SET007 Axioms: SET007+356.ax


%------------------------------------------------------------------------------
% File     : SET007+356 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Cartesian Categories
% 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    : cat_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  172 (   9 unit)
%            Number of atoms       : 1113 ( 198 equality)
%            Maximal formula depth :   34 (   9 average)
%            Number of connectives : 1044 ( 103 ~  ;   6  |; 510  &)
%                                         (   9 <=>; 416 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   34 (   1 propositional; 0-4 arity)
%            Number of functors    :   66 (   1 constant; 0-10 arity)
%            Number of variables   :  609 (   0 singleton; 587 !;  22 ?)
%            Maximal term depth    :    6 (   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_cat_4,axiom,(
    ? [A] :
      ( l1_cat_4(A)
      & v2_cat_4(A) ) )).

fof(rc2_cat_4,axiom,(
    ? [A] :
      ( l1_cat_4(A)
      & v2_cat_1(A)
      & v2_cat_4(A) ) )).

fof(fc1_cat_4,axiom,(
    ! [A,B] :
      ( v2_cat_1(k5_cat_4(A,B))
      & v2_cat_4(k5_cat_4(A,B)) ) )).

fof(rc3_cat_4,axiom,(
    ? [A] :
      ( l1_cat_4(A)
      & v2_cat_1(A)
      & v2_cat_4(A)
      & v3_cat_4(A) ) )).

fof(rc4_cat_4,axiom,(
    ? [A] :
      ( l2_cat_4(A)
      & v5_cat_4(A) ) )).

fof(rc5_cat_4,axiom,(
    ? [A] :
      ( l2_cat_4(A)
      & v2_cat_1(A)
      & v5_cat_4(A) ) )).

fof(fc2_cat_4,axiom,(
    ! [A,B] :
      ( v2_cat_1(k23_cat_4(A,B))
      & v5_cat_4(k23_cat_4(A,B)) ) )).

fof(rc6_cat_4,axiom,(
    ? [A] :
      ( l2_cat_4(A)
      & v2_cat_1(A)
      & v5_cat_4(A)
      & v6_cat_4(A) ) )).

fof(d1_cat_4,axiom,(
    $true )).

fof(d2_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( r1_cat_1(A,B,C)
              <=> ( k6_cat_1(A,B,C) != k1_xboole_0
                  & k6_cat_1(A,C,B) != k1_xboole_0
                  & ? [D] :
                      ( m1_cat_1(D,A,B,C)
                      & ? [E] :
                          ( m1_cat_1(E,A,C,B)
                          & k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
                          & k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) ) ) ) ) ) ) ) )).

fof(d3_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v1_cat_4(A)
      <=> ! [B] :
            ( v1_finset_1(B)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,B,u1_cat_1(A))
                  & m2_relset_1(C,B,u1_cat_1(A)) )
               => ? [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                    & ? [E] :
                        ( m1_cat_3(E,A,D,B)
                        & k4_cat_3(A,B,E) = C
                        & r1_cat_3(A,D,B,E) ) ) ) ) ) ) )).

fof(t1_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v1_cat_4(A)
      <=> ( ? [B] :
              ( m1_subset_1(B,u1_cat_1(A))
              & v6_cat_1(B,A) )
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ? [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                      & ? [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                          & ? [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                              & k2_cat_1(A,E) = D
                              & k2_cat_1(A,F) = D
                              & k3_cat_1(A,E) = B
                              & k3_cat_1(A,F) = C
                              & r2_cat_3(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(d4_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => k1_cat_4(A) = u1_cat_4(A) ) )).

fof(d5_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k2_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u2_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) )).

fof(d6_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k3_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u3_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) )).

fof(d7_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k4_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u4_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) )).

fof(d8_cat_4,axiom,(
    ! [A,B] : k5_cat_4(A,B) = g1_cat_4(k1_tarski(A),k1_tarski(B),k10_pboole(k1_tarski(B),A),k10_pboole(k1_tarski(B),A),k1_cat_1(B,B,B),k10_pboole(k1_tarski(A),B),k1_algstr_1(A),k9_funct_2(A,A,A),k9_funct_2(A,A,B),k9_funct_2(A,A,B)) )).

fof(t2_cat_4,axiom,(
    ! [A,B] : g1_cat_1(u1_cat_1(k5_cat_4(A,B)),u2_cat_1(k5_cat_4(A,B)),u3_cat_1(k5_cat_4(A,B)),u4_cat_1(k5_cat_4(A,B)),u5_cat_1(k5_cat_4(A,B)),u6_cat_1(k5_cat_4(A,B))) = k8_cat_1(A,B) )).

fof(t3_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
     => C = A ) )).

fof(t4_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
         => C = D ) ) )).

fof(t5_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u2_cat_1(k5_cat_4(A,B)))
     => C = B ) )).

fof(t6_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u2_cat_1(k5_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(k5_cat_4(A,B)))
         => C = D ) ) )).

fof(t7_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k5_cat_4(A,B)))
             => r2_hidden(E,k6_cat_1(k5_cat_4(A,B),C,D)) ) ) ) )).

fof(t8_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k5_cat_4(A,B)))
             => m1_cat_1(E,k5_cat_4(A,B),C,D) ) ) ) )).

fof(t9_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
         => k6_cat_1(k5_cat_4(A,B),C,D) != k1_xboole_0 ) ) )).

