SET007 Axioms: SET007+202.ax


%------------------------------------------------------------------------------
% File     : SET007+202 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Introduction to Categories and Functors
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  196 (  42 unit)
%            Number of atoms       : 1211 ( 240 equality)
%            Maximal formula depth :   22 (   8 average)
%            Number of connectives : 1068 (  53 ~  ;  25  |; 371  &)
%                                         (  27 <=>; 592 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-4 arity)
%            Number of functors    :   39 (   1 constant; 0-6 arity)
%            Number of variables   :  644 (   0 singleton; 620 !;  24 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_cat_1,axiom,(
    ? [A] :
      ( l1_cat_1(A)
      & v1_cat_1(A) ) )).

fof(rc2_cat_1,axiom,(
    ? [A] :
      ( l1_cat_1(A)
      & v2_cat_1(A) ) )).

fof(rc3_cat_1,axiom,(
    ? [A] :
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A) ) )).

fof(t1_cat_1,axiom,(
    $true )).

fof(t2_cat_1,axiom,(
    $true )).

fof(t3_cat_1,axiom,(
    $true )).

fof(t4_cat_1,axiom,(
    ! [A,B,C,D] :
      ( ~ v1_xboole_0(D)
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,A,D)
            & m2_relset_1(E,A,D) )
         => ( ( r1_tarski(B,A)
              & r1_tarski(k2_funct_2(A,D,E,B),C) )
           => ( v1_funct_1(k2_partfun1(A,D,E,B))
              & v1_funct_2(k2_partfun1(A,D,E,B),B,C)
              & m2_relset_1(k2_partfun1(A,D,E,B),B,C) ) ) ) ) )).

fof(d1_cat_1,axiom,(
    ! [A,B,C] : k1_cat_1(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C) )).

fof(t5_cat_1,axiom,(
    $true )).

fof(t6_cat_1,axiom,(
    $true )).

fof(t7_cat_1,axiom,(
    ! [A,B,C] :
      ( k1_relat_1(k1_cat_1(A,B,C)) = k1_tarski(k4_tarski(A,B))
      & k1_relat_1(k1_cat_1(A,B,C)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) ) )).

fof(t8_cat_1,axiom,(
    ! [A,B,C] : k1_funct_1(k1_cat_1(A,B,C),k4_tarski(A,B)) = C )).

fof(t9_cat_1,axiom,(
    ! [A,B,C,D] :
      ( m1_subset_1(D,k1_tarski(A))
     => ! [E] :
          ( m1_subset_1(E,k1_tarski(B))
         => k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)) = C ) ) )).

fof(d2_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) ) ) )).

fof(d3_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) )).

fof(d4_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))
               => k4_cat_1(A,B,C) = k1_funct_1(u5_cat_1(A),k4_tarski(C,B)) ) ) ) ) )).

fof(d5_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k5_cat_1(A,B) = k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) ) ) )).

fof(t10_cat_1,axiom,(
    $true )).

fof(t11_cat_1,axiom,(
    $true )).

fof(t12_cat_1,axiom,(
    $true )).

fof(t13_cat_1,axiom,(
    $true )).

fof(t14_cat_1,axiom,(
    $true )).

fof(t15_cat_1,axiom,(
    $true )).

fof(t16_cat_1,axiom,(
    $true )).

fof(t17_cat_1,axiom,(
    $true )).

fof(t18_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                  <=> ( k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C ) ) ) ) ) ) )).

fof(t19_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)) != k1_xboole_0 ) ) )).

fof(d7_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(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
               => ! [D] :
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ( m1_cat_1(D,A,B,C)
                    <=> r2_hidden(D,k6_cat_1(A,B,C)) ) ) ) ) ) ) )).

fof(t20_cat_1,axiom,(
    $true )).

fof(t21_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( r2_hidden(D,k6_cat_1(A,B,C))
                 => m1_cat_1(D,A,B,C) ) ) ) ) )).

fof(t22_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => m1_cat_1(B,A,k2_cat_1(A,B),k3_cat_1(A,B)) ) ) )).

fof(t23_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(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
                   => ( k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C ) ) ) ) ) ) )).

