SET007 Axioms: SET007+412.ax


%------------------------------------------------------------------------------
% File     : SET007+412 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Categorial Categories and Slice Categories
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : cat_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   99 (   0 unit)
%            Number of atoms       :  807 ( 135 equality)
%            Maximal formula depth :   30 (   9 average)
%            Number of connectives :  744 (  36 ~  ;   0  |; 359  &)
%                                         (  17 <=>; 332 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   19 (   0 propositional; 1-3 arity)
%            Number of functors    :   68 (   6 constant; 0-6 arity)
%            Number of variables   :  379 (   0 singleton; 351 !;  28 ?)
%            Maximal term depth    :    6 (   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_cat_5,axiom,(
    ? [A] :
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A)
      & v1_cat_5(A) ) )).

fof(rc2_cat_5,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v2_cat_5(A) ) )).

fof(cc1_cat_5,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( ( v2_cat_1(A)
          & v3_cat_5(A) )
       => ( v2_cat_1(A)
          & v1_cat_5(A) ) ) ) )).

fof(rc3_cat_5,axiom,(
    ? [A] :
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A)
      & v1_cat_5(A)
      & v3_cat_5(A) ) )).

fof(cc2_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => v3_cat_5(B) ) ) )).

fof(rc4_cat_5,axiom,(
    ? [A] :
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A)
      & v1_cat_5(A)
      & v3_cat_5(A)
      & v4_cat_5(A) ) )).

fof(fc1_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ~ v1_xboole_0(k12_cat_5(A,B)) ) )).

fof(fc2_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ~ v1_xboole_0(k13_cat_5(A,B)) ) )).

fof(t1_cat_5,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ! [B] :
          ( l1_cat_1(B)
         => ( ( g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
              & v2_cat_1(A) )
           => v2_cat_1(B) ) ) ) )).

fof(d1_cat_5,axiom,(
    ! [A] :
      ( l1_cat_1(A)
     => ( v1_cat_5(A)
      <=> ! [B] :
            ( m1_subset_1(B,u2_cat_1(A))
           => ? [C] : B = k4_tarski(k1_domain_1(u1_cat_1(A),u1_cat_1(A),k2_cat_1(A,B),k3_cat_1(A,B)),C) ) ) ) )).

fof(t2_cat_5,axiom,(
    ! [A] :
      ( ( v1_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k2_cat_1(A,B) = k17_mcart_1(B)
            & k3_cat_1(A,B) = k18_mcart_1(B)
            & B = k4_tarski(k1_domain_1(u1_cat_1(A),u1_cat_1(A),k2_cat_1(A,B),k3_cat_1(A,B)),k2_mcart_1(B)) ) ) ) )).

fof(t3_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ( m3_cat_2(A,B)
           => g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) ) ) ) )).

fof(t4_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m3_cat_2(C,B)
             => m3_cat_2(C,A) ) ) ) )).

fof(d2_cat_5,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)
                  & m3_cat_2(A,C)
                  & m3_cat_2(B,C) )
              & ? [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                  & m1_subset_1(C,u1_cat_1(B)) )
              & ~ ! [C] :
                    ( ( v1_cat_1(C)
                      & v2_cat_1(C)
                      & l1_cat_1(C) )
                   => ( C = k6_cat_5(A,B)
                    <=> ( u1_cat_1(C) = k3_xboole_0(u1_cat_1(A),u1_cat_1(B))
                        & u2_cat_1(C) = k3_xboole_0(u2_cat_1(A),u2_cat_1(B))
                        & u3_cat_1(C) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),u2_cat_1(B))
                        & u4_cat_1(C) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),u2_cat_1(B))
                        & u5_cat_1(C) = k1_realset1(u5_cat_1(A),u2_cat_1(B))
                        & u6_cat_1(C) = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),u1_cat_1(B)) ) ) ) ) ) ) )).

fof(t5_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m3_cat_2(C,A)
             => ( ~ r2_subset_1(u1_cat_1(B),u1_cat_1(C))
               => k6_cat_5(B,C) = k6_cat_5(C,B) ) ) ) ) )).

fof(t6_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_cat_2(B,A)
         => ! [C] :
              ( m3_cat_2(C,A)
             => ( ~ r2_subset_1(u1_cat_1(B),u1_cat_1(C))
               => ( m3_cat_2(k6_cat_5(B,C),B)
                  & m3_cat_2(k6_cat_5(B,C),C) ) ) ) ) ) )).

fof(d3_cat_5,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] :
                  ( ( v1_cat_1(D)
                    & m3_cat_2(D,B) )
                 => ( D = k7_cat_5(A,B,C)
                  <=> ( u1_cat_1(D) = k2_relat_1(k12_cat_1(A,B,C))
                      & r1_tarski(k2_relat_1(C),u2_cat_1(D))
                      & ! [E] :
                          ( m3_cat_2(E,B)
                         => ( ( u1_cat_1(E) = k2_relat_1(k12_cat_1(A,B,C))
                              & r1_tarski(k2_relat_1(C),u2_cat_1(E)) )
                           => m3_cat_2(D,E) ) ) ) ) ) ) ) ) )).

