SET007 Axioms: SET007+536.ax


%------------------------------------------------------------------------------
% File     : SET007+536 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Composition of Functors and Transformations in Alternativ
% 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    : functor3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   75 (   0 unit)
%            Number of atoms       : 1488 (  37 equality)
%            Maximal formula depth :   32 (  18 average)
%            Number of connectives : 1614 ( 201 ~  ;   5  |; 986  &)
%                                         (   5 <=>; 417 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   29 (   0 propositional; 1-5 arity)
%            Number of functors    :   34 (   1 constant; 0-9 arity)
%            Number of variables   :  474 (   0 singleton; 467 !;   7 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_functor3,axiom,(
    ? [A] :
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v2_altcat_1(A)
      & v6_altcat_1(A)
      & v11_altcat_1(A)
      & v12_altcat_1(A)
      & v1_altcat_2(A) ) )).

fof(rc2_functor3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ? [C] :
          ( l2_functor0(C,A,B)
          & v6_functor0(C,A,B)
          & v8_functor0(C,A,B)
          & v9_functor0(C,A,B)
          & v10_functor0(C,A,B)
          & v11_functor0(C,A,B)
          & v13_functor0(C,A,B)
          & v14_functor0(C,A,B) ) ) )).

fof(rc3_functor3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ? [C] :
          ( l2_functor0(C,A,B)
          & v6_functor0(C,A,B)
          & v8_functor0(C,A,B)
          & v9_functor0(C,A,B)
          & v10_functor0(C,A,B)
          & v11_functor0(C,A,B)
          & v12_functor0(C,A,B)
          & v13_functor0(C,A,B)
          & v14_functor0(C,A,B) ) ) )).

fof(rc4_functor3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ? [C] :
          ( m2_functor0(C,A,B)
          & v6_functor0(C,A,B)
          & v8_functor0(C,A,B)
          & v9_functor0(C,A,B)
          & v10_functor0(C,A,B)
          & v11_functor0(C,A,B)
          & v12_functor0(C,A,B)
          & v13_functor0(C,A,B)
          & v14_functor0(C,A,B)
          & v15_functor0(C,A,B)
          & v16_functor0(C,A,B) ) ) )).

fof(fc1_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v8_functor0(D,A,B)
        & v10_functor0(D,A,B)
        & v13_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v8_functor0(E,B,C)
        & v10_functor0(E,B,C)
        & v13_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v8_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v10_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v13_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) )).

fof(fc2_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v8_functor0(D,A,B)
        & v11_functor0(D,A,B)
        & v14_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v8_functor0(E,B,C)
        & v11_functor0(E,B,C)
        & v14_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v8_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v10_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v13_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) )).

fof(fc3_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v8_functor0(D,A,B)
        & v10_functor0(D,A,B)
        & v13_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v8_functor0(E,B,C)
        & v11_functor0(E,B,C)
        & v14_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v8_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v11_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v14_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) )).

fof(fc4_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v8_functor0(D,A,B)
        & v11_functor0(D,A,B)
        & v14_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v8_functor0(E,B,C)
        & v10_functor0(E,B,C)
        & v13_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v8_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v11_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v14_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) )).

fof(t1_functor3,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,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_altcat_1(A,B,C))
                         => ! [G] :
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(A,B,E))
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_altcat_1(A,E,D))
                                     => ( ( k5_altcat_1(A,B,C,D,F,G) = k5_altcat_1(A,B,E,D,H,I)
                                          & k5_altcat_1(A,C,B,C,k1_altcat_3(A,B,C,F),F) = k8_altcat_1(A,C)
                                          & k5_altcat_1(A,E,D,E,I,k1_altcat_3(A,E,D,I)) = k8_altcat_1(A,E) )
                                       => ( k1_altcat_1(A,B,C) = k1_xboole_0
                                          | k1_altcat_1(A,C,B) = k1_xboole_0
                                          | k1_altcat_1(A,C,D) = k1_xboole_0
                                          | k1_altcat_1(A,D,E) = k1_xboole_0
                                          | k1_altcat_1(A,E,D) = k1_xboole_0
                                          | k5_altcat_1(A,C,B,E,k1_altcat_3(A,B,C,F),H) = k5_altcat_1(A,C,D,E,G,k1_altcat_3(A,E,D,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t2_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v8_functor0(D,A,B)
                    & v10_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( l2_functor0(E,B,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => k4_functor0(A,C,k13_functor0(A,B,C,D,E),F,G) = k5_relat_1(k5_functor0(A,B,D,F,G),k4_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G))) ) ) ) ) ) ) ) )).

