SET007 Axioms: SET007+299.ax


%------------------------------------------------------------------------------
% File     : SET007+299 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Natural transformations.  Discrete 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    : nattra_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  109 (  10 unit)
%            Number of atoms       :  946 ( 105 equality)
%            Maximal formula depth :   32 (  12 average)
%            Number of connectives :  898 (  61 ~  ;   0  |; 386  &)
%                                         (  22 <=>; 429 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   28 (   1 propositional; 0-6 arity)
%            Number of functors    :   56 (   4 constant; 0-7 arity)
%            Number of variables   :  504 (   0 singleton; 489 !;  15 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_nattra_1,axiom,(
    ? [A] :
      ( l1_cat_1(A)
      & v2_cat_1(A)
      & v2_nattra_1(A) ) )).

fof(rc2_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ? [B] :
          ( m3_cat_2(B,A)
          & v1_cat_1(B)
          & v2_cat_1(B)
          & v2_nattra_1(B) ) ) )).

fof(t1_nattra_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,A)
                        & m2_relset_1(E,C,A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,D,B)
                            & m2_relset_1(F,D,B) )
                         => ! [G] :
                              ( ( ~ v1_xboole_0(G)
                                & m1_subset_1(G,k1_zfmisc_1(C)) )
                             => ! [H] :
                                  ( ( ~ v1_xboole_0(H)
                                    & m1_subset_1(H,k1_zfmisc_1(D)) )
                                 => k1_nattra_1(k2_zfmisc_1(C,D),k2_zfmisc_1(A,B),k9_cat_2(C,D,A,B,E,F),k12_mcart_1(C,D,G,H)) = k9_cat_2(G,H,A,B,k1_nattra_1(C,A,E,G),k1_nattra_1(D,B,F,H)) ) ) ) ) ) ) ) ) )).

fof(t2_nattra_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(A)) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & m2_relset_1(G,k12_mcart_1(A,A,C,C),C) )
                             => ( G = k1_realset1(E,C)
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & m2_relset_1(H,k12_mcart_1(B,B,D,D),D) )
                                   => ( H = k1_realset1(F,D)
                                     => k2_nattra_1(A,B,C,D,G,H) = k1_realset1(k10_cat_2(A,B,E,F),k12_mcart_1(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) )).

fof(t3_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_cat_1(C,A,B,B)
             => r2_hidden(C,k6_cat_1(A,B,B)) ) ) ) )).

fof(t4_nattra_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u2_cat_1(k8_cat_1(A,B)))
     => ! [D] :
          ( m1_subset_1(D,u2_cat_1(k8_cat_1(A,B)))
         => C = D ) ) )).

fof(t5_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => r2_hidden(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k10_cat_1(A,B),k10_cat_1(A,B)),k10_cat_1(A,B)),u5_cat_1(A)) ) ) )).

fof(t6_nattra_1,axiom,(
    ! [A,B] : u5_cat_1(k8_cat_1(A,B)) = k1_tarski(k4_tarski(k4_tarski(B,B),B)) )).

fof(t7_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => m3_cat_2(k8_cat_1(B,k10_cat_1(A,B)),A) ) ) )).

fof(t8_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ( u3_cat_1(B) = k7_relat_1(u3_cat_1(A),u2_cat_1(B))
            & u4_cat_1(B) = k7_relat_1(u4_cat_1(A),u2_cat_1(B))
            & u5_cat_1(B) = k1_realset1(u5_cat_1(A),u2_cat_1(B))
            & u6_cat_1(B) = k7_relat_1(u6_cat_1(A),u1_cat_1(B)) ) ) ) )).

fof(t9_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u2_cat_1(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,C,B)
                    & m2_relset_1(D,C,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,B)
                        & m2_relset_1(E,C,B) )
                     => ( ( D = k1_nattra_1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C)
                          & E = k1_nattra_1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & m2_relset_1(F,k2_zfmisc_1(C,C),C) )
                           => ( F = k1_realset1(u5_cat_1(A),C)
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,B,C)
                                    & m2_relset_1(G,B,C) )
                                 => ( G = k1_nattra_1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)
                                   => m3_cat_2(g1_cat_1(B,C,D,E,F,G),A) ) ) ) ) ) ) ) ) ) ) )).

