SET007 Axioms: SET007+17.ax


%------------------------------------------------------------------------------
% File     : SET007+17 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Partial 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    : partfun1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  215 (  86 unit)
%            Number of atoms       :  735 (  83 equality)
%            Maximal formula depth :   15 (   5 average)
%            Number of connectives :  533 (  13 ~  ;   0  |; 276  &)
%                                         (  15 <=>; 229 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :   40 (  12 constant; 0-6 arity)
%            Number of variables   :  457 (   0 singleton; 443 !;  14 ?)
%            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_partfun1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) )).

fof(rc2_partfun1,axiom,(
    ! [A,B] :
    ? [C] :
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) )).

fof(fc1_partfun1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) )).

fof(rc3_partfun1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_relat_2(B)
      & v3_relat_2(B)
      & v4_relat_2(B)
      & v8_relat_2(B)
      & v1_partfun1(B,A,A) ) )).

fof(cc1_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) )).

fof(fc2_partfun1,axiom,(
    ! [A] :
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A))
      & v3_relat_2(k6_relat_1(A))
      & v4_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) )).

fof(t1_partfun1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r1_tarski(D,k2_zfmisc_1(E,F)) )
     => r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))) ) )).

fof(t2_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ~ ( ! [C] :
                  ( r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) )
              & ! [C] :
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C) )
                 => k2_xboole_0(A,B) != C ) ) ) ) )).

fof(t3_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( k2_xboole_0(A,B) = C
               => ! [D] :
                    ( r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                   => k1_funct_1(A,D) = k1_funct_1(B,D) ) ) ) ) ) )).

fof(t4_partfun1,axiom,(
    $true )).

fof(t5_partfun1,axiom,(
    $true )).

fof(t6_partfun1,axiom,(
    $true )).

fof(t7_partfun1,axiom,(
    $true )).

fof(t8_partfun1,axiom,(
    $true )).

fof(t9_partfun1,axiom,(
    $true )).

fof(t10_partfun1,axiom,(
    k2_relat_1(k1_xboole_0) = k1_xboole_0 )).

fof(t11_partfun1,axiom,(
    $true )).

fof(t12_partfun1,axiom,(
    $true )).

fof(t13_partfun1,axiom,(
    $true )).

fof(t14_partfun1,axiom,(
    $true )).

fof(t15_partfun1,axiom,(
    $true )).

fof(t16_partfun1,axiom,(
    $true )).

fof(t17_partfun1,axiom,(
    $true )).

fof(t18_partfun1,axiom,(
    $true )).

fof(t19_partfun1,axiom,(
    $true )).

fof(t20_partfun1,axiom,(
    $true )).

fof(t21_partfun1,axiom,(
    $true )).

fof(t22_partfun1,axiom,(
    $true )).

fof(t23_partfun1,axiom,(
    $true )).

fof(t24_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funct_1(A)
        & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) )).

fof(t25_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) )).

fof(t26_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ~ ( r2_hidden(C,k2_relat_1(D))
          & ! [E] :
              ( m1_subset_1(E,A)
             => ~ ( r2_hidden(E,k4_relset_1(A,B,D))
                  & C = k1_funct_1(D,E) ) ) ) ) )).

fof(t27_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,k4_relset_1(A,B,D))
       => r2_hidden(k1_funct_1(D,C),B) ) ) )).

fof(t28_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(k4_relset_1(A,B,D),C)
       => ( v1_funct_1(D)
          & m2_relset_1(D,C,B) ) ) ) )).

fof(t29_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(k2_relat_1(D),C)
       => ( v1_funct_1(D)
          & m2_relset_1(D,A,C) ) ) ) )).

fof(t30_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(A,C)
       => ( v1_funct_1(D)
          & m2_relset_1(D,C,B) ) ) ) )).

fof(t31_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(B,C)
       => ( v1_funct_1(D)
          & m2_relset_1(D,A,C) ) ) ) )).

fof(t32_partfun1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(E)
        & m2_relset_1(E,A,B) )
     => ( ( r1_tarski(A,C)
          & r1_tarski(B,D) )
       => ( v1_funct_1(E)
          & m2_relset_1(E,C,D) ) ) ) )).

fof(t33_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ( r1_tarski(C,D)
           => ( v1_funct_1(C)
              & m2_relset_1(C,A,B) ) ) ) ) )).

