ( k1_funct_1(k3_funct_5(D),C) = E
                  & k1_relat_1(E) = B
                  & r1_tarski(k2_relat_1(E),k2_relat_1(D))
                  & ! [F] :
                      ( r2_hidden(F,B)
                     => k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(C,F)) ) ) ) ) ) )).

fof(t37_funct_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(k3_funct_5(B)))
       => ( v1_relat_1(k1_funct_1(k3_funct_5(B),A))
          & v1_funct_1(k1_funct_1(k3_funct_5(B),A)) ) ) ) )).

fof(t38_funct_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r2_hidden(A,k1_relat_1(k3_funct_5(B)))
              & C = k1_funct_1(k3_funct_5(B),A) )
           => ( k1_relat_1(C) = k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B)))))
              & r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B)))
              & r1_tarski(k2_relat_1(C),k2_relat_1(B))
              & ! [D] :
                  ( r2_hidden(D,k1_relat_1(C))
                 => ( k1_funct_1(C,D) = k1_funct_1(B,k4_tarski(A,D))
                    & r2_hidden(k4_tarski(A,D),k1_relat_1(B)) ) ) ) ) ) ) )).

fof(t39_funct_5,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ~ ( k2_zfmisc_1(A,B) != k1_xboole_0
          & k1_relat_1(D) = k2_zfmisc_1(A,B)
          & r2_hidden(C,B)
          & ! [E] :
              ( ( v1_relat_1(E)
                & v1_funct_1(E) )
             => ~ ( k1_funct_1(k5_funct_5(D),C) = E
                  & k1_relat_1(E) = A
                  & r1_tarski(k2_relat_1(E),k2_relat_1(D))
                  & ! [F] :
                      ( r2_hidden(F,A)
                     => k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)) ) ) ) ) ) )).

fof(t40_funct_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(k5_funct_5(B)))
       => ( v1_relat_1(k1_funct_1(k5_funct_5(B),A))
          & v1_funct_1(k1_funct_1(k5_funct_5(B),A)) ) ) ) )).

fof(t41_funct_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r2_hidden(A,k1_relat_1(k5_funct_5(B)))
              & C = k1_funct_1(k5_funct_5(B),A) )
           => ( k1_relat_1(C) = k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A))))
              & r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B)))
              & r1_tarski(k2_relat_1(C),k2_relat_1(B))
              & ! [D] :
                  ( r2_hidden(D,k1_relat_1(C))
                 => ( k1_funct_1(C,D) = k1_funct_1(B,k4_tarski(D,A))
                    & r2_hidden(k4_tarski(D,A),k1_relat_1(B)) ) ) ) ) ) ) )).

fof(t42_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( k1_relat_1(C) = k2_zfmisc_1(A,B)
       => ( r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C)))
          & r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C))) ) ) ) )).

fof(t43_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A)))
        & r1_tarski(k2_relat_1(k5_funct_5(A)),k4_partfun1(k1_funct_5(k1_relat_1(A)),k2_relat_1(A))) ) ) )).

fof(t44_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
       => ( r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A))
          & r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C))) ) ) ) )).

fof(t45_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(A,k1_relat_1(C))
              & D = k1_funct_1(C,A)
              & r2_hidden(B,k1_relat_1(D)) )
           => ( r2_hidden(k4_tarski(A,B),k1_relat_1(k4_funct_5(C)))
              & k1_funct_1(k4_funct_5(C),k4_tarski(A,B)) = k1_funct_1(D,B)
              & r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) ) ) ) ) )).

fof(t46_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(A,k1_relat_1(C))
              & D = k1_funct_1(C,A)
              & r2_hidden(B,k1_relat_1(D)) )
           => ( r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C)))
              & k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) = k1_funct_1(D,B)
              & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) ) ) ) ) )).

fof(t47_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
       => ( r1_tarski(k2_relat_1(k4_funct_5(C)),B)
          & r1_tarski(k2_relat_1(k6_funct_5(C)),B) ) ) ) )).

fof(t48_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
       => ( r1_tarski(k2_relat_1(k4_funct_5(C)),B)
          & r1_tarski(k2_relat_1(k6_funct_5(C)),B) ) ) ) )).

fof(t49_funct_5,axiom,
    ( k3_funct_5(k1_xboole_0) = k1_xboole_0
    & k5_funct_5(k1_xboole_0) = k1_xboole_0 )).

fof(t50_funct_5,axiom,
    ( k4_funct_5(k1_xboole_0) = k1_xboole_0
    & k6_funct_5(k1_xboole_0) = k1_xboole_0 )).

fof(t51_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( k1_relat_1(C) = k2_zfmisc_1(A,B)
              & k1_relat_1(D) = k2_zfmisc_1(A,B)
              & k3_funct_5(C) = k3_funct_5(D) )
           => C = D ) ) ) )).

fof(t52_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( k1_relat_1(C) = k2_zfmisc_1(A,B)
              & k1_relat_1(D) = k2_zfmisc_1(A,B)
              & k5_funct_5(C) = k5_funct_5(D) )
           => C = D ) ) ) )).