fof(t10_nattra_1,axiom,(
    ! [A] :
      ( ( v1_cat_1(A)
        & v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v1_cat_1(B)
            & m3_cat_2(B,A) )
         => ( ( u1_cat_1(B) = u1_cat_1(A)
              & u2_cat_1(B) = u2_cat_1(A) )
           => B = A ) ) ) )).

fof(d1_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ( k6_cat_1(A,D,E) != k1_xboole_0
                       => ! [F] :
                            ( m1_cat_1(F,A,D,E)
                           => k3_nattra_1(A,B,C,D,E,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) ) ) ) ) ) ) ) )).

fof(t11_nattra_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,C,A)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(C))
                         => ! [G] :
                              ( m1_subset_1(G,u1_cat_1(C))
                             => ( k6_cat_1(C,F,G) != k1_xboole_0
                               => ! [H] :
                                    ( m1_cat_1(H,C,F,G)
                                   => k3_nattra_1(C,B,k14_cat_1(C,A,B,D,E),F,G,H) = k3_nattra_1(A,B,E,k13_cat_1(C,A,D,F),k13_cat_1(C,A,D,G),k3_nattra_1(C,A,D,F,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t12_nattra_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] :
                        ( 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)
                                 => k3_nattra_1(A,B,C,E,F,G) = k3_nattra_1(A,B,D,E,F,G) ) ) ) )
                   => C = D ) ) ) ) ) )).

fof(t13_nattra_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,u1_cat_1(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_cat_1(B))
                         => ~ ( k6_cat_1(B,D,E) != k1_xboole_0
                              & k6_cat_1(B,E,F) != k1_xboole_0
                              & ~ ! [G] :
                                    ( m1_cat_1(G,B,D,E)
                                   => ! [H] :
                                        ( m1_cat_1(H,B,E,F)
                                       => k3_nattra_1(B,A,C,D,F,k9_cat_1(B,D,E,F,G,H)) = k9_cat_1(A,k13_cat_1(B,A,C,D),k13_cat_1(B,A,C,E),k13_cat_1(B,A,C,F),k3_nattra_1(B,A,C,D,E,G),k3_nattra_1(B,A,C,E,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t14_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ( k3_nattra_1(A,B,C,D,D,k10_cat_1(A,D)) = k10_cat_1(B,E)
                       => k13_cat_1(A,B,C,D) = E ) ) ) ) ) ) )).

fof(t15_nattra_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,u1_cat_1(B))
                 => k3_nattra_1(B,A,C,D,D,k10_cat_1(B,D)) = k10_cat_1(A,k13_cat_1(B,A,C,D)) ) ) ) ) )).

fof(t16_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k6_cat_1(A,B,C) != k1_xboole_0
               => ! [D] :
                    ( m1_cat_1(D,A,B,C)
                   => k3_nattra_1(A,A,k15_cat_1(A),B,C,D) = D ) ) ) ) ) )).

fof(t17_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ( ~ r1_xboole_0(k6_cat_1(A,B,C),k6_cat_1(A,D,E))
                       => ( B = D
                          & C = E ) ) ) ) ) ) ) )).

fof(d2_nattra_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_subset_1(E,u1_cat_1(A))
                       => k6_cat_1(B,k13_cat_1(A,B,C,E),k13_cat_1(A,B,D,E)) != k1_xboole_0 ) ) ) ) ) ) )).

fof(t18_nattra_1,axiom,(
    $true )).

fof(t19_nattra_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_cat_1(E,A,B)
                     => ( ( r1_nattra_1(A,B,C,D)
                          & r1_nattra_1(A,B,D,E) )
                       => r1_nattra_1(A,B,C,E) ) ) ) ) ) ) )).

fof(d3_nattra_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] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_cat_1(A),u2_cat_1(B))
                          & m2_relset_1(E,u1_cat_1(A),u2_cat_1(B)) )
                       => ( m1_nattra_1(E,A,B,C,D)
                        <=> ! [F] :
                              ( m1_subset_1(F,u1_cat_1(A))
                             => m1_cat_1(k8_funct_2(u1_cat_1(A),u2_cat_1(B),E,F),B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)) ) ) ) ) ) ) ) ) )).