fof(t10_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
     => v6_cat_1(C,k5_cat_4(A,B)) ) )).

fof(t11_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(k5_cat_4(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k5_cat_4(A,B)))
             => r2_cat_3(k5_cat_4(A,B),C,D,E) ) ) ) )).

fof(d9_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_4(A) )
     => ( v3_cat_4(A)
      <=> ( v6_cat_1(u1_cat_4(A),A)
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ( k3_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u3_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = B
                    & k3_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u4_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = C
                    & r2_cat_3(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u2_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u3_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u4_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) ) ) ) ) ) ) )).

fof(t12_cat_4,axiom,(
    ! [A,B] : v3_cat_4(k5_cat_4(A,B)) )).

fof(t13_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => v6_cat_1(k1_cat_4(A),A) ) )).

fof(t14_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_cat_1(C,A,B,k1_cat_4(A))
             => ! [D] :
                  ( m1_cat_1(D,A,B,k1_cat_4(A))
                 => C = D ) ) ) ) )).

fof(t15_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,k1_cat_4(A)) != k1_xboole_0 ) ) )).

fof(d10_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_cat_1(C,A,B,k1_cat_4(A))
             => C = k6_cat_4(A,B) ) ) ) )).

fof(t16_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_4(A,B) = k10_cat_3(A,B,k1_cat_4(A)) ) ) )).

fof(t17_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( k2_cat_1(A,k6_cat_4(A,B)) = B
            & k3_cat_1(A,k6_cat_4(A,B)) = k1_cat_4(A) ) ) ) )).

fof(t18_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,k1_cat_4(A)) = k6_domain_1(u2_cat_1(A),k6_cat_4(A,B)) ) ) )).

fof(t19_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k2_cat_1(A,k3_cat_4(A,B,C)) = k2_cat_4(A,B,C)
                & k3_cat_1(A,k3_cat_4(A,B,C)) = B ) ) ) ) )).

fof(t20_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k2_cat_1(A,k4_cat_4(A,B,C)) = k2_cat_4(A,B,C)
                & k3_cat_1(A,k4_cat_4(A,B,C)) = C ) ) ) ) )).

fof(t21_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k6_cat_1(A,k2_cat_4(A,B,C),B) != k1_xboole_0
                & k6_cat_1(A,k2_cat_4(A,B,C),C) != k1_xboole_0 ) ) ) ) )).

fof(t22_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => r2_cat_3(A,k2_cat_4(A,B,C),k7_cat_4(A,B,C),k8_cat_4(A,B,C)) ) ) ) )).

fof(t23_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => v1_cat_4(A) ) )).

fof(t24_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                  & k6_cat_1(A,C,B) != k1_xboole_0
                  & ~ ( v1_cat_3(k7_cat_4(A,B,C),A)
                      & v1_cat_3(k8_cat_4(A,B,C),A) ) ) ) ) ) )).

fof(d11_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,D,B)
                     => ! [F] :
                          ( m1_cat_1(F,A,D,C)
                         => ~ ( k6_cat_1(A,D,B) != k1_xboole_0
                              & k6_cat_1(A,D,C) != k1_xboole_0
                              & ~ ! [G] :
                                    ( m1_cat_1(G,A,D,k2_cat_4(A,B,C))
                                   => ( G = k9_cat_4(A,B,C,D,E,F)
                                    <=> ( k9_cat_1(A,D,k2_cat_4(A,B,C),B,G,k7_cat_4(A,B,C)) = E
                                        & k9_cat_1(A,D,k2_cat_4(A,B,C),C,G,k8_cat_4(A,B,C)) = F ) ) ) ) ) ) ) ) ) ) )).

fof(t25_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,B,D) != k1_xboole_0
                      & k6_cat_1(A,B,k2_cat_4(A,C,D)) = k1_xboole_0 ) ) ) ) ) )).

fof(t26_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k9_cat_4(A,B,C,k2_cat_4(A,B,C),k7_cat_4(A,B,C),k8_cat_4(A,B,C)) = k10_cat_1(A,k2_cat_4(A,B,C)) ) ) ) )).

fof(t27_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] :
                              ( m1_cat_1(G,A,B,D)
                             => ! [H] :
                                  ( m1_cat_1(H,A,E,B)
                                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                      & k6_cat_1(A,B,D) != k1_xboole_0
                                      & k6_cat_1(A,E,B) != k1_xboole_0
                                      & k9_cat_4(A,C,D,E,k9_cat_1(A,E,B,C,H,F),k9_cat_1(A,E,B,D,H,G)) != k9_cat_1(A,E,B,k2_cat_4(A,C,D),H,k9_cat_4(A,C,D,B,F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t28_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] :
                              ( m1_cat_1(G,A,B,D)
                             => ! [H] :
                                  ( m1_cat_1(H,A,B,D)
                                 => ( k9_cat_4(A,C,D,B,E,G) = k9_cat_4(A,C,D,B,F,H)
                                   => ( k6_cat_1(A,B,C) = k1_xboole_0
                                      | k6_cat_1(A,B,D) = k1_xboole_0
                                      | ( E = F
                                        & G = H ) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,B,D)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,B,D) != k1_xboole_0
                              & ( v3_cat_1(E,A)
                                | v3_cat_1(F,A) )
                              & ~ v3_cat_1(k9_cat_4(A,C,D,B,E,F),A) ) ) ) ) ) ) ) )).