fof(t24_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(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)
                             => ( F = G
                               => ( k6_cat_1(A,B,C) = k1_xboole_0
                                  | k6_cat_1(A,D,E) = k1_xboole_0
                                  | ( B = D
                                    & C = E ) ) ) ) ) ) ) ) ) ) )).

fof(t25_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(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_tarski(D)
                   => ! [E] :
                        ( m1_cat_1(E,A,B,C)
                       => D = E ) ) ) ) ) ) )).

fof(t26_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(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)
                 => ( ! [E] :
                        ( m1_cat_1(E,A,B,C)
                       => D = E )
                   => ( k6_cat_1(A,B,C) = k1_xboole_0
                      | k6_cat_1(A,B,C) = k1_tarski(D) ) ) ) ) ) ) )).

fof(t27_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(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)
                         => ~ ( r2_tarski(k6_cat_1(A,B,C),k6_cat_1(A,D,E))
                              & k6_cat_1(A,B,C) = k1_tarski(F)
                              & ! [G] :
                                  ( m1_cat_1(G,A,D,E)
                                 => k6_cat_1(A,D,E) != k1_tarski(G) ) ) ) ) ) ) ) ) )).

fof(d8_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( v2_cat_1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))
                  <=> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B)
                   => ( k1_funct_1(u3_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B)
                      & k1_funct_1(u4_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)
                          & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) )
                       => k1_funct_1(u5_cat_1(A),k4_tarski(D,k1_funct_1(u5_cat_1(A),k4_tarski(C,B)))) = k1_funct_1(u5_cat_1(A),k4_tarski(k1_funct_1(u5_cat_1(A),k4_tarski(D,C)),B)) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B
                & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(A))
                   => ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = B
                     => k1_funct_1(u5_cat_1(A),k4_tarski(k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),C)) = C ) )
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(A))
                   => ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = B
                     => k1_funct_1(u5_cat_1(A),k4_tarski(C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))) = C ) ) ) ) ) ) ) )).

fof(t28_cat_1,axiom,(
    $true )).

fof(t29_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( ( ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))
                  <=> k2_cat_1(A,C) = k3_cat_1(A,B) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ( k2_cat_1(A,C) = k3_cat_1(A,B)
                   => ( k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)
                      & k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( ( k2_cat_1(A,D) = k3_cat_1(A,C)
                          & k2_cat_1(A,C) = k3_cat_1(A,B) )
                       => k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D)) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ( k2_cat_1(A,k5_cat_1(A,B)) = B
                & k3_cat_1(A,k5_cat_1(A,B)) = B
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(A))
                   => ( k3_cat_1(A,C) = B
                     => k4_cat_1(A,C,k5_cat_1(A,B)) = C ) )
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(A))
                   => ( k2_cat_1(A,C) = B
                     => k4_cat_1(A,k5_cat_1(A,B),C) = C ) ) ) ) )
       => v2_cat_1(A) ) ) )).

fof(d9_cat_1,axiom,(
    ! [A,B] : k8_cat_1(A,B) = g1_cat_1(k1_tarski(A),k1_tarski(B),k7_cat_1(B,A),k7_cat_1(B,A),k1_cat_1(B,B,B),k7_cat_1(A,B)) )).

fof(t30_cat_1,axiom,(
    $true )).

fof(t31_cat_1,axiom,(
    $true )).

fof(t32_cat_1,axiom,(
    ! [A,B] : m1_subset_1(A,u1_cat_1(k8_cat_1(A,B))) )).

fof(t33_cat_1,axiom,(
    ! [A,B] : m1_subset_1(A,u2_cat_1(k8_cat_1(B,A))) )).

fof(t34_cat_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
     => C = A ) )).

fof(t35_cat_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u2_cat_1(k8_cat_1(A,B)))
     => C = B ) )).

fof(t36_cat_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k8_cat_1(A,B)))
             => r2_hidden(E,k6_cat_1(k8_cat_1(A,B),C,D)) ) ) ) )).

fof(t37_cat_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(k8_cat_1(A,B)))
             => m1_cat_1(E,k8_cat_1(A,B),C,D) ) ) ) )).

