SET007 Axioms: SET007+322.ax


%------------------------------------------------------------------------------
% File     : SET007+322 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Isomorphisms 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    : isocat_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   85 (   6 unit)
%            Number of atoms       :  787 (  25 equality)
%            Maximal formula depth :   31 (  12 average)
%            Number of connectives :  703 (   1 ~  ;   0  |; 286  &)
%                                         (   5 <=>; 411 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   1 propositional; 0-6 arity)
%            Number of functors    :   34 (   1 constant; 0-9 arity)
%            Number of variables   :  416 (   0 singleton; 406 !;  10 ?)
%            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(t1_isocat_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => v2_funct_1(k15_funct_3(A,B)) ) ) ) )).

fof(t2_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( k2_relat_1(k16_cat_2(A,B)) = u2_cat_1(A)
            & k2_relat_1(k17_cat_2(B,A)) = u2_cat_1(A) ) ) ) )).

fof(t3_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ! [D] :
                  ( m1_subset_1(D,u2_cat_1(B))
                 => ( v5_cat_1(D,B)
                   => v5_cat_1(k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,D),A) ) ) ) ) ) )).

fof(t4_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m2_cat_1(D,B,A)
                 => ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k14_cat_1(A,A,B,k15_cat_1(A),C),C)
                    & r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),k14_cat_1(B,A,A,D,k15_cat_1(A)),D) ) ) ) ) ) )).

fof(t5_isocat_1,axiom,(
    $true )).

fof(t6_isocat_1,axiom,(
    $true )).

fof(t7_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ( r1_nattra_1(A,B,C,D)
                   => ! [E] :
                        ( m1_nattra_1(E,A,B,C,D)
                       => ! [F] :
                            ( m1_subset_1(F,u1_cat_1(A))
                           => r2_hidden(k5_nattra_1(A,B,C,D,E,F),k6_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F))) ) ) ) ) ) ) ) )).

fof(t8_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ( ( r1_nattra_1(A,B,D,E)
                                  & r1_nattra_1(B,C,F,G) )
                               => r1_nattra_1(A,C,k14_cat_1(A,B,C,D,F),k14_cat_1(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(t9_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ( r1_nattra_1(A,B,C,D)
                   => ! [E] :
                        ( m1_nattra_1(E,A,B,C,D)
                       => ( v1_nattra_1(E,A,B,C,D)
                         => ! [F] :
                              ( m1_subset_1(F,u1_cat_1(A))
                             => r1_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)) ) ) ) ) ) ) ) ) )).

fof(d1_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
                & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
             => ( m2_cat_1(C,A,B)
              <=> ( ! [D] :
                      ( m1_subset_1(D,u1_cat_1(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_cat_1(B))
                          & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
                        & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(A))
                         => ( k2_cat_1(A,E) = k3_cat_1(A,D)
                           => k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) ) ) )).

fof(t10_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ( v8_cat_1(C,B,A)
               => ! [D] :
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ? [E] :
                        ( m1_subset_1(E,u2_cat_1(B))
                        & k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,E) = D ) ) ) ) ) ) )).

fof(t11_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ( v8_cat_1(C,B,A)
               => ! [D] :
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ? [E] :
                        ( m1_subset_1(E,u1_cat_1(B))
                        & k13_cat_1(B,A,C,E) = D ) ) ) ) ) ) )).

fof(t12_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v2_funct_1(C)
               => v2_funct_1(k12_cat_1(A,B,C)) ) ) ) ) )).

fof(d2_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v8_cat_1(C,A,B)
               => k3_isocat_1(A,B,C) = k2_funct_1(C) ) ) ) ) )).

fof(d3_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v8_cat_1(C,A,B)
              <=> ( v2_funct_1(C)
                  & k2_relat_1(C) = u2_cat_1(B) ) ) ) ) ) )).

fof(t13_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v8_cat_1(C,A,B)
               => v8_cat_1(k3_isocat_1(A,B,C),B,A) ) ) ) ) )).

fof(t14_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v8_cat_1(C,A,B)
               => k2_funct_1(k12_cat_1(A,B,C)) = k12_cat_1(B,A,k3_isocat_1(A,B,C)) ) ) ) ) )).

