SET007 Axioms: SET007+237.ax


%------------------------------------------------------------------------------
% File     : SET007+237 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subcategories and Products of 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  118 (  13 unit)
%            Number of atoms       :  891 (  94 equality)
%            Maximal formula depth :   21 (  10 average)
%            Number of connectives :  833 (  60 ~  ;   1  |; 416  &)
%                                         (   9 <=>; 347 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-4 arity)
%            Number of functors    :   56 (   1 constant; 0-6 arity)
%            Number of variables   :  454 (   0 singleton; 443 !;  11 ?)
%            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(fc1_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ~ v1_xboole_0(k5_cat_2(A,B)) ) )).

fof(rc1_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ? [B] :
          ( m3_cat_2(B,A)
          & v1_cat_1(B)
          & v2_cat_1(B) ) ) )).

fof(fc2_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v1_cat_1(k11_cat_2(A,B))
        & v2_cat_1(k11_cat_2(A,B)) ) ) )).

fof(t1_cat_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,B),C)
                    & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
                 => ( v1_funct_1(k3_funct_5(D))
                    & v1_funct_2(k3_funct_5(D),A,k1_fraenkel(B,C))
                    & m2_relset_1(k3_funct_5(D),A,k1_fraenkel(B,C)) ) ) ) ) ) )).

fof(t2_cat_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,A),C)
                    & m2_relset_1(D,k2_zfmisc_1(B,A),C) )
                 => ( v1_funct_1(k5_funct_5(D))
                    & v1_funct_2(k5_funct_5(D),A,k1_fraenkel(B,C))
                    & m2_relset_1(k5_funct_5(D),A,k1_fraenkel(B,C)) ) ) ) ) ) )).

fof(t3_cat_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),k2_cat_2(A,B,C,F),D),E) ) ) ) ) ) ) )).

fof(t4_cat_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(A,C,k1_cat_2(B,A,C,k1_fraenkel(A,C),k3_cat_2(A,B,C,F),E),D) ) ) ) ) ) ) )).

fof(d1_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(B))
             => k4_cat_2(A,B,C) = k10_pboole(u2_cat_1(A),k10_cat_1(B,C)) ) ) ) )).

fof(t5_cat_2,axiom,(
    $true )).

fof(t6_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(B))
                 => k8_funct_2(u2_cat_1(B),u2_cat_1(A),k4_cat_2(B,A,C),D) = k10_cat_1(A,C) ) ) ) ) )).

fof(t7_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(B))
                 => k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k4_cat_2(B,A,C)),D) = C ) ) ) ) )).

fof(d2_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( C = k5_cat_2(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> m2_cat_1(D,A,B) ) ) ) ) )).

fof(d3_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( m1_cat_2(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,C)
                   => m2_cat_1(D,A,B) ) ) ) ) ) )).

fof(d4_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( m3_cat_2(B,A)
          <=> ( r1_tarski(u1_cat_1(B),u1_cat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_cat_1(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_cat_1(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_cat_1(A))
                             => ( ( C = E
                                  & D = F )
                               => r1_tarski(k6_cat_1(B,C,D),k6_cat_1(A,E,F)) ) ) ) ) )
              & r1_tarski(u5_cat_1(B),u5_cat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_cat_1(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                     => ( C = D
                       => k10_cat_1(B,C) = k10_cat_1(A,D) ) ) ) ) ) ) ) )).

fof(t8_cat_2,axiom,(
    $true )).

fof(t9_cat_2,axiom,(
    $true )).

fof(t10_cat_2,axiom,(
    $true )).

fof(t11_cat_2,axiom,(
    $true )).

fof(t12_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(B))
             => m1_subset_1(C,u1_cat_1(A)) ) ) ) )).

fof(t13_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => r1_tarski(u2_cat_1(B),u2_cat_1(A)) ) ) )).

fof(t14_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(B))
             => m1_subset_1(C,u2_cat_1(A)) ) ) ) )).