fof(t30_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( k6_cat_1(A,B,k2_cat_4(A,B,k1_cat_4(A))) != k1_xboole_0
            & k6_cat_1(A,B,k2_cat_4(A,k1_cat_4(A),B)) != k1_xboole_0 ) ) ) )).

fof(d12_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k10_cat_4(A,B) = k8_cat_4(A,k1_cat_4(A),B) ) ) )).

fof(d13_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k11_cat_4(A,B) = k9_cat_4(A,k1_cat_4(A),B,B,k6_cat_4(A,B),k10_cat_1(A,B)) ) ) )).

fof(d14_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k12_cat_4(A,B) = k7_cat_4(A,B,k1_cat_4(A)) ) ) )).

fof(d15_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k13_cat_4(A,B) = k9_cat_4(A,B,k1_cat_4(A),B,k10_cat_1(A,B),k6_cat_4(A,B)) ) ) )).

fof(t31_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( k9_cat_1(A,B,k2_cat_4(A,k1_cat_4(A),B),B,k11_cat_4(A,B),k10_cat_4(A,B)) = k10_cat_1(A,B)
            & k9_cat_1(A,k2_cat_4(A,k1_cat_4(A),B),B,k2_cat_4(A,k1_cat_4(A),B),k10_cat_4(A,B),k11_cat_4(A,B)) = k10_cat_1(A,k2_cat_4(A,k1_cat_4(A),B))
            & k9_cat_1(A,B,k2_cat_4(A,B,k1_cat_4(A)),B,k13_cat_4(A,B),k12_cat_4(A,B)) = k10_cat_1(A,B)
            & k9_cat_1(A,k2_cat_4(A,B,k1_cat_4(A)),B,k2_cat_4(A,B,k1_cat_4(A)),k12_cat_4(A,B),k13_cat_4(A,B)) = k10_cat_1(A,k2_cat_4(A,B,k1_cat_4(A))) ) ) ) )).

fof(t32_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( r1_cat_1(A,B,k2_cat_4(A,B,k1_cat_4(A)))
            & r1_cat_1(A,B,k2_cat_4(A,k1_cat_4(A),B)) ) ) ) )).

fof(d16_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k14_cat_4(A,B,C) = k9_cat_4(A,C,B,k2_cat_4(A,B,C),k8_cat_4(A,B,C),k7_cat_4(A,B,C)) ) ) ) )).

fof(t33_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k6_cat_1(A,k2_cat_4(A,B,C),k2_cat_4(A,C,B)) != k1_xboole_0 ) ) ) )).

fof(t34_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k9_cat_1(A,k2_cat_4(A,C,B),k2_cat_4(A,B,C),k2_cat_4(A,C,B),k14_cat_4(A,C,B),k14_cat_4(A,B,C)) = k10_cat_1(A,k2_cat_4(A,C,B)) ) ) ) )).

fof(t35_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => r1_cat_1(A,k2_cat_4(A,B,C),k2_cat_4(A,C,B)) ) ) ) )).

fof(d17_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k15_cat_4(A,B) = k9_cat_4(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) ) ) )).

fof(t36_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,k2_cat_4(A,B,B)) != k1_xboole_0 ) ) )).

fof(t37_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => k9_cat_4(A,C,C,B,D,D) = k9_cat_1(A,B,C,k2_cat_4(A,C,C),D,k15_cat_4(A,C)) ) ) ) ) ) )).

fof(d18_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k16_cat_4(A,B,C,D) = k9_cat_4(A,B,k2_cat_4(A,C,D),k2_cat_4(A,k2_cat_4(A,B,C),D),k9_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,C),B,k7_cat_4(A,k2_cat_4(A,B,C),D),k7_cat_4(A,B,C)),k9_cat_4(A,C,D,k2_cat_4(A,k2_cat_4(A,B,C),D),k9_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,C),C,k7_cat_4(A,k2_cat_4(A,B,C),D),k8_cat_4(A,B,C)),k8_cat_4(A,k2_cat_4(A,B,C),D))) ) ) ) ) )).

fof(d19_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k17_cat_4(A,B,C,D) = k9_cat_4(A,k2_cat_4(A,B,C),D,k2_cat_4(A,B,k2_cat_4(A,C,D)),k9_cat_4(A,B,C,k2_cat_4(A,B,k2_cat_4(A,C,D)),k7_cat_4(A,B,k2_cat_4(A,C,D)),k9_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,C,D),C,k8_cat_4(A,B,k2_cat_4(A,C,D)),k7_cat_4(A,C,D))),k9_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,C,D),D,k8_cat_4(A,B,k2_cat_4(A,C,D)),k8_cat_4(A,C,D))) ) ) ) ) )).

fof(t38_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ( k6_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D))) != k1_xboole_0
                    & k6_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D)) != k1_xboole_0 ) ) ) ) ) )).

fof(t39_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ( k9_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D)),k17_cat_4(A,B,C,D),k16_cat_4(A,B,C,D)) = k10_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)))
                    & k9_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D),k16_cat_4(A,B,C,D),k17_cat_4(A,B,C,D)) = k10_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D)) ) ) ) ) ) )).