fof(t15_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ( v8_cat_1(C,A,B)
               => r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k3_isocat_1(B,A,k3_isocat_1(A,B,C)),C) ) ) ) ) )).

fof(t16_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ( v8_cat_1(C,B,A)
               => ( r4_nattra_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),k2_isocat_1(A,B,A,k3_isocat_1(B,A,C),C),k1_isocat_1(A))
                  & r4_nattra_1(u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),k2_isocat_1(B,A,B,C,k3_isocat_1(B,A,C)),k1_isocat_1(B)) ) ) ) ) ) )).

fof(t17_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ( ( v8_cat_1(D,A,B)
                          & v8_cat_1(E,B,C) )
                       => v8_cat_1(k2_isocat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) )).

fof(d4_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( r1_isocat_1(A,B)
          <=> ? [C] :
                ( m2_cat_1(C,A,B)
                & v8_cat_1(C,A,B) ) ) ) ) )).

fof(t18_isocat_1,axiom,(
    $true )).

fof(t19_isocat_1,axiom,(
    $true )).

fof(t20_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ( ( r1_isocat_1(A,B)
                  & r1_isocat_1(B,C) )
               => r1_isocat_1(A,C) ) ) ) ) )).

fof(t21_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : r1_isocat_1(k11_cat_2(k8_cat_1(B,C),A),A) ) )).

fof(t22_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => r1_isocat_1(k11_cat_2(A,B),k11_cat_2(B,A)) ) ) )).

fof(t23_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => r1_isocat_1(k11_cat_2(k11_cat_2(A,B),C),k11_cat_2(A,k11_cat_2(B,C))) ) ) ) )).

fof(t24_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ( ( r1_isocat_1(A,B)
                      & r1_isocat_1(C,D) )
                   => r1_isocat_1(k11_cat_2(A,C),k11_cat_2(B,D)) ) ) ) ) ) )).

fof(d5_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ( r1_nattra_1(A,B,D,E)
                       => ! [F] :
                            ( m1_nattra_1(F,A,B,D,E)
                           => ! [G] :
                                ( m2_cat_1(G,B,C)
                               => k4_isocat_1(A,B,C,D,E,F,G) = k7_funct_2(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),F,G) ) ) ) ) ) ) ) ) )).

fof(d6_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,B,C)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ( r1_nattra_1(B,C,D,E)
                       => ! [F] :
                            ( m2_cat_1(F,A,B)
                           => ! [G] :
                                ( m1_nattra_1(G,B,C,D,E)
                               => k5_isocat_1(A,B,C,D,E,F,G) = k7_funct_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k12_cat_1(A,B,F),G) ) ) ) ) ) ) ) ) )).

fof(t25_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ( r1_nattra_1(A,B,D,E)
                       => ! [F] :
                            ( m2_cat_1(F,C,A)
                           => ! [G] :
                                ( m1_nattra_1(G,A,B,D,E)
                               => ! [H] :
                                    ( m1_subset_1(H,u1_cat_1(C))
                                   => k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k5_isocat_1(C,A,B,D,E,F,G),H) = k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t26_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ( r1_nattra_1(A,B,D,E)
                       => ! [F] :
                            ( m1_nattra_1(F,A,B,D,E)
                           => ! [G] :
                                ( m2_cat_1(G,B,C)
                               => ! [H] :
                                    ( m1_subset_1(H,u1_cat_1(A))
                                   => k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k4_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t27_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ( ( r2_nattra_1(A,B,D,E)
                                  & r2_nattra_1(B,C,F,G) )
                               => r2_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(d7_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ( r2_nattra_1(A,B,D,E)
                       => ! [F] :
                            ( m2_nattra_1(F,A,B,D,E)
                           => ! [G] :
                                ( m2_cat_1(G,B,C)
                               => k6_isocat_1(A,B,C,D,E,F,G) = k4_isocat_1(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t28_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ( r2_nattra_1(A,B,D,E)
                       => ! [F] :
                            ( m2_nattra_1(F,A,B,D,E)
                           => ! [G] :
                                ( m2_cat_1(G,B,C)
                               => ! [H] :
                                    ( m1_subset_1(H,u1_cat_1(A))
                                   => k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(d8_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,B,C)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ( r2_nattra_1(B,C,D,E)
                       => ! [F] :
                            ( m2_cat_1(F,A,B)
                           => ! [G] :
                                ( m2_nattra_1(G,B,C,D,E)
                               => k7_isocat_1(A,B,C,D,E,F,G) = k5_isocat_1(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t29_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ( r2_nattra_1(A,B,D,E)
                       => ! [F] :
                            ( m2_cat_1(F,C,A)
                           => ! [G] :
                                ( m2_nattra_1(G,A,B,D,E)
                               => ! [H] :
                                    ( m1_subset_1(H,u1_cat_1(C))
                                   => k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k7_isocat_1(C,A,B,D,E,F,G),H) = k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t30_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ! [D] :
                  ( m2_cat_1(D,B,A)
                 => ( r2_nattra_1(B,A,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_cat_1(B))
                       => k6_cat_1(A,k13_cat_1(B,A,C,E),k13_cat_1(B,A,D,E)) != k1_xboole_0 ) ) ) ) ) ) )).