fof(t7_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m3_cat_2(C,B)
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ( r1_tarski(k2_relat_1(D),u2_cat_1(C))
                   => m2_cat_1(D,A,C) ) ) ) ) ) )).

fof(t8_cat_5,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)
             => m2_cat_1(C,A,k7_cat_5(A,B,C)) ) ) ) )).

fof(t9_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m3_cat_2(C,B)
             => ! [D] :
                  ( m2_cat_1(D,A,C)
                 => ! [E] :
                      ( m2_cat_1(E,A,B)
                     => ( D = E
                       => k7_cat_5(A,C,D) = k7_cat_5(A,B,E) ) ) ) ) ) ) )).

fof(d4_cat_5,axiom,(
    ! [A] :
      ( v2_cat_5(A)
    <=> ! [B] :
          ( r2_hidden(B,A)
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) )).

fof(d5_cat_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v2_cat_5(A)
      <=> ! [B] :
            ( m1_subset_1(B,A)
           => ( v2_cat_1(B)
              & l1_cat_1(B) ) ) ) ) )).

fof(d6_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v3_cat_5(A)
      <=> ( v2_cat_5(u1_cat_1(A))
          & ! [B] :
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] :
                  ( ( v2_cat_1(C)
                    & l1_cat_1(C) )
                 => ( B = C
                   => k10_cat_1(A,B) = k4_tarski(k4_tarski(C,C),k15_cat_1(C)) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( ( v2_cat_1(C)
                    & l1_cat_1(C) )
                 => ! [D] :
                      ( ( v2_cat_1(D)
                        & l1_cat_1(D) )
                     => ~ ( C = k2_cat_1(A,B)
                          & D = k3_cat_1(A,B)
                          & ! [E] :
                              ( m2_cat_1(E,C,D)
                             => B != k4_tarski(k4_tarski(C,D),E) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] :
                      ( ( v2_cat_1(D)
                        & l1_cat_1(D) )
                     => ! [E] :
                          ( ( v2_cat_1(E)
                            & l1_cat_1(E) )
                         => ! [F] :
                              ( ( v2_cat_1(F)
                                & l1_cat_1(F) )
                             => ! [G] :
                                  ( m2_cat_1(G,D,E)
                                 => ! [H] :
                                      ( m2_cat_1(H,E,F)
                                     => ( ( B = k4_tarski(k4_tarski(D,E),G)
                                          & C = k4_tarski(k4_tarski(E,F),H) )
                                       => k4_cat_1(A,B,C) = k4_tarski(k4_tarski(D,F),k14_cat_1(D,E,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t10_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( ( g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
              & v3_cat_5(A) )
           => v3_cat_5(B) ) ) ) )).

fof(t11_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v3_cat_5(k8_cat_1(A,k4_tarski(k4_tarski(A,A),k15_cat_1(A)))) ) )).

fof(t12_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) )).

fof(t13_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k2_cat_1(A,B) = k4_cat_5(A,B)
            & k3_cat_1(A,B) = k5_cat_5(A,B) ) ) ) )).

fof(t14_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ( ( u1_cat_1(A) = u1_cat_1(B)
              & u2_cat_1(A) = u2_cat_1(B) )
           => g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) ) ) ) )).

fof(t15_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ( r1_tarski(u2_cat_1(A),u2_cat_1(B))
           => m3_cat_2(A,B) ) ) ) )).

fof(d7_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k10_cat_5(A) = A ) )).

fof(t16_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k10_cat_5(B) = B ) ) )).

fof(t17_cat_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ~ ( ! [C] :
                  ( m1_cat_5(C,A)
                 => ! [D] :
                      ( m1_cat_5(D,A)
                     => ! [E] :
                          ( m1_cat_5(E,A)
                         => ! [F] :
                              ( m2_cat_1(F,C,D)
                             => ! [G] :
                                  ( m2_cat_1(G,D,E)
                                 => ( ( r2_hidden(F,B)
                                      & r2_hidden(G,B) )
                                   => r2_hidden(k14_cat_1(C,D,E,F,G),B) ) ) ) ) ) )
              & ! [C] :
                  ( m1_cat_5(C,A)
                 => r2_hidden(k15_cat_1(C),B) )
              & ! [C] :
                  ( ( v1_cat_1(C)
                    & v2_cat_1(C)
                    & v3_cat_5(C)
                    & l1_cat_1(C) )
                 => ~ ( u1_cat_1(C) = A
                      & ! [D] :
                          ( m1_cat_5(D,A)
                         => ! [E] :
                              ( m1_cat_5(E,A)
                             => ! [F] :
                                  ( m2_cat_1(F,D,E)
                                 => ( m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(D),u2_cat_1(E))),k1_domain_1(A,A,D,E),F),u2_cat_1(C))
                                  <=> r2_hidden(F,B) ) ) ) ) ) ) ) ) ) )).