fof(t40_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => r1_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D))) ) ) ) ) )).

fof(d20_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] :
                              ( m1_cat_1(G,A,D,E)
                             => k18_cat_4(A,B,C,D,E,F,G) = k9_cat_4(A,C,E,k2_cat_4(A,B,D),k9_cat_1(A,k2_cat_4(A,B,D),B,C,k7_cat_4(A,B,D),F),k9_cat_1(A,k2_cat_4(A,B,D),D,E,k8_cat_4(A,B,D),G)) ) ) ) ) ) ) ) )).

fof(t41_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                          & k6_cat_1(A,D,E) != k1_xboole_0
                          & k6_cat_1(A,k2_cat_4(A,B,D),k2_cat_4(A,C,E)) = k1_xboole_0 ) ) ) ) ) ) )).

fof(t42_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k18_cat_4(A,B,B,C,C,k10_cat_1(A,B),k10_cat_1(A,C)) = k10_cat_1(A,k2_cat_4(A,B,C)) ) ) ) )).

fof(t43_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] :
                              ( m1_cat_1(G,A,B,C)
                             => ! [H] :
                                  ( m1_cat_1(H,A,D,E)
                                 => ! [I] :
                                      ( m1_cat_1(I,A,F,B)
                                     => ! [J] :
                                          ( m1_cat_1(J,A,F,D)
                                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                              & k6_cat_1(A,D,E) != k1_xboole_0
                                              & k6_cat_1(A,F,B) != k1_xboole_0
                                              & k6_cat_1(A,F,D) != k1_xboole_0
                                              & k9_cat_1(A,F,k2_cat_4(A,B,D),k2_cat_4(A,C,E),k9_cat_4(A,B,D,F,I,J),k18_cat_4(A,B,C,D,E,G,H)) != k9_cat_4(A,C,E,F,k9_cat_1(A,F,B,C,I,G),k9_cat_1(A,F,D,E,J,H)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t44_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,B,D)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,B,D) != k1_xboole_0
                              & k9_cat_4(A,C,D,B,E,F) != k9_cat_1(A,B,k2_cat_4(A,B,B),k2_cat_4(A,C,D),k15_cat_4(A,B),k18_cat_4(A,B,C,B,D,E,F)) ) ) ) ) ) ) ) )).

fof(t45_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_cat_1(A))
                             => ! [H] :
                                  ( m1_cat_1(H,A,B,C)
                                 => ! [I] :
                                      ( m1_cat_1(I,A,D,E)
                                     => ! [J] :
                                          ( m1_cat_1(J,A,F,B)
                                         => ! [K] :
                                              ( m1_cat_1(K,A,G,D)
                                             => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                                  & k6_cat_1(A,D,E) != k1_xboole_0
                                                  & k6_cat_1(A,F,B) != k1_xboole_0
                                                  & k6_cat_1(A,G,D) != k1_xboole_0
                                                  & k9_cat_1(A,k2_cat_4(A,F,G),k2_cat_4(A,B,D),k2_cat_4(A,C,E),k18_cat_4(A,F,B,G,D,J,K),k18_cat_4(A,B,C,D,E,H,I)) != k18_cat_4(A,F,C,G,E,k9_cat_1(A,F,B,C,J,H),k9_cat_1(A,G,D,E,K,I)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d21_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v4_cat_4(A)
      <=> ! [B] :
            ( v1_finset_1(B)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,B,u1_cat_1(A))
                  & m2_relset_1(C,B,u1_cat_1(A)) )
               => ? [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                    & ? [E] :
                        ( m2_cat_3(E,A,D,B)
                        & k3_cat_3(A,B,E) = C
                        & r3_cat_3(A,D,B,E) ) ) ) ) ) ) )).

fof(t46_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v4_cat_4(A)
      <=> ( ? [B] :
              ( m1_subset_1(B,u1_cat_1(A))
              & v7_cat_1(B,A) )
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ? [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                      & ? [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                          & ? [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                              & k2_cat_1(A,E) = B
                              & k2_cat_1(A,F) = C
                              & k3_cat_1(A,E) = D
                              & k3_cat_1(A,F) = D
                              & r4_cat_3(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(d22_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => k19_cat_4(A) = u5_cat_4(A) ) )).

fof(d23_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k20_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u6_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) )).

fof(d24_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k21_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u7_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) )).

fof(d25_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k22_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u8_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) )).

fof(d26_cat_4,axiom,(
    ! [A,B] : k23_cat_4(A,B) = g2_cat_4(k1_tarski(A),k1_tarski(B),k10_pboole(k1_tarski(B),A),k10_pboole(k1_tarski(B),A),k1_cat_1(B,B,B),k10_pboole(k1_tarski(A),B),k1_algstr_1(A),k9_funct_2(A,A,A),k9_funct_2(A,A,B),k9_funct_2(A,A,B)) )).

fof(t47_cat_4,axiom,(
    ! [A,B] : g1_cat_1(u1_cat_1(k23_cat_4(A,B)),u2_cat_1(k23_cat_4(A,B)),u3_cat_1(k23_cat_4(A,B)),u4_cat_1(k23_cat_4(A,B)),u5_cat_1(k23_cat_4(A,B)),u6_cat_1(k23_cat_4(A,B))) = k8_cat_1(A,B) )).

fof(t48_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
     => C = A ) )).