fof(d4_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m1_nattra_1(D,A,B,C,C)
                 => ( D = k4_nattra_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_cat_1(A))
                       => k8_funct_2(u1_cat_1(A),u2_cat_1(B),D,E) = k10_cat_1(B,k13_cat_1(A,B,C,E)) ) ) ) ) ) ) )).

fof(d5_nattra_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))
                           => k5_nattra_1(A,B,C,D,E,F) = k8_funct_2(u1_cat_1(A),u2_cat_1(B),E,F) ) ) ) ) ) ) ) )).

fof(d6_nattra_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_cat_1(E,A,B)
                     => ( ( r1_nattra_1(A,B,C,D)
                          & r1_nattra_1(A,B,D,E) )
                       => ! [F] :
                            ( m1_nattra_1(F,A,B,C,D)
                           => ! [G] :
                                ( m1_nattra_1(G,A,B,D,E)
                               => ! [H] :
                                    ( m1_nattra_1(H,A,B,C,E)
                                   => ( H = k6_nattra_1(A,B,C,D,E,F,G)
                                    <=> ! [I] :
                                          ( m1_subset_1(I,u1_cat_1(A))
                                         => k5_nattra_1(A,B,C,E,H,I) = k9_cat_1(B,k13_cat_1(A,B,C,I),k13_cat_1(A,B,D,I),k13_cat_1(A,B,E,I),k5_nattra_1(A,B,C,D,F,I),k5_nattra_1(A,B,D,E,G,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_nattra_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)
                 => ( r1_nattra_1(B,A,C,D)
                   => ! [E] :
                        ( m1_nattra_1(E,B,A,C,D)
                       => ! [F] :
                            ( m1_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) )
                             => E = F ) ) ) ) ) ) ) ) )).

fof(t21_nattra_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,u1_cat_1(B))
                 => k5_nattra_1(B,A,C,C,k4_nattra_1(B,A,C),D) = k10_cat_1(A,k13_cat_1(B,A,C,D)) ) ) ) ) )).

fof(t22_nattra_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)
                       => ( k6_nattra_1(A,B,C,D,D,E,k4_nattra_1(A,B,D)) = E
                          & k6_nattra_1(A,B,C,C,D,k4_nattra_1(A,B,C),E) = E ) ) ) ) ) ) ) )).

fof(t23_nattra_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_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,B)
                         => ( ( r1_nattra_1(A,B,C,D)
                              & r1_nattra_1(A,B,D,E)
                              & r1_nattra_1(A,B,E,F) )
                           => ! [G] :
                                ( m1_nattra_1(G,A,B,C,D)
                               => ! [H] :
                                    ( m1_nattra_1(H,A,B,D,E)
                                   => ! [I] :
                                        ( m1_nattra_1(I,A,B,E,F)
                                       => k6_nattra_1(A,B,C,D,F,G,k6_nattra_1(A,B,D,E,F,H,I)) = k6_nattra_1(A,B,C,E,F,k6_nattra_1(A,B,C,D,E,G,H),I) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_nattra_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)
                 => ( r2_nattra_1(A,B,C,D)
                  <=> ( 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))
                             => ! [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)
                                       => k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k3_nattra_1(A,B,C,F,G,H),k5_nattra_1(A,B,C,D,E,G)) = k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,F),k3_nattra_1(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_nattra_1,axiom,(
    $true )).

fof(t25_nattra_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_cat_1(E,A,B)
                     => ( ( r2_nattra_1(A,B,C,D)
                          & r2_nattra_1(A,B,D,E) )
                       => r2_nattra_1(A,B,C,E) ) ) ) ) ) ) )).