fof(t31_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ! [D] :
                  ( m2_cat_1(D,B,A)
                 => ( r2_nattra_1(B,A,C,D)
                   => ! [E] :
                        ( m2_nattra_1(E,B,A,C,D)
                       => ! [F] :
                            ( m2_nattra_1(F,B,A,C,D)
                           => ( ! [G] :
                                  ( m1_subset_1(G,u1_cat_1(B))
                                 => k5_nattra_1(B,A,C,D,E,G) = k5_nattra_1(B,A,C,D,F,G) )
                             => r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),E,F) ) ) ) ) ) ) ) ) )).

fof(t32_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,B,C)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_cat_1(G,C,A)
                             => ! [H] :
                                  ( m2_nattra_1(H,B,C,D,E)
                                 => ! [I] :
                                      ( m2_nattra_1(I,B,C,E,F)
                                     => ( ( r2_nattra_1(B,C,D,E)
                                          & r2_nattra_1(B,C,E,F) )
                                       => r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,F,k8_nattra_1(B,C,D,E,F,H,I),G),k8_nattra_1(B,A,k2_isocat_1(B,C,A,D,G),k2_isocat_1(B,C,A,E,G),k2_isocat_1(B,C,A,F,G),k6_isocat_1(B,C,A,D,E,H,G),k6_isocat_1(B,C,A,E,F,I,G))) ) ) ) ) ) ) ) ) ) ) )).

fof(t33_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ! [H] :
                                  ( m2_nattra_1(H,B,C,E,F)
                                 => ! [I] :
                                      ( m2_nattra_1(I,B,C,F,G)
                                     => ( ( r2_nattra_1(B,C,E,F)
                                          & r2_nattra_1(B,C,F,G) )
                                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,G,D,k8_nattra_1(B,C,E,F,G,H,I)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,E),k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k7_isocat_1(A,B,C,E,F,D,H),k7_isocat_1(A,B,C,F,G,D,I))) ) ) ) ) ) ) ) ) ) ) )).

