SET007 Axioms: SET007+339.ax


%------------------------------------------------------------------------------
% File     : SET007+339 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Isomorphisms Between Functor 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   83 (   3 unit)
%            Number of atoms       :  813 (  44 equality)
%            Maximal formula depth :   22 (  13 average)
%            Number of connectives :  754 (  24 ~  ;   0  |; 333  &)
%                                         (   8 <=>; 389 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   20 (   1 propositional; 0-6 arity)
%            Number of functors    :   58 (   1 constant; 0-9 arity)
%            Number of variables   :  438 (   0 singleton; 432 !;   6 ?)
%            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_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k1_fraenkel(B,C))
                    & m2_relset_1(D,A,k1_fraenkel(B,C)) )
                 => r4_nattra_1(A,k1_fraenkel(B,C),A,k1_fraenkel(B,C),k2_cat_2(A,B,C,k1_isocat_2(A,B,C,D)),D) ) ) ) ) )).

fof(t2_isocat_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k1_fraenkel(B,C))
                    & m2_relset_1(D,A,k1_fraenkel(B,C)) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => k1_funct_1(k1_isocat_2(A,B,C,D),k4_tarski(E,F)) = k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),D,E),F) ) ) ) ) ) ) )).

fof(t3_isocat_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k1_tarski(A),B)
            & m2_relset_1(C,k1_tarski(A),B) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k1_tarski(A),B)
                & m2_relset_1(D,k1_tarski(A),B) )
             => ( k1_funct_1(C,A) = k1_funct_1(D,A)
               => r4_nattra_1(k1_tarski(A),B,k1_tarski(A),B,C,D) ) ) ) ) )).

fof(t4_isocat_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => r2_hidden(k8_funct_2(A,B,D,C),k2_relat_1(D)) ) ) ) ) )).

fof(t5_isocat_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k2_zfmisc_1(B,C))
                    & m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,k2_zfmisc_1(B,C))
                        & m2_relset_1(E,A,k2_zfmisc_1(B,C)) )
                     => ( ( r4_nattra_1(A,B,A,B,k7_funct_2(A,k2_zfmisc_1(B,C),B,D,k9_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),B,E,k9_funct_3(B,C)))
                          & r4_nattra_1(A,C,A,C,k7_funct_2(A,k2_zfmisc_1(B,C),C,D,k10_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),C,E,k10_funct_3(B,C))) )
                       => r4_nattra_1(A,k2_zfmisc_1(B,C),A,k2_zfmisc_1(B,C),D,E) ) ) ) ) ) ) )).

fof(t6_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k4_cat_1(A,B,k10_cat_1(A,k3_cat_1(A,B))) = B ) ) )).

fof(t7_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => k4_cat_1(A,k10_cat_1(A,k2_cat_1(A,B)),B) = B ) ) )).

fof(t8_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(k12_nattra_1(A,B)))
            <=> m2_cat_1(C,A,B) ) ) ) )).

fof(t9_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(k12_nattra_1(A,B)))
             => ? [D] :
                  ( m2_cat_1(D,A,B)
                  & ? [E] :
                      ( m2_cat_1(E,A,B)
                      & ? [F] :
                          ( m2_nattra_1(F,A,B,D,E)
                          & r2_nattra_1(A,B,D,E)
                          & k2_cat_1(k12_nattra_1(A,B),C) = D
                          & k3_cat_1(k12_nattra_1(A,B),C) = E
                          & C = k4_tarski(k4_tarski(D,E),F) ) ) ) ) ) ) )).

fof(d1_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m2_cat_1(D,k12_nattra_1(A,B),B)
                 => ( D = k2_isocat_2(A,B,C)
                  <=> ! [E] :
                        ( m2_cat_1(E,A,B)
                       => ! [F] :
                            ( m2_cat_1(F,A,B)
                           => ! [G] :
                                ( m2_nattra_1(G,A,B,E,F)
                               => ( r2_nattra_1(A,B,E,F)
                                 => k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k5_nattra_1(A,B,E,F,G,C) ) ) ) ) ) ) ) ) ) )).