fof(d8_nattra_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)
                 => ( r2_nattra_1(A,B,C,D)
                   => ! [E] :
                        ( m1_nattra_1(E,A,B,C,D)
                       => ( m2_nattra_1(E,A,B,C,D)
                        <=> ! [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)
                                       => k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k3_nattra_1(A,B,C,F,G,H),k5_nattra_1(A,B,C,D,E,G)) = k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,F),k3_nattra_1(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d9_nattra_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_cat_1(E,A,B)
                     => ( ( r2_nattra_1(A,B,C,D)
                          & r2_nattra_1(A,B,D,E) )
                       => ! [F] :
                            ( m2_nattra_1(F,A,B,C,D)
                           => ! [G] :
                                ( m2_nattra_1(G,A,B,D,E)
                               => k8_nattra_1(A,B,C,D,E,F,G) = k6_nattra_1(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t26_nattra_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)
                 => ( r2_nattra_1(A,B,C,D)
                   => ! [E] :
                        ( m2_nattra_1(E,A,B,C,D)
                       => ( k8_nattra_1(A,B,C,D,D,E,k7_nattra_1(A,B,D)) = E
                          & k8_nattra_1(A,B,C,C,D,k7_nattra_1(A,B,C),E) = E ) ) ) ) ) ) ) )).

fof(t27_nattra_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_cat_1(E,B,A)
                     => ( ( r2_nattra_1(B,A,C,D)
                          & r2_nattra_1(B,A,D,E) )
                       => ! [F] :
                            ( m2_nattra_1(F,B,A,C,D)
                           => ! [G] :
                                ( m2_nattra_1(G,B,A,D,E)
                               => ! [H] :
                                    ( m1_subset_1(H,u1_cat_1(B))
                                   => k5_nattra_1(B,A,C,E,k8_nattra_1(B,A,C,D,E,F,G),H) = k9_cat_1(A,k13_cat_1(B,A,C,H),k13_cat_1(B,A,D,H),k13_cat_1(B,A,E,H),k5_nattra_1(B,A,C,D,F,H),k5_nattra_1(B,A,D,E,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t28_nattra_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_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,B)
                         => ! [G] :
                              ( m2_nattra_1(G,A,B,C,D)
                             => ! [H] :
                                  ( m2_nattra_1(H,A,B,D,E)
                                 => ( ( r2_nattra_1(A,B,C,D)
                                      & r2_nattra_1(A,B,D,E)
                                      & r2_nattra_1(A,B,E,F) )
                                   => ! [I] :
                                        ( m2_nattra_1(I,A,B,E,F)
                                       => k8_nattra_1(A,B,C,D,F,G,k8_nattra_1(A,B,D,E,F,H,I)) = k8_nattra_1(A,B,C,E,F,k8_nattra_1(A,B,C,D,E,G,H),I) ) ) ) ) ) ) ) ) ) ) )).

fof(d10_nattra_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] :
                      ( 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))
                           => v5_cat_1(k5_nattra_1(A,B,C,D,E,F),B) ) ) ) ) ) ) ) )).

fof(d11_nattra_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)
                 => ( r3_nattra_1(A,B,C,D)
                  <=> ( r2_nattra_1(A,B,C,D)
                      & ? [E] :
                          ( m2_nattra_1(E,A,B,C,D)
                          & v1_nattra_1(E,A,B,C,D) ) ) ) ) ) ) ) )).

fof(d12_nattra_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_nattra_1(F,A,B,D,C)
                             => ( F = k9_nattra_1(A,B,C,D,E)
                              <=> ! [G] :
                                    ( m1_subset_1(G,u1_cat_1(A))
                                   => k5_nattra_1(A,B,D,C,F,G) = k11_cat_1(B,k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(d13_nattra_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)
                          & v1_nattra_1(E,A,B,C,D) )
                       => k10_nattra_1(A,B,C,D,E) = k9_nattra_1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t29_nattra_1,axiom,(
    $true )).

fof(t30_nattra_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)
                          & v1_nattra_1(E,A,B,C,D) )
                       => ! [F] :
                            ( m1_subset_1(F,u1_cat_1(A))
                           => k5_nattra_1(A,B,D,C,k10_nattra_1(A,B,C,D,E),F) = k11_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k5_nattra_1(A,B,C,D,E,F)) ) ) ) ) ) ) ) )).

fof(t31_nattra_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)
                 => ( r3_nattra_1(A,B,C,D)
                   => r3_nattra_1(A,B,D,C) ) ) ) ) ) )).

fof(t32_nattra_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_cat_1(E,A,B)
                     => ( ( r3_nattra_1(A,B,C,D)
                          & r3_nattra_1(A,B,D,E) )
                       => r3_nattra_1(A,B,C,E) ) ) ) ) ) ) )).

