SET007 Axioms: SET007+525.ax


%------------------------------------------------------------------------------
% File     : SET007+525 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Categories Without Uniqueness of cod and dom
% Version  : [Urb08] axioms.
% English  : Some Properties of the Morphisms and the Functors

% 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    : altcat_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   78 (   0 unit)
%            Number of atoms       : 1030 ( 116 equality)
%            Maximal formula depth :   28 (  12 average)
%            Number of connectives : 1103 ( 151 ~  ;  47  |; 541  &)
%                                         (  12 <=>; 352 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   37 (   0 propositional; 1-5 arity)
%            Number of functors    :   20 (   1 constant; 0-6 arity)
%            Number of variables   :  303 (   0 singleton; 302 !;   1 ?)
%            Maximal term depth    :    3 (   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(fc1_altcat_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k1_altcat_1(A,B,B)) ) )).

fof(fc2_altcat_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_altcat_3(k8_altcat_1(A,B),A,B,B)
        & v2_altcat_3(k8_altcat_1(A,B),A,B,B)
        & v4_altcat_3(k8_altcat_1(A,B),A,B,B)
        & v5_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) )).

fof(fc3_altcat_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_altcat_3(k8_altcat_1(A,B),A,B,B)
        & v2_altcat_3(k8_altcat_1(A,B),A,B,B)
        & v3_altcat_3(k8_altcat_1(A,B),A,B,B)
        & v4_altcat_3(k8_altcat_1(A,B),A,B,B)
        & v5_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) )).

fof(rc1_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ? [B] :
          ( m1_altcat_2(B,A)
          & ~ v3_struct_0(B)
          & v2_altcat_1(B)
          & v6_altcat_1(B)
          & v11_altcat_1(B)
          & v12_altcat_1(B)
          & v1_altcat_2(B)
          & v2_altcat_2(B,A)
          & v3_altcat_2(B,A) ) ) )).

fof(fc4_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k1_altcat_4(A))
        & v2_altcat_1(k1_altcat_4(A))
        & v6_altcat_1(k1_altcat_4(A))
        & v11_altcat_1(k1_altcat_4(A))
        & v12_altcat_1(k1_altcat_4(A))
        & v1_altcat_2(k1_altcat_4(A))
        & v3_altcat_2(k1_altcat_4(A),A) ) ) )).

fof(fc5_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k2_altcat_4(A))
        & v2_altcat_1(k2_altcat_4(A))
        & v6_altcat_1(k2_altcat_4(A))
        & v11_altcat_1(k2_altcat_4(A))
        & v12_altcat_1(k2_altcat_4(A))
        & v1_altcat_2(k2_altcat_4(A))
        & v3_altcat_2(k2_altcat_4(A),A) ) ) )).

fof(fc6_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k3_altcat_4(A))
        & v2_altcat_1(k3_altcat_4(A))
        & v6_altcat_1(k3_altcat_4(A))
        & v11_altcat_1(k3_altcat_4(A))
        & v12_altcat_1(k3_altcat_4(A))
        & v1_altcat_2(k3_altcat_4(A))
        & v3_altcat_2(k3_altcat_4(A),A) ) ) )).

fof(fc7_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k4_altcat_4(A))
        & v2_altcat_1(k4_altcat_4(A))
        & v6_altcat_1(k4_altcat_4(A))
        & v11_altcat_1(k4_altcat_4(A))
        & v12_altcat_1(k4_altcat_4(A))
        & v1_altcat_2(k4_altcat_4(A))
        & v3_altcat_2(k4_altcat_4(A),A) ) ) )).

fof(fc8_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k5_altcat_4(A))
        & v2_altcat_1(k5_altcat_4(A))
        & v6_altcat_1(k5_altcat_4(A))
        & v11_altcat_1(k5_altcat_4(A))
        & v12_altcat_1(k5_altcat_4(A))
        & v1_altcat_2(k5_altcat_4(A))
        & v3_altcat_2(k5_altcat_4(A),A) ) ) )).

