SET007 Axioms: SET007+333.ax


%------------------------------------------------------------------------------
% File     : SET007+333 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Products and Coproducts in 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  130 (   7 unit)
%            Number of atoms       : 1019 ( 155 equality)
%            Maximal formula depth :   35 (  11 average)
%            Number of connectives :  933 (  44 ~  ;   4  |; 362  &)
%                                         (  34 <=>; 489 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   1 propositional; 0-4 arity)
%            Number of functors    :   39 (   5 constant; 0-6 arity)
%            Number of variables   :  547 (   0 singleton; 539 !;   8 ?)
%            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(d1_cat_3,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( r2_hidden(D,A)
             => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ) )).

fof(t1_cat_3,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ( ! [E] :
                    ( r2_hidden(E,A)
                   => k4_finseq_4(A,B,C,E) = k4_finseq_4(A,B,D,E) )
               => C = D ) ) ) ) )).

fof(t2_cat_3,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( m1_subset_1(D,C)
         => ( r2_hidden(B,A)
           => k4_finseq_4(A,C,k1_cat_3(C,A,D),B) = D ) ) ) )).

fof(t3_cat_3,axiom,(
    $true )).

fof(t4_cat_3,axiom,(
    $true )).

fof(t5_cat_3,axiom,(
    $true )).

fof(t6_cat_3,axiom,(
    $true )).

fof(t7_cat_3,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ( A != B
       => ! [D] :
            ( m1_subset_1(D,C)
           => ! [E] :
                ( m1_subset_1(E,C)
               => ( k4_finseq_4(k2_tarski(A,B),C,k5_funct_4(C,A,B,D,E),A) = D
                  & k4_finseq_4(k2_tarski(A,B),C,k5_funct_4(C,A,B,D,E),B) = E ) ) ) ) ) )).

fof(d2_cat_3,axiom,(
    $true )).

fof(d3_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u1_cat_1(A))
                & m2_relset_1(D,B,u1_cat_1(A)) )
             => ( D = k3_cat_3(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u1_cat_1(A),D,E) = k2_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) )).

fof(d4_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u1_cat_1(A))
                & m2_relset_1(D,B,u1_cat_1(A)) )
             => ( D = k4_cat_3(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u1_cat_1(A),D,E) = k3_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) )).

fof(t8_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => k3_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C)) = k1_cat_3(u1_cat_1(B),A,k2_cat_1(B,C)) ) ) )).

fof(t9_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => k4_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C)) = k1_cat_3(u1_cat_1(B),A,k3_cat_1(B,C)) ) ) )).

fof(t10_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => k3_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E)) = k5_funct_4(u1_cat_1(C),A,B,k2_cat_1(C,D),k2_cat_1(C,E)) ) ) ) )).

fof(t11_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => k4_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E)) = k5_funct_4(u1_cat_1(C),A,B,k3_cat_1(C,D),k3_cat_1(C,E)) ) ) ) )).

fof(d5_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u2_cat_1(k2_oppcat_1(A)))
                & m2_relset_1(D,B,u2_cat_1(k2_oppcat_1(A))) )
             => ( D = k5_cat_3(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u2_cat_1(k2_oppcat_1(A)),D,E) = k5_oppcat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) )).

fof(t12_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => k5_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C)) = k1_cat_3(u2_cat_1(k2_oppcat_1(B)),A,k5_oppcat_1(B,C)) ) ) )).

fof(t13_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ( A != B
               => k5_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E)) = k5_funct_4(u2_cat_1(k2_oppcat_1(C)),A,B,k5_oppcat_1(C,D),k5_oppcat_1(C,E)) ) ) ) ) )).

fof(t14_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u2_cat_1(B))
            & m2_relset_1(C,A,u2_cat_1(B)) )
         => k5_cat_3(k2_oppcat_1(B),A,k5_cat_3(B,A,C)) = C ) ) )).

fof(d6_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(k2_oppcat_1(A)))
            & m2_relset_1(C,B,u2_cat_1(k2_oppcat_1(A))) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u2_cat_1(A))
                & m2_relset_1(D,B,u2_cat_1(A)) )
             => ( D = k6_cat_3(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u2_cat_1(A),D,E) = k6_oppcat_1(A,k4_finseq_4(B,u2_cat_1(k2_oppcat_1(A)),C,E)) ) ) ) ) ) )).

fof(t15_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(k2_oppcat_1(B)))
         => k6_cat_3(B,A,k1_cat_3(u2_cat_1(k2_oppcat_1(B)),A,C)) = k1_cat_3(u2_cat_1(B),A,k6_oppcat_1(B,C)) ) ) )).

fof(t16_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ( A != B
       => ! [D] :
            ( m1_subset_1(D,u2_cat_1(k2_oppcat_1(C)))
           => ! [E] :
                ( m1_subset_1(E,u2_cat_1(k2_oppcat_1(C)))
               => k6_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(k2_oppcat_1(C)),A,B,D,E)) = k5_funct_4(u2_cat_1(C),A,B,k6_oppcat_1(C,D),k6_oppcat_1(C,E)) ) ) ) ) )).