fof(t49_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
         => C = D ) ) )).

fof(t50_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u2_cat_1(k23_cat_4(A,B)))
     => C = B ) )).

fof(t51_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u2_cat_1(k23_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(k23_cat_4(A,B)))
         => C = D ) ) )).

fof(t52_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k23_cat_4(A,B)))
             => r2_hidden(E,k6_cat_1(k23_cat_4(A,B),C,D)) ) ) ) )).

fof(t53_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k23_cat_4(A,B)))
             => m1_cat_1(E,k23_cat_4(A,B),C,D) ) ) ) )).

fof(t54_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
         => k6_cat_1(k23_cat_4(A,B),C,D) != k1_xboole_0 ) ) )).

fof(t55_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
     => v7_cat_1(C,k23_cat_4(A,B)) ) )).

fof(t56_cat_4,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(k23_cat_4(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k23_cat_4(A,B)))
             => r4_cat_3(k23_cat_4(A,B),C,D,E) ) ) ) )).

fof(d27_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l2_cat_4(A) )
     => ( v6_cat_4(A)
      <=> ( v7_cat_1(u5_cat_4(A),A)
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ( k2_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u7_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = B
                    & k2_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u8_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = C
                    & r4_cat_3(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u6_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u7_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u8_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) ) ) ) ) ) ) )).

fof(t57_cat_4,axiom,(
    ! [A,B] : v6_cat_4(k23_cat_4(A,B)) )).

fof(t58_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => v7_cat_1(k19_cat_4(A),A) ) )).

fof(t59_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_cat_1(C,A,k19_cat_4(A),B)
             => ! [D] :
                  ( m1_cat_1(D,A,k19_cat_4(A),B)
                 => C = D ) ) ) ) )).

fof(d28_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_cat_1(C,A,k19_cat_4(A),B)
             => C = k24_cat_4(A,B) ) ) ) )).

fof(t60_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,k19_cat_4(A),B) != k1_xboole_0 ) ) )).

fof(t61_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k24_cat_4(A,B) = k11_cat_3(A,k19_cat_4(A),B) ) ) )).

fof(t62_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( k2_cat_1(A,k24_cat_4(A,B)) = k19_cat_4(A)
            & k3_cat_1(A,k24_cat_4(A,B)) = B ) ) ) )).

fof(t63_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,k19_cat_4(A),B) = k6_domain_1(u2_cat_1(A),k24_cat_4(A,B)) ) ) )).

fof(t64_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k2_cat_1(A,k21_cat_4(A,B,C)) = B
                & k3_cat_1(A,k21_cat_4(A,B,C)) = k20_cat_4(A,B,C) ) ) ) ) )).

fof(t65_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k2_cat_1(A,k22_cat_4(A,B,C)) = C
                & k3_cat_1(A,k22_cat_4(A,B,C)) = k20_cat_4(A,B,C) ) ) ) ) )).

fof(t66_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k6_cat_1(A,B,k20_cat_4(A,B,C)) != k1_xboole_0
                & k6_cat_1(A,C,k20_cat_4(A,B,C)) != k1_xboole_0 ) ) ) ) )).

fof(t67_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => r4_cat_3(A,k20_cat_4(A,B,C),k21_cat_4(A,B,C),k22_cat_4(A,B,C)) ) ) ) )).

fof(t68_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => v4_cat_4(A) ) )).

fof(t69_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                  & k6_cat_1(A,C,B) != k1_xboole_0
                  & ~ ( v2_cat_3(k21_cat_4(A,B,C),A)
                      & v2_cat_3(k22_cat_4(A,B,C),A) ) ) ) ) ) )).

fof(d29_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,D)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ~ ( k6_cat_1(A,B,D) != k1_xboole_0
                              & k6_cat_1(A,C,D) != k1_xboole_0
                              & ~ ! [G] :
                                    ( m1_cat_1(G,A,k20_cat_4(A,B,C),D)
                                   => ( G = k27_cat_4(A,B,C,D,E,F)
                                    <=> ( k9_cat_1(A,B,k20_cat_4(A,B,C),D,k25_cat_4(A,B,C),G) = E
                                        & k9_cat_1(A,C,k20_cat_4(A,B,C),D,k26_cat_4(A,B,C),G) = F ) ) ) ) ) ) ) ) ) ) )).

fof(t70_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,D,C) != k1_xboole_0
                      & k6_cat_1(A,k20_cat_4(A,B,D),C) = k1_xboole_0 ) ) ) ) ) )).

fof(t71_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k27_cat_4(A,B,C,k20_cat_4(A,B,C),k25_cat_4(A,B,C),k26_cat_4(A,B,C)) = k10_cat_1(A,k20_cat_4(A,B,C)) ) ) ) )).

fof(t72_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] :
                              ( m1_cat_1(G,A,D,C)
                             => ! [H] :
                                  ( m1_cat_1(H,A,C,E)
                                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                      & k6_cat_1(A,D,C) != k1_xboole_0
                                      & k6_cat_1(A,C,E) != k1_xboole_0
                                      & k27_cat_4(A,B,D,E,k9_cat_1(A,B,C,E,F,H),k9_cat_1(A,D,C,E,G,H)) != k9_cat_1(A,k20_cat_4(A,B,D),C,E,k27_cat_4(A,B,D,C,F,G),H) ) ) ) ) ) ) ) ) ) )).