fof(t1_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_altcat_1(A,B,C))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,B,D))
                         => ! [G] :
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ( ( F = k5_altcat_1(A,B,C,D,E,G)
                                  & k5_altcat_1(A,C,D,C,G,k1_altcat_3(A,C,D,G)) = k8_altcat_1(A,C) )
                               => ( k1_altcat_1(A,B,C) = k1_xboole_0
                                  | k1_altcat_1(A,C,D) = k1_xboole_0
                                  | k1_altcat_1(A,D,C) = k1_xboole_0
                                  | E = k5_altcat_1(A,B,D,C,F,k1_altcat_3(A,C,D,G)) ) ) ) ) ) ) ) ) ) )).

fof(t2_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_altcat_1(A,B,C))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,C))
                         => ! [G] :
                              ( m1_subset_1(G,k1_altcat_1(A,D,B))
                             => ( ( F = k5_altcat_1(A,D,B,C,G,E)
                                  & k5_altcat_1(A,B,D,B,k1_altcat_3(A,D,B,G),G) = k8_altcat_1(A,B) )
                               => ( k1_altcat_1(A,D,B) = k1_xboole_0
                                  | k1_altcat_1(A,B,D) = k1_xboole_0
                                  | k1_altcat_1(A,B,C) = k1_xboole_0
                                  | E = k5_altcat_1(A,B,D,C,k1_altcat_3(A,D,B,G),F) ) ) ) ) ) ) ) ) ) )).

fof(t3_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v3_altcat_3(D,A,B,C)
                   => ( k1_altcat_1(A,B,C) = k1_xboole_0
                      | k1_altcat_1(A,C,B) = k1_xboole_0
                      | v3_altcat_3(k1_altcat_3(A,B,C,D),A,C,B) ) ) ) ) ) ) )).

fof(t4_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_altcat_3(k8_altcat_1(A,B),A,B,B)
            & v4_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ) )).

fof(t5_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ! [E] :
                      ( m1_subset_1(E,k1_altcat_1(A,C,B))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,C,B))
                         => ( ( k5_altcat_1(A,B,C,B,D,F) = k8_altcat_1(A,B)
                              & k5_altcat_1(A,C,B,C,E,D) = k8_altcat_1(A,C) )
                           => ( k1_altcat_1(A,B,C) = k1_xboole_0
                              | k1_altcat_1(A,C,B) = k1_xboole_0
                              | E = F ) ) ) ) ) ) ) ) )).

fof(t6_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => v2_altcat_3(D,A,B,C) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,B) != k1_xboole_0
                        & ~ v3_altcat_3(D,A,B,C) ) ) ) ) ) ) )).

fof(t7_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ! [E] :
                      ( m1_subset_1(E,k1_altcat_1(A,B,C))
                     => ( ( v9_altcat_3(D,A,B,C)
                          & v9_altcat_3(E,A,B,C) )
                       => ( ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ v8_altcat_3(F,A) )
                          | D = E ) ) ) ) ) ) ) )).

fof(t8_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v7_altcat_3(B,A)
                   => v4_altcat_3(D,A,B,C) ) ) ) ) ) )).

fof(t9_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(A,C,B))
                 => ( v6_altcat_3(B,A)
                   => v5_altcat_3(D,A,C,B) ) ) ) ) ) )).

fof(t10_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v7_altcat_3(B,A)
                  & r2_altcat_3(A,C,B) )
               => v7_altcat_3(C,A) ) ) ) ) )).

fof(t11_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v6_altcat_3(B,A)
                  & r2_altcat_3(A,B,C) )
               => v6_altcat_3(C,A) ) ) ) ) )).

fof(t12_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v6_altcat_3(B,A)
                  & v7_altcat_3(C,A) )
               => ( k1_altcat_1(A,C,B) = k1_xboole_0
                  | ( v6_altcat_3(C,A)
                    & v7_altcat_3(B,A) ) ) ) ) ) ) )).

fof(t13_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k8_functor0(A,B,C,D,D,k8_altcat_1(A,D)) = k8_altcat_1(B,k3_functor0(A,B,C,D)) ) ) ) ) )).

fof(t14_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v18_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => v2_funct_2(k7_functor0(A,B,C,E,D),k1_altcat_1(A,E,D),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E))) ) ) ) ) ) ) )).

fof(t15_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v17_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => v2_funct_1(k7_functor0(A,B,C,E,D)) ) ) ) ) ) ) )).

