SET007 Axioms: SET007+20.ax


%------------------------------------------------------------------------------
% File     : SET007+20 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Functions from a Set to a Set
% 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  214 (  70 unit)
%            Number of atoms       : 1129 ( 220 equality)
%            Maximal formula depth :   17 (   6 average)
%            Number of connectives :  986 (  71 ~  ;  28  |; 550  &)
%                                         (  14 <=>; 323 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :   78 (  39 constant; 0-6 arity)
%            Number of variables   :  539 (   0 singleton; 515 !;  24 ?)
%            Maximal term depth    :    3 (   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(rc1_funct_2,axiom,(
    ! [A,B] :
    ? [C] :
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) )).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] :
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) )).

fof(fc1_funct_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) )).

fof(fc2_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) )).

fof(cc2_funct_2,axiom,(
    ! [A,B,C] :
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) )).

fof(cc3_funct_2,axiom,(
    ! [A,B,C] :
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) )).

fof(rc2_funct_2,axiom,(
    ! [A] :
    ? [B] :
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) )).

fof(cc4_funct_2,axiom,(
    ! [A,B] :
      ( m1_relset_1(B,A,A)
     => ( ( v1_funct_1(B)
          & v1_partfun1(B,A,A)
          & v1_relat_2(B)
          & v1_funct_2(B,A,A) )
       => ( v1_funct_1(B)
          & v2_funct_1(B)
          & v1_funct_2(B,A,A)
          & v2_funct_2(B,A,A)
          & v3_funct_2(B,A,A) ) ) ) )).

fof(cc5_funct_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) )).

fof(cc6_funct_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) )).

fof(d1_funct_2,axiom,(
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) )).

fof(t1_funct_2,axiom,(
    $true )).

fof(t2_funct_2,axiom,(
    $true )).

fof(t3_funct_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funct_1(A)
        & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A))
        & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) )).

fof(t4_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) )).

fof(t5_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( k1_relat_1(C) = A
          & ! [D] :
              ( r2_hidden(D,A)
             => r2_hidden(k1_funct_1(C,D),B) ) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & m2_relset_1(C,A,B) ) ) ) )).

fof(t6_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) ) ) ) )).

fof(t7_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) )).

fof(t8_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(k2_relat_1(D),C)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(D)
            & v1_funct_2(D,A,C)
            & m2_relset_1(D,A,C) ) ) ) ) )).

fof(t9_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(B,C)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(D)
            & v1_funct_2(D,A,C)
            & m2_relset_1(D,A,C) ) ) ) ) )).

fof(d2_funct_2,axiom,(
    ! [A,B,C] :
      ( C = k1_funct_2(A,B)
    <=> ! [D] :
          ( r2_hidden(D,C)
        <=> ? [E] :
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) )).

fof(t10_funct_2,axiom,(
    $true )).

fof(t11_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => r2_hidden(C,k1_funct_2(A,B)) ) ) )).

fof(t12_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => r2_hidden(B,k1_funct_2(A,A)) ) )).

fof(t13_funct_2,axiom,(
    $true )).

fof(t14_funct_2,axiom,(
    ! [A] :
      ( A != k1_xboole_0
     => k1_funct_2(A,k1_xboole_0) = k1_xboole_0 ) )).

fof(t15_funct_2,axiom,(
    $true )).

fof(t16_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ! [D] :
            ~ ( r2_hidden(D,B)
              & ! [E] :
                  ~ ( r2_hidden(E,A)
                    & D = k1_funct_1(C,E) ) )
       => ( B = k1_xboole_0
          | k2_relat_1(C) = B ) ) ) )).

fof(t17_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ~ ( r2_hidden(C,B)
          & k2_relat_1(D) = B
          & ! [E] :
              ~ ( r2_hidden(E,A)
                & k1_funct_1(D,E) = C ) ) ) )).

fof(t18_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] :
                ( r2_hidden(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) )).