fof(t34_partfun1,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) )
         => ( ( k4_relset_1(A,B,C) = k4_relset_1(A,B,D)
              & ! [E] :
                  ( m1_subset_1(E,A)
                 => ( r2_hidden(E,k4_relset_1(A,B,C))
                   => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) )
           => C = D ) ) ) )).

fof(t35_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
         => ( ( k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E)
              & ! [F,G] :
                  ( r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D))
                 => k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) ) )
           => D = E ) ) ) )).

fof(t36_partfun1,axiom,(
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
     => k5_relat_1(k6_relat_1(A),C) = C ) )).

fof(t37_partfun1,axiom,(
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
     => k5_relat_1(C,k6_relat_1(B)) = C ) )).

fof(t38_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ( ! [D] :
            ( m1_subset_1(D,A)
           => ! [E] :
                ( m1_subset_1(E,A)
               => ( ( r2_hidden(D,k4_relset_1(A,B,C))
                    & r2_hidden(E,k4_relset_1(A,B,C))
                    & k1_funct_1(C,D) = k1_funct_1(C,E) )
                 => D = E ) ) )
       => v2_funct_1(C) ) ) )).

fof(t39_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_1(C)
       => ( v1_funct_1(k2_funct_1(C))
          & m2_relset_1(k2_funct_1(C),B,A) ) ) ) )).

fof(t40_partfun1,axiom,(
    $true )).

fof(t41_partfun1,axiom,(
    $true )).

fof(t42_partfun1,axiom,(
    $true )).

fof(t43_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( v1_funct_1(k8_relset_1(A,B,D,C))
        & m2_relset_1(k8_relset_1(A,B,D,C),C,B) ) ) )).

fof(t44_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( v1_funct_1(k8_relset_1(A,B,D,C))
        & m2_relset_1(k8_relset_1(A,B,D,C),A,B) ) ) )).

fof(t45_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( v1_funct_1(k9_relset_1(A,B,C,D))
        & m2_relset_1(k9_relset_1(A,B,C,D),A,C) ) ) )).

fof(t46_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( v1_funct_1(k9_relset_1(A,B,C,D))
        & m2_relset_1(k9_relset_1(A,B,C,D),A,B) ) ) )).

fof(t47_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_funct_1(k7_relat_1(k8_relat_1(A,C),B))
        & m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) ) ) )).

fof(t48_partfun1,axiom,(
    $true )).

fof(t49_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ~ ( r2_hidden(C,k9_relat_1(D,A))
          & ! [E] :
              ( m1_subset_1(E,A)
             => ~ ( r2_hidden(E,k4_relset_1(A,B,D))
                  & C = k1_funct_1(D,E) ) ) ) ) )).

fof(t50_partfun1,axiom,(
    $true )).

fof(t51_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => k9_relat_1(C,A) = k2_relat_1(C) ) )).

fof(t52_partfun1,axiom,(
    $true )).

fof(t53_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => k10_relat_1(C,B) = k4_relset_1(A,B,C) ) )).

fof(t54_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => ( k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0
        & k2_relat_1(B) = k1_xboole_0 ) ) )).

fof(t55_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( k1_relat_1(C) = k1_xboole_0
       => ( v1_funct_1(C)
          & m2_relset_1(C,A,B) ) ) ) )).

fof(t56_partfun1,axiom,(
    ! [A,B] :
      ( v1_funct_1(k1_xboole_0)
      & m2_relset_1(k1_xboole_0,A,B) ) )).

fof(t57_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => B = k1_xboole_0 ) )).

fof(t58_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_xboole_0,A) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,k1_xboole_0,B) )
         => C = D ) ) )).

fof(t59_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => v2_funct_1(B) ) )).

fof(t60_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_xboole_0,A) )
     => k9_relat_1(C,B) = k1_xboole_0 ) )).

fof(t61_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_xboole_0,A) )
     => k10_relat_1(C,B) = k1_xboole_0 ) )).

fof(t62_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,k1_xboole_0) )
     => ( k4_relset_1(A,k1_xboole_0,B) = k1_xboole_0
        & k2_relat_1(B) = k1_xboole_0 ) ) )).

fof(t63_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( k2_relat_1(C) = k1_xboole_0
       => ( v1_funct_1(C)
          & m2_relset_1(C,A,B) ) ) ) )).

fof(t64_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,k1_xboole_0) )
     => B = k1_xboole_0 ) )).