fof(t17_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u2_cat_1(B))
            & m2_relset_1(C,A,u2_cat_1(B)) )
         => k6_cat_3(B,A,k5_cat_3(B,A,C)) = C ) ) )).

fof(d7_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] :
              ( m1_subset_1(D,u2_cat_1(A))
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,u2_cat_1(A))
                    & m2_relset_1(E,B,u2_cat_1(A)) )
                 => ( E = k7_cat_3(A,B,C,D)
                  <=> ! [F] :
                        ( r2_hidden(F,B)
                       => k4_finseq_4(B,u2_cat_1(A),E,F) = k4_cat_1(A,D,k4_finseq_4(B,u2_cat_1(A),C,F)) ) ) ) ) ) ) )).

fof(d8_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] :
              ( m1_subset_1(D,u2_cat_1(A))
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,u2_cat_1(A))
                    & m2_relset_1(E,B,u2_cat_1(A)) )
                 => ( E = k8_cat_3(A,B,C,D)
                  <=> ! [F] :
                        ( r2_hidden(F,B)
                       => k4_finseq_4(B,u2_cat_1(A),E,F) = k4_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,F),D) ) ) ) ) ) ) )).

fof(t18_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] :
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ( A != B
                   => k7_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E),F) = k5_funct_4(u2_cat_1(C),A,B,k4_cat_1(C,F,D),k4_cat_1(C,F,E)) ) ) ) ) ) )).

fof(t19_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] :
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ( A != B
                   => k8_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,E,F),D) = k5_funct_4(u2_cat_1(C),A,B,k4_cat_1(C,E,D),k4_cat_1(C,F,D)) ) ) ) ) ) )).

fof(t20_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( k3_cat_3(B,A,D) = k1_cat_3(u1_cat_1(B),A,k3_cat_1(B,C))
               => ( k3_cat_3(B,A,k7_cat_3(B,A,D,C)) = k1_cat_3(u1_cat_1(B),A,k2_cat_1(B,C))
                  & k4_cat_3(B,A,k7_cat_3(B,A,D,C)) = k4_cat_3(B,A,D) ) ) ) ) ) )).

fof(t21_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( k4_cat_3(B,A,D) = k1_cat_3(u1_cat_1(B),A,k2_cat_1(B,C))
               => ( k3_cat_3(B,A,k8_cat_3(B,A,D,C)) = k3_cat_3(B,A,D)
                  & k4_cat_3(B,A,k8_cat_3(B,A,D,C)) = k1_cat_3(u1_cat_1(B),A,k3_cat_1(B,C)) ) ) ) ) ) )).

fof(d9_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u2_cat_1(A))
                & m2_relset_1(D,B,u2_cat_1(A)) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,u2_cat_1(A))
                    & m2_relset_1(E,B,u2_cat_1(A)) )
                 => ( E = k9_cat_3(A,B,C,D)
                  <=> ! [F] :
                        ( r2_hidden(F,B)
                       => k4_finseq_4(B,u2_cat_1(A),E,F) = k4_cat_1(A,k4_finseq_4(B,u2_cat_1(A),D,F),k4_finseq_4(B,u2_cat_1(A),C,F)) ) ) ) ) ) ) )).

fof(t22_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u2_cat_1(B))
            & m2_relset_1(C,A,u2_cat_1(B)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( k3_cat_3(B,A,C) = k4_cat_3(B,A,D)
               => ( k3_cat_3(B,A,k9_cat_3(B,A,C,D)) = k3_cat_3(B,A,D)
                  & k4_cat_3(B,A,k9_cat_3(B,A,C,D)) = k4_cat_3(B,A,C) ) ) ) ) ) )).

fof(t23_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] :
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ! [G] :
                      ( m1_subset_1(G,u2_cat_1(C))
                     => ( A != B
                       => k9_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E),k5_funct_4(u2_cat_1(C),A,B,F,G)) = k5_funct_4(u2_cat_1(C),A,B,k4_cat_1(C,F,D),k4_cat_1(C,G,E)) ) ) ) ) ) ) )).

fof(t24_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => k7_cat_3(B,A,D,C) = k9_cat_3(B,A,D,k1_cat_3(u2_cat_1(B),A,C)) ) ) ) )).

fof(t25_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => k8_cat_3(B,A,D,C) = k9_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C),D) ) ) ) )).

fof(d10_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v1_cat_3(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u2_cat_1(A))
                & k3_cat_1(A,C) = k2_cat_1(A,B)
                & k4_cat_1(A,C,B) = k10_cat_1(A,k3_cat_1(A,B)) ) ) ) ) )).

fof(d11_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v2_cat_3(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u2_cat_1(A))
                & k2_cat_1(A,C) = k3_cat_1(A,B)
                & k4_cat_1(A,B,C) = k10_cat_1(A,k2_cat_1(A,B)) ) ) ) ) )).