fof(t3_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v8_functor0(D,A,B)
                    & v11_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( l2_functor0(E,B,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => k4_functor0(A,C,k13_functor0(A,B,C,D,E),F,G) = k5_relat_1(k7_functor0(A,B,D,F,G),k4_functor0(B,C,E,k3_functor0(A,B,D,G),k3_functor0(A,B,D,F))) ) ) ) ) ) ) ) )).

fof(t4_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => k13_functor0(A,B,B,C,k11_functor0(B)) = g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) ) ) ) )).

fof(t5_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => k13_functor0(A,A,B,k12_functor0(A),C) = g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) ) ) ) )).

fof(t6_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_altcat_2(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v8_functor0(D,A,B)
                    & v10_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v8_functor0(E,B,C)
                        & v10_functor0(E,B,C)
                        & l2_functor0(E,B,C) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(A,F,G))
                                 => ( k1_altcat_1(A,F,G) != k1_xboole_0
                                   => k6_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k6_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t7_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_altcat_2(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v8_functor0(D,A,B)
                    & v11_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v8_functor0(E,B,C)
                        & v11_functor0(E,B,C)
                        & l2_functor0(E,B,C) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(A,F,G))
                                 => ( k1_altcat_1(A,F,G) != k1_xboole_0
                                   => k6_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k8_functor0(B,C,E,k3_functor0(A,B,D,G),k3_functor0(A,B,D,F),k8_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t8_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_altcat_2(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v8_functor0(D,A,B)
                    & v10_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v8_functor0(E,B,C)
                        & v11_functor0(E,B,C)
                        & l2_functor0(E,B,C) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(A,F,G))
                                 => ( k1_altcat_1(A,F,G) != k1_xboole_0
                                   => k8_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k8_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t9_functor3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_altcat_2(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v8_functor0(D,C,B)
                    & v10_functor0(D,C,B)
                    & l2_functor0(D,C,B) )
                 => ! [E] :
                      ( ( v8_functor0(E,A,C)
                        & v11_functor0(E,A,C)
                        & l2_functor0(E,A,C) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_altcat_1(A,F,G))
                                 => ( k1_altcat_1(A,F,G) != k1_xboole_0
                                   => k8_functor0(A,B,k13_functor0(A,C,B,E,D),F,G,H) = k6_functor0(C,B,D,k3_functor0(A,C,E,G),k3_functor0(A,C,E,F),k8_functor0(A,C,E,F,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t10_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ( ( r1_functor2(A,B,D,E)
                                  & r1_functor2(B,C,F,G) )
                               => r1_functor2(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(d1_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( m1_functor2(F,A,B,D,E)
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ( r1_functor2(A,B,D,E)
                               => ! [H] :
                                    ( m1_functor2(H,A,C,k1_functor3(A,B,C,D,G),k1_functor3(A,B,C,E,G))
                                   => ( H = k5_functor3(A,B,C,D,E,F,G)
                                    <=> ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => k1_funct_1(H,I) = k6_functor0(B,C,G,k3_functor0(A,B,D,I),k3_functor0(A,B,E,I),k2_functor2(A,B,D,E,F,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t11_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,C,B)
                    & m2_functor0(D,C,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,C,B)
                        & m2_functor0(E,C,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,A)
                            & m2_functor0(F,B,A) )
                         => ! [G] :
                              ( m1_functor2(G,C,B,D,E)
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(C))
                                 => ( r1_functor2(C,B,D,E)
                                   => k2_functor2(C,A,k1_functor3(C,B,A,D,F),k1_functor3(C,B,A,E,F),k5_functor3(C,B,A,D,E,G,F),H) = k6_functor0(B,A,F,k3_functor0(C,B,D,H),k3_functor0(C,B,E,H),k2_functor2(C,B,D,E,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(d2_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,B,C)
                    & m2_functor0(D,B,C) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,A,B)
                            & m2_functor0(F,A,B) )
                         => ! [G] :
                              ( m1_functor2(G,B,C,D,E)
                             => ( r1_functor2(B,C,D,E)
                               => ! [H] :
                                    ( m1_functor2(H,A,C,k1_functor3(A,B,C,F,D),k1_functor3(A,B,C,F,E))
                                   => ( H = k6_functor3(A,B,C,D,E,F,G)
                                    <=> ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => k1_funct_1(H,I) = k2_functor2(B,C,D,E,G,k3_functor0(A,B,F,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,C,A)
                    & m2_functor0(D,C,A) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,A,B)
                            & m2_functor0(F,A,B) )
                         => ! [G] :
                              ( m1_functor2(G,A,B,E,F)
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(C))
                                 => ( r1_functor2(A,B,E,F)
                                   => k2_functor2(C,B,k1_functor3(C,A,B,D,E),k1_functor3(C,A,B,D,F),k6_functor3(C,A,B,E,F,D,G),H) = k2_functor2(A,B,E,F,G,k3_functor0(C,A,D,H)) ) ) ) ) ) ) ) ) ) )).