fof(t16_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v10_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)))
                         => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                              & v18_functor0(C,A,B)
                              & v8_functor0(C,A,B)
                              & ! [G] :
                                  ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                 => F != k6_functor0(A,B,C,D,E,G) ) ) ) ) ) ) ) ) )).

fof(t17_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)))
                         => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                              & v18_functor0(C,A,B)
                              & v8_functor0(C,A,B)
                              & ! [G] :
                                  ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                 => F != k8_functor0(A,B,C,D,E,G) ) ) ) ) ) ) ) ) )).

fof(t18_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( v1_altcat_3(F,A,D,E)
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v1_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) ) ) )).

fof(t19_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( v2_altcat_3(F,A,D,E)
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v2_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) ) ) )).

fof(t20_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( v3_altcat_3(F,A,D,E)
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v3_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) ) ) )).

fof(t21_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_altcat_3(A,D,E)
                       => r2_altcat_3(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) )).

fof(t22_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( v1_altcat_3(F,A,D,E)
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v2_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) ) ) )).

fof(t23_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( v2_altcat_3(F,A,D,E)
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v1_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) ) ) )).

fof(t24_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( v3_altcat_3(F,A,D,E)
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v3_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) ) ) )).

fof(t25_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_altcat_3(A,D,E)
                       => r2_altcat_3(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) )).

fof(t26_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( ( v18_functor0(C,A,B)
                              & v17_functor0(C,A,B)
                              & v1_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v1_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) )).

fof(t27_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( ( v18_functor0(C,A,B)
                              & v17_functor0(C,A,B)
                              & v2_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v2_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) )).

fof(t28_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( ( v18_functor0(C,A,B)
                              & v17_functor0(C,A,B)
                              & v3_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v3_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) )).

fof(t29_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( v18_functor0(C,A,B)
                          & v17_functor0(C,A,B)
                          & r2_altcat_3(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
                       => ( k1_altcat_1(A,D,E) = k1_xboole_0
                          | k1_altcat_1(A,E,D) = k1_xboole_0
                          | r2_altcat_3(A,D,E) ) ) ) ) ) ) ) )).

fof(t30_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( ( v18_functor0(C,A,B)
                              & v17_functor0(C,A,B)
                              & v1_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v2_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) )).

fof(t31_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( ( v18_functor0(C,A,B)
                              & v17_functor0(C,A,B)
                              & v2_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v1_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) )).

fof(t32_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,D,E))
                         => ( ( v18_functor0(C,A,B)
                              & v17_functor0(C,A,B)
                              & v3_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
                           => ( k1_altcat_1(A,D,E) = k1_xboole_0
                              | k1_altcat_1(A,E,D) = k1_xboole_0
                              | v3_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) )).

fof(t33_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( v18_functor0(C,A,B)
                          & v17_functor0(C,A,B)
                          & r2_altcat_3(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
                       => ( k1_altcat_1(A,D,E) = k1_xboole_0
                          | k1_altcat_1(A,E,D) = k1_xboole_0
                          | r2_altcat_3(A,D,E) ) ) ) ) ) ) ) )).

fof(t34_altcat_4,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( u1_struct_0(A) = u1_struct_0(B)
              & u1_altcat_1(A) = u1_altcat_1(B) )
           => v2_altcat_2(B,A) ) ) ) )).

fof(t35_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( u1_struct_0(A) = u1_struct_0(B)
              & u1_altcat_1(A) = u1_altcat_1(B) )
           => ( v2_altcat_2(B,A)
              & v3_altcat_2(B,A) ) ) ) ) )).

fof(t36_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v3_altcat_2(C,B)
                & m1_altcat_2(C,B) )
             => ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v3_altcat_2(C,A)
                & m1_altcat_2(C,A) ) ) ) ) )).