fof(t26_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v1_cat_3(B,A)
           => v4_cat_1(B,A) ) ) ) )).

fof(t27_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v2_cat_3(B,A)
           => v3_cat_1(B,A) ) ) ) )).

fof(t28_cat_3,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))
             => ( ( v1_cat_3(B,A)
                  & v1_cat_3(C,A)
                  & k2_cat_1(A,C) = k3_cat_1(A,B) )
               => v1_cat_3(k4_cat_1(A,B,C),A) ) ) ) ) )).

fof(t29_cat_3,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))
             => ( ( v2_cat_3(B,A)
                  & v2_cat_3(C,A)
                  & k2_cat_1(A,C) = k3_cat_1(A,B) )
               => v2_cat_3(k4_cat_1(A,B,C),A) ) ) ) ) )).

fof(t30_cat_3,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)
                  & v1_cat_3(k4_cat_1(A,C,B),A) )
               => v1_cat_3(B,A) ) ) ) ) )).

fof(t31_cat_3,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)
                  & v2_cat_3(k4_cat_1(A,C,B),A) )
               => v2_cat_3(C,A) ) ) ) ) )).

fof(t32_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( ( v1_cat_3(B,A)
              & v3_cat_1(B,A) )
           => v5_cat_1(B,A) ) ) ) )).

fof(t33_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( ( v2_cat_3(B,A)
              & v4_cat_1(B,A) )
           => v5_cat_1(B,A) ) ) ) )).

fof(t34_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v5_cat_1(B,A)
          <=> ( v1_cat_3(B,A)
              & v2_cat_3(B,A) ) ) ) ) )).

fof(t35_cat_3,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] :
                  ( m2_cat_1(D,A,B)
                 => ( v1_cat_3(C,A)
                   => v1_cat_3(k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,C),B) ) ) ) ) ) )).

fof(t36_cat_3,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] :
                  ( m2_cat_1(D,A,B)
                 => ( v2_cat_3(C,A)
                   => v2_cat_3(k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,C),B) ) ) ) ) ) )).

fof(t37_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v1_cat_3(B,A)
          <=> v2_cat_3(k5_oppcat_1(A,B),k2_oppcat_1(A)) ) ) ) )).

fof(t38_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v2_cat_3(B,A)
          <=> v1_cat_3(k5_oppcat_1(A,B),k2_oppcat_1(A)) ) ) ) )).

fof(d12_cat_3,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(C,A)
               => ! [D] :
                    ( m1_cat_1(D,A,B,C)
                   => D = k10_cat_3(A,B,C) ) ) ) ) ) )).

fof(t39_cat_3,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)
               => ( k2_cat_1(A,k10_cat_3(A,C,B)) = C
                  & k3_cat_1(A,k10_cat_3(A,C,B)) = B ) ) ) ) ) )).

fof(t40_cat_3,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,u2_cat_1(A))
                 => ( ( v6_cat_1(B,A)
                      & k2_cat_1(A,D) = C
                      & k3_cat_1(A,D) = B )
                   => k10_cat_3(A,C,B) = D ) ) ) ) ) )).

fof(t41_cat_3,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(C,A)
                   => k10_cat_3(A,B,C) = D ) ) ) ) ) )).

fof(d13_cat_3,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)
               => ! [D] :
                    ( m1_cat_1(D,A,B,C)
                   => D = k11_cat_3(A,B,C) ) ) ) ) ) )).

fof(t42_cat_3,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)
               => ( k2_cat_1(A,k11_cat_3(A,B,C)) = B
                  & k3_cat_1(A,k11_cat_3(A,B,C)) = C ) ) ) ) ) )).

fof(t43_cat_3,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,u2_cat_1(A))
                 => ( ( v7_cat_1(B,A)
                      & k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C )
                   => k11_cat_3(A,B,C) = D ) ) ) ) ) )).

fof(t44_cat_3,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)
                 => ( v7_cat_1(B,A)
                   => k11_cat_3(A,B,C) = D ) ) ) ) ) )).

fof(d14_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( m1_cat_3(D,A,B,C)
              <=> k3_cat_3(A,C,D) = k1_cat_3(u1_cat_1(A),C,B) ) ) ) ) )).

fof(t45_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] :
              ( m1_cat_3(E,C,D,A)
             => ( r2_hidden(B,A)
               => k2_cat_1(C,k4_finseq_4(A,u2_cat_1(C),E,B)) = D ) ) ) ) )).

fof(t46_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
                & m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
             => m1_cat_3(C,A,B,k1_xboole_0) ) ) ) )).

fof(t47_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u2_cat_1(B))
             => ( k2_cat_1(B,D) = C
               => m1_cat_3(k2_cat_3(u2_cat_1(B),A,D),B,C,k1_tarski(A)) ) ) ) ) )).