fof(t19_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ~ ( B = k1_xboole_0
                & C != k1_xboole_0
                & A != k1_xboole_0 )
           => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
              & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)
              & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) ) ) ) ) )).

fof(t20_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ( k2_relat_1(D) = B
              & k2_relat_1(E) = C )
           => ( B = k1_xboole_0
              | C = k1_xboole_0
              | k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C ) ) ) ) )).

fof(t21_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) )).

fof(t22_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( B != k1_xboole_0
       => ( k2_relat_1(C) = B
        <=> ! [D] :
              ( D != k1_xboole_0
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,D)
                    & m2_relset_1(E,B,D) )
                 => ! [F] :
                      ( ( v1_funct_1(F)
                        & v1_funct_2(F,B,D)
                        & m2_relset_1(F,B,D) )
                     => ( k1_partfun1(A,B,B,D,C,E) = k1_partfun1(A,B,B,D,C,F)
                       => E = F ) ) ) ) ) ) ) )).

fof(t23_funct_2,axiom,(
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) )).

fof(t24_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,A)
            & m2_relset_1(D,B,A) )
         => ( k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B)
           => k2_relat_1(C) = B ) ) ) )).

fof(t25_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => ( v2_funct_1(C)
        <=> ! [D,E] :
              ( ( r2_hidden(D,A)
                & r2_hidden(E,A)
                & k1_funct_1(C,D) = k1_funct_1(C,E) )
             => D = E ) ) ) ) )).

fof(t26_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( v2_funct_1(k1_partfun1(A,B,B,C,D,E))
           => ( ( C = k1_xboole_0
                & B != k1_xboole_0 )
              | ( B = k1_xboole_0
                & A != k1_xboole_0 )
              | v2_funct_1(D) ) ) ) ) )).

fof(t27_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ~ ( A != k1_xboole_0
          & B != k1_xboole_0
          & ~ ( v2_funct_1(C)
            <=> ! [D,E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,D,A)
                    & m2_relset_1(E,D,A) )
                 => ! [F] :
                      ( ( v1_funct_1(F)
                        & v1_funct_2(F,D,A)
                        & m2_relset_1(F,D,A) )
                     => ( k1_partfun1(D,A,A,B,E,C) = k1_partfun1(D,A,A,B,F,C)
                       => E = F ) ) ) ) ) ) )).

fof(t28_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ( k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C
              & v2_funct_1(E) )
           => ( C = k1_xboole_0
              | k2_relat_1(D) = B ) ) ) ) )).

fof(t29_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,A)
            & m2_relset_1(D,B,A) )
         => ( k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A)
           => ( B = k1_xboole_0
              | ( v2_funct_1(C)
                & k2_relat_1(D) = A ) ) ) ) ) )).

fof(t30_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ( v2_funct_1(k1_partfun1(A,B,B,C,D,E))
              & k2_relat_1(D) = B )
           => ( ( C = k1_xboole_0
                & B != k1_xboole_0 )
              | ( v2_funct_1(D)
                & v2_funct_1(E) ) ) ) ) ) )).

fof(t31_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( v2_funct_1(C)
          & k2_relat_1(C) = B )
       => ( v1_funct_1(k2_funct_1(C))
          & v1_funct_2(k2_funct_1(C),B,A)
          & m2_relset_1(k2_funct_1(C),B,A) ) ) ) )).

fof(t32_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( ( v2_funct_1(D)
          & r2_hidden(C,A) )
       => ( B = k1_xboole_0
          | k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) = C ) ) ) )).

fof(t33_funct_2,axiom,(
    $true )).

fof(t34_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,A)
            & m2_relset_1(D,B,A) )
         => ( ( k2_relat_1(C) = B
              & v2_funct_1(C)
              & ! [E,F] :
                  ( ( ( r2_hidden(E,B)
                      & k1_funct_1(D,E) = F )
                   => ( r2_hidden(F,A)
                      & k1_funct_1(C,F) = E ) )
                  & ( ( r2_hidden(F,A)
                      & k1_funct_1(C,F) = E )
                   => ( r2_hidden(E,B)
                      & k1_funct_1(D,E) = F ) ) ) )
           => ( A = k1_xboole_0
              | B = k1_xboole_0
              | D = k2_funct_1(C) ) ) ) ) )).