fof(t38_cat_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
         => k6_cat_1(k8_cat_1(A,B),C,D) != k1_xboole_0 ) ) )).

fof(t39_cat_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
         => ! [E] :
              ( m1_subset_1(E,u1_cat_1(k8_cat_1(A,B)))
             => ! [F] :
                  ( m1_subset_1(F,u1_cat_1(k8_cat_1(A,B)))
                 => ! [G] :
                      ( m1_cat_1(G,k8_cat_1(A,B),C,D)
                     => ! [H] :
                          ( m1_cat_1(H,k8_cat_1(A,B),E,F)
                         => G = H ) ) ) ) ) ) )).

fof(t40_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,B) = k3_cat_1(A,C)
              <=> r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A))) ) ) ) ) )).

fof(t41_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,B) = k3_cat_1(A,C)
               => k4_cat_1(A,C,B) = k1_funct_1(u5_cat_1(A),k4_tarski(B,C)) ) ) ) ) )).

fof(t42_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = k3_cat_1(A,B)
               => ( k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)
                  & k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) ) ) ) ) ) )).

fof(t43_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( ( k2_cat_1(A,D) = k3_cat_1(A,C)
                      & k2_cat_1(A,C) = k3_cat_1(A,B) )
                   => k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D)) ) ) ) ) ) )).

fof(t44_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( k2_cat_1(A,k5_cat_1(A,B)) = B
            & k3_cat_1(A,k5_cat_1(A,B)) = B ) ) ) )).

fof(t45_cat_1,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))
             => ( k5_cat_1(A,B) = k5_cat_1(A,C)
               => B = C ) ) ) ) )).

fof(t46_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k3_cat_1(A,C) = B
               => k4_cat_1(A,C,k5_cat_1(A,B)) = C ) ) ) ) )).

fof(t47_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = B
               => k4_cat_1(A,k5_cat_1(A,B),C) = C ) ) ) ) )).

fof(d10_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v3_cat_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u2_cat_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ( ( k2_cat_1(A,C) = k2_cat_1(A,D)
                        & k3_cat_1(A,C) = k2_cat_1(A,B)
                        & k3_cat_1(A,D) = k2_cat_1(A,B)
                        & k4_cat_1(A,C,B) = k4_cat_1(A,D,B) )
                     => C = D ) ) ) ) ) ) )).

fof(d11_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v4_cat_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u2_cat_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ( ( k2_cat_1(A,C) = k3_cat_1(A,B)
                        & k2_cat_1(A,D) = k3_cat_1(A,B)
                        & k3_cat_1(A,C) = k3_cat_1(A,D)
                        & k4_cat_1(A,B,C) = k4_cat_1(A,B,D) )
                     => C = D ) ) ) ) ) ) )).

fof(d12_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v5_cat_1(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u2_cat_1(A))
                & k2_cat_1(A,C) = k3_cat_1(A,B)
                & k3_cat_1(A,C) = k2_cat_1(A,B)
                & k4_cat_1(A,C,B) = k5_cat_1(A,k3_cat_1(A,B))
                & k4_cat_1(A,B,C) = k5_cat_1(A,k2_cat_1(A,B)) ) ) ) ) )).

fof(t48_cat_1,axiom,(
    $true )).

fof(t49_cat_1,axiom,(
    $true )).

fof(t50_cat_1,axiom,(
    $true )).

fof(t51_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,C,D) != k1_xboole_0
                              & ~ r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) ) ) ) ) ) ) ) )).

fof(t52_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,C,D) != k1_xboole_0
                      & k6_cat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) )).

fof(d13_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,C,D) != k1_xboole_0
                              & k9_cat_1(A,B,C,D,E,F) != k4_cat_1(A,E,F) ) ) ) ) ) ) ) )).

fof(t53_cat_1,axiom,(
    $true )).

fof(t54_cat_1,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))
             => ! [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,C,D)
                             => ! [H] :
                                  ( m1_cat_1(H,A,D,E)
                                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                      & k6_cat_1(A,C,D) != k1_xboole_0
                                      & k6_cat_1(A,D,E) != k1_xboole_0
                                      & k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H)) != k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) ) ) ) ) ) ) ) ) ) )).