fof(t48_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] :
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ( ( k2_cat_1(C,E) = D
                      & k2_cat_1(C,F) = D )
                   => m1_cat_3(k5_funct_4(u2_cat_1(C),A,B,E,F),C,D,k2_tarski(A,B)) ) ) ) ) ) )).

fof(t49_cat_3,axiom,(
    $true )).

fof(t50_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u2_cat_1(B))
             => ! [E] :
                  ( m1_cat_3(E,B,C,A)
                 => ( k3_cat_1(B,D) = C
                   => m1_cat_3(k7_cat_3(B,A,E,D),B,k2_cat_1(B,D),A) ) ) ) ) ) )).

fof(t51_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ! [E] :
                  ( m1_cat_3(E,B,C,A)
                 => ( k3_cat_3(B,A,D) = k4_cat_3(B,A,E)
                   => m1_cat_3(k9_cat_3(B,A,D,E),B,C,A) ) ) ) ) ) )).

fof(t52_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => ! [D] :
              ( m1_cat_3(D,B,k3_cat_1(B,C),A)
             => k8_cat_3(k2_oppcat_1(B),A,k5_cat_3(B,A,D),k5_oppcat_1(B,C)) = k5_cat_3(B,A,k7_cat_3(B,A,D,C)) ) ) ) )).

fof(d15_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( r1_cat_3(A,B,C,D)
              <=> ( m1_cat_3(D,A,B,C)
                  & ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_cat_3(F,A,E,C)
                         => ~ ( k4_cat_3(A,C,D) = k4_cat_3(A,C,F)
                              & ! [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(G,k6_cat_1(A,E,B))
                                      & ! [H] :
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ( r2_hidden(H,k6_cat_1(A,E,B))
                                           => ( ! [I] :
                                                  ( r2_hidden(I,C)
                                                 => k4_cat_1(A,H,k4_finseq_4(C,u2_cat_1(A),D,I)) = k4_finseq_4(C,u2_cat_1(A),F,I) )
                                            <=> G = H ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t53_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_cat_1(B))
             => ! [E] :
                  ( m1_cat_3(E,B,C,A)
                 => ! [F] :
                      ( m1_cat_3(F,B,D,A)
                     => ( ( r1_cat_3(B,C,A,E)
                          & r1_cat_3(B,D,A,F)
                          & k4_cat_3(B,A,E) = k4_cat_3(B,A,F) )
                       => r1_cat_1(B,C,D) ) ) ) ) ) ) )).

fof(t54_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_cat_3(D,B,C,A)
             => ( ( r1_cat_3(B,C,A,D)
                  & ! [E,F] :
                      ~ ( r2_hidden(E,A)
                        & r2_hidden(F,A)
                        & k6_cat_1(B,k3_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),k3_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,F))) = k1_xboole_0 ) )
               => ! [E] :
                    ( r2_hidden(E,A)
                   => v1_cat_3(k4_finseq_4(A,u2_cat_1(B),D,E),B) ) ) ) ) ) )).

fof(t55_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
                & m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
             => ( r1_cat_3(A,B,k1_xboole_0,C)
              <=> v6_cat_1(B,A) ) ) ) ) )).

fof(t56_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_cat_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u2_cat_1(B))
                 => ! [F] :
                      ( m1_cat_3(F,B,C,A)
                     => ( ( r1_cat_3(B,C,A,F)
                          & k2_cat_1(B,E) = D
                          & k3_cat_1(B,E) = C
                          & v5_cat_1(E,B) )
                       => r1_cat_3(B,D,A,k7_cat_3(B,A,F,E)) ) ) ) ) ) ) )).

fof(t57_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => r1_cat_3(B,C,k1_tarski(A),k2_cat_3(u2_cat_1(B),A,k10_cat_1(B,C))) ) ) )).

fof(t58_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_cat_3(D,B,C,A)
             => ( ( r1_cat_3(B,C,A,D)
                  & ! [E] :
                      ( r2_hidden(E,A)
                     => v6_cat_1(k3_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),B) ) )
               => v6_cat_1(C,B) ) ) ) ) )).

fof(d16_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_cat_3(A,B,C,D)
                  <=> ( k2_cat_1(A,C) = B
                      & k2_cat_1(A,D) = B
                      & ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(F,k6_cat_1(A,E,k3_cat_1(A,C)))
                                      & r2_hidden(G,k6_cat_1(A,E,k3_cat_1(A,D)))
                                      & ! [H] :
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ~ ( r2_hidden(H,k6_cat_1(A,E,B))
                                              & ! [I] :
                                                  ( m1_subset_1(I,u2_cat_1(A))
                                                 => ( r2_hidden(I,k6_cat_1(A,E,B))
                                                   => ( ( k4_cat_1(A,I,C) = F
                                                        & k4_cat_1(A,I,D) = G )
                                                    <=> H = I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t59_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] :
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ( A != B
                   => ( r2_cat_3(C,D,E,F)
                    <=> r1_cat_3(C,D,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,E,F)) ) ) ) ) ) ) )).