fof(t18_cat_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_cat_1(C)
                & v2_cat_1(C)
                & v3_cat_5(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v1_cat_1(D)
                    & v2_cat_1(D)
                    & v3_cat_5(D)
                    & l1_cat_1(D) )
                 => ( ( u1_cat_1(C) = A
                      & ! [E] :
                          ( m1_cat_5(E,A)
                         => ! [F] :
                              ( m1_cat_5(F,A)
                             => ! [G] :
                                  ( m2_cat_1(G,E,F)
                                 => ( m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(E),u2_cat_1(F))),k1_domain_1(A,A,E,F),G),u2_cat_1(C))
                                  <=> r2_hidden(G,B) ) ) ) )
                      & u1_cat_1(D) = A
                      & ! [E] :
                          ( m1_cat_5(E,A)
                         => ! [F] :
                              ( m1_cat_5(F,A)
                             => ! [G] :
                                  ( m2_cat_1(G,E,F)
                                 => ( m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(E),u2_cat_1(F))),k1_domain_1(A,A,E,F),G),u2_cat_1(D))
                                  <=> r2_hidden(G,B) ) ) ) ) )
                   => C = D ) ) ) ) ) )).

fof(d8_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ( v4_cat_5(A)
      <=> ! [B] :
            ( ( v2_cat_1(B)
              & l1_cat_1(B) )
           => ! [C] :
                ( ( v2_cat_1(C)
                  & l1_cat_1(C) )
               => ( ( m1_subset_1(B,u1_cat_1(A))
                    & m1_subset_1(C,u1_cat_1(A)) )
                 => ! [D] :
                      ( m2_cat_1(D,B,C)
                     => m1_subset_1(k4_tarski(k4_tarski(B,C),D),u2_cat_1(A)) ) ) ) ) ) ) )).

fof(t19_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & v4_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & v4_cat_5(B)
            & l1_cat_1(B) )
         => ( u1_cat_1(A) = u1_cat_1(B)
           => g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) ) ) ) )).

fof(t20_cat_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ? [B] :
          ( v1_cat_1(B)
          & v2_cat_1(B)
          & v3_cat_5(B)
          & v4_cat_5(B)
          & l1_cat_1(B)
          & u1_cat_1(B) = A ) ) )).

fof(t21_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & v4_cat_5(B)
            & l1_cat_1(B) )
         => ( r1_tarski(u1_cat_1(A),u1_cat_1(B))
           => m3_cat_2(A,B) ) ) ) )).

fof(t22_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & v3_cat_5(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,C)
                     => ( D = E
                       => k7_cat_5(A,B,D) = k7_cat_5(A,C,E) ) ) ) ) ) ) )).

fof(d9_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k12_cat_5(A,B) = k3_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k6_domain_1(u1_cat_1(A),B)) ) ) )).

fof(d10_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => k13_cat_5(A,B) = k3_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k6_domain_1(u1_cat_1(A),B)) ) ) )).

fof(t23_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( r2_hidden(C,k12_cat_5(A,B))
              <=> k3_cat_1(A,C) = B ) ) ) ) )).

fof(t24_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( r2_hidden(C,k13_cat_5(A,B))
              <=> k2_cat_1(A,C) = B ) ) ) ) )).

fof(t25_cat_5,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) = k5_subset_1(u2_cat_1(A),k13_cat_5(A,B),k12_cat_5(A,C)) ) ) ) )).

fof(t26_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ( r2_hidden(B,k13_cat_5(A,k2_cat_1(A,B)))
            & r2_hidden(B,k12_cat_5(A,k3_cat_1(A,B))) ) ) ) )).

fof(t27_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m2_subset_1(C,u2_cat_1(A),k12_cat_5(A,k2_cat_1(A,B)))
             => r2_hidden(k4_cat_1(A,C,B),k12_cat_5(A,k3_cat_1(A,B))) ) ) ) )).

fof(t28_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m2_subset_1(C,u2_cat_1(A),k13_cat_5(A,k3_cat_1(A,B)))
             => r2_hidden(k4_cat_1(A,B,C),k13_cat_5(A,k2_cat_1(A,B))) ) ) ) )).