fof(t10_isocat_2,axiom,(
    $true )).

fof(t11_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : r1_isocat_1(k12_nattra_1(k8_cat_1(B,C),A),A) ) )).

fof(t12_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => k13_cat_1(B,C,k14_cat_2(A,B,C,D,E),F) = k13_cat_1(k11_cat_2(A,B),C,D,k12_cat_2(A,B,E,F)) ) ) ) ) ) ) )).

fof(t13_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => ( ( k6_cat_1(A,C,D) != k1_xboole_0
                              & k6_cat_1(B,E,F) != k1_xboole_0 )
                          <=> k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) != k1_xboole_0 ) ) ) ) ) ) ) )).

fof(t14_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => ( k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) != k1_xboole_0
                           => ! [G] :
                                ( m1_subset_1(G,u2_cat_1(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u2_cat_1(B))
                                   => ( m1_cat_1(k13_cat_2(A,B,G,H),k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F))
                                    <=> ( m1_cat_1(G,A,C,D)
                                        & m1_cat_1(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                     => ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
                       => ! [F] :
                            ( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
                           => ! [G] :
                                ( m1_subset_1(G,u1_cat_1(A))
                               => ( r2_nattra_1(B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G))
                                  & m2_nattra_1(k1_funct_1(k3_funct_5(F),G),B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) )).

fof(d2_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => k3_isocat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E) ) ) ) ) ) )).

fof(t16_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => ! [G] :
                              ( m1_subset_1(G,u2_cat_1(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u2_cat_1(B))
                                 => ( ( r2_hidden(G,k6_cat_1(A,C,D))
                                      & r2_hidden(H,k6_cat_1(B,E,F)) )
                                   => r2_hidden(k13_cat_2(A,B,G,H),k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F))) ) ) ) ) ) ) ) ) ) )).

fof(t17_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ( k6_cat_1(A,E,F) != k1_xboole_0
                           => ! [G] :
                                ( m1_cat_1(G,A,E,F)
                               => ( r2_nattra_1(B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F))
                                  & m2_nattra_1(k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,G)),B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F)) ) ) ) ) ) ) ) ) ) )).

fof(d3_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => k4_isocat_2(A,B,C,D,E) = k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,E)) ) ) ) ) ) )).

fof(t18_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => r2_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) ) ) ) ) )).

fof(t19_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => k5_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),k4_isocat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,E,k10_cat_1(B,F))) ) ) ) ) ) ) )).

fof(t20_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k7_nattra_1(B,C,k14_cat_2(A,B,C,D,E)),k4_isocat_2(A,B,C,D,k10_cat_1(A,E))) ) ) ) ) ) )).

fof(t21_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(A))
                         => ( k2_cat_1(A,E) = k3_cat_1(A,F)
                           => ! [G] :
                                ( m2_nattra_1(G,B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E)))
                               => ( r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),G,k4_isocat_2(A,B,C,D,F))
                                 => r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k4_isocat_2(A,B,C,D,k4_cat_1(A,F,E)),k8_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),G,k4_isocat_2(A,B,C,D,E))) ) ) ) ) ) ) ) ) ) )).

fof(d4_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,A,k12_nattra_1(B,C))
                     => ( E = k5_isocat_2(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u2_cat_1(A))
                           => k8_funct_2(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),E,F) = k4_tarski(k4_tarski(k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k3_cat_1(A,F))),k4_isocat_2(A,B,C,D,F)) ) ) ) ) ) ) ) )).

fof(t22_isocat_2,axiom,(
    $true )).

fof(t23_isocat_2,axiom,(
    $true )).

fof(t24_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E) = k14_cat_2(A,B,C,D,E) ) ) ) ) ) )).

fof(t25_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => m2_cat_1(k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E),B,C) ) ) ) ) ) )).

fof(t26_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                     => ( r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
                       => r4_nattra_1(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,E) ) ) ) ) ) ) )).