fof(t65_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,k1_xboole_0) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,B,k1_xboole_0) )
         => C = D ) ) )).

fof(t66_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,k1_xboole_0) )
     => v2_funct_1(B) ) )).

fof(t67_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,k1_xboole_0) )
     => k9_relat_1(C,B) = k1_xboole_0 ) )).

fof(t68_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,k1_xboole_0) )
     => k10_relat_1(C,B) = k1_xboole_0 ) )).

fof(t69_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_tarski(A),B) )
     => r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))) ) )).

fof(t70_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_tarski(A),B) )
     => v2_funct_1(C) ) )).

fof(t71_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,k1_tarski(A),B) )
     => r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))) ) )).

fof(t72_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( ( k1_relat_1(D) = k1_tarski(A)
          & r2_hidden(A,B)
          & r2_hidden(k1_funct_1(D,A),C) )
       => ( v1_funct_1(D)
          & m2_relset_1(D,B,C) ) ) ) )).

fof(t73_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,k1_tarski(B)) )
     => ( r2_hidden(C,k4_relset_1(A,k1_tarski(B),D))
       => k1_funct_1(D,C) = B ) ) )).

fof(t74_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,k1_tarski(B)) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,k1_tarski(B)) )
         => ( k4_relset_1(A,k1_tarski(B),C) = k4_relset_1(A,k1_tarski(B),D)
           => C = D ) ) ) )).

fof(d1_partfun1,axiom,(
    $true )).

fof(d2_partfun1,axiom,(
    $true )).

fof(d3_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k3_partfun1(A,B,C) = k7_relat_1(k8_relat_1(C,A),B) ) )).

fof(t75_partfun1,axiom,(
    $true )).

fof(t76_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_tarski(k3_partfun1(C,A,B),C) ) )).

fof(t77_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C))
        & r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) ) ) )).

fof(t78_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))
      <=> ( r2_hidden(A,k1_relat_1(D))
          & r2_hidden(A,B)
          & r2_hidden(k1_funct_1(D,A),C) ) ) ) )).

fof(t79_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( ( r2_hidden(A,k1_relat_1(D))
          & r2_hidden(A,B)
          & r2_hidden(k1_funct_1(D,A),C) )
       => k1_funct_1(k3_partfun1(D,B,C),A) = k1_funct_1(D,A) ) ) )).

fof(t80_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))
       => k1_funct_1(k3_partfun1(D,B,C),A) = k1_funct_1(D,A) ) ) )).

fof(t81_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( r1_tarski(C,D)
           => r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B)) ) ) ) )).

fof(t82_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r1_tarski(A,B)
       => r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C)) ) ) )).

fof(t83_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r1_tarski(A,B)
       => r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B)) ) ) )).

fof(t84_partfun1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_relat_1(E)
        & v1_funct_1(E) )
     => ( ( r1_tarski(A,B)
          & r1_tarski(C,D) )
       => r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D)) ) ) )).

fof(t85_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => C = k3_partfun1(C,A,B) ) ) )).

fof(t86_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => A = k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) ) )).

fof(t87_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => k3_partfun1(C,A,B) = C ) )).

fof(t88_partfun1,axiom,(
    $true )).

fof(t89_partfun1,axiom,(
    $true )).

fof(t90_partfun1,axiom,(
    $true )).

fof(t91_partfun1,axiom,(
    ! [A,B] : k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0 )).

fof(t92_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ! [E] :
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)) ) ) )).

fof(t93_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ! [E] :
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A)
           => k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)) = k3_partfun1(k5_relat_1(D,E),C,B) ) ) ) )).

fof(t94_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v2_funct_1(C)
       => v2_funct_1(k3_partfun1(C,A,B)) ) ) )).

fof(t95_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v2_funct_1(C)
       => k2_funct_1(k3_partfun1(C,A,B)) = k3_partfun1(k2_funct_1(C),B,A) ) ) )).

fof(t96_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B) ) )).

fof(t97_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => k9_relset_1(B,C,A,k3_partfun1(D,B,C)) = k3_partfun1(D,B,k3_xboole_0(A,C)) ) )).

fof(d4_partfun1,axiom,(
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
     => ( v1_partfun1(C,A,B)
      <=> k4_relset_1(A,B,C) = A ) ) )).

fof(t98_partfun1,axiom,(
    $true )).