fof(t34_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_cat_1(G,C,D)
                             => ! [H] :
                                  ( m2_cat_1(H,C,D)
                                 => ! [I] :
                                      ( m2_nattra_1(I,C,D,G,H)
                                     => ( r2_nattra_1(C,D,G,H)
                                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k7_isocat_1(A,B,D,k2_isocat_1(B,C,D,F,G),k2_isocat_1(B,C,D,F,H),E,k7_isocat_1(B,C,D,G,H,F,I)),k7_isocat_1(A,C,D,G,H,k2_isocat_1(A,B,C,E,F),I)) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,A,C)
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => ! [G] :
                              ( m2_cat_1(G,C,D)
                             => ! [H] :
                                  ( m2_cat_1(H,D,B)
                                 => ! [I] :
                                      ( m2_nattra_1(I,C,D,F,G)
                                     => ( r2_nattra_1(C,D,F,G)
                                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_isocat_1(A,C,B,k2_isocat_1(C,D,B,F,H),k2_isocat_1(C,D,B,G,H),E,k6_isocat_1(C,D,B,F,G,I,H)),k6_isocat_1(A,D,B,k2_isocat_1(A,C,D,E,F),k2_isocat_1(A,C,D,E,G),k7_isocat_1(A,C,D,F,G,E,I),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,C,D)
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => ! [G] :
                              ( m2_cat_1(G,D,A)
                             => ! [H] :
                                  ( m2_cat_1(H,A,B)
                                 => ! [I] :
                                      ( m2_nattra_1(I,C,D,E,F)
                                     => ( r2_nattra_1(C,D,E,F)
                                       => r4_nattra_1(u1_cat_1(C),u2_cat_1(B),u1_cat_1(C),u2_cat_1(B),k6_isocat_1(C,D,B,E,F,I,k2_isocat_1(D,A,B,G,H)),k6_isocat_1(C,A,B,k2_isocat_1(C,D,A,E,G),k2_isocat_1(C,D,A,F,G),k6_isocat_1(C,D,A,E,F,I,G),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t37_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,E,D,k7_nattra_1(B,C,E)),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))) ) ) ) ) ) )).

fof(t38_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k6_isocat_1(A,B,C,D,D,k7_nattra_1(A,B,D),E),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))) ) ) ) ) ) )).

fof(t39_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ! [D] :
                  ( m2_cat_1(D,B,A)
                 => ! [E] :
                      ( m2_nattra_1(E,B,A,C,D)
                     => ( r2_nattra_1(B,A,C,D)
                       => r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k7_isocat_1(B,B,A,C,D,k1_isocat_1(B),E),E) ) ) ) ) ) ) )).

fof(t40_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_nattra_1(E,A,B,C,D)
                     => ( r2_nattra_1(A,B,C,D)
                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k6_isocat_1(A,B,B,C,D,E,k1_isocat_1(B)),E) ) ) ) ) ) ) )).

fof(d9_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ! [H] :
                                  ( m2_nattra_1(H,A,B,D,E)
                                 => ! [I] :
                                      ( m2_nattra_1(I,B,C,F,G)
                                     => k8_isocat_1(A,B,C,D,E,F,G,H,I) = k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,F),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,H,F),k7_isocat_1(A,B,C,F,G,E,I)) ) ) ) ) ) ) ) ) ) )).

fof(t41_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ! [H] :
                                  ( m2_nattra_1(H,A,B,D,E)
                                 => ! [I] :
                                      ( m2_nattra_1(I,B,C,F,G)
                                     => ( ( r2_nattra_1(A,B,D,E)
                                          & r2_nattra_1(B,C,F,G) )
                                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,E,F,G,H,I),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k7_isocat_1(A,B,C,F,G,D,I),k6_isocat_1(A,B,C,D,E,H,G))) ) ) ) ) ) ) ) ) ) ) )).

fof(t42_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_nattra_1(E,A,B,C,D)
                     => ( r2_nattra_1(A,B,C,D)
                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k8_isocat_1(A,B,B,C,D,k1_isocat_1(B),k1_isocat_1(B),E,k7_nattra_1(B,B,k1_isocat_1(B))),E) ) ) ) ) ) ) )).

fof(t43_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ! [D] :
                  ( m2_cat_1(D,B,A)
                 => ! [E] :
                      ( m2_nattra_1(E,B,A,C,D)
                     => ( r2_nattra_1(B,A,C,D)
                       => r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k8_isocat_1(B,B,A,k1_isocat_1(B),k1_isocat_1(B),C,D,k7_nattra_1(B,B,k1_isocat_1(B)),E),E) ) ) ) ) ) ) )).