fof(t60_cat_3,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,B,D) != k1_xboole_0
                      & ~ ! [E] :
                            ( m1_cat_1(E,A,B,C)
                           => ! [F] :
                                ( m1_cat_1(F,A,B,D)
                               => ( r2_cat_3(A,B,E,F)
                                <=> ! [G] :
                                      ( m1_subset_1(G,u1_cat_1(A))
                                     => ~ ( k6_cat_1(A,G,C) != k1_xboole_0
                                          & k6_cat_1(A,G,D) != k1_xboole_0
                                          & ~ ( k6_cat_1(A,G,B) != k1_xboole_0
                                              & ! [H] :
                                                  ( m1_cat_1(H,A,G,C)
                                                 => ! [I] :
                                                      ( m1_cat_1(I,A,G,D)
                                                     => ? [J] :
                                                          ( m1_cat_1(J,A,G,B)
                                                          & ! [K] :
                                                              ( m1_cat_1(K,A,G,B)
                                                             => ( ( k9_cat_1(A,G,B,C,K,E) = H
                                                                  & k9_cat_1(A,G,B,D,K,F) = I )
                                                              <=> J = K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t61_cat_3,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,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ! [G] :
                              ( m1_subset_1(G,u2_cat_1(A))
                             => ( ( r2_cat_3(A,B,D,E)
                                  & r2_cat_3(A,C,F,G)
                                  & k3_cat_1(A,D) = k3_cat_1(A,F)
                                  & k3_cat_1(A,E) = k3_cat_1(A,G) )
                               => r1_cat_1(A,B,C) ) ) ) ) ) ) ) ) )).

fof(t62_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_cat_3(A,B,C,D)
                   => ( k6_cat_1(A,k3_cat_1(A,C),k3_cat_1(A,D)) = k1_xboole_0
                      | k6_cat_1(A,k3_cat_1(A,D),k3_cat_1(A,C)) = k1_xboole_0
                      | ( v1_cat_3(C,A)
                        & v1_cat_3(D,A) ) ) ) ) ) ) ) )).

fof(t63_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ( ( r2_cat_3(A,B,C,D)
                          & r2_hidden(E,k6_cat_1(A,B,B))
                          & k4_cat_1(A,E,C) = C
                          & k4_cat_1(A,E,D) = D )
                       => E = k10_cat_1(A,B) ) ) ) ) ) ) )).

fof(t64_cat_3,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,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ( ( r2_cat_3(A,B,D,E)
                              & k2_cat_1(A,F) = C
                              & k3_cat_1(A,F) = B
                              & v5_cat_1(F,A) )
                           => r2_cat_3(A,C,k4_cat_1(A,F,D),k4_cat_1(A,F,E)) ) ) ) ) ) ) ) )).

fof(t65_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( ( r2_cat_3(A,B,C,D)
                      & v6_cat_1(k3_cat_1(A,D),A) )
                   => r1_cat_1(A,B,k3_cat_1(A,C)) ) ) ) ) ) )).

fof(t66_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( ( r2_cat_3(A,B,C,D)
                      & v6_cat_1(k3_cat_1(A,C),A) )
                   => r1_cat_1(A,B,k3_cat_1(A,D)) ) ) ) ) ) )).

fof(d17_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( m2_cat_3(D,A,B,C)
              <=> k4_cat_3(A,C,D) = k1_cat_3(u1_cat_1(A),C,B) ) ) ) ) )).

fof(t67_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] :
              ( m2_cat_3(E,C,D,A)
             => ( r2_hidden(B,A)
               => k3_cat_1(C,k4_finseq_4(A,u2_cat_1(C),E,B)) = D ) ) ) ) )).

fof(t68_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
                & m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
             => m2_cat_3(C,A,B,k1_xboole_0) ) ) ) )).

fof(t69_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u2_cat_1(B))
             => ( k3_cat_1(B,D) = C
               => m2_cat_3(k2_cat_3(u2_cat_1(B),A,D),B,C,k1_tarski(A)) ) ) ) ) )).

fof(t70_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] :
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ( ( k3_cat_1(C,E) = D
                      & k3_cat_1(C,F) = D )
                   => m2_cat_3(k5_funct_4(u2_cat_1(C),A,B,E,F),C,D,k2_tarski(A,B)) ) ) ) ) ) )).

fof(t71_cat_3,axiom,(
    $true )).

fof(t72_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u2_cat_1(B))
             => ! [E] :
                  ( m2_cat_3(E,B,C,A)
                 => ( k2_cat_1(B,D) = C
                   => m2_cat_3(k8_cat_3(B,A,E,D),B,k3_cat_1(B,D),A) ) ) ) ) ) )).

fof(t73_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m2_cat_3(D,B,C,A)
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,u2_cat_1(B))
                    & m2_relset_1(E,A,u2_cat_1(B)) )
                 => ( k3_cat_3(B,A,D) = k4_cat_3(B,A,E)
                   => m2_cat_3(k9_cat_3(B,A,D,E),B,C,A) ) ) ) ) ) )).