fof(t37_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(B,E,F))
                                 => ( ( E = C
                                      & F = D
                                      & G = H )
                                   => ( k1_altcat_1(B,E,F) = k1_xboole_0
                                      | ( ( v4_altcat_3(G,A,C,D)
                                         => v4_altcat_3(H,B,E,F) )
                                        & ( v5_altcat_3(G,A,C,D)
                                         => v5_altcat_3(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(A,D,C))
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_altcat_1(B,E,F))
                                     => ! [J] :
                                          ( m1_subset_1(J,k1_altcat_1(B,F,E))
                                         => ( ( E = C
                                              & F = D
                                              & G = I
                                              & H = J )
                                           => ( k1_altcat_1(B,E,F) = k1_xboole_0
                                              | k1_altcat_1(B,F,E) = k1_xboole_0
                                              | ( ( r1_altcat_3(A,C,D,G,H)
                                                 => r1_altcat_3(B,E,F,I,J) )
                                                & ( r1_altcat_3(B,E,F,I,J)
                                                 => r1_altcat_3(A,C,D,G,H) )
                                                & ( r1_altcat_3(A,D,C,H,G)
                                                 => r1_altcat_3(B,F,E,J,I) )
                                                & ( r1_altcat_3(B,F,E,J,I)
                                                 => r1_altcat_3(A,D,C,H,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v2_altcat_2(B,A)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(B,E,F))
                                 => ( ( E = C
                                      & F = D
                                      & G = H )
                                   => ( k1_altcat_1(B,E,F) = k1_xboole_0
                                      | k1_altcat_1(B,F,E) = k1_xboole_0
                                      | ( ( v1_altcat_3(G,A,C,D)
                                         => v1_altcat_3(H,B,E,F) )
                                        & ( v2_altcat_3(G,A,C,D)
                                         => v2_altcat_3(H,B,E,F) )
                                        & ( v3_altcat_3(G,A,C,D)
                                         => v3_altcat_3(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(B,E,F))
                                 => ( ( E = C
                                      & F = D
                                      & G = H )
                                   => ( k1_altcat_1(B,E,F) = k1_xboole_0
                                      | k1_altcat_1(B,F,E) = k1_xboole_0
                                      | ( ( v1_altcat_3(H,B,E,F)
                                         => v1_altcat_3(G,A,C,D) )
                                        & ( v2_altcat_3(H,B,E,F)
                                         => v2_altcat_3(G,A,C,D) )
                                        & ( v3_altcat_3(H,B,E,F)
                                         => v3_altcat_3(G,A,C,D) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ( B = k1_altcat_4(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,k1_altcat_1(A,C,D))
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( k1_altcat_1(A,C,D) != k1_xboole_0
                              & v4_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) )).

fof(d2_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ( B = k2_altcat_4(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,k1_altcat_1(A,C,D))
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( k1_altcat_1(A,C,D) != k1_xboole_0
                              & v5_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) )).

fof(d3_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ( B = k3_altcat_4(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,k1_altcat_1(A,C,D))
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( k1_altcat_1(A,C,D) != k1_xboole_0
                              & k1_altcat_1(A,D,C) != k1_xboole_0
                              & v1_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) )).

fof(d4_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ( B = k4_altcat_4(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,k1_altcat_1(A,C,D))
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( k1_altcat_1(A,C,D) != k1_xboole_0
                              & k1_altcat_1(A,D,C) != k1_xboole_0
                              & v2_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) )).

fof(d5_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ( B = k5_altcat_4(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,k1_altcat_1(A,C,D))
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( k1_altcat_1(A,C,D) != k1_xboole_0
                              & k1_altcat_1(A,D,C) != k1_xboole_0
                              & v3_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) )).

fof(t41_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k5_altcat_4(A))
        & v2_altcat_1(k5_altcat_4(A))
        & v3_altcat_2(k5_altcat_4(A),k3_altcat_4(A))
        & m1_altcat_2(k5_altcat_4(A),k3_altcat_4(A)) ) ) )).

fof(t42_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k5_altcat_4(A))
        & v2_altcat_1(k5_altcat_4(A))
        & v3_altcat_2(k5_altcat_4(A),k4_altcat_4(A))
        & m1_altcat_2(k5_altcat_4(A),k4_altcat_4(A)) ) ) )).

fof(t43_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k4_altcat_4(A))
        & v2_altcat_1(k4_altcat_4(A))
        & v3_altcat_2(k4_altcat_4(A),k1_altcat_4(A))
        & m1_altcat_2(k4_altcat_4(A),k1_altcat_4(A)) ) ) )).

fof(t44_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k3_altcat_4(A))
        & v2_altcat_1(k3_altcat_4(A))
        & v3_altcat_2(k3_altcat_4(A),k2_altcat_4(A))
        & m1_altcat_2(k3_altcat_4(A),k2_altcat_4(A)) ) ) )).