fof(t73_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] :
                              ( m1_cat_1(G,A,D,C)
                             => ! [H] :
                                  ( m1_cat_1(H,A,D,C)
                                 => ( k27_cat_4(A,B,D,C,E,G) = k27_cat_4(A,B,D,C,F,H)
                                   => ( k6_cat_1(A,B,C) = k1_xboole_0
                                      | k6_cat_1(A,D,C) = k1_xboole_0
                                      | ( E = F
                                        & G = H ) ) ) ) ) ) ) ) ) ) ) )).

fof(t74_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,D,C)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,D,C) != k1_xboole_0
                              & ( v4_cat_1(E,A)
                                | v4_cat_1(F,A) )
                              & ~ v4_cat_1(k27_cat_4(A,B,D,C,E,F),A) ) ) ) ) ) ) ) )).

fof(t75_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( r1_cat_1(A,B,k20_cat_4(A,B,k19_cat_4(A)))
            & r1_cat_1(A,B,k20_cat_4(A,k19_cat_4(A),B)) ) ) ) )).

fof(t76_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => r1_cat_1(A,k20_cat_4(A,B,C),k20_cat_4(A,C,B)) ) ) ) )).

fof(t77_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => r1_cat_1(A,k20_cat_4(A,k20_cat_4(A,B,C),D),k20_cat_4(A,B,k20_cat_4(A,C,D))) ) ) ) ) )).

fof(d30_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k28_cat_4(A,B) = k27_cat_4(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) ) ) )).

fof(d31_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_cat_1(F,A,B,D)
                         => ! [G] :
                              ( m1_cat_1(G,A,C,E)
                             => k29_cat_4(A,B,C,D,E,F,G) = k27_cat_4(A,B,C,k20_cat_4(A,D,E),k9_cat_1(A,B,D,k20_cat_4(A,D,E),F,k25_cat_4(A,D,E)),k9_cat_1(A,C,E,k20_cat_4(A,D,E),G,k26_cat_4(A,D,E))) ) ) ) ) ) ) ) )).

fof(t78_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                          & k6_cat_1(A,D,E) != k1_xboole_0
                          & k6_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,E)) = k1_xboole_0 ) ) ) ) ) ) )).

fof(t79_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => k29_cat_4(A,B,C,B,C,k10_cat_1(A,B),k10_cat_1(A,C)) = k10_cat_1(A,k20_cat_4(A,B,C)) ) ) ) )).

fof(t80_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] :
                              ( m1_cat_1(G,A,B,C)
                             => ! [H] :
                                  ( m1_cat_1(H,A,D,E)
                                 => ! [I] :
                                      ( m1_cat_1(I,A,C,F)
                                     => ! [J] :
                                          ( m1_cat_1(J,A,E,F)
                                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                              & k6_cat_1(A,D,E) != k1_xboole_0
                                              & k6_cat_1(A,C,F) != k1_xboole_0
                                              & k6_cat_1(A,E,F) != k1_xboole_0
                                              & k9_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,E),F,k29_cat_4(A,B,D,C,E,G,H),k27_cat_4(A,C,E,F,I,J)) != k27_cat_4(A,B,D,F,k9_cat_1(A,B,C,F,G,I),k9_cat_1(A,D,E,F,H,J)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t81_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,D,C)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,D,C) != k1_xboole_0
                              & k9_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,C),C,k29_cat_4(A,B,D,C,C,E,F),k28_cat_4(A,C)) != k27_cat_4(A,B,D,C,E,F) ) ) ) ) ) ) ) )).

fof(t82_cat_4,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_cat_1(A))
                             => ! [H] :
                                  ( m1_cat_1(H,A,B,C)
                                 => ! [I] :
                                      ( m1_cat_1(I,A,D,E)
                                     => ! [J] :
                                          ( m1_cat_1(J,A,C,F)
                                         => ! [K] :
                                              ( m1_cat_1(K,A,E,G)
                                             => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                                  & k6_cat_1(A,D,E) != k1_xboole_0
                                                  & k6_cat_1(A,C,F) != k1_xboole_0
                                                  & k6_cat_1(A,E,G) != k1_xboole_0
                                                  & k9_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,E),k20_cat_4(A,F,G),k29_cat_4(A,B,D,C,E,H,I),k29_cat_4(A,C,E,F,G,J,K)) != k29_cat_4(A,B,D,F,G,k9_cat_1(A,B,C,F,H,J),k9_cat_1(A,D,E,G,I,K)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_l1_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => l1_cat_1(A) ) )).

fof(existence_l1_cat_4,axiom,(
    ? [A] : l1_cat_4(A) )).

fof(dt_l2_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => l1_cat_1(A) ) )).

fof(existence_l2_cat_4,axiom,(
    ? [A] : l2_cat_4(A) )).

fof(abstractness_v2_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => ( v2_cat_4(A)
       => A = g1_cat_4(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A),u1_cat_4(A),u2_cat_4(A),u3_cat_4(A),u4_cat_4(A)) ) ) )).

fof(abstractness_v5_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => ( v5_cat_4(A)
       => A = g2_cat_4(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A),u5_cat_4(A),u6_cat_4(A),u7_cat_4(A),u8_cat_4(A)) ) ) )).