fof(t99_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ( ( v1_partfun1(C,A,B)
          & B = k1_xboole_0 )
       => A = k1_xboole_0 ) ) )).

fof(t100_partfun1,axiom,(
    $true )).

fof(t101_partfun1,axiom,(
    $true )).

fof(t102_partfun1,axiom,(
    $true )).

fof(t103_partfun1,axiom,(
    $true )).

fof(t104_partfun1,axiom,(
    $true )).

fof(t105_partfun1,axiom,(
    $true )).

fof(t106_partfun1,axiom,(
    $true )).

fof(t107_partfun1,axiom,(
    $true )).

fof(t108_partfun1,axiom,(
    $true )).

fof(t109_partfun1,axiom,(
    $true )).

fof(t110_partfun1,axiom,(
    $true )).

fof(t111_partfun1,axiom,(
    $true )).

fof(t112_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => v1_partfun1(B,k1_xboole_0,A) ) )).

fof(t113_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_partfun1(k3_partfun1(C,A,B),A,B)
       => r1_tarski(A,k1_relat_1(C)) ) ) )).

fof(t114_partfun1,axiom,(
    ! [A,B] :
      ( v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B)
     => A = k1_xboole_0 ) )).

fof(t115_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r1_tarski(A,k1_relat_1(C))
          & r1_tarski(k2_relat_1(C),B) )
       => v1_partfun1(k3_partfun1(C,A,B),A,B) ) ) )).

fof(t116_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_partfun1(k3_partfun1(C,A,B),A,B)
       => r1_tarski(k9_relat_1(C,A),B) ) ) )).

fof(t117_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r1_tarski(A,k1_relat_1(C))
          & r1_tarski(k9_relat_1(C,A),B) )
       => v1_partfun1(k3_partfun1(C,A,B),A,B) ) ) )).

fof(d5_partfun1,axiom,(
    ! [A,B,C] :
      ( C = k4_partfun1(A,B)
    <=> ! [D] :
          ( r2_hidden(D,C)
        <=> ? [E] :
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & r1_tarski(k1_relat_1(E),A)
              & r1_tarski(k2_relat_1(E),B) ) ) ) )).

fof(t118_partfun1,axiom,(
    $true )).

fof(t119_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => r2_hidden(C,k4_partfun1(A,B)) ) )).

fof(t120_partfun1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(C,k4_partfun1(A,B))
     => ( v1_funct_1(C)
        & m2_relset_1(C,A,B) ) ) )).

fof(t121_partfun1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k4_partfun1(A,B))
     => ( v1_funct_1(C)
        & m2_relset_1(C,A,B) ) ) )).

fof(t122_partfun1,axiom,(
    ! [A] : k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0) )).

fof(t123_partfun1,axiom,(
    ! [A] : k4_partfun1(A,k1_xboole_0) = k1_tarski(k1_xboole_0) )).

fof(t124_partfun1,axiom,(
    $true )).

fof(t125_partfun1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,B)
     => r1_tarski(k4_partfun1(A,C),k4_partfun1(B,C)) ) )).

fof(t126_partfun1,axiom,(
    ! [A,B] : r1_tarski(k4_partfun1(k1_xboole_0,A),k4_partfun1(B,A)) )).

fof(t127_partfun1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,B)
     => r1_tarski(k4_partfun1(C,A),k4_partfun1(C,B)) ) )).

fof(t128_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)) ) )).

fof(d6_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ! [C] :
                ( r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
               => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) )).

fof(t129_partfun1,axiom,(
    $true )).

fof(t130_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ? [C] :
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & k2_xboole_0(A,B) = C ) ) ) ) )).

fof(t131_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ? [C] :
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & r1_tarski(A,C)
                & r1_tarski(B,C) ) ) ) ) )).

fof(t132_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
           => ( r1_partfun1(A,B)
            <=> ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) )).

fof(t133_partfun1,axiom,(
    $true )).

fof(t134_partfun1,axiom,(
    $true )).

fof(t135_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => r1_partfun1(A,B) ) ) ) )).

fof(t136_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & r1_partfun1(A,B) )
           => A = B ) ) ) )).

fof(t137_partfun1,axiom,(
    $true )).

fof(t138_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => r1_partfun1(A,B) ) ) ) )).

fof(t139_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(A,C)
                  & r1_tarski(B,C) )
               => r1_partfun1(A,B) ) ) ) ) )).