fof(d14_nattra_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)
                 => ( r3_nattra_1(A,B,C,D)
                   => ! [E] :
                        ( m2_nattra_1(E,A,B,C,D)
                       => ( m3_nattra_1(E,A,B,C,D)
                        <=> v1_nattra_1(E,A,B,C,D) ) ) ) ) ) ) ) )).

fof(t33_nattra_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)
             => m3_nattra_1(k7_nattra_1(A,B,C),A,B,C,C) ) ) ) )).

fof(t34_nattra_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_cat_1(E,A,B)
                     => ( ( r3_nattra_1(A,B,C,D)
                          & r3_nattra_1(A,B,D,E) )
                       => ! [F] :
                            ( m3_nattra_1(F,A,B,C,D)
                           => ! [G] :
                                ( m3_nattra_1(G,A,B,D,E)
                               => m3_nattra_1(k8_nattra_1(A,B,C,D,E,F,G),A,B,C,E) ) ) ) ) ) ) ) ) )).

fof(d15_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( m4_nattra_1(C,A,B)
              <=> ! [D] :
                    ~ ( r2_hidden(D,C)
                      & ! [E] :
                          ( m2_cat_1(E,A,B)
                         => ! [F] :
                              ( m2_cat_1(F,A,B)
                             => ! [G] :
                                  ( m2_nattra_1(G,A,B,E,F)
                                 => ~ ( D = k4_tarski(k4_tarski(E,F),G)
                                      & r2_nattra_1(A,B,E,F) ) ) ) ) ) ) ) ) ) )).

fof(d16_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m4_nattra_1(C,A,B)
             => ( C = k11_nattra_1(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,C)
                  <=> ? [E] :
                        ( m2_cat_1(E,A,B)
                        & ? [F] :
                            ( m2_cat_1(F,A,B)
                            & ? [G] :
                                ( m2_nattra_1(G,A,B,E,F)
                                & D = k4_tarski(k4_tarski(E,F),G)
                                & r2_nattra_1(A,B,E,F) ) ) ) ) ) ) ) ) )).

fof(d17_nattra_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,C,D)
                            & m2_relset_1(F,C,D) )
                         => ( r4_nattra_1(A,B,C,D,E,F)
                          <=> ( A = C
                              & ! [G] :
                                  ( m1_subset_1(G,A)
                                 => k8_funct_2(A,B,E,G) = k1_funct_1(F,G) ) ) ) ) ) ) ) ) ) )).

fof(t35_nattra_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)
                      <=> r2_hidden(k4_tarski(k4_tarski(C,D),E),k11_nattra_1(A,B)) ) ) ) ) ) ) )).

fof(d18_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v1_cat_1(C)
                & v2_cat_1(C)
                & l1_cat_1(C) )
             => ( C = k12_nattra_1(A,B)
              <=> ( u1_cat_1(C) = k7_cat_2(A,B)
                  & u2_cat_1(C) = k11_nattra_1(A,B)
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ( k2_cat_1(C,D) = k1_mcart_1(k1_mcart_1(D))
                        & k3_cat_1(C,D) = k2_mcart_1(k1_mcart_1(D)) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(C))
                         => ( k2_cat_1(C,E) = k3_cat_1(C,D)
                           => r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C))) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(C))
                         => ~ ( r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C)))
                              & ! [F] :
                                  ( m2_cat_1(F,A,B)
                                 => ! [G] :
                                      ( m2_cat_1(G,A,B)
                                     => ! [H] :
                                          ( m2_cat_1(H,A,B)
                                         => ! [I] :
                                              ( m2_nattra_1(I,A,B,F,G)
                                             => ! [J] :
                                                  ( m2_nattra_1(J,A,B,G,H)
                                                 => ~ ( D = k4_tarski(k4_tarski(F,G),I)
                                                      & E = k4_tarski(k4_tarski(G,H),J)
                                                      & k1_funct_1(u5_cat_1(C),k13_cat_2(C,C,E,D)) = k4_tarski(k4_tarski(F,H),k8_nattra_1(A,B,F,G,H,I,J)) ) ) ) ) ) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_cat_1(C))
                     => ! [E] :
                          ( m2_cat_1(E,A,B)
                         => ( E = D
                           => k10_cat_1(C,D) = k4_tarski(k4_tarski(E,E),k7_nattra_1(A,B,E)) ) ) ) ) ) ) ) ) )).