fof(dt_k1_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => m1_subset_1(k1_cat_4(A),u1_cat_1(A)) ) )).

fof(dt_k2_cat_4,axiom,(
    ! [A,B,C] :
      ( ( l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k2_cat_4(A,B,C),u1_cat_1(A)) ) )).

fof(dt_k3_cat_4,axiom,(
    ! [A,B,C] :
      ( ( l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k3_cat_4(A,B,C),u2_cat_1(A)) ) )).

fof(dt_k4_cat_4,axiom,(
    ! [A,B,C] :
      ( ( l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k4_cat_4(A,B,C),u2_cat_1(A)) ) )).

fof(dt_k5_cat_4,axiom,(
    ! [A,B] :
      ( v2_cat_4(k5_cat_4(A,B))
      & l1_cat_4(k5_cat_4(A,B)) ) )).

fof(dt_k6_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k6_cat_4(A,B),A,B,k1_cat_4(A)) ) )).

fof(dt_k7_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_cat_1(k7_cat_4(A,B,C),A,k2_cat_4(A,B,C),B) ) )).

fof(redefinition_k7_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => k7_cat_4(A,B,C) = k3_cat_4(A,B,C) ) )).

fof(dt_k8_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_cat_1(k8_cat_4(A,B,C),A,k2_cat_4(A,B,C),C) ) )).

fof(redefinition_k8_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => k8_cat_4(A,B,C) = k4_cat_4(A,B,C) ) )).

fof(dt_k9_cat_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A))
        & m1_cat_1(E,A,D,B)
        & m1_cat_1(F,A,D,C) )
     => m1_cat_1(k9_cat_4(A,B,C,D,E,F),A,D,k2_cat_4(A,B,C)) ) )).

fof(dt_k10_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k10_cat_4(A,B),A,k2_cat_4(A,k1_cat_4(A),B),B) ) )).

fof(dt_k11_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k11_cat_4(A,B),A,B,k2_cat_4(A,k1_cat_4(A),B)) ) )).

fof(dt_k12_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k12_cat_4(A,B),A,k2_cat_4(A,B,k1_cat_4(A)),B) ) )).

fof(dt_k13_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k13_cat_4(A,B),A,B,k2_cat_4(A,B,k1_cat_4(A))) ) )).

fof(dt_k14_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_cat_1(k14_cat_4(A,B,C),A,k2_cat_4(A,B,C),k2_cat_4(A,C,B)) ) )).

fof(dt_k15_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k15_cat_4(A,B),A,B,k2_cat_4(A,B,B)) ) )).

fof(dt_k16_cat_4,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A)) )
     => m1_cat_1(k16_cat_4(A,B,C,D),A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D))) ) )).

fof(dt_k17_cat_4,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A)) )
     => m1_cat_1(k17_cat_4(A,B,C,D),A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D)) ) )).

fof(dt_k18_cat_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A))
        & m1_subset_1(E,u1_cat_1(A))
        & m1_cat_1(F,A,B,C)
        & m1_cat_1(G,A,D,E) )
     => m1_cat_1(k18_cat_4(A,B,C,D,E,F,G),A,k2_cat_4(A,B,D),k2_cat_4(A,C,E)) ) )).

fof(dt_k19_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => m1_subset_1(k19_cat_4(A),u1_cat_1(A)) ) )).

fof(dt_k20_cat_4,axiom,(
    ! [A,B,C] :
      ( ( l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k20_cat_4(A,B,C),u1_cat_1(A)) ) )).

fof(dt_k21_cat_4,axiom,(
    ! [A,B,C] :
      ( ( l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k21_cat_4(A,B,C),u2_cat_1(A)) ) )).

fof(dt_k22_cat_4,axiom,(
    ! [A,B,C] :
      ( ( l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k22_cat_4(A,B,C),u2_cat_1(A)) ) )).

fof(dt_k23_cat_4,axiom,(
    ! [A,B] :
      ( v5_cat_4(k23_cat_4(A,B))
      & l2_cat_4(k23_cat_4(A,B)) ) )).

fof(dt_k24_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k24_cat_4(A,B),A,k19_cat_4(A),B) ) )).

fof(dt_k25_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_cat_1(k25_cat_4(A,B,C),A,B,k20_cat_4(A,B,C)) ) )).

fof(redefinition_k25_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => k25_cat_4(A,B,C) = k21_cat_4(A,B,C) ) )).

fof(dt_k26_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_cat_1(k26_cat_4(A,B,C),A,C,k20_cat_4(A,B,C)) ) )).

fof(redefinition_k26_cat_4,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => k26_cat_4(A,B,C) = k22_cat_4(A,B,C) ) )).

fof(dt_k27_cat_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A))
        & m1_cat_1(E,A,B,D)
        & m1_cat_1(F,A,C,D) )
     => m1_cat_1(k27_cat_4(A,B,C,D,E,F),A,k20_cat_4(A,B,C),D) ) )).

fof(dt_k28_cat_4,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k28_cat_4(A,B),A,k20_cat_4(A,B,B),B) ) )).

fof(dt_k29_cat_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( v2_cat_1(A)
        & v6_cat_4(A)
        & l2_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A))
        & m1_subset_1(E,u1_cat_1(A))
        & m1_cat_1(F,A,B,D)
        & m1_cat_1(G,A,C,E) )
     => m1_cat_1(k29_cat_4(A,B,C,D,E,F,G),A,k20_cat_4(A,B,C),k20_cat_4(A,D,E)) ) )).