fof(t35_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( k2_relat_1(C) = B
          & v2_funct_1(C) )
       => ( B = k1_xboole_0
          | ( k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A)
            & k5_relat_1(k2_funct_1(C),C) = k6_partfun1(B) ) ) ) ) )).

fof(t36_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,A)
            & m2_relset_1(D,B,A) )
         => ( ( k2_relat_1(C) = B
              & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A)
              & v2_funct_1(C) )
           => ( A = k1_xboole_0
              | B = k1_xboole_0
              | D = k2_funct_1(C) ) ) ) ) )).

fof(t37_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ~ ( B != k1_xboole_0
          & ? [D] :
              ( v1_funct_1(D)
              & v1_funct_2(D,B,A)
              & m2_relset_1(D,B,A)
              & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) )
          & ~ v2_funct_1(C) ) ) )).

fof(t38_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(C,A)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(k2_partfun1(A,B,D,C))
            & v1_funct_2(k2_partfun1(A,B,D,C),C,B)
            & m2_relset_1(k2_partfun1(A,B,D,C),C,B) ) ) ) ) )).

fof(t39_funct_2,axiom,(
    $true )).

fof(t40_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(A,C)
       => k2_partfun1(A,B,D,C) = D ) ) )).

fof(t41_funct_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m2_relset_1(E,A,B) )
     => ( ( r2_hidden(C,A)
          & r2_hidden(k1_funct_1(E,C),D) )
       => ( B = k1_xboole_0
          | k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) ) ) ) )).

fof(t42_funct_2,axiom,(
    $true )).

fof(t43_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] :
            ( ? [F] :
                ( r2_hidden(F,A)
                & r2_hidden(F,C)
                & E = k1_funct_1(D,F) )
           => r2_hidden(E,k9_relat_1(D,C)) ) ) ) )).

fof(t44_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => r1_tarski(k9_relat_1(D,C),B) ) )).

fof(t45_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => k2_funct_2(A,B,C,A) = k2_relat_1(C) ) ) )).

fof(t46_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] :
            ( r2_hidden(E,k10_relat_1(D,C))
          <=> ( r2_hidden(E,A)
              & r2_hidden(k1_funct_1(D,E),C) ) ) ) ) )).

fof(t47_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => r1_tarski(k10_relat_1(D,C),A) ) )).

fof(t48_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => k3_funct_2(A,B,C,B) = A ) ) )).

fof(t49_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ! [D] :
            ~ ( r2_hidden(D,B)
              & k3_funct_2(A,B,C,k1_tarski(D)) = k1_xboole_0 )
      <=> k2_relat_1(C) = B ) ) )).

fof(t50_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(C,A)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) ) ) ) )).

fof(t51_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => k3_funct_2(A,B,C,k2_funct_2(A,B,C,A)) = A ) ) )).

fof(t52_funct_2,axiom,(
    $true )).

fof(t53_funct_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m2_relset_1(E,A,B) )
     => ! [F] :
          ( ( v1_funct_1(F)
            & v1_funct_2(F,B,C)
            & m2_relset_1(F,B,C) )
         => ~ ( ( C = k1_xboole_0
               => B = k1_xboole_0 )
              & ( B = k1_xboole_0
               => A = k1_xboole_0 )
              & ~ r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) ) ) ) )).

fof(t54_funct_2,axiom,(
    $true )).

fof(t55_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_xboole_0
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_xboole_0,A)
          & m2_relset_1(B,k1_xboole_0,A) ) ) ) )).

fof(t56_funct_2,axiom,(
    $true )).

fof(t57_funct_2,axiom,(
    $true )).

fof(t58_funct_2,axiom,(
    $true )).

fof(t59_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_xboole_0,A)
        & m2_relset_1(C,k1_xboole_0,A) )
     => k2_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0 ) )).