fof(t44_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,B)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ! [H] :
                                  ( m2_cat_1(H,B,C)
                                 => ! [I] :
                                      ( m2_cat_1(I,C,D)
                                     => ! [J] :
                                          ( m2_cat_1(J,C,D)
                                         => ! [K] :
                                              ( m2_nattra_1(K,A,B,E,F)
                                             => ! [L] :
                                                  ( m2_nattra_1(L,B,C,G,H)
                                                 => ! [M] :
                                                      ( m2_nattra_1(M,C,D,I,J)
                                                     => ( ( r2_nattra_1(A,B,E,F)
                                                          & r2_nattra_1(B,C,G,H)
                                                          & r2_nattra_1(C,D,I,J) )
                                                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k8_isocat_1(A,C,D,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,F,H),I,J,k8_isocat_1(A,B,C,E,F,G,H,K,L),M),k8_isocat_1(A,B,D,E,F,k2_isocat_1(B,C,D,G,I),k2_isocat_1(B,C,D,H,J),K,k8_isocat_1(B,C,D,G,H,I,J,L,M))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t45_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ! [G] :
                              ( m2_nattra_1(G,B,C,E,F)
                             => ( r2_nattra_1(B,C,E,F)
                               => r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,F,D,G),k8_isocat_1(A,B,C,D,D,E,F,k7_nattra_1(A,B,D),G)) ) ) ) ) ) ) ) ) )).

fof(t46_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,B,C)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ! [F] :
                          ( m2_cat_1(F,C,A)
                         => ! [G] :
                              ( m2_nattra_1(G,B,C,D,E)
                             => ( r2_nattra_1(B,C,D,E)
                               => r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,E,G,F),k8_isocat_1(B,C,A,D,E,F,F,G,k7_nattra_1(C,A,F))) ) ) ) ) ) ) ) ) )).

fof(t47_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,B)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ! [H] :
                                  ( m2_cat_1(H,B,C)
                                 => ! [I] :
                                      ( m2_cat_1(I,B,C)
                                     => ! [J] :
                                          ( m2_nattra_1(J,A,B,D,E)
                                         => ! [K] :
                                              ( m2_nattra_1(K,A,B,E,F)
                                             => ! [L] :
                                                  ( m2_nattra_1(L,B,C,G,H)
                                                 => ! [M] :
                                                      ( m2_nattra_1(M,B,C,H,I)
                                                     => ( ( r2_nattra_1(A,B,D,E)
                                                          & r2_nattra_1(A,B,E,F)
                                                          & r2_nattra_1(B,C,G,H)
                                                          & r2_nattra_1(B,C,H,I) )
                                                       => r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,F,G,I,k8_nattra_1(A,B,D,E,F,J,K),k8_nattra_1(B,C,G,H,I,L,M)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,H),k2_isocat_1(A,B,C,F,I),k8_isocat_1(A,B,C,D,E,G,H,J,L),k8_isocat_1(A,B,C,E,F,H,I,K,M))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t48_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => ! [G] :
                              ( m2_cat_1(G,B,C)
                             => ! [H] :
                                  ( m2_cat_1(H,B,C)
                                 => ( r3_nattra_1(B,C,G,H)
                                   => ( r3_nattra_1(B,D,k2_isocat_1(B,C,D,G,F),k2_isocat_1(B,C,D,H,F))
                                      & r3_nattra_1(A,C,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,E,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t49_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m2_cat_1(D,B,A)
                 => ! [E] :
                      ( m2_cat_1(E,A,A)
                     => ( r3_nattra_1(A,A,E,k1_isocat_1(A))
                       => ( r3_nattra_1(A,B,k2_isocat_1(A,A,B,E,C),C)
                          & r3_nattra_1(B,A,k2_isocat_1(B,A,A,D,E),D) ) ) ) ) ) ) ) )).

fof(d10_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( r2_isocat_1(A,B)
          <=> ? [C] :
                ( m2_cat_1(C,A,B)
                & ? [D] :
                    ( m2_cat_1(D,B,A)
                    & r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
                    & r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) ) ) ) ) ) )).

fof(t50_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( r1_isocat_1(A,B)
           => r2_isocat_1(A,B) ) ) ) )).

fof(t51_isocat_1,axiom,(
    $true )).

fof(t52_isocat_1,axiom,(
    $true )).

fof(t53_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ( ( r2_isocat_1(A,B)
                  & r2_isocat_1(B,C) )
               => r2_isocat_1(A,C) ) ) ) ) )).