fof(dt_u1_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => m1_subset_1(u1_cat_4(A),u1_cat_1(A)) ) )).

fof(dt_u2_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => ( v1_funct_1(u2_cat_4(A))
        & v1_funct_2(u2_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A))
        & m2_relset_1(u2_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A)) ) ) )).

fof(dt_u3_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => ( v1_funct_1(u3_cat_4(A))
        & v1_funct_2(u3_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u3_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) )).

fof(dt_u4_cat_4,axiom,(
    ! [A] :
      ( l1_cat_4(A)
     => ( v1_funct_1(u4_cat_4(A))
        & v1_funct_2(u4_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u4_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) )).

fof(dt_u5_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => m1_subset_1(u5_cat_4(A),u1_cat_1(A)) ) )).

fof(dt_u6_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => ( v1_funct_1(u6_cat_4(A))
        & v1_funct_2(u6_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A))
        & m2_relset_1(u6_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A)) ) ) )).

fof(dt_u7_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => ( v1_funct_1(u7_cat_4(A))
        & v1_funct_2(u7_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u7_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) )).

fof(dt_u8_cat_4,axiom,(
    ! [A] :
      ( l2_cat_4(A)
     => ( v1_funct_1(u8_cat_4(A))
        & v1_funct_2(u8_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u8_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) )).

fof(dt_g1_cat_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B)
        & m1_subset_1(G,A)
        & v1_funct_1(H)
        & v1_funct_2(H,k2_zfmisc_1(A,A),A)
        & m1_relset_1(H,k2_zfmisc_1(A,A),A)
        & v1_funct_1(I)
        & v1_funct_2(I,k2_zfmisc_1(A,A),B)
        & m1_relset_1(I,k2_zfmisc_1(A,A),B)
        & v1_funct_1(J)
        & v1_funct_2(J,k2_zfmisc_1(A,A),B)
        & m1_relset_1(J,k2_zfmisc_1(A,A),B) )
     => ( v2_cat_4(g1_cat_4(A,B,C,D,E,F,G,H,I,J))
        & l1_cat_4(g1_cat_4(A,B,C,D,E,F,G,H,I,J)) ) ) )).

fof(free_g1_cat_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B)
        & m1_subset_1(G,A)
        & v1_funct_1(H)
        & v1_funct_2(H,k2_zfmisc_1(A,A),A)
        & m1_relset_1(H,k2_zfmisc_1(A,A),A)
        & v1_funct_1(I)
        & v1_funct_2(I,k2_zfmisc_1(A,A),B)
        & m1_relset_1(I,k2_zfmisc_1(A,A),B)
        & v1_funct_1(J)
        & v1_funct_2(J,k2_zfmisc_1(A,A),B)
        & m1_relset_1(J,k2_zfmisc_1(A,A),B) )
     => ! [K,L,M,N,O,P,Q,R,S,T] :
          ( g1_cat_4(A,B,C,D,E,F,G,H,I,J) = g1_cat_4(K,L,M,N,O,P,Q,R,S,T)
         => ( A = K
            & B = L
            & C = M
            & D = N
            & E = O
            & F = P
            & G = Q
            & H = R
            & I = S
            & J = T ) ) ) )).

fof(dt_g2_cat_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B)
        & m1_subset_1(G,A)
        & v1_funct_1(H)
        & v1_funct_2(H,k2_zfmisc_1(A,A),A)
        & m1_relset_1(H,k2_zfmisc_1(A,A),A)
        & v1_funct_1(I)
        & v1_funct_2(I,k2_zfmisc_1(A,A),B)
        & m1_relset_1(I,k2_zfmisc_1(A,A),B)
        & v1_funct_1(J)
        & v1_funct_2(J,k2_zfmisc_1(A,A),B)
        & m1_relset_1(J,k2_zfmisc_1(A,A),B) )
     => ( v5_cat_4(g2_cat_4(A,B,C,D,E,F,G,H,I,J))
        & l2_cat_4(g2_cat_4(A,B,C,D,E,F,G,H,I,J)) ) ) )).

fof(free_g2_cat_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B)
        & m1_subset_1(G,A)
        & v1_funct_1(H)
        & v1_funct_2(H,k2_zfmisc_1(A,A),A)
        & m1_relset_1(H,k2_zfmisc_1(A,A),A)
        & v1_funct_1(I)
        & v1_funct_2(I,k2_zfmisc_1(A,A),B)
        & m1_relset_1(I,k2_zfmisc_1(A,A),B)
        & v1_funct_1(J)
        & v1_funct_2(J,k2_zfmisc_1(A,A),B)
        & m1_relset_1(J,k2_zfmisc_1(A,A),B) )
     => ! [K,L,M,N,O,P,Q,R,S,T] :
          ( g2_cat_4(A,B,C,D,E,F,G,H,I,J) = g2_cat_4(K,L,M,N,O,P,Q,R,S,T)
         => ( A = K
            & B = L
            & C = M
            & D = N
            & E = O
            & F = P
            & G = Q
            & H = R
            & I = S
            & J = T ) ) ) )).
%------------------------------------------------------------------------------