fof(t27_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                     => ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
                       => ! [F] :
                            ( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
                           => ( r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
                              & ? [G] :
                                  ( m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
                                  & ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C))
                                        & m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) )
                                     => ( r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H)
                                       => ! [I] :
                                            ( m1_subset_1(I,u1_cat_1(A))
                                           => k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I) = k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                     => ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
                       => ! [F] :
                            ( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
                           => ! [G] :
                                ( m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
                               => ( G = k6_isocat_2(A,B,C,D,E,F)
                                <=> ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C))
                                        & m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) )
                                     => ( r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H)
                                       => ! [I] :
                                            ( m1_subset_1(I,u1_cat_1(A))
                                           => k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I) = k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t28_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k7_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D)),k6_isocat_2(A,B,C,D,D,k7_nattra_1(k11_cat_2(A,B),C,D))) ) ) ) ) )).

fof(t29_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                     => ! [F] :
                          ( m2_cat_1(F,k11_cat_2(A,B),C)
                         => ( ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
                              & r2_nattra_1(k11_cat_2(A,B),C,E,F) )
                           => ! [G] :
                                ( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
                               => ! [H] :
                                    ( m2_nattra_1(H,k11_cat_2(A,B),C,E,F)
                                   => r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,F,k8_nattra_1(k11_cat_2(A,B),C,D,E,F,G,H)),k8_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F),k6_isocat_2(A,B,C,D,E,G),k6_isocat_2(A,B,C,E,F,H))) ) ) ) ) ) ) ) ) ) )).

fof(t30_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                     => ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
                       => ! [F] :
                            ( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
                           => ! [G] :
                                ( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
                               => ( r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,E,F),k6_isocat_2(A,B,C,D,E,G))
                                 => r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),F,G) ) ) ) ) ) ) ) ) ) )).

fof(t31_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k12_nattra_1(B,C))
                 => ? [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                      & r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),D,k5_isocat_2(A,B,C,E)) ) ) ) ) ) )).

fof(t32_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] :
                      ( m2_cat_1(E,k11_cat_2(A,B),C)
                     => ( r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
                       => ! [F] :
                            ( m2_nattra_1(F,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
                           => ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
                              & ? [G] :
                                  ( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
                                  & r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),F,k6_isocat_2(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) )).

fof(d6_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C)))
                 => ( D = k7_isocat_2(A,B,C)
                  <=> ! [E] :
                        ( m2_cat_1(E,k11_cat_2(A,B),C)
                       => ! [F] :
                            ( m2_cat_1(F,k11_cat_2(A,B),C)
                           => ( r2_nattra_1(k11_cat_2(A,B),C,E,F)
                             => ! [G] :
                                  ( m2_nattra_1(G,k11_cat_2(A,B),C,E,F)
                                 => k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k4_tarski(k4_tarski(k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F)),k6_isocat_2(A,B,C,E,F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t33_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => v8_cat_1(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ) ) )).

fof(t34_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => r1_isocat_1(k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ) ) )).

fof(t35_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,B,C)
                         => ( r2_nattra_1(A,B,D,E)
                           => ! [G] :
                                ( m2_nattra_1(G,A,B,D,E)
                               => k6_isocat_1(A,B,C,D,E,G,F) = k5_relat_1(G,F) ) ) ) ) ) ) ) ) )).

fof(d7_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => k11_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),B,D,k8_isocat_2(B,C)) ) ) ) ) )).

fof(d8_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => k12_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),C,D,k9_isocat_2(B,C)) ) ) ) ) )).

fof(t36_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,C)
                     => ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),D)
                        & r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),E) ) ) ) ) ) ) )).

fof(t37_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => ! [E] :
                      ( m2_cat_1(E,A,k11_cat_2(B,C))
                     => ( ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E))
                          & r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) )
                       => r4_nattra_1(u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),D,E) ) ) ) ) ) ) )).