fof(d11_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( r2_isocat_1(A,B)
           => ! [C] :
                ( m2_cat_1(C,A,B)
               => ( m1_isocat_1(C,A,B)
                <=> ? [D] :
                      ( m2_cat_1(D,B,A)
                      & r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
                      & r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) ) ) ) ) ) ) )).

fof(t54_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m1_isocat_1(k1_isocat_1(A),A,A) ) )).

fof(t55_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ( ( r2_isocat_1(A,B)
                  & r2_isocat_1(B,C) )
               => ! [D] :
                    ( m1_isocat_1(D,A,B)
                   => ! [E] :
                        ( m1_isocat_1(E,B,C)
                       => m1_isocat_1(k2_isocat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) )).

fof(t56_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( r2_isocat_1(A,B)
           => ! [C] :
                ( m1_isocat_1(C,A,B)
               => ? [D] :
                    ( m1_isocat_1(D,B,A)
                    & r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
                    & r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) ) ) ) ) ) )).

fof(t57_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m2_cat_1(D,B,A)
                 => ( r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
                   => v10_cat_1(C,A,B) ) ) ) ) ) )).

fof(t58_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( r2_isocat_1(A,B)
           => ! [C] :
                ( m1_isocat_1(C,A,B)
               => ( v9_cat_1(C,A,B)
                  & v10_cat_1(C,A,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_cat_1(B))
                     => ? [E] :
                          ( m1_subset_1(E,u1_cat_1(A))
                          & r1_cat_1(B,D,k13_cat_1(A,B,C,E)) ) ) ) ) ) ) ) )).

fof(dt_m1_isocat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m1_isocat_1(C,A,B)
         => m2_cat_1(C,A,B) ) ) )).

fof(existence_m1_isocat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m1_isocat_1(C,A,B) ) )).

fof(symmetry_r1_isocat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( r1_isocat_1(A,B)
       => r1_isocat_1(B,A) ) ) )).

fof(reflexivity_r1_isocat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => r1_isocat_1(A,A) ) )).

fof(symmetry_r2_isocat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( r2_isocat_1(A,B)
       => r2_isocat_1(B,A) ) ) )).

fof(reflexivity_r2_isocat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => r2_isocat_1(A,A) ) )).

fof(dt_k1_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m2_cat_1(k1_isocat_1(A),A,A) ) )).

fof(redefinition_k1_isocat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k1_isocat_1(A) = k15_cat_1(A) ) )).

fof(dt_k2_isocat_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,B,C) )
     => m2_cat_1(k2_isocat_1(A,B,C,D,E),A,C) ) )).

fof(redefinition_k2_isocat_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,B,C) )
     => k2_isocat_1(A,B,C,D,E) = k5_relat_1(D,E) ) )).

fof(dt_k3_isocat_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => m2_cat_1(k3_isocat_1(A,B,C),B,A) ) )).

fof(dt_k4_isocat_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( 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,B)
        & m1_nattra_1(F,A,B,D,E)
        & m2_cat_1(G,B,C) )
     => m1_nattra_1(k4_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)) ) )).

fof(dt_k5_isocat_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( 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,B,C)
        & m2_cat_1(E,B,C)
        & m2_cat_1(F,A,B)
        & m1_nattra_1(G,B,C,D,E) )
     => m1_nattra_1(k5_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)) ) )).

fof(dt_k6_isocat_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( 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,B)
        & m2_nattra_1(F,A,B,D,E)
        & m2_cat_1(G,B,C) )
     => m2_nattra_1(k6_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)) ) )).

fof(dt_k7_isocat_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( 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,B,C)
        & m2_cat_1(E,B,C)
        & m2_cat_1(F,A,B)
        & m2_nattra_1(G,B,C,D,E) )
     => m2_nattra_1(k7_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)) ) )).

fof(dt_k8_isocat_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( 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,B)
        & m2_cat_1(F,B,C)
        & m2_cat_1(G,B,C)
        & m2_nattra_1(H,A,B,D,E)
        & m2_nattra_1(I,B,C,F,G) )
     => m2_nattra_1(k8_isocat_1(A,B,C,D,E,F,G,H,I),A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G)) ) )).
%------------------------------------------------------------------------------