fof(t140_partfun1,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_relat_1(E)
                & v1_funct_1(E) )
             => ( ( r1_partfun1(C,E)
                  & r1_tarski(D,C) )
               => r1_partfun1(D,E) ) ) ) ) )).

fof(t141_partfun1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_partfun1(k1_xboole_0,A) ) )).

fof(t142_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C) ) )).

fof(t143_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,k1_tarski(B)) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,k1_tarski(B)) )
         => r1_partfun1(C,D) ) ) )).

fof(t144_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_partfun1(k7_relat_1(B,A),B) ) )).

fof(t145_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_partfun1(k8_relat_1(A,B),B) ) )).

fof(t146_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C) ) )).

fof(t147_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_partfun1(k3_partfun1(C,A,B),C) ) )).

fof(t148_partfun1,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) )
         => ( ( v1_partfun1(C,A,B)
              & v1_partfun1(D,A,B)
              & r1_partfun1(C,D) )
           => C = D ) ) ) )).

fof(t149_partfun1,axiom,(
    $true )).

fof(t150_partfun1,axiom,(
    $true )).

fof(t151_partfun1,axiom,(
    $true )).

fof(t152_partfun1,axiom,(
    $true )).

fof(t153_partfun1,axiom,(
    $true )).

fof(t154_partfun1,axiom,(
    $true )).

fof(t155_partfun1,axiom,(
    $true )).

fof(t156_partfun1,axiom,(
    $true )).

fof(t157_partfun1,axiom,(
    $true )).

fof(t158_partfun1,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)
                & m2_relset_1(E,A,B) )
             => ( ( r1_partfun1(C,E)
                  & r1_partfun1(D,E)
                  & v1_partfun1(E,A,B) )
               => r1_partfun1(C,D) ) ) ) ) )).

fof(t159_partfun1,axiom,(
    $true )).

fof(t160_partfun1,axiom,(
    $true )).

fof(t161_partfun1,axiom,(
    $true )).

fof(t162_partfun1,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)
                    & m2_relset_1(E,A,B) )
                 => ~ ( v1_partfun1(E,A,B)
                      & r1_partfun1(C,E)
                      & r1_partfun1(D,E) ) ) ) ) ) )).

fof(d7_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( D = k5_partfun1(A,B,C)
        <=> ! [E] :
              ( r2_hidden(E,D)
            <=> ? [F] :
                  ( v1_funct_1(F)
                  & m2_relset_1(F,A,B)
                  & F = E
                  & v1_partfun1(F,A,B)
                  & r1_partfun1(C,F) ) ) ) ) )).

fof(t163_partfun1,axiom,(
    $true )).

fof(t164_partfun1,axiom,(
    $true )).

fof(t165_partfun1,axiom,(
    $true )).

fof(t166_partfun1,axiom,(
    $true )).

fof(t167_partfun1,axiom,(
    $true )).

fof(t168_partfun1,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)
            & m2_relset_1(D,A,B) ) ) ) )).

fof(t169_partfun1,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) )
         => ( r2_hidden(D,k5_partfun1(A,B,C))
           => v1_partfun1(D,A,B) ) ) ) )).

fof(t170_partfun1,axiom,(
    $true )).

fof(t171_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( r2_hidden(D,k5_partfun1(A,B,C))
           => r1_partfun1(C,D) ) ) ) )).

fof(t172_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,A,k1_xboole_0) )
     => ( A != k1_xboole_0
       => k5_partfun1(A,k1_xboole_0,B) = k1_xboole_0 ) ) )).

fof(t173_partfun1,axiom,(
    $true )).

fof(t174_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ( v1_partfun1(C,A,B)
      <=> k5_partfun1(A,B,C) = k1_tarski(C) ) ) )).

fof(t175_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => k5_partfun1(k1_xboole_0,A,B) = k1_tarski(B) ) )).

fof(t176_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0) ) )).

fof(t177_partfun1,axiom,(
    $true )).

fof(t178_partfun1,axiom,(
    $true )).

fof(t179_partfun1,axiom,(
    $true )).

fof(t180_partfun1,axiom,(
    $true )).

fof(t181_partfun1,axiom,(
    $true )).

fof(t182_partfun1,axiom,(
    $true )).

fof(t183_partfun1,axiom,(
    $true )).

fof(t184_partfun1,axiom,(
    $true )).