fof(t13_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,B,C)
                    & m2_functor0(D,B,C) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( ( v15_functor0(G,C,A)
                                & m2_functor0(G,C,A) )
                             => ! [H] :
                                  ( m1_functor2(H,B,C,D,E)
                                 => ! [I] :
                                      ( m1_functor2(I,B,C,E,F)
                                     => ( ( r1_functor2(B,C,D,E)
                                          & r1_functor2(B,C,E,F) )
                                       => r6_pboole(u1_struct_0(B),k5_functor3(B,C,A,D,F,k3_functor2(B,C,D,E,F,H,I),G),k3_functor2(B,A,k1_functor3(B,C,A,D,G),k1_functor3(B,C,A,E,G),k1_functor3(B,C,A,F,G),k5_functor3(B,C,A,D,E,H,G),k5_functor3(B,C,A,E,F,I,G))) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ! [H] :
                                  ( m1_functor2(H,B,C,E,F)
                                 => ! [I] :
                                      ( m1_functor2(I,B,C,F,G)
                                     => ( ( r1_functor2(B,C,E,F)
                                          & r1_functor2(B,C,F,G) )
                                       => r6_pboole(u1_struct_0(A),k6_functor3(A,B,C,E,G,D,k3_functor2(B,C,E,F,G,H,I)),k3_functor2(A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,D,G),k6_functor3(A,B,C,E,F,D,H),k6_functor3(A,B,C,F,G,D,I))) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_altcat_1(D)
                    & v12_altcat_1(D)
                    & l2_altcat_1(D) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( ( v15_functor0(G,C,D)
                                & m2_functor0(G,C,D) )
                             => ! [H] :
                                  ( ( v15_functor0(H,C,D)
                                    & m2_functor0(H,C,D) )
                                 => ! [I] :
                                      ( m1_functor2(I,C,D,G,H)
                                     => ( r1_functor2(C,D,G,H)
                                       => r6_pboole(u1_struct_0(A),k6_functor3(A,B,D,k1_functor3(B,C,D,F,G),k1_functor3(B,C,D,F,H),E,k6_functor3(B,C,D,G,H,F,I)),k6_functor3(A,C,D,G,H,k1_functor3(A,B,C,E,F),I)) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_altcat_1(D)
                    & v12_altcat_1(D)
                    & l2_altcat_1(D) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,C)
                        & m2_functor0(E,A,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,C,D)
                            & m2_functor0(F,C,D) )
                         => ! [G] :
                              ( ( v15_functor0(G,C,D)
                                & m2_functor0(G,C,D) )
                             => ! [H] :
                                  ( ( v15_functor0(H,D,B)
                                    & m2_functor0(H,D,B) )
                                 => ! [I] :
                                      ( m1_functor2(I,C,D,F,G)
                                     => ( r1_functor2(C,D,F,G)
                                       => r6_pboole(u1_struct_0(A),k6_functor3(A,C,B,k1_functor3(C,D,B,F,H),k1_functor3(C,D,B,G,H),E,k5_functor3(C,D,B,F,G,I,H)),k5_functor3(A,D,B,k1_functor3(A,C,D,E,F),k1_functor3(A,C,D,E,G),k6_functor3(A,C,D,F,G,E,I),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t17_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_altcat_1(D)
                    & v12_altcat_1(D)
                    & l2_altcat_1(D) )
                 => ! [E] :
                      ( ( v15_functor0(E,C,D)
                        & m2_functor0(E,C,D) )
                     => ! [F] :
                          ( ( v15_functor0(F,C,D)
                            & m2_functor0(F,C,D) )
                         => ! [G] :
                              ( ( v15_functor0(G,D,A)
                                & m2_functor0(G,D,A) )
                             => ! [H] :
                                  ( ( v15_functor0(H,A,B)
                                    & m2_functor0(H,A,B) )
                                 => ! [I] :
                                      ( m1_functor2(I,C,D,E,F)
                                     => ( r1_functor2(C,D,E,F)
                                       => r6_pboole(u1_struct_0(C),k5_functor3(C,D,B,E,F,I,k1_functor3(D,A,B,G,H)),k5_functor3(C,A,B,k1_functor3(C,D,A,E,G),k1_functor3(C,D,A,F,G),k5_functor3(C,D,A,E,F,I,G),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => r6_pboole(u1_struct_0(A),k6_functor3(A,B,C,E,E,D,k4_functor2(B,C,E)),k4_functor2(A,C,k1_functor3(A,B,C,D,E))) ) ) ) ) ) )).