fof(t74_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( m1_cat_3(D,B,C,A)
              <=> m2_cat_3(k5_cat_3(B,A,D),k2_oppcat_1(B),k3_oppcat_1(B,C),A) ) ) ) ) )).

fof(t75_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u2_cat_1(k2_oppcat_1(B)))
            & m2_relset_1(C,A,u2_cat_1(k2_oppcat_1(B))) )
         => ! [D] :
              ( m1_subset_1(D,u1_cat_1(k2_oppcat_1(B)))
             => ( m2_cat_3(C,k2_oppcat_1(B),D,A)
              <=> m1_cat_3(k6_cat_3(B,A,C),B,k4_oppcat_1(B,D),A) ) ) ) ) )).

fof(t76_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u2_cat_1(B))
         => ! [D] :
              ( m2_cat_3(D,B,k2_cat_1(B,C),A)
             => k7_cat_3(k2_oppcat_1(B),A,k5_cat_3(B,A,D),k5_oppcat_1(B,C)) = k5_cat_3(B,A,k8_cat_3(B,A,D,C)) ) ) ) )).

fof(d18_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( r3_cat_3(A,B,C,D)
              <=> ( m2_cat_3(D,A,B,C)
                  & ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m2_cat_3(F,A,E,C)
                         => ~ ( k3_cat_3(A,C,D) = k3_cat_3(A,C,F)
                              & ! [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(G,k6_cat_1(A,B,E))
                                      & ! [H] :
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ( r2_hidden(H,k6_cat_1(A,B,E))
                                           => ( ! [I] :
                                                  ( r2_hidden(I,C)
                                                 => k4_cat_1(A,k4_finseq_4(C,u2_cat_1(A),D,I),H) = k4_finseq_4(C,u2_cat_1(A),F,I) )
                                            <=> G = H ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t77_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( r1_cat_3(B,C,A,D)
              <=> r3_cat_3(k2_oppcat_1(B),k3_oppcat_1(B,C),A,k5_cat_3(B,A,D)) ) ) ) ) )).

fof(t78_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_cat_1(B))
             => ! [E] :
                  ( m2_cat_3(E,B,C,A)
                 => ! [F] :
                      ( m2_cat_3(F,B,D,A)
                     => ( ( r3_cat_3(B,C,A,E)
                          & r3_cat_3(B,D,A,F)
                          & k3_cat_3(B,A,E) = k3_cat_3(B,A,F) )
                       => r1_cat_1(B,C,D) ) ) ) ) ) ) )).

fof(t79_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m2_cat_3(D,B,C,A)
             => ( ( r3_cat_3(B,C,A,D)
                  & ! [E,F] :
                      ~ ( r2_hidden(E,A)
                        & r2_hidden(F,A)
                        & k6_cat_1(B,k2_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),k2_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,F))) = k1_xboole_0 ) )
               => ! [E] :
                    ( r2_hidden(E,A)
                   => v2_cat_3(k4_finseq_4(A,u2_cat_1(B),D,E),B) ) ) ) ) ) )).

fof(t80_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_cat_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u2_cat_1(B))
                 => ! [F] :
                      ( m2_cat_3(F,B,C,A)
                     => ( ( r3_cat_3(B,C,A,F)
                          & k2_cat_1(B,E) = C
                          & k3_cat_1(B,E) = D
                          & v5_cat_1(E,B) )
                       => r3_cat_3(B,D,A,k8_cat_3(B,A,F,E)) ) ) ) ) ) ) )).

fof(t81_cat_3,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m2_cat_3(C,A,B,k1_xboole_0)
             => ( r3_cat_3(A,B,k1_xboole_0,C)
              <=> v7_cat_1(B,A) ) ) ) ) )).

fof(t82_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => r3_cat_3(B,C,k1_tarski(A),k2_cat_3(u2_cat_1(B),A,k10_cat_1(B,C))) ) ) )).

fof(t83_cat_3,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] :
              ( m2_cat_3(D,B,C,A)
             => ( ( r3_cat_3(B,C,A,D)
                  & ! [E] :
                      ( r2_hidden(E,A)
                     => v7_cat_1(k2_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),B) ) )
               => v7_cat_1(C,B) ) ) ) ) )).

fof(d19_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r4_cat_3(A,B,C,D)
                  <=> ( k3_cat_1(A,C) = B
                      & k3_cat_1(A,D) = B
                      & ! [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(F,k6_cat_1(A,k2_cat_1(A,C),E))
                                      & r2_hidden(G,k6_cat_1(A,k2_cat_1(A,D),E))
                                      & ! [H] :
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ~ ( r2_hidden(H,k6_cat_1(A,B,E))
                                              & ! [I] :
                                                  ( m1_subset_1(I,u2_cat_1(A))
                                                 => ( r2_hidden(I,k6_cat_1(A,B,E))
                                                   => ( ( k4_cat_1(A,C,I) = F
                                                        & k4_cat_1(A,D,I) = G )
                                                    <=> H = I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t84_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_cat_3(A,B,C,D)
                  <=> r4_cat_3(k2_oppcat_1(A),k3_oppcat_1(A,B),k5_oppcat_1(A,C),k5_oppcat_1(A,D)) ) ) ) ) ) )).