fof(t15_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(B))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( C = D
                   => ( k2_cat_1(B,C) = k2_cat_1(A,D)
                      & k3_cat_1(B,C) = k3_cat_1(A,D) ) ) ) ) ) ) )).

fof(t16_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] :
                              ( m1_cat_1(G,B,C,D)
                             => ( ( C = E
                                  & D = F )
                               => ( k6_cat_1(B,C,D) = k1_xboole_0
                                  | m1_cat_1(G,A,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t17_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(B))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(B))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ( ( C = E
                              & D = F
                              & k2_cat_1(B,D) = k3_cat_1(B,C) )
                           => k4_cat_1(B,C,D) = k4_cat_1(A,E,F) ) ) ) ) ) ) ) )).

fof(t18_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m3_cat_2(A,A) ) )).

fof(t19_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => m2_cat_1(k15_cat_1(B),B,A) ) ) )).

fof(d5_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => k8_cat_2(A,B) = k15_cat_1(B) ) ) )).

fof(t20_cat_2,axiom,(
    $true )).

fof(t21_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(B))
             => k8_funct_2(u2_cat_1(B),u2_cat_1(A),k8_cat_2(A,B),C) = C ) ) ) )).

fof(t22_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(B))
             => k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k8_cat_2(A,B)),C) = C ) ) ) )).

fof(t23_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(B))
             => k13_cat_1(B,A,k8_cat_2(A,B),C) = C ) ) ) )).

fof(t24_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => v10_cat_1(k8_cat_2(A,B),B,A) ) ) )).

fof(t25_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ( v9_cat_1(k8_cat_2(A,B),B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_cat_1(B))
               => ! [D] :
                    ( m1_subset_1(D,u1_cat_1(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_cat_1(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_cat_1(A))
                           => ( ( C = E
                                & D = F )
                             => k6_cat_1(B,C,D) = k6_cat_1(A,E,F) ) ) ) ) ) ) ) ) )).

fof(d6_cat_2,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( r1_cat_2(A,B)
          <=> ( m3_cat_2(A,B)
              & ! [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(B))
                         => ! [F] :
                              ( m1_subset_1(F,u1_cat_1(B))
                             => ( ( C = E
                                  & D = F )
                               => k6_cat_1(A,C,D) = k6_cat_1(B,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t26_cat_2,axiom,(
    $true )).

fof(t27_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ( r1_cat_2(B,A)
          <=> v9_cat_1(k8_cat_2(A,B),B,A) ) ) ) )).

fof(d7_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => k11_cat_2(A,B) = g1_cat_1(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)),k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)),k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B))) ) ) )).

fof(t32_cat_2,axiom,(
    $true )).

fof(t33_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( u1_cat_1(k11_cat_2(A,B)) = k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B))
            & u2_cat_1(k11_cat_2(A,B)) = k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B))
            & u3_cat_1(k11_cat_2(A,B)) = k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B))
            & u4_cat_1(k11_cat_2(A,B)) = k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B))
            & u5_cat_1(k11_cat_2(A,B)) = k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B))
            & u6_cat_1(k11_cat_2(A,B)) = k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B)) ) ) ) )).

fof(t34_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(B))
                 => m1_subset_1(k1_domain_1(u1_cat_1(A),u1_cat_1(B),C,D),u1_cat_1(k11_cat_2(A,B))) ) ) ) ) )).

fof(t35_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(k11_cat_2(A,B)))
             => ? [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                  & ? [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                      & C = k12_cat_2(A,B,D,E) ) ) ) ) ) )).

fof(t36_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(B))
                 => m1_subset_1(k1_domain_1(u2_cat_1(A),u2_cat_1(B),C,D),u2_cat_1(k11_cat_2(A,B))) ) ) ) ) )).

fof(t37_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(k11_cat_2(A,B)))
             => ? [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                  & ? [E] :
                      ( m1_subset_1(E,u2_cat_1(B))
                      & C = k13_cat_2(A,B,D,E) ) ) ) ) ) )).