fof(t19_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => r6_pboole(u1_struct_0(A),k5_functor3(A,B,C,D,D,k4_functor2(A,B,D),E),k4_functor2(A,C,k1_functor3(A,B,C,D,E))) ) ) ) ) ) )).

fof(t20_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_functor2(E,A,B,C,D)
                     => ( r1_functor2(A,B,C,D)
                       => r6_pboole(u1_struct_0(A),k5_functor3(A,B,B,C,D,E,k12_functor0(B)),E) ) ) ) ) ) ) )).

fof(t21_functor3,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,B,A)
                & m2_functor0(C,B,A) )
             => ! [D] :
                  ( ( v15_functor0(D,B,A)
                    & m2_functor0(D,B,A) )
                 => ! [E] :
                      ( m1_functor2(E,B,A,C,D)
                     => ( r1_functor2(B,A,C,D)
                       => r6_pboole(u1_struct_0(B),k6_functor3(B,B,A,C,D,k12_functor0(B),E),E) ) ) ) ) ) ) )).

fof(d3_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ! [H] :
                                  ( m1_functor2(H,A,B,D,E)
                                 => ! [I] :
                                      ( m1_functor2(I,B,C,F,G)
                                     => k7_functor3(A,B,C,D,E,F,G,H,I) = k3_functor2(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,F),k1_functor3(A,B,C,E,G),k5_functor3(A,B,C,D,E,H,F),k6_functor3(A,B,C,F,G,E,I)) ) ) ) ) ) ) ) ) ) )).

fof(t22_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,B,C)
                    & m2_functor0(D,B,C) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,C,A)
                            & m2_functor0(F,C,A) )
                         => ! [G] :
                              ( ( v15_functor0(G,C,A)
                                & m2_functor0(G,C,A) )
                             => ! [H] :
                                  ( m1_functor2(H,B,C,D,E)
                                 => ! [I] :
                                      ( m2_functor2(I,C,A,F,G)
                                     => ( ( r1_functor2(B,C,D,E)
                                          & r2_functor2(C,A,F,G) )
                                       => r6_pboole(u1_struct_0(B),k7_functor3(B,C,A,D,E,F,G,H,I),k3_functor2(B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,D,G),k1_functor3(B,C,A,E,G),k6_functor3(B,C,A,F,G,D,I),k5_functor3(B,C,A,D,E,H,G))) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_functor2(E,A,B,C,D)
                     => ( r1_functor2(A,B,C,D)
                       => r6_pboole(u1_struct_0(A),k7_functor3(A,B,B,C,D,k12_functor0(B),k12_functor0(B),E,k4_functor2(B,B,k12_functor0(B))),E) ) ) ) ) ) ) )).