fof(d9_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => ! [E] :
                      ( m2_cat_1(E,A,k11_cat_2(B,C))
                     => ! [F] :
                          ( m2_nattra_1(F,A,k11_cat_2(B,C),D,E)
                         => k13_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),B,D,E,F,k8_isocat_2(B,C)) ) ) ) ) ) ) )).

fof(d10_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => ! [E] :
                      ( m2_cat_1(E,A,k11_cat_2(B,C))
                     => ! [F] :
                          ( m2_nattra_1(F,A,k11_cat_2(B,C),D,E)
                         => k14_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),C,D,E,F,k9_isocat_2(B,C)) ) ) ) ) ) ) )).

fof(t38_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => ! [E] :
                      ( m2_cat_1(E,A,k11_cat_2(B,C))
                     => ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
                       => ( r2_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E))
                          & r2_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) ) ) ) ) ) ) ) )).

fof(t39_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => ! [E] :
                      ( m2_cat_1(E,A,k11_cat_2(B,C))
                     => ! [F] :
                          ( m2_cat_1(F,A,k11_cat_2(B,C))
                         => ! [G] :
                              ( m2_cat_1(G,A,k11_cat_2(B,C))
                             => ( ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
                                  & r2_nattra_1(A,k11_cat_2(B,C),F,G) )
                               => ! [H] :
                                    ( m2_nattra_1(H,A,k11_cat_2(B,C),D,E)
                                   => ! [I] :
                                        ( m2_nattra_1(I,A,k11_cat_2(B,C),F,G)
                                       => ( ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,E,H),k13_isocat_2(A,B,C,F,G,I))
                                            & r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,E,H),k14_isocat_2(A,B,C,F,G,I)) )
                                         => r4_nattra_1(u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_nattra_1(A,B,k11_isocat_2(A,B,C,D)),k13_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D)))
                    & r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_nattra_1(A,C,k12_isocat_2(A,B,C,D)),k14_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D))) ) ) ) ) ) )).

fof(t41_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,k11_cat_2(B,C))
                 => ! [E] :
                      ( m2_cat_1(E,A,k11_cat_2(B,C))
                     => ! [F] :
                          ( m2_cat_1(F,A,k11_cat_2(B,C))
                         => ( ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
                              & r2_nattra_1(A,k11_cat_2(B,C),E,F) )
                           => ! [G] :
                                ( m2_nattra_1(G,A,k11_cat_2(B,C),D,E)
                               => ! [H] :
                                    ( m2_nattra_1(H,A,k11_cat_2(B,C),E,F)
                                   => ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E),k11_isocat_2(A,B,C,F),k13_isocat_2(A,B,C,D,E,G),k13_isocat_2(A,B,C,E,F,H)))
                                      & r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E),k12_isocat_2(A,B,C,F),k14_isocat_2(A,B,C,D,E,G),k14_isocat_2(A,B,C,E,F,H))) ) ) ) ) ) ) ) ) ) ) )).

fof(t42_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_cat_1(A))
                             => ( k6_cat_1(A,F,G) != k1_xboole_0
                               => ! [H] :
                                    ( m1_cat_1(H,A,F,G)
                                   => k3_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F,G,H) = k13_cat_2(B,C,k3_nattra_1(A,B,D,F,G,H),k3_nattra_1(A,C,E,F,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t43_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(A))
                         => k13_cat_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F) = k12_cat_2(B,C,k13_cat_1(A,B,D,F),k13_cat_1(A,C,E,F)) ) ) ) ) ) ) )).

fof(t44_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,C)
                         => ! [G] :
                              ( m2_cat_1(G,A,C)
                             => ( ( r1_nattra_1(A,B,D,E)
                                  & r1_nattra_1(A,C,F,G) )
                               => r1_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(d11_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,C)
                         => ! [G] :
                              ( m2_cat_1(G,A,C)
                             => ( ( r1_nattra_1(A,B,D,E)
                                  & r1_nattra_1(A,C,F,G) )
                               => ! [H] :
                                    ( m1_nattra_1(H,A,B,D,E)
                                   => ! [I] :
                                        ( m1_nattra_1(I,A,C,F,G)
                                       => k15_isocat_2(A,B,C,D,E,F,G,H,I) = k14_funct_3(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),H,I) ) ) ) ) ) ) ) ) ) ) )).