fof(t85_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] :
              ( m1_subset_1(E,u2_cat_1(C))
             => ! [F] :
                  ( m1_subset_1(F,u2_cat_1(C))
                 => ( A != B
                   => ( r4_cat_3(C,D,E,F)
                    <=> r3_cat_3(C,D,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,E,F)) ) ) ) ) ) ) )).

fof(t86_cat_3,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,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ! [G] :
                              ( m1_subset_1(G,u2_cat_1(A))
                             => ( ( r4_cat_3(A,B,D,E)
                                  & r4_cat_3(A,C,F,G)
                                  & k2_cat_1(A,D) = k2_cat_1(A,F)
                                  & k2_cat_1(A,E) = k2_cat_1(A,G) )
                               => r1_cat_1(A,B,C) ) ) ) ) ) ) ) ) )).

fof(t87_cat_3,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,D,C) != k1_xboole_0
                      & ~ ! [E] :
                            ( m1_cat_1(E,A,B,C)
                           => ! [F] :
                                ( m1_cat_1(F,A,D,C)
                               => ( r4_cat_3(A,C,E,F)
                                <=> ! [G] :
                                      ( m1_subset_1(G,u1_cat_1(A))
                                     => ~ ( k6_cat_1(A,B,G) != k1_xboole_0
                                          & k6_cat_1(A,D,G) != k1_xboole_0
                                          & ~ ( k6_cat_1(A,C,G) != k1_xboole_0
                                              & ! [H] :
                                                  ( m1_cat_1(H,A,B,G)
                                                 => ! [I] :
                                                      ( m1_cat_1(I,A,D,G)
                                                     => ? [J] :
                                                          ( m1_cat_1(J,A,C,G)
                                                          & ! [K] :
                                                              ( m1_cat_1(K,A,C,G)
                                                             => ( ( k9_cat_1(A,B,C,G,E,K) = H
                                                                  & k9_cat_1(A,D,C,G,F,K) = I )
                                                              <=> J = K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t88_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r4_cat_3(A,B,C,D)
                   => ( k6_cat_1(A,k2_cat_1(A,C),k2_cat_1(A,D)) = k1_xboole_0
                      | k6_cat_1(A,k2_cat_1(A,D),k2_cat_1(A,C)) = k1_xboole_0
                      | ( v2_cat_3(C,A)
                        & v2_cat_3(D,A) ) ) ) ) ) ) ) )).

fof(t89_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ( ( r4_cat_3(A,B,C,D)
                          & r2_hidden(E,k6_cat_1(A,B,B))
                          & k4_cat_1(A,C,E) = C
                          & k4_cat_1(A,D,E) = D )
                       => E = k10_cat_1(A,B) ) ) ) ) ) ) )).

fof(t90_cat_3,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,u2_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ( ( r4_cat_3(A,B,D,E)
                              & k2_cat_1(A,F) = B
                              & k3_cat_1(A,F) = C
                              & v5_cat_1(F,A) )
                           => r4_cat_3(A,C,k4_cat_1(A,D,F),k4_cat_1(A,E,F)) ) ) ) ) ) ) ) )).

fof(t91_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( ( r4_cat_3(A,B,C,D)
                      & v7_cat_1(k2_cat_1(A,D),A) )
                   => r1_cat_1(A,k2_cat_1(A,C),B) ) ) ) ) ) )).

fof(t92_cat_3,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))
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( ( r4_cat_3(A,B,C,D)
                      & v7_cat_1(k2_cat_1(A,C),A) )
                   => r1_cat_1(A,k2_cat_1(A,D),B) ) ) ) ) ) )).

fof(s1_cat_3,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s1_cat_3,f2_s1_cat_3)
      & m2_relset_1(A,f1_s1_cat_3,f2_s1_cat_3)
      & ! [B] :
          ( r2_hidden(B,f1_s1_cat_3)
         => k4_finseq_4(f1_s1_cat_3,f2_s1_cat_3,A,B) = f3_s1_cat_3(B) ) ) )).