fof(t24_functor3,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,B,A)
                & m2_functor0(C,B,A) )
             => ! [D] :
                  ( ( v15_functor0(D,B,A)
                    & m2_functor0(D,B,A) )
                 => ! [E] :
                      ( m1_functor2(E,B,A,C,D)
                     => ( r1_functor2(B,A,C,D)
                       => r6_pboole(u1_struct_0(B),k7_functor3(B,B,A,k12_functor0(B),k12_functor0(B),C,D,k4_functor2(B,B,k12_functor0(B)),E),E) ) ) ) ) ) ) )).

fof(t25_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,B,C)
                    & m2_functor0(D,B,C) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,C,A)
                            & m2_functor0(F,C,A) )
                         => ! [G] :
                              ( m1_functor2(G,B,C,D,E)
                             => ( r1_functor2(B,C,D,E)
                               => r6_pboole(u1_struct_0(B),k5_functor3(B,C,A,D,E,G,F),k7_functor3(B,C,A,D,E,F,F,G,k4_functor2(C,A,F))) ) ) ) ) ) ) ) ) )).

fof(t26_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( m1_functor2(G,B,C,E,F)
                             => ( r1_functor2(B,C,E,F)
                               => r6_pboole(u1_struct_0(A),k6_functor3(A,B,C,E,F,D,G),k7_functor3(A,B,C,D,D,E,F,k4_functor2(A,B,D),G)) ) ) ) ) ) ) ) ) )).

fof(t27_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_altcat_1(D)
                    & v11_altcat_1(D)
                    & v12_altcat_1(D)
                    & l2_altcat_1(D) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,A,B)
                            & m2_functor0(F,A,B) )
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ! [H] :
                                  ( ( v15_functor0(H,B,C)
                                    & m2_functor0(H,B,C) )
                                 => ! [I] :
                                      ( ( v15_functor0(I,C,D)
                                        & m2_functor0(I,C,D) )
                                     => ! [J] :
                                          ( ( v15_functor0(J,C,D)
                                            & m2_functor0(J,C,D) )
                                         => ! [K] :
                                              ( m1_functor2(K,A,B,E,F)
                                             => ! [L] :
                                                  ( m1_functor2(L,B,C,G,H)
                                                 => ! [M] :
                                                      ( m1_functor2(M,C,D,I,J)
                                                     => ( ( r1_functor2(A,B,E,F)
                                                          & r1_functor2(B,C,G,H)
                                                          & r1_functor2(C,D,I,J) )
                                                       => r6_pboole(u1_struct_0(A),k7_functor3(A,B,D,E,F,k1_functor3(B,C,D,G,I),k1_functor3(B,C,D,H,J),K,k7_functor3(B,C,D,G,H,I,J,L,M)),k7_functor3(A,C,D,k1_functor3(A,B,C,E,G),k1_functor3(A,B,C,F,H),I,J,k7_functor3(A,B,C,E,F,G,H,K,L),M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t28_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,B,C)
                    & m2_functor0(D,B,C) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,C,A)
                            & m2_functor0(F,C,A) )
                         => ! [G] :
                              ( m2_functor2(G,B,C,D,E)
                             => ( r2_functor2(B,C,D,E)
                               => m2_functor2(k5_functor3(B,C,A,D,E,G,F),B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,E,F)) ) ) ) ) ) ) ) ) )).

fof(t29_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( m2_functor2(G,B,C,E,F)
                             => ( r2_functor2(B,C,E,F)
                               => m2_functor2(k6_functor3(A,B,C,E,F,D,G),A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F)) ) ) ) ) ) ) ) ) )).