fof(t185_partfun1,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_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D))
           => r1_partfun1(C,D) ) ) ) )).

fof(t186_partfun1,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)
              & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) ) ) ) )).

fof(s1_partfun1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_partfun1
      & ! [B] :
          ( r2_hidden(B,f1_s1_partfun1)
         => ( ( p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f2_s1_partfun1(B) )
            & ( ~ p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f3_s1_partfun1(B) ) ) ) ) )).

fof(s2_partfun1,axiom,
    ( ( ! [A,B] :
          ( ( r2_hidden(A,f1_s2_partfun1)
            & p1_s2_partfun1(A,B) )
         => r2_hidden(B,f2_s2_partfun1) )
      & ! [A,B,C] :
          ( ( r2_hidden(A,f1_s2_partfun1)
            & p1_s2_partfun1(A,B)
            & p1_s2_partfun1(A,C) )
         => B = C ) )
   => ? [A] :
        ( v1_funct_1(A)
        & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1)
        & ! [B] :
            ( r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A))
          <=> ( r2_hidden(B,f1_s2_partfun1)
              & ? [C] : p1_s2_partfun1(B,C) ) )
        & ! [B] :
            ( r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A))
           => p1_s2_partfun1(B,k1_funct_1(A,B)) ) ) )).

fof(s3_partfun1,axiom,
    ( ! [A] :
        ( p1_s3_partfun1(A)
       => r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1) )
   => ? [A] :
        ( v1_funct_1(A)
        & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1)
        & ! [B] :
            ( r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A))
          <=> ( r2_hidden(B,f1_s3_partfun1)
              & p1_s3_partfun1(B) ) )
        & ! [B] :
            ( r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A))
           => k1_funct_1(A,B) = f3_s3_partfun1(B) ) ) )).

fof(s4_partfun1,axiom,
    ( ( ! [A,B,C] :
          ( ( r2_hidden(A,f1_s4_partfun1)
            & r2_hidden(B,f2_s4_partfun1)
            & p1_s4_partfun1(A,B,C) )
         => r2_hidden(C,f3_s4_partfun1) )
      & ! [A,B,C,D] :
          ( ( r2_hidden(A,f1_s4_partfun1)
            & r2_hidden(B,f2_s4_partfun1)
            & p1_s4_partfun1(A,B,C)
            & p1_s4_partfun1(A,B,D) )
         => C = D ) )
   => ? [A] :
        ( v1_funct_1(A)
        & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1)
        & ! [B,C] :
            ( r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A))
          <=> ( r2_hidden(B,f1_s4_partfun1)
              & r2_hidden(C,f2_s4_partfun1)
              & ? [D] : p1_s4_partfun1(B,C,D) ) )
        & ! [B,C] :
            ( r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A))
           => p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))) ) ) )).

fof(s5_partfun1,axiom,
    ( ! [A,B] :
        ( p1_s5_partfun1(A,B)
       => r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1) )
   => ? [A] :
        ( v1_funct_1(A)
        & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1)
        & ! [B,C] :
            ( r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A))
          <=> ( r2_hidden(B,f1_s5_partfun1)
              & r2_hidden(C,f2_s5_partfun1)
              & p1_s5_partfun1(B,C) ) )
        & ! [B,C] :
            ( r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A))
           => k1_funct_1(A,k4_tarski(B,C)) = f4_s5_partfun1(B,C) ) ) )).

fof(symmetry_r1_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_partfun1(A,B)
       => r1_partfun1(B,A) ) ) )).

fof(reflexivity_r1_partfun1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_partfun1(A,A) ) )).

fof(dt_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F))
        & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) )).

fof(redefinition_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) )).

fof(dt_k2_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_partfun1(A,B,C,D))
        & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) )).

fof(redefinition_k2_partfun1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) )).

fof(dt_k3_partfun1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funct_1(k3_partfun1(A,B,C))
        & m2_relset_1(k3_partfun1(A,B,C),B,C) ) ) )).

fof(dt_k4_partfun1,axiom,(
    $true )).

fof(dt_k5_partfun1,axiom,(
    $true )).

fof(dt_k6_partfun1,axiom,(
    ! [A] :
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) )).

fof(redefinition_k6_partfun1,axiom,(
    ! [A] : k6_partfun1(A) = k6_relat_1(A) )).
%------------------------------------------------------------------------------