fof(t55_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)) ) ) )).

fof(t56_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,B) != k1_xboole_0 ) ) )).

fof(t57_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => k9_cat_1(A,B,C,C,D,k10_cat_1(A,C)) = D ) ) ) ) ) )).

fof(t58_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D ) ) ) ) ) )).

fof(t59_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k9_cat_1(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) = k10_cat_1(A,B) ) ) )).

fof(t60_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => ( v3_cat_1(D,A)
                    <=> ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] :
                              ( m1_cat_1(F,A,E,B)
                             => ! [G] :
                                  ( m1_cat_1(G,A,E,B)
                                 => ( k9_cat_1(A,E,B,C,F,D) = k9_cat_1(A,E,B,C,G,D)
                                   => ( k6_cat_1(A,E,B) = k1_xboole_0
                                      | F = G ) ) ) ) ) ) ) ) ) ) ) )).

fof(t61_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ( ( v3_cat_1(E,A)
                              & v3_cat_1(F,A) )
                           => ( k6_cat_1(A,B,C) = k1_xboole_0
                              | k6_cat_1(A,C,D) = k1_xboole_0
                              | v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) ) ) ) ) ) ) ) ) )).

fof(t62_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ( v3_cat_1(k9_cat_1(A,B,C,D,E,F),A)
                           => ( k6_cat_1(A,B,C) = k1_xboole_0
                              | k6_cat_1(A,C,D) = k1_xboole_0
                              | v3_cat_1(E,A) ) ) ) ) ) ) ) ) )).

fof(t63_cat_1,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))
             => ! [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)
                       => ( k6_cat_1(A,B,C) = k1_xboole_0
                          | k6_cat_1(A,C,B) = k1_xboole_0
                          | v3_cat_1(E,A) ) ) ) ) ) ) ) )).

fof(t64_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => v3_cat_1(k10_cat_1(A,B),A) ) ) )).

fof(t65_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => ( v4_cat_1(D,A)
                    <=> ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] :
                              ( m1_cat_1(F,A,C,E)
                             => ! [G] :
                                  ( m1_cat_1(G,A,C,E)
                                 => ( k9_cat_1(A,B,C,E,D,F) = k9_cat_1(A,B,C,E,D,G)
                                   => ( k6_cat_1(A,C,E) = k1_xboole_0
                                      | F = G ) ) ) ) ) ) ) ) ) ) ) )).

fof(t66_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ( ( v4_cat_1(E,A)
                              & v4_cat_1(F,A) )
                           => ( k6_cat_1(A,B,C) = k1_xboole_0
                              | k6_cat_1(A,C,D) = k1_xboole_0
                              | v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) ) ) ) ) ) ) ) ) )).

fof(t67_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ( v4_cat_1(k9_cat_1(A,B,C,D,E,F),A)
                           => ( k6_cat_1(A,B,C) = k1_xboole_0
                              | k6_cat_1(A,C,D) = k1_xboole_0
                              | v4_cat_1(F,A) ) ) ) ) ) ) ) ) )).

fof(t68_cat_1,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))
             => ! [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)
                       => ( k6_cat_1(A,B,C) = k1_xboole_0
                          | k6_cat_1(A,C,B) = k1_xboole_0
                          | v4_cat_1(D,A) ) ) ) ) ) ) ) )).

fof(t69_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => v4_cat_1(k10_cat_1(A,B),A) ) ) )).

fof(t70_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => ( v5_cat_1(D,A)
                    <=> ( k6_cat_1(A,C,B) != k1_xboole_0
                        & ? [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(t71_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,C,B) != k1_xboole_0
                      & ? [E] :
                          ( m1_cat_1(E,A,C,B)
                          & ? [F] :
                              ( m1_cat_1(F,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,F) = k10_cat_1(A,B)
                              & E != F ) ) ) ) ) ) ) )).

fof(d14_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( v5_cat_1(D,A)
                   => ( k6_cat_1(A,B,C) = k1_xboole_0
                      | ! [E] :
                          ( m1_cat_1(E,A,C,B)
                         => ( E = k11_cat_1(A,B,C,D)
                          <=> ( 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(t72_cat_1,axiom,(
    $true )).