fof(t30_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ! [H] :
                                  ( m2_functor2(H,A,B,D,E)
                                 => ! [I] :
                                      ( m2_functor2(I,B,C,F,G)
                                     => ( ( r2_functor2(A,B,D,E)
                                          & r2_functor2(B,C,F,G) )
                                       => ( r2_functor2(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G))
                                          & m2_functor2(k7_functor3(A,B,C,D,E,F,G,H,I),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t31_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,A,B)
                            & m2_functor0(F,A,B) )
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ! [H] :
                                  ( ( v15_functor0(H,B,C)
                                    & m2_functor0(H,B,C) )
                                 => ! [I] :
                                      ( ( v15_functor0(I,B,C)
                                        & m2_functor0(I,B,C) )
                                     => ! [J] :
                                          ( m2_functor2(J,B,C,G,H)
                                         => ! [K] :
                                              ( m2_functor2(K,B,C,H,I)
                                             => ! [L] :
                                                  ( m1_functor2(L,A,B,D,E)
                                                 => ! [M] :
                                                      ( m1_functor2(M,A,B,E,F)
                                                     => ( ( r2_functor2(A,B,D,E)
                                                          & r2_functor2(A,B,E,F)
                                                          & r2_functor2(B,C,G,H)
                                                          & r2_functor2(B,C,H,I) )
                                                       => r6_pboole(u1_struct_0(A),k7_functor3(A,B,C,D,F,G,I,k3_functor2(A,B,D,E,F,L,M),k5_functor2(B,C,G,H,I,J,K)),k3_functor2(A,C,k1_functor3(A,B,C,D,G),k1_functor3(A,B,C,E,H),k1_functor3(A,B,C,F,I),k7_functor3(A,B,C,D,E,G,H,L,J),k7_functor3(A,B,C,E,F,H,I,M,K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t32_functor3,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,B,A)
                & m2_functor0(C,B,A) )
             => ! [D] :
                  ( ( v15_functor0(D,B,A)
                    & m2_functor0(D,B,A) )
                 => ! [E] :
                      ( m2_functor2(E,B,A,C,D)
                     => ( ( r2_functor2(B,A,C,D)
                          & r1_functor2(B,A,D,C)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => v3_altcat_3(k2_functor2(B,A,C,D,E,F),A,k3_functor0(B,A,C,F),k3_functor0(B,A,D,F)) ) )
                       => ( r2_functor2(B,A,D,C)
                          & ? [F] :
                              ( m2_functor2(F,B,A,D,C)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ( k1_funct_1(F,G) = k1_altcat_3(A,k3_functor0(B,A,C,G),k3_functor0(B,A,D,G),k2_functor2(B,A,C,D,E,G))
                                    & v3_altcat_3(k2_functor2(B,A,D,C,F,G),A,k3_functor0(B,A,D,G),k3_functor0(B,A,C,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ( r1_functor3(A,B,C,D)
                  <=> ( r2_functor2(A,B,C,D)
                      & r1_functor2(A,B,D,C)
                      & ? [E] :
                          ( m2_functor2(E,A,B,C,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => v3_altcat_3(k2_functor2(A,B,C,D,E,F),B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F)) ) ) ) ) ) ) ) ) )).

fof(d5_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ( r1_functor3(A,B,C,D)
                   => ! [E] :
                        ( m2_functor2(E,A,B,C,D)
                       => ( m1_functor3(E,A,B,C,D)
                        <=> ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => v3_altcat_3(k2_functor2(A,B,C,D,E,F),B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F)) ) ) ) ) ) ) ) ) )).

fof(t33_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ( ( r1_functor3(A,B,C,D)
                          & r1_functor3(A,B,D,E) )
                       => r1_functor3(A,B,C,E) ) ) ) ) ) ) )).

fof(t34_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( m1_functor3(F,A,B,C,D)
                         => ! [G] :
                              ( m1_functor3(G,A,B,D,E)
                             => ( ( r1_functor3(A,B,C,D)
                                  & r1_functor3(A,B,D,E) )
                               => m1_functor3(k5_functor2(A,B,C,D,E,F,G),A,B,C,E) ) ) ) ) ) ) ) ) )).