fof(t45_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,C)
                         => ! [G] :
                              ( m2_cat_1(G,A,C)
                             => ( ( r1_nattra_1(A,B,D,E)
                                  & r1_nattra_1(A,C,F,G) )
                               => ! [H] :
                                    ( m1_nattra_1(H,A,B,D,E)
                                   => ! [I] :
                                        ( m1_nattra_1(I,A,C,F,G)
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_cat_1(A))
                                           => k5_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k15_isocat_2(A,B,C,D,E,F,G,H,I),J) = k13_cat_2(B,C,k5_nattra_1(A,B,D,E,H,J),k5_nattra_1(A,C,F,G,I,J)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t46_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,C)
                         => ! [G] :
                              ( m2_cat_1(G,A,C)
                             => ( ( r2_nattra_1(A,B,D,E)
                                  & r2_nattra_1(A,C,F,G) )
                               => r2_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(d12_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,C)
                         => ! [G] :
                              ( m2_cat_1(G,A,C)
                             => ( ( r2_nattra_1(A,B,D,E)
                                  & r2_nattra_1(A,C,F,G) )
                               => ! [H] :
                                    ( m2_nattra_1(H,A,B,D,E)
                                   => ! [I] :
                                        ( m2_nattra_1(I,A,C,F,G)
                                       => k16_isocat_2(A,B,C,D,E,F,G,H,I) = k15_isocat_2(A,B,C,D,E,F,G,H,I) ) ) ) ) ) ) ) ) ) ) )).

fof(t47_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,C)
                         => ! [G] :
                              ( m2_cat_1(G,A,C)
                             => ( ( r2_nattra_1(A,B,D,E)
                                  & r2_nattra_1(A,C,F,G) )
                               => ! [H] :
                                    ( m2_nattra_1(H,A,B,D,E)
                                   => ! [I] :
                                        ( m2_nattra_1(I,A,C,F,G)
                                       => ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k16_isocat_2(A,B,C,D,E,F,G,H,I)),H)
                                          & r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k16_isocat_2(A,B,C,D,E,F,G,H,I)),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d13_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C)))
                 => ( D = k17_isocat_2(A,B,C)
                  <=> ! [E] :
                        ( m2_cat_1(E,A,k11_cat_2(B,C))
                       => ! [F] :
                            ( m2_cat_1(F,A,k11_cat_2(B,C))
                           => ( r2_nattra_1(A,k11_cat_2(B,C),E,F)
                             => ! [G] :
                                  ( m2_nattra_1(G,A,k11_cat_2(B,C),E,F)
                                 => k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k4_tarski(k4_tarski(k4_tarski(k11_isocat_2(A,B,C,E),k11_isocat_2(A,B,C,F)),k13_isocat_2(A,B,C,E,F,G)),k4_tarski(k4_tarski(k12_isocat_2(A,B,C,E),k12_isocat_2(A,B,C,F)),k14_isocat_2(A,B,C,E,F,G))) ) ) ) ) ) ) ) ) ) )).

fof(t48_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => v8_cat_1(k17_isocat_2(A,B,C),k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) ) ) ) )).

fof(t49_isocat_2,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => r1_isocat_1(k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) ) ) ) )).

fof(dt_k1_isocat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,k1_fraenkel(B,C))
        & m1_relset_1(D,A,k1_fraenkel(B,C)) )
     => ( v1_funct_1(k1_isocat_2(A,B,C,D))
        & v1_funct_2(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C)
        & m2_relset_1(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C) ) ) )).

fof(redefinition_k1_isocat_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,k1_fraenkel(B,C))
        & m1_relset_1(D,A,k1_fraenkel(B,C)) )
     => k1_isocat_2(A,B,C,D) = k4_funct_5(D) ) )).