fof(d11_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( ( v1_cat_1(C)
                & v2_cat_1(C)
                & v1_cat_5(C)
                & l1_cat_1(C) )
             => ( C = k14_cat_5(A,B)
              <=> ( u1_cat_1(C) = k12_cat_5(A,B)
                  & ! [D] :
                      ( m2_subset_1(D,u2_cat_1(A),k12_cat_5(A,B))
                     => ! [E] :
                          ( m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B))
                         => ! [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                             => ( ( k2_cat_1(A,E) = k3_cat_1(A,F)
                                  & D = k4_cat_1(A,F,E) )
                               => m1_subset_1(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,D,E),F),u2_cat_1(C)) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ? [E] :
                          ( m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B))
                          & ? [F] :
                              ( m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B))
                              & ? [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                  & D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,E,F),G)
                                  & k2_cat_1(A,F) = k3_cat_1(A,G)
                                  & E = k4_cat_1(A,G,F) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(C))
                         => ! [F] :
                              ( m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B))
                             => ! [G] :
                                  ( m2_subset_1(G,u2_cat_1(A),k12_cat_5(A,B))
                                 => ! [H] :
                                      ( m2_subset_1(H,u2_cat_1(A),k12_cat_5(A,B))
                                     => ! [I] :
                                          ( m1_subset_1(I,u2_cat_1(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u2_cat_1(A))
                                             => ( ( D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,G),I)
                                                  & E = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,G,H),J) )
                                               => k4_cat_1(C,D,E) = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,H),k4_cat_1(A,I,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d12_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( ( v1_cat_1(C)
                & v2_cat_1(C)
                & v1_cat_5(C)
                & l1_cat_1(C) )
             => ( C = k15_cat_5(A,B)
              <=> ( u1_cat_1(C) = k13_cat_5(A,B)
                  & ! [D] :
                      ( m2_subset_1(D,u2_cat_1(A),k13_cat_5(A,B))
                     => ! [E] :
                          ( m2_subset_1(E,u2_cat_1(A),k13_cat_5(A,B))
                         => ! [F] :
                              ( m1_subset_1(F,u2_cat_1(A))
                             => ( ( k2_cat_1(A,F) = k3_cat_1(A,D)
                                  & k4_cat_1(A,D,F) = E )
                               => m1_subset_1(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,D,E),F),u2_cat_1(C)) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ? [E] :
                          ( m2_subset_1(E,u2_cat_1(A),k13_cat_5(A,B))
                          & ? [F] :
                              ( m2_subset_1(F,u2_cat_1(A),k13_cat_5(A,B))
                              & ? [G] :
                                  ( m1_subset_1(G,u2_cat_1(A))
                                  & D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,E,F),G)
                                  & k2_cat_1(A,G) = k3_cat_1(A,E)
                                  & k4_cat_1(A,E,G) = F ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ! [E] :
                          ( m1_subset_1(E,u2_cat_1(C))
                         => ! [F] :
                              ( m2_subset_1(F,u2_cat_1(A),k13_cat_5(A,B))
                             => ! [G] :
                                  ( m2_subset_1(G,u2_cat_1(A),k13_cat_5(A,B))
                                 => ! [H] :
                                      ( m2_subset_1(H,u2_cat_1(A),k13_cat_5(A,B))
                                     => ! [I] :
                                          ( m1_subset_1(I,u2_cat_1(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u2_cat_1(A))
                                             => ( ( D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,G),I)
                                                  & E = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,G,H),J) )
                                               => k4_cat_1(C,D,E) = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,H),k4_cat_1(A,I,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(k14_cat_5(A,B)))
             => ( C = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k17_cat_5(A,B,C),k18_cat_5(A,B,C)),k16_cat_5(A,B,C))
                & k2_cat_1(A,k18_cat_5(A,B,C)) = k3_cat_1(A,k16_cat_5(A,B,C))
                & k17_cat_5(A,B,C) = k4_cat_1(A,k16_cat_5(A,B,C),k18_cat_5(A,B,C))
                & k2_cat_1(k14_cat_5(A,B),C) = k17_cat_5(A,B,C)
                & k3_cat_1(k14_cat_5(A,B),C) = k18_cat_5(A,B,C) ) ) ) ) )).

fof(t30_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m2_subset_1(C,u2_cat_1(A),k12_cat_5(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k14_cat_5(A,B)))
                 => ( D = C
                   => k10_cat_1(k14_cat_5(A,B),D) = k1_domain_1(u1_cat_1(k11_cat_2(k14_cat_5(A,B),k14_cat_5(A,B))),u2_cat_1(A),k12_cat_2(k14_cat_5(A,B),k14_cat_5(A,B),D,D),k10_cat_1(A,k2_cat_1(A,C))) ) ) ) ) ) )).

fof(t31_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(k15_cat_5(A,B)))
             => ( C = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k20_cat_5(A,B,C),k21_cat_5(A,B,C)),k19_cat_5(A,B,C))
                & k2_cat_1(A,k19_cat_5(A,B,C)) = k3_cat_1(A,k20_cat_5(A,B,C))
                & k4_cat_1(A,k20_cat_5(A,B,C),k19_cat_5(A,B,C)) = k21_cat_5(A,B,C)
                & k2_cat_1(k15_cat_5(A,B),C) = k20_cat_5(A,B,C)
                & k3_cat_1(k15_cat_5(A,B),C) = k21_cat_5(A,B,C) ) ) ) ) )).