fof(t60_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_xboole_0,A)
        & m2_relset_1(C,k1_xboole_0,A) )
     => k3_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0 ) )).

fof(t61_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_tarski(A),B)
        & m2_relset_1(C,k1_tarski(A),B) )
     => ( B != k1_xboole_0
       => r2_hidden(k1_funct_1(C,A),B) ) ) )).

fof(t62_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_tarski(A),B)
        & m2_relset_1(C,k1_tarski(A),B) )
     => ( B != k1_xboole_0
       => k2_relat_1(C) = k1_tarski(k1_funct_1(C,A)) ) ) )).

fof(t63_funct_2,axiom,(
    $true )).

fof(t64_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k1_tarski(A),B)
        & m2_relset_1(D,k1_tarski(A),B) )
     => ( B != k1_xboole_0
       => r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A))) ) ) )).

fof(t65_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,k1_tarski(B))
        & m2_relset_1(D,A,k1_tarski(B)) )
     => ( r2_hidden(C,A)
       => k1_funct_1(D,C) = B ) ) )).

fof(t66_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,k1_tarski(B))
        & m2_relset_1(C,A,k1_tarski(B)) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,k1_tarski(B))
            & m2_relset_1(D,A,k1_tarski(B)) )
         => C = D ) ) )).

fof(t67_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( k4_relset_1(A,A,B) = A
        & r1_tarski(k2_relat_1(B),A) ) ) )).

fof(t68_funct_2,axiom,(
    $true )).

fof(t69_funct_2,axiom,(
    $true )).

fof(t70_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( r2_hidden(B,A)
           => k1_funct_1(k5_relat_1(C,D),B) = k1_funct_1(D,k1_funct_1(C,B)) ) ) ) )).

fof(t71_funct_2,axiom,(
    $true )).

fof(t72_funct_2,axiom,(
    $true )).

fof(t73_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( ( k2_relat_1(B) = A
              & k2_relat_1(C) = A )
           => k2_relat_1(k4_funct_2(A,B,C)) = A ) ) ) )).

fof(t74_funct_2,axiom,(
    ! [A,B] :
      ( m2_relset_1(B,A,A)
     => ( k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B
        & k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B ) ) )).

fof(t75_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( ( k4_funct_2(A,B,C) = B
              & k2_relat_1(B) = A )
           => C = k6_partfun1(A) ) ) ) )).

fof(t76_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( ( k4_funct_2(A,C,B) = B
              & v2_funct_1(B) )
           => C = k6_partfun1(A) ) ) ) )).

fof(t77_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( v2_funct_1(B)
      <=> ! [C,D] :
            ( ( r2_hidden(C,A)
              & r2_hidden(D,A)
              & k1_funct_1(B,C) = k1_funct_1(B,D) )
           => C = D ) ) ) )).

fof(t78_funct_2,axiom,(
    $true )).

fof(t79_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => k2_funct_2(A,A,B,A) = k2_relat_1(B) ) )).

fof(t80_funct_2,axiom,(
    $true )).

fof(t81_funct_2,axiom,(
    $true )).

fof(t82_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A ) )).

fof(d3_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_2(C,A,B)
      <=> k2_relat_1(C) = B ) ) )).

fof(d4_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v3_funct_2(C,A,B)
      <=> ( v2_funct_1(C)
          & v2_funct_2(C,A,B) ) ) ) )).

fof(t83_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( ( v2_funct_1(B)
          & k2_relat_1(B) = A )
       => ( v1_funct_1(B)
          & v1_funct_2(B,A,A)
          & v3_funct_2(B,A,A)
          & m2_relset_1(B,A,A) ) ) ) )).

fof(t84_funct_2,axiom,(
    $true )).

fof(t85_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( v2_funct_1(B)
       => ! [C,D] :
            ( ( r2_hidden(C,A)
              & r2_hidden(D,A)
              & k1_funct_1(B,C) = k1_funct_1(B,D) )
           => C = D ) ) ) )).