fof(t38_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(B))
                 => ( k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k2_cat_1(A,C),k2_cat_1(B,D))
                    & k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k3_cat_1(A,C),k3_cat_1(B,D)) ) ) ) ) ) )).

fof(t39_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(B))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(B))
                         => ( ( k2_cat_1(A,D) = k3_cat_1(A,C)
                              & k2_cat_1(B,F) = k3_cat_1(B,E) )
                           => k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F)) = k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) ) ) ) ) ) ) ) )).

fof(t40_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(B))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(B))
                         => ( k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,D,F)) = k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E))
                           => k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F)) = k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) ) ) ) ) ) ) ) )).

fof(t41_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(B))
                 => k10_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,D)) = k13_cat_2(A,B,k10_cat_1(A,C),k10_cat_1(B,D)) ) ) ) ) )).

fof(t42_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [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(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) = k2_zfmisc_1(k6_cat_1(A,C,D),k6_cat_1(B,E,F)) ) ) ) ) ) ) )).

fof(t43_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_cat_1(E,A,C,D)
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_cat_1(B))
                             => ! [H] :
                                  ( m1_cat_1(H,B,F,G)
                                 => ~ ( k6_cat_1(A,C,D) != k1_xboole_0
                                      & k6_cat_1(B,F,G) != k1_xboole_0
                                      & ~ m1_cat_1(k13_cat_2(A,B,E,H),k11_cat_2(A,B),k12_cat_2(A,B,C,F),k12_cat_2(A,B,D,G)) ) ) ) ) ) ) ) ) ) )).

fof(t44_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => m2_cat_1(k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)),B,C) ) ) ) ) ) )).

fof(t45_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => m2_cat_1(k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)),A,C) ) ) ) ) ) )).

fof(d8_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => k14_cat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)) ) ) ) ) ) )).

fof(t46_cat_2,axiom,(
    $true )).

fof(t47_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(B))
                         => k8_funct_2(u2_cat_1(B),u2_cat_1(C),k14_cat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,k10_cat_1(A,E),F)) ) ) ) ) ) ) )).

fof(t48_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,k14_cat_2(A,B,C,D,E)),F) = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)) ) ) ) ) ) ) )).

fof(d9_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => k15_cat_2(A,B,C,D,E) = k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)) ) ) ) ) ) )).

fof(t49_cat_2,axiom,(
    $true )).

fof(t50_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => k8_funct_2(u2_cat_1(A),u2_cat_1(C),k15_cat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,F,k10_cat_1(B,E))) ) ) ) ) ) ) )).

fof(t51_cat_2,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,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k15_cat_2(A,B,C,D,F)),E) = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)) ) ) ) ) ) ) )).

fof(t52_cat_2,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] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C))
                    & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C))
                        & m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) )
                     => ~ ( ! [F] :
                              ( m1_subset_1(F,u1_cat_1(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_cat_1(B))
                                 => k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,G),k10_cat_1(A,F)) = k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,F),k10_cat_1(B,G)) ) )
                          & ! [F] :
                              ( m1_subset_1(F,u2_cat_1(B))
                             => ! [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)) ) )
                          & ! [F] :
                              ( m2_cat_1(F,k11_cat_2(B,A),C)
                             => ~ ! [G] :
                                    ( m1_subset_1(G,u2_cat_1(B))
                                   => ! [H] :
                                        ( m1_subset_1(H,u2_cat_1(A))
                                       => k8_funct_2(u2_cat_1(k11_cat_2(B,A)),u2_cat_1(C),F,k13_cat_2(B,A,G,H)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,G)),H),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,H)),G)) ) ) ) ) ) ) ) ) ) )).

fof(t53_cat_2,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] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C))
                    & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C))
                        & m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) )
                     => ( ? [F] :
                            ( m2_cat_1(F,k11_cat_2(B,A),C)
                            & ! [G] :
                                ( m1_subset_1(G,u1_cat_1(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_cat_1(B))
                                   => ( k15_cat_2(B,A,C,F,G) = k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,G)
                                      & k14_cat_2(B,A,C,F,H) = k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,H) ) ) ) )
                       => ! [F] :
                            ( m1_subset_1(F,u2_cat_1(B))
                           => ! [G] :
                                ( m1_subset_1(G,u2_cat_1(A))
                               => k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)) ) ) ) ) ) ) ) ) )).