fof(t35_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,B,C)
                    & m2_functor0(D,B,C) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,C,A)
                            & m2_functor0(F,C,A) )
                         => ! [G] :
                              ( m1_functor3(G,B,C,D,E)
                             => ( r1_functor3(B,C,D,E)
                               => ( r1_functor3(B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,E,F))
                                  & m1_functor3(k5_functor3(B,C,A,D,E,G,F),B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,E,F)) ) ) ) ) ) ) ) ) ) )).

fof(t36_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( m1_functor3(G,B,C,E,F)
                             => ( r1_functor3(B,C,E,F)
                               => ( r1_functor3(A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F))
                                  & m1_functor3(k6_functor3(A,B,C,E,F,D,G),A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F)) ) ) ) ) ) ) ) ) ) )).

fof(t37_functor3,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] :
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v15_functor0(F,B,C)
                            & m2_functor0(F,B,C) )
                         => ! [G] :
                              ( ( v15_functor0(G,B,C)
                                & m2_functor0(G,B,C) )
                             => ! [H] :
                                  ( m1_functor3(H,A,B,D,E)
                                 => ! [I] :
                                      ( m1_functor3(I,B,C,F,G)
                                     => ( ( r1_functor3(A,B,D,E)
                                          & r1_functor3(B,C,F,G) )
                                       => ( r1_functor3(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G))
                                          & m1_functor3(k7_functor3(A,B,C,D,E,F,G,H,I),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_functor3(E,A,B,C,D)
                     => ( r1_functor3(A,B,C,D)
                       => ! [F] :
                            ( m1_functor3(F,A,B,D,C)
                           => ( F = k8_functor3(A,B,C,D,E)
                            <=> ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => k1_funct_1(F,G) = k1_altcat_3(B,k3_functor0(A,B,C,G),k3_functor0(A,B,D,G),k2_functor2(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) )).

fof(t38_functor3,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,B,A)
                & m2_functor0(C,B,A) )
             => ! [D] :
                  ( ( v15_functor0(D,B,A)
                    & m2_functor0(D,B,A) )
                 => ! [E] :
                      ( m1_functor3(E,B,A,C,D)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( r1_functor3(B,A,C,D)
                           => k2_functor2(B,A,D,C,k8_functor3(B,A,C,D,E),F) = k1_altcat_3(A,k3_functor0(B,A,C,F),k3_functor0(B,A,D,F),k2_functor2(B,A,C,D,E,F)) ) ) ) ) ) ) ) )).

fof(t39_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_functor3(E,A,B,C,D)
                     => ( r1_functor3(A,B,C,D)
                       => r6_pboole(u1_struct_0(A),k5_functor2(A,B,D,C,D,k8_functor3(A,B,C,D,E),E),k4_functor2(A,B,D)) ) ) ) ) ) ) )).

fof(t40_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_functor3(E,A,B,C,D)
                     => ( r1_functor3(A,B,C,D)
                       => r6_pboole(u1_struct_0(A),k5_functor2(A,B,C,D,C,E,k8_functor3(A,B,C,D,E)),k4_functor2(A,B,C)) ) ) ) ) ) ) )).

fof(t41_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_functor3(E,A,B,C,D)
                     => ( r1_functor3(A,B,C,D)
                       => r6_pboole(u1_struct_0(A),k8_functor3(A,B,D,C,k8_functor3(A,B,C,D,E)),E) ) ) ) ) ) ) )).

fof(t42_functor3,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] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,A,B)
                        & m2_functor0(E,A,B) )
                     => ! [F] :
                          ( m1_functor3(F,A,B,C,E)
                         => ! [G] :
                              ( m1_functor3(G,A,B,E,D)
                             => ! [H] :
                                  ( m1_functor3(H,A,B,C,D)
                                 => ( ( r6_pboole(u1_struct_0(A),H,k5_functor2(A,B,C,E,D,F,G))
                                      & r1_functor3(A,B,C,E)
                                      & r1_functor3(A,B,E,D) )
                                   => r6_pboole(u1_struct_0(A),k8_functor3(A,B,C,D,H),k5_functor2(A,B,D,E,C,k8_functor3(A,B,E,D,G),k8_functor3(A,B,C,E,F))) ) ) ) ) ) ) ) ) ) )).