fof(t36_nattra_1,axiom,(
    $true )).

fof(t37_nattra_1,axiom,(
    $true )).

fof(t38_nattra_1,axiom,(
    $true )).

fof(t39_nattra_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)
                     => ! [F] :
                          ( m1_subset_1(F,u2_cat_1(k12_nattra_1(A,B)))
                         => ( F = k4_tarski(k4_tarski(C,D),E)
                           => ( k2_cat_1(k12_nattra_1(A,B),F) = C
                              & k3_cat_1(k12_nattra_1(A,B),F) = D ) ) ) ) ) ) ) ) )).

fof(t40_nattra_1,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)))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k12_nattra_1(A,B)))
                 => ! [E] :
                      ( m1_cat_1(E,k12_nattra_1(A,B),C,D)
                     => ~ ( k6_cat_1(k12_nattra_1(A,B),C,D) != k1_xboole_0
                          & ! [F] :
                              ( m2_cat_1(F,A,B)
                             => ! [G] :
                                  ( m2_cat_1(G,A,B)
                                 => ! [H] :
                                      ( m2_nattra_1(H,A,B,F,G)
                                     => ~ ( C = F
                                          & D = G
                                          & E = k4_tarski(k4_tarski(F,G),H) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_nattra_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_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_cat_1(F,A,B)
                         => ! [G] :
                              ( m2_nattra_1(G,A,B,E,F)
                             => ! [H] :
                                  ( m2_nattra_1(H,A,B,C,D)
                                 => ! [I] :
                                      ( m1_subset_1(I,u2_cat_1(k12_nattra_1(A,B)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u2_cat_1(k12_nattra_1(A,B)))
                                         => ( ( I = k4_tarski(k4_tarski(E,F),G)
                                              & J = k4_tarski(k4_tarski(C,D),H) )
                                           => ( r2_hidden(k13_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,B),J,I),k1_relat_1(u5_cat_1(k12_nattra_1(A,B))))
                                            <=> r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),F,C) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t42_nattra_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_cat_1(E,A,B)
                     => ! [F] :
                          ( m2_nattra_1(F,A,B,C,D)
                         => ! [G] :
                              ( m2_nattra_1(G,A,B,D,E)
                             => ! [H] :
                                  ( m1_subset_1(H,u2_cat_1(k12_nattra_1(A,B)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u2_cat_1(k12_nattra_1(A,B)))
                                     => ( ( H = k4_tarski(k4_tarski(C,D),F)
                                          & I = k4_tarski(k4_tarski(D,E),G) )
                                       => k4_cat_1(k12_nattra_1(A,B),H,I) = k4_tarski(k4_tarski(C,E),k8_nattra_1(A,B,C,D,E,F,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(d19_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v2_nattra_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u2_cat_1(A))
           => ? [C] :
                ( m1_subset_1(C,u1_cat_1(A))
                & B = k10_cat_1(A,C) ) ) ) ) )).

fof(t43_nattra_1,axiom,(
    $true )).

fof(t44_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v2_nattra_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,B) = k1_tarski(k10_cat_1(A,B)) ) ) )).

fof(t45_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v2_nattra_1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ? [C] :
                  ( v1_finset_1(C)
                  & C = k6_cat_1(A,B,B)
                  & k4_card_1(C) = np__1 ) )
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => ( B != C
                   => k6_cat_1(A,B,C) = k1_xboole_0 ) ) ) ) ) ) )).

fof(t46_nattra_1,axiom,(
    ! [A,B] : v2_nattra_1(k8_cat_1(A,B)) )).

fof(t47_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v2_nattra_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => v2_nattra_1(B) ) ) )).

fof(t48_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( ( v2_nattra_1(A)
              & v2_nattra_1(B) )
           => v2_nattra_1(k11_cat_2(A,B)) ) ) ) )).