fof(t86_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & v3_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( k5_funct_2(A,B,C) = C
           => B = k6_partfun1(A) ) ) ) )).

fof(t87_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & v3_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( k5_funct_2(A,B,C) = k6_partfun1(A)
           => C = k6_funct_2(A,B) ) ) ) )).

fof(t88_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( k5_funct_2(A,B,k6_funct_2(A,B)) = k6_partfun1(A)
        & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A) ) ) )).

fof(t89_funct_2,axiom,(
    $true )).

fof(t90_funct_2,axiom,(
    $true )).

fof(t91_funct_2,axiom,(
    $true )).

fof(t92_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m2_relset_1(C,A,A) )
     => ( r1_tarski(B,A)
       => ( k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B
          & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B ) ) ) )).

fof(t93_funct_2,axiom,(
    $true )).

fof(t94_funct_2,axiom,(
    $true )).

fof(t95_funct_2,axiom,(
    $true )).

fof(t96_funct_2,axiom,(
    $true )).

fof(t97_funct_2,axiom,(
    $true )).

fof(t98_funct_2,axiom,(
    $true )).

fof(t99_funct_2,axiom,(
    $true )).

fof(t100_funct_2,axiom,(
    $true )).

fof(t101_funct_2,axiom,(
    $true )).

fof(t102_funct_2,axiom,(
    $true )).

fof(t103_funct_2,axiom,(
    $true )).

fof(t104_funct_2,axiom,(
    $true )).

fof(t105_funct_2,axiom,(
    $true )).

fof(t106_funct_2,axiom,(
    $true )).

fof(t107_funct_2,axiom,(
    $true )).

fof(t108_funct_2,axiom,(
    $true )).

fof(t109_funct_2,axiom,(
    $true )).

fof(t110_funct_2,axiom,(
    $true )).

fof(t111_funct_2,axiom,(
    $true )).

fof(t112_funct_2,axiom,(
    $true )).

fof(t113_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] :
                ( m1_subset_1(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) )).

fof(t114_funct_2,axiom,(
    $true )).

fof(t115_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ~ ( r2_hidden(E,k2_funct_2(A,B,D,C))
            & ! [F] :
                ~ ( r2_hidden(F,A)
                  & r2_hidden(F,C)
                  & E = k1_funct_1(D,F) ) ) ) )).

fof(t116_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] :
          ~ ( r2_hidden(E,k2_funct_2(A,B,D,C))
            & ! [F] :
                ( m1_subset_1(F,A)
               => ~ ( r2_hidden(F,C)
                    & E = k1_funct_1(D,F) ) ) ) ) )).

fof(t117_funct_2,axiom,(
    $true )).

fof(t118_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,k2_zfmisc_1(A,B),C)
            & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
         => ( ! [F,G] :
                ( ( r2_hidden(F,A)
                  & r2_hidden(G,B) )
               => k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) )
           => D = E ) ) ) )).

fof(t119_funct_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v1_funct_1(F)
        & v1_funct_2(F,k2_zfmisc_1(A,B),C)
        & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
     => ( ( r2_hidden(D,A)
          & r2_hidden(E,B) )
       => ( C = k1_xboole_0
          | r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) ) ) ) )).

fof(t120_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,k2_zfmisc_1(A,B),C)
            & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
         => ( ! [F] :
                ( m1_subset_1(F,A)
               => ! [G] :
                    ( m1_subset_1(G,B)
                   => k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) ) )
           => D = E ) ) ) )).

fof(t121_funct_2,axiom,(
    ! [A,B,C] :
      ( r2_hidden(C,k1_funct_2(A,B))
     => ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) ) ) )).

fof(t122_funct_2,axiom,(
    $true )).

fof(t123_funct_2,axiom,(
    $true )).

fof(t124_funct_2,axiom,(
    $true )).

fof(t125_funct_2,axiom,(
    $true )).

fof(t126_funct_2,axiom,(
    $true )).