fof(t73_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( v5_cat_1(D,A)
                   => ( k6_cat_1(A,B,C) = k1_xboole_0
                      | ( v3_cat_1(D,A)
                        & v4_cat_1(D,A) ) ) ) ) ) ) ) )).

fof(t74_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => v5_cat_1(k10_cat_1(A,B),A) ) ) )).

fof(t75_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ( ( v5_cat_1(E,A)
                              & v5_cat_1(F,A) )
                           => ( k6_cat_1(A,B,C) = k1_xboole_0
                              | k6_cat_1(A,C,D) = k1_xboole_0
                              | v5_cat_1(k9_cat_1(A,B,C,D,E,F),A) ) ) ) ) ) ) ) ) )).

fof(t76_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( v5_cat_1(D,A)
                   => ( k6_cat_1(A,B,C) = k1_xboole_0
                      | v5_cat_1(k11_cat_1(A,B,C,D),A) ) ) ) ) ) ) )).

fof(t77_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] :
                          ( m1_cat_1(F,A,C,D)
                         => ( ( v5_cat_1(E,A)
                              & v5_cat_1(F,A) )
                           => ( k6_cat_1(A,B,C) = k1_xboole_0
                              | k6_cat_1(A,C,D) = k1_xboole_0
                              | k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) = k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E)) ) ) ) ) ) ) ) ) )).

fof(d15_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v6_cat_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_cat_1(A))
               => ( k6_cat_1(A,C,B) != k1_xboole_0
                  & ? [D] :
                      ( m1_cat_1(D,A,C,B)
                      & ! [E] :
                          ( m1_cat_1(E,A,C,B)
                         => D = E ) ) ) ) ) ) ) )).

fof(d16_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v7_cat_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_cat_1(A))
               => ( k6_cat_1(A,B,C) != k1_xboole_0
                  & ? [D] :
                      ( m1_cat_1(D,A,B,C)
                      & ! [E] :
                          ( m1_cat_1(E,A,B,C)
                         => D = E ) ) ) ) ) ) ) )).

fof(d17_cat_1,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
                  & ? [D] :
                      ( m1_cat_1(D,A,B,C)
                      & v5_cat_1(D,A) ) ) ) ) ) ) )).

fof(t78_cat_1,axiom,(
    $true )).

fof(t79_cat_1,axiom,(
    $true )).

fof(t80_cat_1,axiom,(
    $true )).

fof(t81_cat_1,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(t82_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v7_cat_1(B,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_tarski(D) ) ) ) ) ) )).

fof(t83_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v7_cat_1(B,A)
           => ! [C] :
                ( m1_cat_1(C,A,B,B)
               => k10_cat_1(A,B) = C ) ) ) ) )).

fof(t84_cat_1,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))
             => ( ( v7_cat_1(B,A)
                  & v7_cat_1(C,A) )
               => r1_cat_1(A,B,C) ) ) ) ) )).

fof(t85_cat_1,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))
             => ( ( v7_cat_1(B,A)
                  & r1_cat_1(A,B,C) )
               => v7_cat_1(C,A) ) ) ) ) )).

fof(t86_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v6_cat_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_cat_1(A))
               => ? [D] :
                    ( m1_cat_1(D,A,C,B)
                    & k6_cat_1(A,C,B) = k1_tarski(D) ) ) ) ) ) )).

fof(t87_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v6_cat_1(B,A)
           => ! [C] :
                ( m1_cat_1(C,A,B,B)
               => k10_cat_1(A,B) = C ) ) ) ) )).

fof(t88_cat_1,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))
             => ( ( v6_cat_1(B,A)
                  & v6_cat_1(C,A) )
               => r1_cat_1(A,B,C) ) ) ) ) )).

fof(t89_cat_1,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))
             => ( ( v6_cat_1(B,A)
                  & r1_cat_1(A,C,B) )
               => v6_cat_1(C,A) ) ) ) ) )).