fof(t54_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => m2_cat_1(k9_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),A) ) ) )).

fof(t55_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => m2_cat_1(k10_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),B) ) ) )).

fof(d10_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => k16_cat_2(A,B) = k9_funct_3(u2_cat_1(A),u2_cat_1(B)) ) ) )).

fof(d11_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => k17_cat_2(A,B) = k10_funct_3(u2_cat_1(A),u2_cat_1(B)) ) ) )).

fof(t56_cat_2,axiom,(
    $true )).

fof(t57_cat_2,axiom,(
    $true )).

fof(t58_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(B))
                 => k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(A),k16_cat_2(A,B),k13_cat_2(A,B,C,D)) = C ) ) ) ) )).

fof(t59_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(B))
                 => k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(A),k12_cat_1(k11_cat_2(A,B),A,k16_cat_2(A,B)),k12_cat_2(A,B,C,D)) = C ) ) ) ) )).

fof(t60_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(B))
                 => k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(B),k17_cat_2(A,B),k13_cat_2(A,B,C,D)) = D ) ) ) ) )).

fof(t61_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(B))
                 => k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(B),k12_cat_1(k11_cat_2(A,B),B,k17_cat_2(A,B)),k12_cat_2(A,B,C,D)) = D ) ) ) ) )).

fof(t62_cat_2,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,A,C)
                     => m2_cat_1(k14_funct_3(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,k11_cat_2(B,C)) ) ) ) ) ) )).

fof(t63_cat_2,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,A,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => k8_funct_2(u1_cat_1(A),u1_cat_1(k11_cat_2(B,C)),k12_cat_1(A,k11_cat_2(B,C),k18_cat_2(A,B,C,D,E)),F) = k12_cat_2(B,C,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F),k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,E),F)) ) ) ) ) ) ) )).

fof(t64_cat_2,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] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F) = k18_cat_2(k11_cat_2(A,C),B,D,k14_cat_1(k11_cat_2(A,C),A,B,k16_cat_2(A,C),E),k14_cat_1(k11_cat_2(A,C),C,D,k17_cat_2(A,C),F)) ) ) ) ) ) ) )).

fof(t65_cat_2,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] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => m2_cat_1(k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F),k11_cat_2(A,C),k11_cat_2(B,D)) ) ) ) ) ) ) )).

fof(t66_cat_2,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] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => ! [G] :
                              ( m1_subset_1(G,u1_cat_1(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_cat_1(C))
                                 => k8_funct_2(u1_cat_1(k11_cat_2(A,C)),u1_cat_1(k11_cat_2(B,D)),k12_cat_1(k11_cat_2(A,C),k11_cat_2(B,D),k19_cat_2(A,C,B,D,E,F)),k12_cat_2(A,C,G,H)) = k12_cat_2(B,D,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,E),G),k8_funct_2(u1_cat_1(C),u1_cat_1(D),k12_cat_1(C,D,F),H)) ) ) ) ) ) ) ) ) )).

fof(dt_m1_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_cat_2(C,A,B)
         => ~ v1_xboole_0(C) ) ) )).

fof(existence_m1_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m1_cat_2(C,A,B) ) )).

fof(dt_m2_cat_2,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_cat_2(C,A,B) )
     => ! [D] :
          ( m2_cat_2(D,A,B,C)
         => m2_cat_1(D,A,B) ) ) )).

fof(existence_m2_cat_2,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_cat_2(C,A,B) )
     => ? [D] : m2_cat_2(D,A,B,C) ) )).

fof(redefinition_m2_cat_2,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_cat_2(C,A,B) )
     => ! [D] :
          ( m2_cat_2(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) )).

fof(dt_m3_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) )).