fof(t127_funct_2,axiom,(
    $true )).

fof(t128_funct_2,axiom,(
    $true )).

fof(t129_funct_2,axiom,(
    $true )).

fof(t130_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ( k4_relset_1(A,B,C) = A
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & m2_relset_1(C,A,B) ) ) ) )).

fof(t131_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ( v1_partfun1(C,A,B)
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & m2_relset_1(C,A,B) ) ) ) )).

fof(t132_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & m2_relset_1(C,A,B) )
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | v1_partfun1(C,A,B) ) ) ) )).

fof(t133_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => v1_partfun1(k3_partfun1(C,A,B),A,B) ) ) )).

fof(t134_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => v1_partfun1(k3_partfun1(B,A,A),A,A) ) )).

fof(t135_funct_2,axiom,(
    $true )).

fof(t136_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ~ ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
          & ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ? [E] :
                  ( r2_hidden(E,k4_relset_1(A,B,C))
                  & k1_funct_1(D,E) != k1_funct_1(C,E) ) ) ) ) )).

fof(t137_funct_2,axiom,(
    $true )).

fof(t138_funct_2,axiom,(
    $true )).

fof(t139_funct_2,axiom,(
    $true )).

fof(t140_funct_2,axiom,(
    $true )).

fof(t141_funct_2,axiom,(
    ! [A,B] : r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B)) )).

fof(t142_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( r1_partfun1(C,D)
           => ( ( B = k1_xboole_0
                & A != k1_xboole_0 )
              | C = D ) ) ) ) )).

fof(t143_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( r1_partfun1(B,C)
           => B = C ) ) ) )).

fof(t144_funct_2,axiom,(
    $true )).

fof(t145_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ( B = k1_xboole_0
             => A = k1_xboole_0 )
           => ( r1_partfun1(C,D)
            <=> ! [E] :
                  ( r2_hidden(E,k4_relset_1(A,B,C))
                 => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) ) ) ) )).

fof(t146_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( r1_partfun1(B,C)
          <=> ! [D] :
                ( r2_hidden(D,k4_relset_1(A,A,B))
               => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) )).

fof(t147_funct_2,axiom,(
    $true )).

fof(t148_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ~ ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
          & ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ~ r1_partfun1(C,D) ) ) ) )).

fof(t149_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,A) )
     => ? [C] :
          ( v1_funct_1(C)
          & v1_funct_2(C,A,A)
          & m2_relset_1(C,A,A)
          & r1_partfun1(B,C) ) ) )).

fof(t150_funct_2,axiom,(
    $true )).

fof(t151_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & v1_funct_2(E,A,B)
                & m2_relset_1(E,A,B) )
             => ( ( r1_partfun1(C,E)
                  & r1_partfun1(D,E) )
               => ( ( B = k1_xboole_0
                    & A != k1_xboole_0 )
                  | r1_partfun1(C,D) ) ) ) ) ) )).

fof(t152_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,A,A) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,A)
                & m2_relset_1(D,A,A) )
             => ( ( r1_partfun1(B,D)
                  & r1_partfun1(C,D) )
               => r1_partfun1(B,C) ) ) ) ) )).

fof(t153_funct_2,axiom,(
    $true )).

fof(t154_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ~ ( ( B = k1_xboole_0
               => A = k1_xboole_0 )
              & r1_partfun1(C,D)
              & ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ~ ( r1_partfun1(C,E)
                      & r1_partfun1(D,E) ) ) ) ) ) )).

fof(t155_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( r1_partfun1(C,D)
           => ( ( B = k1_xboole_0
                & A != k1_xboole_0 )
              | r2_hidden(D,k5_partfun1(A,B,C)) ) ) ) ) )).

fof(t156_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( r1_partfun1(B,C)
           => r2_hidden(C,k5_partfun1(A,A,B)) ) ) ) )).

fof(t157_funct_2,axiom,(
    $true )).

fof(t158_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( r2_hidden(D,k5_partfun1(A,B,C))
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) )).

fof(t159_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)) ) )).