fof(t90_cat_1,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))
             => ! [D] :
                  ( m1_cat_1(D,A,B,C)
                 => ( v6_cat_1(B,A)
                   => ( k6_cat_1(A,B,C) = k1_xboole_0
                      | v3_cat_1(D,A) ) ) ) ) ) ) )).

fof(t91_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => r1_cat_1(A,B,B) ) ) )).

fof(t92_cat_1,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)
               => r1_cat_1(A,C,B) ) ) ) ) )).

fof(t93_cat_1,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ( ( r1_cat_1(A,B,C)
                      & r1_cat_1(A,C,D) )
                   => r1_cat_1(A,B,D) ) ) ) ) ) )).

fof(d18_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ( m2_cat_1(C,A,B)
              <=> ( ! [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_cat_1(B))
                          & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u3_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
                        & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u4_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                         => ( r2_hidden(k4_tarski(E,D),k1_relat_1(u5_cat_1(A)))
                           => k1_funct_1(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D))) = k1_funct_1(u5_cat_1(B),k4_tarski(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) ) ) ) ) ) ) ) )).

fof(t94_cat_1,axiom,(
    $true )).

fof(t95_cat_1,axiom,(
    $true )).

fof(t96_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ( ( ! [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_cat_1(B))
                          & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
                        & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                         => ( k2_cat_1(A,E) = k3_cat_1(A,D)
                           => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) )
               => m2_cat_1(C,A,B) ) ) ) ) )).

fof(t97_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ? [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                      & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) ) ) ) ) )).

fof(t98_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
                    & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) ) ) ) ) )).

fof(t99_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ( k2_cat_1(A,E) = k3_cat_1(A,D)
                       => ( k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
                          & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) ) )).

fof(t100_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B))
                    & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) )
                 => ( ( ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,E)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)) )
                      & ! [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                         => ( k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E))
                            & k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k3_cat_1(A,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) )
                      & ! [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                         => ! [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                             => ( k2_cat_1(A,F) = k3_cat_1(A,E)
                               => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)) ) ) ) )
                   => m2_cat_1(C,A,B) ) ) ) ) ) )).

fof(d19_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ? [E] :
                        ( m1_subset_1(E,u1_cat_1(B))
                        & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) ) )
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B))
                      & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) )
                   => ( D = k12_cat_1(A,B,C)
                    <=> ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_cat_1(B))
                             => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),E)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),F)
                               => k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E) = F ) ) ) ) ) ) ) ) ) )).

fof(t101_cat_1,axiom,(
    $true )).

fof(t102_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ? [E] :
                        ( m1_subset_1(E,u1_cat_1(B))
                        & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
               => ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_cat_1(B))
                       => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
                         => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E ) ) ) ) ) ) ) )).

fof(t103_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
                       => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E ) ) ) ) ) ) )).

fof(t104_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) )).

fof(t105_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
                    & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) )).

fof(d20_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k13_cat_1(A,B,C,D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) ) ) ) ) )).

fof(t106_cat_1,axiom,(
    $true )).

fof(t107_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
                       => k13_cat_1(A,B,C,D) = E ) ) ) ) ) ) )).

fof(t108_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k13_cat_1(A,B,C,D)) ) ) ) ) )).

fof(t109_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( k13_cat_1(A,B,C,k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
                    & k13_cat_1(A,B,C,k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) )).

fof(t110_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) )).

fof(t111_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m2_cat_1(k6_partfun1(u2_cat_1(A)),A,A) ) )).

fof(t112_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k14_cat_1(A,B,C,D,E)),F) = k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,E),k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F)) ) ) ) ) ) ) )).

fof(t113_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => k13_cat_1(A,C,k14_cat_1(A,B,C,D,E),F) = k13_cat_1(B,C,E,k13_cat_1(A,B,D,F)) ) ) ) ) ) ) )).

fof(d21_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k15_cat_1(A) = k6_partfun1(u2_cat_1(A)) ) )).

fof(t114_cat_1,axiom,(
    $true )).

fof(t115_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B) = B ) ) )).

fof(t116_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k8_funct_2(u1_cat_1(A),u1_cat_1(A),k12_cat_1(A,A,k15_cat_1(A)),B) = B ) ) )).