fof(t49_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v2_nattra_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)
                 => ( r1_nattra_1(B,A,C,D)
                   => r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),C,D) ) ) ) ) ) )).

fof(t50_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v2_nattra_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,B,A)
             => ! [D] :
                  ( m1_nattra_1(D,B,A,C,C)
                 => r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),D,k7_nattra_1(B,A,C)) ) ) ) ) )).

fof(t51_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( v2_nattra_1(A)
           => v2_nattra_1(k12_nattra_1(B,A)) ) ) ) )).

fof(t52_nattra_1,axiom,(
    ! [A] :
      ( ( v1_cat_1(A)
        & v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v2_nattra_1(A)
       => k13_nattra_1(A) = A ) ) )).

fof(t53_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k13_nattra_1(k13_nattra_1(A)) = k13_nattra_1(A) ) )).

fof(t54_nattra_1,axiom,(
    ! [A,B] : k13_nattra_1(k8_cat_1(A,B)) = k8_cat_1(A,B) )).

fof(t55_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => k13_nattra_1(k11_cat_2(A,B)) = k11_cat_2(k13_nattra_1(A),k13_nattra_1(B)) ) ) )).

fof(s1_nattra_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s1_nattra_1)
       => ~ r1_xboole_0(f2_s1_nattra_1,f3_s1_nattra_1(A)) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_nattra_1,f2_s1_nattra_1)
        & m2_relset_1(A,f1_s1_nattra_1,f2_s1_nattra_1)
        & ! [B] :
            ( m1_subset_1(B,f1_s1_nattra_1)
           => r2_hidden(k8_funct_2(f1_s1_nattra_1,f2_s1_nattra_1,A,B),f3_s1_nattra_1(B)) ) ) )).

fof(dt_m1_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ! [E] :
          ( m1_nattra_1(E,A,B,C,D)
         => ( v1_funct_1(E)
            & v1_funct_2(E,u1_cat_1(A),u2_cat_1(B))
            & m2_relset_1(E,u1_cat_1(A),u2_cat_1(B)) ) ) ) )).

fof(existence_m1_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ? [E] : m1_nattra_1(E,A,B,C,D) ) )).

fof(dt_m2_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ! [E] :
          ( m2_nattra_1(E,A,B,C,D)
         => m1_nattra_1(E,A,B,C,D) ) ) )).

fof(existence_m2_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ? [E] : m2_nattra_1(E,A,B,C,D) ) )).

fof(dt_m3_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ! [E] :
          ( m3_nattra_1(E,A,B,C,D)
         => m2_nattra_1(E,A,B,C,D) ) ) )).

fof(existence_m3_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ? [E] : m3_nattra_1(E,A,B,C,D) ) )).

fof(dt_m4_nattra_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] :
          ( m4_nattra_1(C,A,B)
         => ~ v1_xboole_0(C) ) ) )).

fof(existence_m4_nattra_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m4_nattra_1(C,A,B) ) )).

fof(reflexivity_r1_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => r1_nattra_1(A,B,C,C) ) )).

fof(reflexivity_r2_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => r2_nattra_1(A,B,C,C) ) )).

fof(reflexivity_r3_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => r3_nattra_1(A,B,C,C) ) )).

fof(symmetry_r4_nattra_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & v1_funct_2(F,C,D)
        & m1_relset_1(F,C,D) )
     => ( r4_nattra_1(A,B,C,D,E,F)
       => r4_nattra_1(A,B,C,D,F,E) ) ) )).

fof(reflexivity_r4_nattra_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & v1_funct_2(F,C,D)
        & m1_relset_1(F,C,D) )
     => r4_nattra_1(A,B,C,D,E,E) ) )).

fof(redefinition_r4_nattra_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & v1_funct_2(F,C,D)
        & m1_relset_1(F,C,D) )
     => ( r4_nattra_1(A,B,C,D,E,F)
      <=> E = F ) ) )).

fof(dt_k1_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,k1_zfmisc_1(A)) )
     => ( v1_funct_1(k1_nattra_1(A,B,C,D))
        & v1_funct_2(k1_nattra_1(A,B,C,D),D,B)
        & m2_relset_1(k1_nattra_1(A,B,C,D),D,B) ) ) )).