fof(t45_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => v4_altcat_3(D,A,B,C) ) ) )
       => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k1_altcat_4(A) ) ) )).

fof(t46_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => v5_altcat_3(D,A,B,C) ) ) )
       => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k2_altcat_4(A) ) ) )).

fof(t47_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ( v1_altcat_3(D,A,B,C)
                      & k1_altcat_1(A,C,B) != k1_xboole_0 ) ) ) )
       => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k3_altcat_4(A) ) ) )).

fof(t48_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ( v2_altcat_3(D,A,B,C)
                      & k1_altcat_1(A,C,B) != k1_xboole_0 ) ) ) )
       => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k4_altcat_4(A) ) ) )).

fof(t49_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ( v3_altcat_3(D,A,B,C)
                      & k1_altcat_1(A,C,B) != k1_xboole_0 ) ) ) )
       => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k5_altcat_4(A) ) ) )).

fof(t50_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k1_altcat_4(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k1_altcat_4(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(k1_altcat_4(A),B,C))
                 => ( k1_altcat_1(k1_altcat_4(A),B,C) != k1_xboole_0
                   => v4_altcat_3(D,k1_altcat_4(A),B,C) ) ) ) ) ) )).

fof(t51_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_altcat_4(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_altcat_4(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(k2_altcat_4(A),B,C))
                 => ( k1_altcat_1(k2_altcat_4(A),B,C) != k1_xboole_0
                   => v5_altcat_3(D,k2_altcat_4(A),B,C) ) ) ) ) ) )).

fof(t52_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_altcat_4(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_altcat_4(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(k5_altcat_4(A),B,C))
                 => ( k1_altcat_1(k5_altcat_4(A),B,C) != k1_xboole_0
                   => ( v3_altcat_3(D,k5_altcat_4(A),B,C)
                      & r2_hidden(k1_altcat_3(k5_altcat_4(A),B,C,D),k1_altcat_1(k5_altcat_4(A),C,B)) ) ) ) ) ) ) )).

fof(t53_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k1_altcat_4(k1_altcat_4(A)) = k1_altcat_4(A) ) )).

fof(t54_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k2_altcat_4(k2_altcat_4(A)) = k2_altcat_4(A) ) )).

fof(t55_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k5_altcat_4(k5_altcat_4(A)) = k5_altcat_4(A) ) )).

fof(t56_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k5_altcat_4(k1_altcat_4(A)) = k5_altcat_4(A) ) )).

fof(t57_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k5_altcat_4(k2_altcat_4(A)) = k5_altcat_4(A) ) )).

fof(t58_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k5_altcat_4(k3_altcat_4(A)) = k5_altcat_4(A) ) )).

fof(t59_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k5_altcat_4(k4_altcat_4(A)) = k5_altcat_4(A) ) )).

fof(dt_k1_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k1_altcat_4(A))
        & v2_altcat_1(k1_altcat_4(A))
        & v6_altcat_1(k1_altcat_4(A))
        & m1_altcat_2(k1_altcat_4(A),A) ) ) )).

fof(dt_k2_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k2_altcat_4(A))
        & v2_altcat_1(k2_altcat_4(A))
        & v6_altcat_1(k2_altcat_4(A))
        & m1_altcat_2(k2_altcat_4(A),A) ) ) )).

fof(dt_k3_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k3_altcat_4(A))
        & v2_altcat_1(k3_altcat_4(A))
        & v6_altcat_1(k3_altcat_4(A))
        & m1_altcat_2(k3_altcat_4(A),A) ) ) )).

fof(dt_k4_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k4_altcat_4(A))
        & v2_altcat_1(k4_altcat_4(A))
        & v6_altcat_1(k4_altcat_4(A))
        & m1_altcat_2(k4_altcat_4(A),A) ) ) )).

fof(dt_k5_altcat_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k5_altcat_4(A))
        & v2_altcat_1(k5_altcat_4(A))
        & v6_altcat_1(k5_altcat_4(A))
        & m1_altcat_2(k5_altcat_4(A),A) ) ) )).
%------------------------------------------------------------------------------