fof(dt_k2_isocat_2,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(A)) )
     => m2_cat_1(k2_isocat_2(A,B,C),k12_nattra_1(A,B),B) ) )).

fof(dt_k3_isocat_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,k11_cat_2(A,B),C)
        & m1_subset_1(E,u2_cat_1(A)) )
     => ( v1_funct_1(k3_isocat_2(A,B,C,D,E))
        & v1_funct_2(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C))
        & m2_relset_1(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)) ) ) )).

fof(dt_k4_isocat_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,k11_cat_2(A,B),C)
        & m1_subset_1(E,u2_cat_1(A)) )
     => m2_nattra_1(k4_isocat_2(A,B,C,D,E),B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) )).

fof(dt_k5_isocat_2,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,k11_cat_2(A,B),C) )
     => m2_cat_1(k5_isocat_2(A,B,C,D),A,k12_nattra_1(B,C)) ) )).

fof(dt_k6_isocat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,k11_cat_2(A,B),C)
        & m2_cat_1(E,k11_cat_2(A,B),C)
        & m2_nattra_1(F,k11_cat_2(A,B),C,D,E) )
     => m2_nattra_1(k6_isocat_2(A,B,C,D,E,F),A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) ) )).

fof(dt_k7_isocat_2,axiom,(
    ! [A,B,C] :
      ( ( 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(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) )).

fof(dt_k8_isocat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m2_cat_1(k8_isocat_2(A,B),k11_cat_2(A,B),A) ) )).

fof(redefinition_k8_isocat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => k8_isocat_2(A,B) = k16_cat_2(A,B) ) )).

fof(dt_k9_isocat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m2_cat_1(k9_isocat_2(A,B),k11_cat_2(A,B),B) ) )).

fof(redefinition_k9_isocat_2,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => k9_isocat_2(A,B) = k17_cat_2(A,B) ) )).

fof(dt_k10_isocat_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,A,C) )
     => m2_cat_1(k10_isocat_2(A,B,C,D,E),A,k11_cat_2(B,C)) ) )).

fof(redefinition_k10_isocat_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,A,C) )
     => k10_isocat_2(A,B,C,D,E) = k13_funct_3(D,E) ) )).

fof(dt_k11_isocat_2,axiom,(
    ! [A,B,C,D] :
      ( ( 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,k11_cat_2(B,C)) )
     => m2_cat_1(k11_isocat_2(A,B,C,D),A,B) ) )).

fof(dt_k12_isocat_2,axiom,(
    ! [A,B,C,D] :
      ( ( 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,k11_cat_2(B,C)) )
     => m2_cat_1(k12_isocat_2(A,B,C,D),A,C) ) )).

fof(dt_k13_isocat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,k11_cat_2(B,C))
        & m2_cat_1(E,A,k11_cat_2(B,C))
        & m2_nattra_1(F,A,k11_cat_2(B,C),D,E) )
     => m2_nattra_1(k13_isocat_2(A,B,C,D,E,F),A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E)) ) )).

fof(dt_k14_isocat_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,k11_cat_2(B,C))
        & m2_cat_1(E,A,k11_cat_2(B,C))
        & m2_nattra_1(F,A,k11_cat_2(B,C),D,E) )
     => m2_nattra_1(k14_isocat_2(A,B,C,D,E,F),A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) ) )).

fof(dt_k15_isocat_2,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,A,C)
        & m2_cat_1(G,A,C)
        & m1_nattra_1(H,A,B,D,E)
        & m1_nattra_1(I,A,C,F,G) )
     => m1_nattra_1(k15_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) )).

fof(dt_k16_isocat_2,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,A,C)
        & m2_cat_1(G,A,C)
        & m2_nattra_1(H,A,B,D,E)
        & m2_nattra_1(I,A,C,F,G) )
     => m2_nattra_1(k16_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) )).

fof(dt_k17_isocat_2,axiom,(
    ! [A,B,C] :
      ( ( 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(k17_isocat_2(A,B,C),k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) ) )).
%------------------------------------------------------------------------------