fof(t43_functor3,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) )
             => r6_pboole(u1_struct_0(A),k8_functor3(A,B,C,C,k9_functor3(A,B,C)),k9_functor3(A,B,C)) ) ) ) )).

fof(dt_m1_functor3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => ! [E] :
          ( m1_functor3(E,A,B,C,D)
         => m2_functor2(E,A,B,C,D) ) ) )).

fof(existence_m1_functor3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => ? [E] : m1_functor3(E,A,B,C,D) ) )).

fof(symmetry_r1_functor3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => ( r1_functor3(A,B,C,D)
       => r1_functor3(A,B,D,C) ) ) )).

fof(reflexivity_r1_functor3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => r1_functor3(A,B,C,C) ) )).

fof(dt_k1_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => ( v9_functor0(k1_functor3(A,B,C,D,E),A,C)
        & v15_functor0(k1_functor3(A,B,C,D,E),A,C)
        & m2_functor0(k1_functor3(A,B,C,D,E),A,C) ) ) )).

fof(redefinition_k1_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => k1_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) )).

fof(dt_k2_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => ( v9_functor0(k2_functor3(A,B,C,D,E),A,C)
        & v15_functor0(k2_functor3(A,B,C,D,E),A,C)
        & m2_functor0(k2_functor3(A,B,C,D,E),A,C) ) ) )).

fof(redefinition_k2_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => k2_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) )).

fof(dt_k3_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => ( v9_functor0(k3_functor3(A,B,C,D,E),A,C)
        & v16_functor0(k3_functor3(A,B,C,D,E),A,C)
        & m2_functor0(k3_functor3(A,B,C,D,E),A,C) ) ) )).

fof(redefinition_k3_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => k3_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) )).

fof(dt_k4_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => ( v9_functor0(k4_functor3(A,B,C,D,E),A,C)
        & v16_functor0(k4_functor3(A,B,C,D,E),A,C)
        & m2_functor0(k4_functor3(A,B,C,D,E),A,C) ) ) )).

fof(redefinition_k4_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => k4_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) )).

fof(dt_k5_functor3,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,A,B)
        & m2_functor0(E,A,B)
        & m1_functor2(F,A,B,D,E)
        & v15_functor0(G,B,C)
        & m2_functor0(G,B,C) )
     => m1_functor2(k5_functor3(A,B,C,D,E,F,G),A,C,k1_functor3(A,B,C,D,G),k1_functor3(A,B,C,E,G)) ) )).

fof(dt_k6_functor3,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,B,C)
        & m2_functor0(D,B,C)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C)
        & v15_functor0(F,A,B)
        & m2_functor0(F,A,B)
        & m1_functor2(G,B,C,D,E) )
     => m1_functor2(k6_functor3(A,B,C,D,E,F,G),A,C,k1_functor3(A,B,C,F,D),k1_functor3(A,B,C,F,E)) ) )).

fof(dt_k7_functor3,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,A,B)
        & m2_functor0(E,A,B)
        & v15_functor0(F,B,C)
        & m2_functor0(F,B,C)
        & v15_functor0(G,B,C)
        & m2_functor0(G,B,C)
        & m1_functor2(H,A,B,D,E)
        & m1_functor2(I,B,C,F,G) )
     => m1_functor2(k7_functor3(A,B,C,D,E,F,G,H,I),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) )).

fof(dt_k8_functor3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & m1_functor3(E,A,B,C,D) )
     => m1_functor3(k8_functor3(A,B,C,D,E),A,B,D,C) ) )).

fof(dt_k9_functor3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B) )
     => m1_functor3(k9_functor3(A,B,C),A,B,C,C) ) )).

fof(redefinition_k9_functor3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B) )
     => k9_functor3(A,B,C) = k1_functor2(A,B,C) ) )).
%------------------------------------------------------------------------------