fof(t160_funct_2,axiom,(
    ! [A,B] : k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B) )).

fof(t161_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C) ) ) )).

fof(t162_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B) ) )).

fof(t163_funct_2,axiom,(
    $true )).

fof(t164_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,k1_tarski(B)) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,k1_tarski(B))
            & m2_relset_1(D,A,k1_tarski(B)) )
         => k5_partfun1(A,k1_tarski(B),C) = k1_tarski(D) ) ) )).

fof(t165_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ( r1_tarski(D,C)
           => r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) ) ) ) )).

fof(t166_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ( ( r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C))
              & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) )
           => r1_tarski(D,C) ) ) ) )).

fof(t167_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ( ( r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))
              & ! [E] : B != k1_tarski(E) )
           => r1_tarski(D,C) ) ) ) )).

fof(t168_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ( ( ! [E] : B != k1_tarski(E)
              & k5_partfun1(A,B,C) = k5_partfun1(A,B,D) )
           => C = D ) ) ) )).

fof(d5_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C))
        & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) )
     => D = k9_funct_2(A,B,C) ) )).

fof(t169_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(C,k1_funct_2(A,B))
       => ( k1_relat_1(C) = A
          & r1_tarski(k2_relat_1(C),B) ) ) ) )).

fof(s1_funct_2,axiom,
    ( ! [A] :
        ~ ( r2_hidden(A,f1_s1_funct_2)
          & ! [B] :
              ~ ( r2_hidden(B,f2_s1_funct_2)
                & p1_s1_funct_2(A,B) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2)
        & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2)
        & ! [B] :
            ( r2_hidden(B,f1_s1_funct_2)
           => p1_s1_funct_2(B,k1_funct_1(A,B)) ) ) )).

fof(s2_funct_2,axiom,
    ( ! [A] :
        ( r2_hidden(A,f1_s2_funct_2)
       => r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2)
        & m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2)
        & ! [B] :
            ( r2_hidden(B,f1_s2_funct_2)
           => k1_funct_1(A,B) = f3_s2_funct_2(B) ) ) )).

fof(s3_funct_2,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s3_funct_2)
       => ? [B] :
            ( m1_subset_1(B,f2_s3_funct_2)
            & p1_s3_funct_2(A,B) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2)
        & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2)
        & ! [B] :
            ( m1_subset_1(B,f1_s3_funct_2)
           => p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)) ) ) )).

fof(s4_funct_2,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2)
      & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2)
      & ! [B] :
          ( m1_subset_1(B,f1_s4_funct_2)
         => k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B) ) ) )).

fof(s5_funct_2,axiom,
    ( ! [A,B] :
        ~ ( r2_hidden(A,f1_s5_funct_2)
          & r2_hidden(B,f2_s5_funct_2)
          & ! [C] :
              ~ ( r2_hidden(C,f3_s5_funct_2)
                & p1_s5_funct_2(A,B,C) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2)
        & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2)
        & ! [B,C] :
            ( ( r2_hidden(B,f1_s5_funct_2)
              & r2_hidden(C,f2_s5_funct_2) )
           => p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))) ) ) )).

fof(s6_funct_2,axiom,
    ( ! [A,B] :
        ( ( r2_hidden(A,f1_s6_funct_2)
          & r2_hidden(B,f2_s6_funct_2) )
       => r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2)
        & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2)
        & ! [B,C] :
            ( ( r2_hidden(B,f1_s6_funct_2)
              & r2_hidden(C,f2_s6_funct_2) )
           => k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C) ) ) )).

fof(s7_funct_2,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s7_funct_2)
       => ! [B] :
            ( m1_subset_1(B,f2_s7_funct_2)
           => ? [C] :
                ( m1_subset_1(C,f3_s7_funct_2)
                & p1_s7_funct_2(A,B,C) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2)
        & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2)
        & ! [B] :
            ( m1_subset_1(B,f1_s7_funct_2)
           => ! [C] :
                ( m1_subset_1(C,f2_s7_funct_2)
               => p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))) ) ) ) )).