fof(t32_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] :
              ( m2_subset_1(C,u2_cat_1(A),k13_cat_5(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k15_cat_5(A,B)))
                 => ( D = C
                   => k10_cat_1(k15_cat_5(A,B),D) = k1_domain_1(u1_cat_1(k11_cat_2(k15_cat_5(A,B),k15_cat_5(A,B))),u2_cat_1(A),k12_cat_2(k15_cat_5(A,B),k15_cat_5(A,B),D,D),k10_cat_1(A,k3_cat_1(A,C))) ) ) ) ) ) )).

fof(d13_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m2_cat_1(C,k14_cat_5(A,k2_cat_1(A,B)),k14_cat_5(A,k3_cat_1(A,B)))
             => ( C = k22_cat_5(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u2_cat_1(k14_cat_5(A,k2_cat_1(A,B))))
                   => k8_funct_2(u2_cat_1(k14_cat_5(A,k2_cat_1(A,B))),u2_cat_1(k14_cat_5(A,k3_cat_1(A,B))),C,D) = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k4_cat_1(A,k17_cat_5(A,k2_cat_1(A,B),D),B),k4_cat_1(A,k18_cat_5(A,k2_cat_1(A,B),D),B)),k16_cat_5(A,k2_cat_1(A,B),D)) ) ) ) ) ) )).

fof(d14_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m2_cat_1(C,k15_cat_5(A,k3_cat_1(A,B)),k15_cat_5(A,k2_cat_1(A,B)))
             => ( C = k23_cat_5(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u2_cat_1(k15_cat_5(A,k3_cat_1(A,B))))
                   => k8_funct_2(u2_cat_1(k15_cat_5(A,k3_cat_1(A,B))),u2_cat_1(k15_cat_5(A,k2_cat_1(A,B))),C,D) = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k4_cat_1(A,B,k20_cat_5(A,k3_cat_1(A,B),D)),k4_cat_1(A,B,k21_cat_5(A,k3_cat_1(A,B),D))),k19_cat_5(A,k3_cat_1(A,B),D)) ) ) ) ) ) )).

fof(t33_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = k3_cat_1(A,B)
               => k22_cat_5(A,k4_cat_1(A,B,C)) = k1_partfun1(u2_cat_1(k14_cat_5(A,k2_cat_1(A,B))),u2_cat_1(k14_cat_5(A,k3_cat_1(A,B))),u2_cat_1(k14_cat_5(A,k2_cat_1(A,C))),u2_cat_1(k14_cat_5(A,k3_cat_1(A,C))),k22_cat_5(A,B),k22_cat_5(A,C)) ) ) ) ) )).

fof(t34_cat_5,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = k3_cat_1(A,B)
               => k23_cat_5(A,k4_cat_1(A,B,C)) = k1_partfun1(u2_cat_1(k15_cat_5(A,k3_cat_1(A,C))),u2_cat_1(k15_cat_5(A,k2_cat_1(A,C))),u2_cat_1(k15_cat_5(A,k3_cat_1(A,B))),u2_cat_1(k15_cat_5(A,k2_cat_1(A,B))),k23_cat_5(A,C),k23_cat_5(A,B)) ) ) ) ) )).