fof(t117_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k12_cat_1(A,A,k15_cat_1(A)) = k6_partfun1(u1_cat_1(A)) ) )).

fof(t118_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k13_cat_1(A,A,k15_cat_1(A),B) = B ) ) )).

fof(d22_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v8_cat_1(C,A,B)
              <=> ( v2_funct_1(C)
                  & k2_relat_1(C) = u2_cat_1(B)
                  & k2_relat_1(k12_cat_1(A,B,C)) = u1_cat_1(B) ) ) ) ) ) )).

fof(d23_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v9_cat_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_cat_1(A))
                       => ( k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) != k1_xboole_0
                         => ! [F] :
                              ( m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))
                             => ( k6_cat_1(A,D,E) != k1_xboole_0
                                & ? [G] :
                                    ( m1_cat_1(G,A,D,E)
                                    & F = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) ) ) ) ) ) ) ) ) ) ) )).

fof(d24_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v10_cat_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_cat_1(A))
                       => ( k6_cat_1(A,D,E) != k1_xboole_0
                         => ! [F] :
                              ( m1_cat_1(F,A,D,E)
                             => ! [G] :
                                  ( m1_cat_1(G,A,D,E)
                                 => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G)
                                   => F = G ) ) ) ) ) ) ) ) ) ) )).

fof(t119_cat_1,axiom,(
    $true )).

fof(t120_cat_1,axiom,(
    $true )).

fof(t121_cat_1,axiom,(
    $true )).

fof(t122_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v8_cat_1(k15_cat_1(A),A,A) ) )).

fof(t123_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( r2_hidden(F,k6_cat_1(A,D,E))
                         => r2_hidden(k1_funct_1(C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) ) ) ) ) )).

fof(t124_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ( k6_cat_1(A,D,E) != k1_xboole_0
                       => ! [F] :
                            ( m1_cat_1(F,A,D,E)
                           => r2_hidden(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) ) ) ) ) ) )).

fof(t125_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ( k6_cat_1(A,D,E) != k1_xboole_0
                       => ! [F] :
                            ( m1_cat_1(F,A,D,E)
                           => m1_cat_1(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) ) ) ) ) ) ) )).

fof(t126_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ~ ( k6_cat_1(A,D,E) != k1_xboole_0
                          & k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) = k1_xboole_0 ) ) ) ) ) ) )).

fof(t127_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ( ( v9_cat_1(D,A,B)
                          & v9_cat_1(E,B,C) )
                       => v9_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) )).

fof(t128_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ( ( v10_cat_1(D,A,B)
                          & v10_cat_1(E,B,C) )
                       => v10_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) )).

fof(t129_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => r1_tarski(k2_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) ) ) ) )).

fof(d25_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => k16_cat_1(A,B,C,D,E) = k2_partfun1(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)) ) ) ) ) ) )).

fof(t130_cat_1,axiom,(
    $true )).

fof(t131_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ( k6_cat_1(A,D,E) != k1_xboole_0
                       => ! [F] :
                            ( m1_cat_1(F,A,D,E)
                           => k1_funct_1(k16_cat_1(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) ) ) ) ) ) ) ) )).

fof(t132_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v9_cat_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_cat_1(A))
                       => k2_relat_1(k16_cat_1(A,B,C,D,E)) = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) ) ) ) ) ) )).

fof(t133_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v10_cat_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_cat_1(A))
                       => v2_funct_1(k16_cat_1(A,B,C,D,E)) ) ) ) ) ) ) )).

fof(dt_m1_cat_1,axiom,(
    ! [A,B,C] :
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => ! [D] :
          ( m1_cat_1(D,A,B,C)
         => m1_subset_1(D,u2_cat_1(A)) ) ) )).

fof(existence_m1_cat_1,axiom,(
    ! [A,B,C] :
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => ? [D] : m1_cat_1(D,A,B,C) ) )).

fof(dt_m2_cat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m2_cat_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
            & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) ) ) ) )).

fof(existence_m2_cat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m2_cat_1(C,A,B) ) )).

fof(dt_l1_cat_1,axiom,(
    $true )).

fof(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) )).