fof(redefinition_k1_nattra_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,k1_zfmisc_1(A)) )
     => k1_nattra_1(A,B,C,D) = k7_relat_1(C,D) ) )).

fof(dt_k2_nattra_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(A))
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(B))
        & v1_funct_1(E)
        & m1_relset_1(E,k12_mcart_1(A,A,C,C),C)
        & v1_funct_1(F)
        & m1_relset_1(F,k12_mcart_1(B,B,D,D),D) )
     => ( v1_funct_1(k2_nattra_1(A,B,C,D,E,F))
        & m2_relset_1(k2_nattra_1(A,B,C,D,E,F),k12_mcart_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k12_mcart_1(A,B,C,D),k12_mcart_1(A,B,C,D)),k12_mcart_1(A,B,C,D)) ) ) )).

fof(redefinition_k2_nattra_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(A))
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(B))
        & v1_funct_1(E)
        & m1_relset_1(E,k12_mcart_1(A,A,C,C),C)
        & v1_funct_1(F)
        & m1_relset_1(F,k12_mcart_1(B,B,D,D),D) )
     => k2_nattra_1(A,B,C,D,E,F) = k3_funct_4(E,F) ) )).

fof(dt_k3_nattra_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m1_subset_1(D,u1_cat_1(A))
        & m1_subset_1(E,u1_cat_1(A))
        & m1_cat_1(F,A,D,E) )
     => m1_cat_1(k3_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) )).

fof(dt_k4_nattra_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) )
     => m1_nattra_1(k4_nattra_1(A,B,C),A,B,C,C) ) )).

fof(dt_k5_nattra_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( 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(D,A,B)
        & m1_nattra_1(E,A,B,C,D)
        & m1_subset_1(F,u1_cat_1(A)) )
     => m1_cat_1(k5_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)) ) )).

fof(dt_k6_nattra_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)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,A,B)
        & m1_nattra_1(F,A,B,C,D)
        & m1_nattra_1(G,A,B,D,E) )
     => m1_nattra_1(k6_nattra_1(A,B,C,D,E,F,G),A,B,C,E) ) )).

fof(dt_k7_nattra_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_nattra_1(k7_nattra_1(A,B,C),A,B,C,C) ) )).

fof(redefinition_k7_nattra_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) )
     => k7_nattra_1(A,B,C) = k4_nattra_1(A,B,C) ) )).

fof(dt_k8_nattra_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)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,A,B)
        & m2_nattra_1(F,A,B,C,D)
        & m2_nattra_1(G,A,B,D,E) )
     => m2_nattra_1(k8_nattra_1(A,B,C,D,E,F,G),A,B,C,E) ) )).

fof(dt_k9_nattra_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B)
        & m1_nattra_1(E,A,B,C,D) )
     => m1_nattra_1(k9_nattra_1(A,B,C,D,E),A,B,D,C) ) )).

fof(dt_k10_nattra_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B)
        & m2_nattra_1(E,A,B,C,D) )
     => m2_nattra_1(k10_nattra_1(A,B,C,D,E),A,B,D,C) ) )).

fof(dt_k11_nattra_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m4_nattra_1(k11_nattra_1(A,B),A,B) ) )).

fof(dt_k12_nattra_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v1_cat_1(k12_nattra_1(A,B))
        & v2_cat_1(k12_nattra_1(A,B))
        & l1_cat_1(k12_nattra_1(A,B)) ) ) )).

fof(dt_k13_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v1_cat_1(k13_nattra_1(A))
        & v2_nattra_1(k13_nattra_1(A))
        & m3_cat_2(k13_nattra_1(A),A) ) ) )).

fof(d20_nattra_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v1_cat_1(B)
            & v2_nattra_1(B)
            & m3_cat_2(B,A) )
         => ( B = k13_nattra_1(A)
          <=> ( u1_cat_1(B) = u1_cat_1(A)
              & u2_cat_1(B) = a_1_0_nattra_1(A) ) ) ) ) )).

fof(fraenkel_a_1_0_nattra_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ( r2_hidden(A,a_1_0_nattra_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_cat_1(B))
            & A = k10_cat_1(B,C) ) ) ) )).
%------------------------------------------------------------------------------