fof(t53_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
              & r1_tarski(k2_relat_1(D),k1_funct_2(A,B))
              & k4_funct_5(C) = k4_funct_5(D) )
           => ( A = k1_xboole_0
              | C = D ) ) ) ) )).

fof(t54_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
              & r1_tarski(k2_relat_1(D),k1_funct_2(A,B))
              & k6_funct_5(C) = k6_funct_5(D) )
           => ( A = k1_xboole_0
              | C = D ) ) ) ) )).

fof(t55_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
       => ( A = k1_xboole_0
          | ( k3_funct_5(k4_funct_5(C)) = C
            & k5_funct_5(k6_funct_5(C)) = C ) ) ) ) )).

fof(t56_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( k1_relat_1(C) = k2_zfmisc_1(A,B)
       => ( k4_funct_5(k3_funct_5(C)) = C
          & k6_funct_5(k5_funct_5(C)) = C ) ) ) )).

fof(t57_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
       => ( k4_funct_5(k3_funct_5(C)) = C
          & k6_funct_5(k5_funct_5(C)) = C ) ) ) )).

fof(t58_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
       => ( r2_hidden(k1_xboole_0,k2_relat_1(C))
          | ( k3_funct_5(k4_funct_5(C)) = C
            & k5_funct_5(k6_funct_5(C)) = C ) ) ) ) )).

fof(t59_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
              & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B))
              & k3_funct_5(C) = k3_funct_5(D) )
           => C = D ) ) ) )).

fof(t60_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
              & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B))
              & k5_funct_5(C) = k5_funct_5(D) )
           => C = D ) ) ) )).

fof(t61_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
              & r1_tarski(k2_relat_1(D),k4_partfun1(A,B))
              & k4_funct_5(C) = k4_funct_5(D) )
           => ( r2_hidden(k1_xboole_0,k2_relat_1(C))
              | r2_hidden(k1_xboole_0,k2_relat_1(D))
              | C = D ) ) ) ) )).

fof(t62_funct_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
              & r1_tarski(k2_relat_1(D),k4_partfun1(A,B))
              & k6_funct_5(C) = k6_funct_5(D) )
           => ( r2_hidden(k1_xboole_0,k2_relat_1(C))
              | r2_hidden(k1_xboole_0,k2_relat_1(D))
              | C = D ) ) ) ) )).

fof(t63_funct_5,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,B)
     => r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)) ) )).

fof(t64_funct_5,axiom,(
    ! [A] : k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0) )).

fof(t65_funct_5,axiom,(
    ! [A,B] :
      ( r2_wellord2(A,k1_funct_2(k1_tarski(B),A))
      & k1_card_1(A) = k1_card_1(k1_funct_2(k1_tarski(B),A)) ) )).

fof(t66_funct_5,axiom,(
    ! [A,B] : k1_funct_2(A,k1_tarski(B)) = k1_tarski(k2_funcop_1(A,B)) )).

fof(t67_funct_5,axiom,(
    ! [A,B,C,D] :
      ( ( r2_wellord2(A,B)
        & r2_wellord2(C,D) )
     => ( r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D))
        & k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)) ) ) )).

fof(t68_funct_5,axiom,(
    ! [A,B,C,D] :
      ( ( k1_card_1(A) = k1_card_1(B)
        & k1_card_1(C) = k1_card_1(D) )
     => k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)) ) )).

fof(t69_funct_5,axiom,(
    ! [A,B,C] :
      ( r1_xboole_0(A,B)
     => ( r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C)))
        & k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) ) ) )).

fof(t70_funct_5,axiom,(
    ! [A,B,C] :
      ( r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C)))
      & k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)) = k1_card_1(k1_funct_2(A,k1_funct_2(B,C))) ) )).

fof(t71_funct_5,axiom,(
    ! [A,B,C] :
      ( r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C)))
      & k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) ) )).

fof(t72_funct_5,axiom,(
    ! [A,B,C] :
      ( A != B
     => ( r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C))
        & k1_card_1(k1_funct_2(C,k2_tarski(A,B))) = k1_card_1(k1_zfmisc_1(C)) ) ) )).

fof(t73_funct_5,axiom,(
    ! [A,B,C] :
      ( A != B
     => ( r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C))
        & k1_card_1(k1_funct_2(k2_tarski(A,B),C)) = k1_card_1(k2_zfmisc_1(C,C)) ) ) )).

fof(s1_funct_5,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_funct_5
      & ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(B,f1_s1_funct_5)
           => k1_funct_1(A,B) = f2_s1_funct_5(B) ) ) ) )).

fof(dt_k1_funct_5,axiom,(
    $true )).

fof(dt_k2_funct_5,axiom,(
    $true )).

fof(dt_k3_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_5(A))
        & v1_funct_1(k3_funct_5(A)) ) ) )).

fof(dt_k4_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k4_funct_5(A))
        & v1_funct_1(k4_funct_5(A)) ) ) )).

fof(dt_k5_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k5_funct_5(A))
        & v1_funct_1(k5_funct_5(A)) ) ) )).

fof(dt_k6_funct_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k6_funct_5(A))
        & v1_funct_1(k6_funct_5(A)) ) ) )).
%------------------------------------------------------------------------------