fof(existence_m3_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ? [B] : m3_cat_2(B,A) ) )).

fof(dt_k1_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(C)
        & m1_fraenkel(D,B,C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,D)
        & m1_relset_1(E,A,D)
        & m1_subset_1(F,A) )
     => m2_fraenkel(k1_cat_2(A,B,C,D,E,F),B,C,D) ) )).

fof(redefinition_k1_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(C)
        & m1_fraenkel(D,B,C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,D)
        & m1_relset_1(E,A,D)
        & m1_subset_1(F,A) )
     => k1_cat_2(A,B,C,D,E,F) = k1_funct_1(E,F) ) )).

fof(dt_k2_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_funct_1(k2_cat_2(A,B,C,D))
        & v1_funct_2(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C))
        & m2_relset_1(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) ) ) )).

fof(redefinition_k2_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => k2_cat_2(A,B,C,D) = k3_funct_5(D) ) )).

fof(dt_k3_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_funct_1(k3_cat_2(A,B,C,D))
        & v1_funct_2(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C))
        & m2_relset_1(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)) ) ) )).

fof(redefinition_k3_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => k3_cat_2(A,B,C,D) = k5_funct_5(D) ) )).

fof(dt_k4_cat_2,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(B)) )
     => m2_cat_1(k4_cat_2(A,B,C),A,B) ) )).

fof(dt_k5_cat_2,axiom,(
    $true )).

fof(dt_k6_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m1_cat_2(D,B,C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,D)
        & m1_relset_1(E,A,D)
        & m1_subset_1(F,A) )
     => m2_cat_2(k6_cat_2(A,B,C,D,E,F),B,C,D) ) )).

fof(redefinition_k6_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m1_cat_2(D,B,C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,D)
        & m1_relset_1(E,A,D)
        & m1_subset_1(F,A) )
     => k6_cat_2(A,B,C,D,E,F) = k1_funct_1(E,F) ) )).

fof(dt_k7_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m1_cat_2(k7_cat_2(A,B),A,B) ) )).

fof(redefinition_k7_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => k7_cat_2(A,B) = k5_cat_2(A,B) ) )).

fof(dt_k8_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m3_cat_2(B,A) )
     => m2_cat_1(k8_cat_2(A,B),B,A) ) )).

fof(dt_k9_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,D)
        & m1_relset_1(F,B,D) )
     => ( v1_funct_1(k9_cat_2(A,B,C,D,E,F))
        & v1_funct_2(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
        & m2_relset_1(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) ) ) )).

fof(redefinition_k9_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,D)
        & m1_relset_1(F,B,D) )
     => k9_cat_2(A,B,C,D,E,F) = k15_funct_3(E,F) ) )).

fof(dt_k10_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(B,B),B) )
     => ( v1_funct_1(k10_cat_2(A,B,C,D))
        & m2_relset_1(k10_cat_2(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) ) ) )).

fof(redefinition_k10_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(B,B),B) )
     => k10_cat_2(A,B,C,D) = k3_funct_4(C,D) ) )).

fof(dt_k11_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v2_cat_1(k11_cat_2(A,B))
        & l1_cat_1(k11_cat_2(A,B)) ) ) )).

fof(dt_k12_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(B)) )
     => m1_subset_1(k12_cat_2(A,B,C,D),u1_cat_1(k11_cat_2(A,B))) ) )).

fof(redefinition_k12_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(B)) )
     => k12_cat_2(A,B,C,D) = k4_tarski(C,D) ) )).

fof(dt_k13_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u2_cat_1(A))
        & m1_subset_1(D,u2_cat_1(B)) )
     => m1_subset_1(k13_cat_2(A,B,C,D),u2_cat_1(k11_cat_2(A,B))) ) )).

fof(redefinition_k13_cat_2,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u2_cat_1(A))
        & m1_subset_1(D,u2_cat_1(B)) )
     => k13_cat_2(A,B,C,D) = k4_tarski(C,D) ) )).