fof(s2_cat_3,axiom,
    ( ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s2_cat_3,f2_s2_cat_3)
        & m2_relset_1(A,f1_s2_cat_3,f2_s2_cat_3)
        & ! [B] :
            ( r2_hidden(B,f1_s2_cat_3)
           => k4_finseq_4(f1_s2_cat_3,f2_s2_cat_3,A,B) = f3_s2_cat_3(B) ) )
    & ! [A] :
        ( ( v1_funct_1(A)
          & v1_funct_2(A,f1_s2_cat_3,f2_s2_cat_3)
          & m2_relset_1(A,f1_s2_cat_3,f2_s2_cat_3) )
       => ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,f1_s2_cat_3,f2_s2_cat_3)
              & m2_relset_1(B,f1_s2_cat_3,f2_s2_cat_3) )
           => ( ( ! [C] :
                    ( r2_hidden(C,f1_s2_cat_3)
                   => k4_finseq_4(f1_s2_cat_3,f2_s2_cat_3,A,C) = f3_s2_cat_3(C) )
                & ! [C] :
                    ( r2_hidden(C,f1_s2_cat_3)
                   => k4_finseq_4(f1_s2_cat_3,f2_s2_cat_3,B,C) = f3_s2_cat_3(C) ) )
             => A = B ) ) ) )).

fof(dt_m1_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ! [D] :
          ( m1_cat_3(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,C,u2_cat_1(A))
            & m2_relset_1(D,C,u2_cat_1(A)) ) ) ) )).

fof(existence_m1_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ? [D] : m1_cat_3(D,A,B,C) ) )).

fof(dt_m2_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ! [D] :
          ( m2_cat_3(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,C,u2_cat_1(A))
            & m2_relset_1(D,C,u2_cat_1(A)) ) ) ) )).

fof(existence_m2_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ? [D] : m2_cat_3(D,A,B,C) ) )).

fof(dt_k1_cat_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k1_cat_3(A,B,C))
        & v1_funct_2(k1_cat_3(A,B,C),B,A)
        & m2_relset_1(k1_cat_3(A,B,C),B,A) ) ) )).

fof(redefinition_k1_cat_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k1_cat_3(A,B,C) = k2_funcop_1(B,C) ) )).

fof(dt_k2_cat_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k2_cat_3(A,B,C))
        & v1_funct_2(k2_cat_3(A,B,C),k1_tarski(B),A)
        & m2_relset_1(k2_cat_3(A,B,C),k1_tarski(B),A) ) ) )).

fof(redefinition_k2_cat_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k2_cat_3(A,B,C) = k3_cqc_lang(B,C) ) )).

fof(dt_k3_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k3_cat_3(A,B,C))
        & v1_funct_2(k3_cat_3(A,B,C),B,u1_cat_1(A))
        & m2_relset_1(k3_cat_3(A,B,C),B,u1_cat_1(A)) ) ) )).

fof(dt_k4_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k4_cat_3(A,B,C))
        & v1_funct_2(k4_cat_3(A,B,C),B,u1_cat_1(A))
        & m2_relset_1(k4_cat_3(A,B,C),B,u1_cat_1(A)) ) ) )).

fof(dt_k5_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k5_cat_3(A,B,C))
        & v1_funct_2(k5_cat_3(A,B,C),B,u2_cat_1(k2_oppcat_1(A)))
        & m2_relset_1(k5_cat_3(A,B,C),B,u2_cat_1(k2_oppcat_1(A))) ) ) )).

fof(dt_k6_cat_3,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(k2_oppcat_1(A)))
        & m1_relset_1(C,B,u2_cat_1(k2_oppcat_1(A))) )
     => ( v1_funct_1(k6_cat_3(A,B,C))
        & v1_funct_2(k6_cat_3(A,B,C),B,u2_cat_1(A))
        & m2_relset_1(k6_cat_3(A,B,C),B,u2_cat_1(A)) ) ) )).

fof(dt_k7_cat_3,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A))
        & m1_subset_1(D,u2_cat_1(A)) )
     => ( v1_funct_1(k7_cat_3(A,B,C,D))
        & v1_funct_2(k7_cat_3(A,B,C,D),B,u2_cat_1(A))
        & m2_relset_1(k7_cat_3(A,B,C,D),B,u2_cat_1(A)) ) ) )).

fof(dt_k8_cat_3,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A))
        & m1_subset_1(D,u2_cat_1(A)) )
     => ( v1_funct_1(k8_cat_3(A,B,C,D))
        & v1_funct_2(k8_cat_3(A,B,C,D),B,u2_cat_1(A))
        & m2_relset_1(k8_cat_3(A,B,C,D),B,u2_cat_1(A)) ) ) )).

fof(dt_k9_cat_3,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,u2_cat_1(A))
        & m1_relset_1(D,B,u2_cat_1(A)) )
     => ( v1_funct_1(k9_cat_3(A,B,C,D))
        & v1_funct_2(k9_cat_3(A,B,C,D),B,u2_cat_1(A))
        & m2_relset_1(k9_cat_3(A,B,C,D),B,u2_cat_1(A)) ) ) )).

fof(dt_k10_cat_3,axiom,(
    ! [A,B,C] :
      ( ( 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(k10_cat_3(A,B,C),A,B,C) ) )).

fof(dt_k11_cat_3,axiom,(
    ! [A,B,C] :
      ( ( 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(k11_cat_3(A,B,C),A,B,C) ) )).
%------------------------------------------------------------------------------