fof(s8_funct_2,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2)
      & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2)
      & ! [B] :
          ( m1_subset_1(B,f1_s8_funct_2)
         => ! [C] :
              ( m1_subset_1(C,f2_s8_funct_2)
             => k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C) ) ) ) )).

fof(s9_funct_2,axiom,
    ( ! [A] :
        ( r2_hidden(A,f1_s9_funct_2)
       => ( ( p1_s9_funct_2(A)
           => r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2) )
          & ( ~ p1_s9_funct_2(A)
           => r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2)
        & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2)
        & ! [B] :
            ( r2_hidden(B,f1_s9_funct_2)
           => ( ( p1_s9_funct_2(B)
               => k1_funct_1(A,B) = f3_s9_funct_2(B) )
              & ( ~ p1_s9_funct_2(B)
               => k1_funct_1(A,B) = f4_s9_funct_2(B) ) ) ) ) )).

fof(s10_funct_2,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2)
      & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2)
      & k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2
      & ! [B] :
          ( m1_subset_1(B,f1_s10_funct_2)
         => ( B != f3_s10_funct_2
           => k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B) ) ) ) )).

fof(s11_funct_2,axiom,
    ( f3_s11_funct_2 != f4_s11_funct_2
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2)
        & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2)
        & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2
        & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2
        & ! [B] :
            ( m1_subset_1(B,f1_s11_funct_2)
           => ~ ( B != f3_s11_funct_2
                & B != f4_s11_funct_2
                & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) ) ) ) )).

fof(s12_funct_2,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s12_funct_2)
       => r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2)
        & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2)
        & ! [B] :
            ( m1_subset_1(B,f1_s12_funct_2)
           => k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B) ) ) )).

fof(s13_funct_2,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s13_funct_2)
       => m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2)
        & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2)
        & ! [B] :
            ( m1_subset_1(B,f1_s13_funct_2)
           => k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B) ) ) )).

fof(s14_funct_2,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s14_funct_2)
       => ? [B] :
            ( m1_subset_1(B,f2_s14_funct_2)
            & p1_s14_funct_2(A,B) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2)
        & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2)
        & ! [B] :
            ( m1_subset_1(B,f1_s14_funct_2)
           => p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)) ) ) )).

fof(dt_k1_funct_2,axiom,(
    $true )).

fof(dt_k2_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) )).

fof(redefinition_k2_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) )).

fof(dt_k3_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)) ) )).

fof(redefinition_k3_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k3_funct_2(A,B,C,D) = k10_relat_1(C,D) ) )).

fof(dt_k4_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v1_funct_1(k4_funct_2(A,B,C))
        & v1_funct_2(k4_funct_2(A,B,C),A,A)
        & m2_relset_1(k4_funct_2(A,B,C),A,A) ) ) )).

fof(redefinition_k4_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => k4_funct_2(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k5_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v1_funct_1(k5_funct_2(A,B,C))
        & v1_funct_2(k5_funct_2(A,B,C),A,A)
        & v3_funct_2(k5_funct_2(A,B,C),A,A)
        & m2_relset_1(k5_funct_2(A,B,C),A,A) ) ) )).

fof(redefinition_k5_funct_2,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => k5_funct_2(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k6_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m1_relset_1(B,A,A) )
     => ( v1_funct_1(k6_funct_2(A,B))
        & v1_funct_2(k6_funct_2(A,B),A,A)
        & v3_funct_2(k6_funct_2(A,B),A,A)
        & m2_relset_1(k6_funct_2(A,B),A,A) ) ) )).

fof(redefinition_k6_funct_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m1_relset_1(B,A,A) )
     => k6_funct_2(A,B) = k2_funct_1(B) ) )).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) )).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) )).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) )).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k9_funct_2,axiom,(
    ! [A,B,C] :
      ( v1_funct_1(k9_funct_2(A,B,C))
      & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C))
      & m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) ) )).
%------------------------------------------------------------------------------