fof(dt_k14_cat_2,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,k11_cat_2(A,B),C)
        & m1_subset_1(E,u1_cat_1(A)) )
     => m2_cat_1(k14_cat_2(A,B,C,D,E),B,C) ) )).

fof(dt_k15_cat_2,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,k11_cat_2(A,B),C)
        & m1_subset_1(E,u1_cat_1(B)) )
     => m2_cat_1(k15_cat_2(A,B,C,D,E),A,C) ) )).

fof(dt_k16_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m2_cat_1(k16_cat_2(A,B),k11_cat_2(A,B),A) ) )).

fof(dt_k17_cat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m2_cat_1(k17_cat_2(A,B),k11_cat_2(A,B),B) ) )).

fof(dt_k18_cat_2,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,A,C) )
     => m2_cat_1(k18_cat_2(A,B,C,D,E),A,k11_cat_2(B,C)) ) )).

fof(redefinition_k18_cat_2,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,A,C) )
     => k18_cat_2(A,B,C,D,E) = k13_funct_3(D,E) ) )).

fof(dt_k19_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & v2_cat_1(D)
        & l1_cat_1(D)
        & m2_cat_1(E,A,C)
        & m2_cat_1(F,B,D) )
     => m2_cat_1(k19_cat_2(A,B,C,D,E,F),k11_cat_2(A,B),k11_cat_2(C,D)) ) )).

fof(redefinition_k19_cat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & v2_cat_1(D)
        & l1_cat_1(D)
        & m2_cat_1(E,A,C)
        & m2_cat_1(F,B,D) )
     => k19_cat_2(A,B,C,D,E,F) = k15_funct_3(E,F) ) )).

fof(t28_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => ( ~ v1_xboole_0(k3_tarski(a_2_0_cat_2(A,B)))
            & m1_subset_1(k3_tarski(a_2_0_cat_2(A,B)),k1_zfmisc_1(u2_cat_1(A))) ) ) ) )).

fof(t29_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( C = k3_tarski(a_2_0_cat_2(A,B))
               => ( v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C))
                  & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B)
                  & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B)
                  & v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C))
                  & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B)
                  & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B)
                  & v1_funct_1(k1_realset1(u5_cat_1(A),C))
                  & m2_relset_1(k1_realset1(u5_cat_1(A),C),k2_zfmisc_1(C,C),C)
                  & v1_funct_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))
                  & v1_funct_2(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C)
                  & m2_relset_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) ) ) ) ) ) )).

fof(t30_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,C,B)
                    & m2_relset_1(D,C,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,B)
                        & m2_relset_1(E,C,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k2_zfmisc_1(C,C),C) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,B,C)
                                & m2_relset_1(G,B,C) )
                             => ( ( C = k3_tarski(a_2_0_cat_2(A,B))
                                  & D = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C)
                                  & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)
                                  & F = k1_realset1(u5_cat_1(A),C)
                                  & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) )
                               => r1_cat_2(g1_cat_1(B,C,D,E,F,G),A) ) ) ) ) ) ) ) ) )).

fof(t31_cat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,C,B)
                    & m2_relset_1(D,C,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,B)
                        & m2_relset_1(E,C,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k2_zfmisc_1(C,C),C) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,B,C)
                                & m2_relset_1(G,B,C) )
                             => ( r1_cat_2(g1_cat_1(B,C,D,E,F,G),A)
                               => ( C = k3_tarski(a_2_0_cat_2(A,B))
                                  & D = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C)
                                  & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)
                                  & F = k1_realset1(u5_cat_1(A),C)
                                  & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) ) ) ) ) ) ) ) ) ) )).

fof(fraenkel_a_2_0_cat_2,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) )
     => ( r2_hidden(A,a_2_0_cat_2(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,u1_cat_1(B))
            & m1_subset_1(E,u1_cat_1(B))
            & A = k6_cat_1(B,D,E)
            & r2_hidden(D,C)
            & r2_hidden(E,C) ) ) ) )).
%------------------------------------------------------------------------------