fof(s1_cat_5,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s1_cat_5)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_cat_5)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_cat_5)
                 => ! [D] :
                      ( m1_subset_1(D,f2_s1_cat_5)
                     => ! [E] :
                          ( m1_subset_1(E,f2_s1_cat_5)
                         => ( ( p1_s1_cat_5(A,B,D)
                              & p1_s1_cat_5(B,C,E) )
                           => ( r2_hidden(f3_s1_cat_5(E,D),f2_s1_cat_5)
                              & p1_s1_cat_5(A,C,f3_s1_cat_5(E,D)) ) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_cat_5)
         => ? [B] :
              ( m1_subset_1(B,f2_s1_cat_5)
              & p1_s1_cat_5(A,A,B)
              & ! [C] :
                  ( m1_subset_1(C,f1_s1_cat_5)
                 => ! [D] :
                      ( m1_subset_1(D,f2_s1_cat_5)
                     => ( ( p1_s1_cat_5(A,C,D)
                         => f3_s1_cat_5(D,B) = D )
                        & ( p1_s1_cat_5(C,A,D)
                         => f3_s1_cat_5(B,D) = D ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_cat_5)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_cat_5)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_cat_5)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s1_cat_5)
                     => ! [E] :
                          ( m1_subset_1(E,f2_s1_cat_5)
                         => ! [F] :
                              ( m1_subset_1(F,f2_s1_cat_5)
                             => ! [G] :
                                  ( m1_subset_1(G,f2_s1_cat_5)
                                 => ( ( p1_s1_cat_5(A,B,E)
                                      & p1_s1_cat_5(B,C,F)
                                      & p1_s1_cat_5(C,D,G) )
                                   => f3_s1_cat_5(G,f3_s1_cat_5(F,E)) = f3_s1_cat_5(f3_s1_cat_5(G,F),E) ) ) ) ) ) ) ) ) )
   => ? [A] :
        ( v1_cat_1(A)
        & v2_cat_1(A)
        & v1_cat_5(A)
        & l1_cat_1(A)
        & u1_cat_1(A) = f1_s1_cat_5
        & ! [B] :
            ( m1_subset_1(B,f1_s1_cat_5)
           => ! [C] :
                ( m1_subset_1(C,f1_s1_cat_5)
               => ! [D] :
                    ( m1_subset_1(D,f2_s1_cat_5)
                   => ( p1_s1_cat_5(B,C,D)
                     => m1_subset_1(k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,B,C),D),u2_cat_1(A)) ) ) ) )
        & ! [B] :
            ( m1_subset_1(B,u2_cat_1(A))
           => ? [C] :
                ( m1_subset_1(C,f1_s1_cat_5)
                & ? [D] :
                    ( m1_subset_1(D,f1_s1_cat_5)
                    & ? [E] :
                        ( m1_subset_1(E,f2_s1_cat_5)
                        & B = k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,C,D),E)
                        & p1_s1_cat_5(C,D,E) ) ) ) )
        & ! [B] :
            ( m1_subset_1(B,u2_cat_1(A))
           => ! [C] :
                ( m1_subset_1(C,u2_cat_1(A))
               => ! [D] :
                    ( m1_subset_1(D,f1_s1_cat_5)
                   => ! [E] :
                        ( m1_subset_1(E,f1_s1_cat_5)
                       => ! [F] :
                            ( m1_subset_1(F,f1_s1_cat_5)
                           => ! [G] :
                                ( m1_subset_1(G,f2_s1_cat_5)
                               => ! [H] :
                                    ( m1_subset_1(H,f2_s1_cat_5)
                                   => ( ( B = k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,E),G)
                                        & C = k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,E,F),H) )
                                     => k4_cat_1(A,B,C) = k4_tarski(k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,F),f3_s1_cat_5(H,G)) ) ) ) ) ) ) ) ) ) )).

fof(s2_cat_5,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s2_cat_5)
       => ? [B] :
            ( m1_subset_1(B,f2_s2_cat_5)
            & p1_s2_cat_5(A,A,B)
            & ! [C] :
                ( m1_subset_1(C,f1_s2_cat_5)
               => ! [D] :
                    ( m1_subset_1(D,f2_s2_cat_5)
                   => ( ( p1_s2_cat_5(A,C,D)
                       => f3_s2_cat_5(D,B) = D )
                      & ( p1_s2_cat_5(C,A,D)
                       => f3_s2_cat_5(B,D) = D ) ) ) ) ) )
   => ! [A] :
        ( ( v1_cat_1(A)
          & v2_cat_1(A)
          & v1_cat_5(A)
          & l1_cat_1(A) )
       => ! [B] :
            ( ( v1_cat_1(B)
              & v2_cat_1(B)
              & v1_cat_5(B)
              & l1_cat_1(B) )
           => ( ( u1_cat_1(A) = f1_s2_cat_5
                & ! [C] :
                    ( m1_subset_1(C,f1_s2_cat_5)
                   => ! [D] :
                        ( m1_subset_1(D,f1_s2_cat_5)
                       => ! [E] :
                            ( m1_subset_1(E,f2_s2_cat_5)
                           => ( p1_s2_cat_5(C,D,E)
                             => m1_subset_1(k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,C,D),E),u2_cat_1(A)) ) ) ) )
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(A))
                   => ? [D] :
                        ( m1_subset_1(D,f1_s2_cat_5)
                        & ? [E] :
                            ( m1_subset_1(E,f1_s2_cat_5)
                            & ? [F] :
                                ( m1_subset_1(F,f2_s2_cat_5)
                                & C = k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,D,E),F)
                                & p1_s2_cat_5(D,E,F) ) ) ) )
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(A))
                   => ! [D] :
                        ( m1_subset_1(D,u2_cat_1(A))
                       => ! [E] :
                            ( m1_subset_1(E,f1_s2_cat_5)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s2_cat_5)
                               => ! [G] :
                                    ( m1_subset_1(G,f1_s2_cat_5)
                                   => ! [H] :
                                        ( m1_subset_1(H,f2_s2_cat_5)
                                       => ! [I] :
                                            ( m1_subset_1(I,f2_s2_cat_5)
                                           => ( ( C = k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,E,F),H)
                                                & D = k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,F,G),I) )
                                             => k4_cat_1(A,C,D) = k4_tarski(k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,E,G),f3_s2_cat_5(I,H)) ) ) ) ) ) ) ) )
                & u1_cat_1(B) = f1_s2_cat_5
                & ! [C] :
                    ( m1_subset_1(C,f1_s2_cat_5)
                   => ! [D] :
                        ( m1_subset_1(D,f1_s2_cat_5)
                       => ! [E] :
                            ( m1_subset_1(E,f2_s2_cat_5)
                           => ( p1_s2_cat_5(C,D,E)
                             => m1_subset_1(k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,C,D),E),u2_cat_1(B)) ) ) ) )
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(B))
                   => ? [D] :
                        ( m1_subset_1(D,f1_s2_cat_5)
                        & ? [E] :
                            ( m1_subset_1(E,f1_s2_cat_5)
                            & ? [F] :
                                ( m1_subset_1(F,f2_s2_cat_5)
                                & C = k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,D,E),F)
                                & p1_s2_cat_5(D,E,F) ) ) ) )
                & ! [C] :
                    ( m1_subset_1(C,u2_cat_1(B))
                   => ! [D] :
                        ( m1_subset_1(D,u2_cat_1(B))
                       => ! [E] :
                            ( m1_subset_1(E,f1_s2_cat_5)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s2_cat_5)
                               => ! [G] :
                                    ( m1_subset_1(G,f1_s2_cat_5)
                                   => ! [H] :
                                        ( m1_subset_1(H,f2_s2_cat_5)
                                       => ! [I] :
                                            ( m1_subset_1(I,f2_s2_cat_5)
                                           => ( ( C = k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,E,F),H)
                                                & D = k1_domain_1(k2_zfmisc_1(f1_s2_cat_5,f1_s2_cat_5),f2_s2_cat_5,k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,F,G),I) )
                                             => k4_cat_1(B,C,D) = k4_tarski(k1_domain_1(f1_s2_cat_5,f1_s2_cat_5,E,G),f3_s2_cat_5(I,H)) ) ) ) ) ) ) ) ) )
             => A = B ) ) ) )).