fof(abstractness_v1_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( v1_cat_1(A)
       => A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ) )).

fof(dt_k1_cat_1,axiom,(
    ! [A,B,C] :
      ( v1_funct_1(k1_cat_1(A,B,C))
      & m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) ) )).

fof(dt_k2_cat_1,axiom,(
    ! [A,B] :
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)) ) )).

fof(dt_k3_cat_1,axiom,(
    ! [A,B] :
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)) ) )).

fof(dt_k4_cat_1,axiom,(
    ! [A,B,C] :
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)) ) )).

fof(dt_k5_cat_1,axiom,(
    ! [A,B] :
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)) ) )).

fof(dt_k6_cat_1,axiom,(
    ! [A,B,C] :
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))) ) )).

fof(dt_k7_cat_1,axiom,(
    ! [A,B] :
      ( v1_funct_1(k7_cat_1(A,B))
      & v1_funct_2(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B))
      & m2_relset_1(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) ) )).

fof(redefinition_k7_cat_1,axiom,(
    ! [A,B] : k7_cat_1(A,B) = k3_cqc_lang(A,B) )).

fof(dt_k8_cat_1,axiom,(
    ! [A,B] :
      ( v1_cat_1(k8_cat_1(A,B))
      & v2_cat_1(k8_cat_1(A,B))
      & l1_cat_1(k8_cat_1(A,B)) ) )).

fof(dt_k9_cat_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & l1_cat_1(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,C)
        & m1_cat_1(F,A,C,D) )
     => m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D) ) )).

fof(dt_k10_cat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k10_cat_1(A,B),A,B,B) ) )).

fof(redefinition_k10_cat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => k10_cat_1(A,B) = k5_cat_1(A,B) ) )).

fof(dt_k11_cat_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_cat_1(D,A,B,C) )
     => m1_cat_1(k11_cat_1(A,B,C,D),A,C,B) ) )).

fof(dt_k12_cat_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
        & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
     => ( v1_funct_1(k12_cat_1(A,B,C))
        & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B))
        & m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) ) ) )).

fof(dt_k13_cat_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m1_subset_1(D,u1_cat_1(A)) )
     => m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)) ) )).

fof(dt_k14_cat_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,B,C) )
     => m2_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) )).

fof(redefinition_k14_cat_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,B,C) )
     => k14_cat_1(A,B,C,D,E) = k5_relat_1(D,E) ) )).

fof(dt_k15_cat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m2_cat_1(k15_cat_1(A),A,A) ) )).

fof(dt_k16_cat_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m1_subset_1(D,u1_cat_1(A))
        & m1_subset_1(E,u1_cat_1(A)) )
     => ( v1_funct_1(k16_cat_1(A,B,C,D,E))
        & v1_funct_2(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))
        & m2_relset_1(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) )).

fof(dt_u1_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u1_cat_1(A)) ) )).

fof(dt_u2_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u2_cat_1(A)) ) )).

fof(dt_u3_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( v1_funct_1(u3_cat_1(A))
        & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) )).

fof(dt_u4_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( v1_funct_1(u4_cat_1(A))
        & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) )).

fof(dt_u5_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( v1_funct_1(u5_cat_1(A))
        & m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)) ) ) )).

fof(dt_u6_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( v1_funct_1(u6_cat_1(A))
        & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
        & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) ) ) )).

fof(dt_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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) )
     => ( v1_cat_1(g1_cat_1(A,B,C,D,E,F))
        & l1_cat_1(g1_cat_1(A,B,C,D,E,F)) ) ) )).

fof(free_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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) )
     => ! [G,H,I,J,K,L] :
          ( g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) )).

fof(d6_cat_1,axiom,(
    ! [A] :
      ( l1_cat_1(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) = a_3_0_cat_1(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_cat_1,axiom,(
    ! [A,B,C,D] :
      ( ( l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(B))
        & m1_subset_1(D,u1_cat_1(B)) )
     => ( r2_hidden(A,a_3_0_cat_1(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u2_cat_1(B))
            & A = E
            & k2_cat_1(B,E) = C
            & k3_cat_1(B,E) = D ) ) ) )).
%------------------------------------------------------------------------------