fof(s3_cat_5,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u2_cat_1(f1_s3_cat_5))
         => ( m1_subset_1(f4_s3_cat_5(A),u2_cat_1(f2_s3_cat_5))
            & ! [B] :
                ( m1_subset_1(B,u2_cat_1(f2_s3_cat_5))
               => ( B = f4_s3_cat_5(A)
                 => ( k2_cat_1(f2_s3_cat_5,B) = f3_s3_cat_5(k2_cat_1(f1_s3_cat_5,A))
                    & k3_cat_1(f2_s3_cat_5,B) = f3_s3_cat_5(k3_cat_1(f1_s3_cat_5,A)) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_cat_1(f1_s3_cat_5))
         => f4_s3_cat_5(k10_cat_1(f1_s3_cat_5,A)) = k10_cat_1(f2_s3_cat_5,f3_s3_cat_5(A)) )
      & ! [A] :
          ( m1_subset_1(A,u2_cat_1(f1_s3_cat_5))
         => ! [B] :
              ( m1_subset_1(B,u2_cat_1(f1_s3_cat_5))
             => ! [C] :
                  ( m1_subset_1(C,u2_cat_1(f2_s3_cat_5))
                 => ! [D] :
                      ( m1_subset_1(D,u2_cat_1(f2_s3_cat_5))
                     => ( ( C = f4_s3_cat_5(A)
                          & D = f4_s3_cat_5(B)
                          & k2_cat_1(f1_s3_cat_5,B) = k3_cat_1(f1_s3_cat_5,A) )
                       => f4_s3_cat_5(k4_cat_1(f1_s3_cat_5,A,B)) = k4_cat_1(f2_s3_cat_5,C,D) ) ) ) ) ) )
   => ? [A] :
        ( m2_cat_1(A,f1_s3_cat_5,f2_s3_cat_5)
        & ! [B] :
            ( m1_subset_1(B,u2_cat_1(f1_s3_cat_5))
           => k8_funct_2(u2_cat_1(f1_s3_cat_5),u2_cat_1(f2_s3_cat_5),A,B) = f4_s3_cat_5(B) ) ) )).

fof(dt_m1_cat_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ! [B] :
          ( m1_cat_5(B,A)
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) )).

fof(existence_m1_cat_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ? [B] : m1_cat_5(B,A) ) )).

fof(redefinition_m1_cat_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ! [B] :
          ( m1_cat_5(B,A)
        <=> m1_subset_1(B,A) ) ) )).

fof(dt_k1_cat_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
     => m1_subset_1(k1_cat_5(A,B,C,D),A) ) )).

fof(redefinition_k1_cat_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
     => k1_cat_5(A,B,C,D) = k17_mcart_1(D) ) )).

fof(dt_k2_cat_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
     => m1_subset_1(k2_cat_5(A,B,C,D),B) ) )).

fof(redefinition_k2_cat_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
     => k2_cat_5(A,B,C,D) = k18_mcart_1(D) ) )).

fof(dt_k3_cat_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k3_cat_5(A,B,C),B) ) )).

fof(redefinition_k3_cat_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => k3_cat_5(A,B,C) = k2_mcart_1(C) ) )).

fof(dt_k4_cat_5,axiom,(
    ! [A,B] :
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k4_cat_5(A,B),u1_cat_1(A)) ) )).

fof(redefinition_k4_cat_5,axiom,(
    ! [A,B] :
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k4_cat_5(A,B) = k17_mcart_1(B) ) )).

fof(dt_k5_cat_5,axiom,(
    ! [A,B] :
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k5_cat_5(A,B),u1_cat_1(A)) ) )).

fof(redefinition_k5_cat_5,axiom,(
    ! [A,B] :
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k5_cat_5(A,B) = k18_mcart_1(B) ) )).

fof(dt_k6_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v1_cat_1(k6_cat_5(A,B))
        & v2_cat_1(k6_cat_5(A,B))
        & l1_cat_1(k6_cat_5(A,B)) ) ) )).

fof(dt_k7_cat_5,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) )
     => ( v1_cat_1(k7_cat_5(A,B,C))
        & m3_cat_2(k7_cat_5(A,B,C),B) ) ) )).

fof(dt_k8_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => ( v2_cat_1(k8_cat_5(A,B))
        & l1_cat_1(k8_cat_5(A,B)) ) ) )).

fof(redefinition_k8_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k8_cat_5(A,B) = k17_mcart_1(B) ) )).

fof(dt_k9_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => ( v2_cat_1(k9_cat_5(A,B))
        & l1_cat_1(k9_cat_5(A,B)) ) ) )).

fof(redefinition_k9_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k9_cat_5(A,B) = k18_mcart_1(B) ) )).

fof(dt_k10_cat_5,axiom,(
    ! [A] :
      ( v2_cat_1(k10_cat_5(A))
      & l1_cat_1(k10_cat_5(A)) ) )).

fof(dt_k11_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m2_cat_1(k11_cat_5(A,B),k10_cat_5(k2_cat_1(A,B)),k10_cat_5(k3_cat_1(A,B))) ) )).

fof(redefinition_k11_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k11_cat_5(A,B) = k2_mcart_1(B) ) )).

fof(dt_k12_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_subset_1(k12_cat_5(A,B),k1_zfmisc_1(u2_cat_1(A))) ) )).

fof(dt_k13_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_subset_1(k13_cat_5(A,B),k1_zfmisc_1(u2_cat_1(A))) ) )).

fof(dt_k14_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ( v1_cat_1(k14_cat_5(A,B))
        & v2_cat_1(k14_cat_5(A,B))
        & v1_cat_5(k14_cat_5(A,B))
        & l1_cat_1(k14_cat_5(A,B)) ) ) )).

fof(dt_k15_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ( v1_cat_1(k15_cat_5(A,B))
        & v2_cat_1(k15_cat_5(A,B))
        & v1_cat_5(k15_cat_5(A,B))
        & l1_cat_1(k15_cat_5(A,B)) ) ) )).

fof(dt_k16_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) )
     => m1_subset_1(k16_cat_5(A,B,C),u2_cat_1(A)) ) )).

fof(redefinition_k16_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) )
     => k16_cat_5(A,B,C) = k2_mcart_1(C) ) )).

fof(dt_k17_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) )
     => m2_subset_1(k17_cat_5(A,B,C),u2_cat_1(A),k12_cat_5(A,B)) ) )).

fof(redefinition_k17_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) )
     => k17_cat_5(A,B,C) = k17_mcart_1(C) ) )).

fof(dt_k18_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) )
     => m2_subset_1(k18_cat_5(A,B,C),u2_cat_1(A),k12_cat_5(A,B)) ) )).

fof(redefinition_k18_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) )
     => k18_cat_5(A,B,C) = k18_mcart_1(C) ) )).

fof(dt_k19_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) )
     => m1_subset_1(k19_cat_5(A,B,C),u2_cat_1(A)) ) )).

fof(redefinition_k19_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) )
     => k19_cat_5(A,B,C) = k2_mcart_1(C) ) )).

fof(dt_k20_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) )
     => m2_subset_1(k20_cat_5(A,B,C),u2_cat_1(A),k13_cat_5(A,B)) ) )).

fof(redefinition_k20_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) )
     => k20_cat_5(A,B,C) = k17_mcart_1(C) ) )).

fof(dt_k21_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) )
     => m2_subset_1(k21_cat_5(A,B,C),u2_cat_1(A),k13_cat_5(A,B)) ) )).

fof(redefinition_k21_cat_5,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) )
     => k21_cat_5(A,B,C) = k18_mcart_1(C) ) )).

fof(dt_k22_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m2_cat_1(k22_cat_5(A,B),k14_cat_5(A,k2_cat_1(A,B)),k14_cat_5(A,k3_cat_1(A,B))) ) )).

fof(dt_k23_cat_5,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m2_cat_1(k23_cat_5(A,B),k15_cat_5(A,k3_cat_1(A,B)),k15_cat_5(A,k2_cat_1(A,B))) ) )).
%------------------------------------------------------------------------------