SET007 Axioms: SET007+697.ax


%------------------------------------------------------------------------------
% File     : SET007+697 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Miscellaneous Facts about Functors
% 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    : yellow20 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   79 (   0 unit)
%            Number of atoms       : 1240 ( 148 equality)
%            Maximal formula depth :   38 (  15 average)
%            Number of connectives : 1318 ( 157 ~  ;   9  |; 676  &)
%                                         (  22 <=>; 454 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   52 (   0 propositional; 1-5 arity)
%            Number of functors    :   59 (  18 constant; 0-6 arity)
%            Number of variables   :  423 (   0 singleton; 403 !;  20 ?)
%            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(fc1_yellow20,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_binop_1(A,B,C))
        & v1_funct_1(k1_binop_1(A,B,C)) ) ) )).

fof(fc2_yellow20,axiom,(
    ! [A,B] :
      ( ( ~ 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)
        & v3_altcat_2(B,A)
        & m1_altcat_2(B,A) )
     => ( v6_functor0(k10_functor0(A,B),B,A)
        & v8_functor0(k10_functor0(A,B),B,A)
        & v9_functor0(k10_functor0(A,B),B,A)
        & v10_functor0(k10_functor0(A,B),B,A)
        & v12_functor0(k10_functor0(A,B),B,A)
        & v13_functor0(k10_functor0(A,B),B,A) ) ) )).

fof(fc3_yellow20,axiom,(
    ! [A,B] :
      ( ( ~ 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)
        & v3_altcat_2(B,A)
        & m1_altcat_2(B,A) )
     => ( v6_functor0(k10_functor0(A,B),B,A)
        & v8_functor0(k10_functor0(A,B),B,A)
        & v9_functor0(k10_functor0(A,B),B,A)
        & v10_functor0(k10_functor0(A,B),B,A)
        & v12_functor0(k10_functor0(A,B),B,A)
        & v13_functor0(k10_functor0(A,B),B,A) ) ) )).

fof(t1_yellow20,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] :
              ( ( v6_functor0(C,A,B)
                & v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v7_functor0(C,A,B)
                  & v21_functor0(C,A,B) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( k3_functor0(A,B,C,D) = E
                        <=> k3_functor0(B,A,k15_functor0(A,B,C),E) = D ) ) ) ) ) ) ) )).

fof(t2_yellow20,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] :
              ( ( v8_functor0(C,A,B)
                & v10_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( ( v8_functor0(D,B,A)
                    & v10_functor0(D,B,A)
                    & l2_functor0(D,B,A) )
                 => ( ( v21_functor0(C,A,B)
                      & D = k15_functor0(A,B,C) )
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k1_altcat_1(A,E,F) != k1_xboole_0
                             => ! [G] :
                                  ( m1_subset_1(G,k1_altcat_1(A,E,F))
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F)))
                                     => ( k6_functor0(A,B,C,E,F,G) = H
                                      <=> k6_functor0(B,A,D,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),H) = G ) ) ) ) ) ) ) ) ) ) ) )).

fof(t3_yellow20,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] :
              ( ( v8_functor0(C,A,B)
                & v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( ( v8_functor0(D,B,A)
                    & v11_functor0(D,B,A)
                    & l2_functor0(D,B,A) )
                 => ( ( v21_functor0(C,A,B)
                      & D = k15_functor0(A,B,C) )
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k1_altcat_1(A,E,F) != k1_xboole_0
                             => ! [G] :
                                  ( m1_subset_1(G,k1_altcat_1(A,E,F))
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E)))
                                     => ( k8_functor0(A,B,C,E,F,G) = H
                                      <=> k8_functor0(B,A,D,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),H) = G ) ) ) ) ) ) ) ) ) ) ) )).

fof(t4_yellow20,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] :
              ( m2_functor0(C,A,B)
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( m2_functor0(D,B,A)
                   => ( k13_functor0(B,A,B,D,C) = k12_functor0(B)
                     => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).

fof(t5_yellow20,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] :
              ( m2_functor0(C,A,B)
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( m2_functor0(D,B,A)
                   => ( k13_functor0(A,B,A,C,D) = k12_functor0(A)
                     => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).

fof(t6_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( ( v15_functor0(D,B,A)
                      & m2_functor0(D,B,A) )
                   => ( ( ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => k3_functor0(A,B,C,k3_functor0(B,A,D,E)) = E )
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => ! [F] :
                                ( m1_subset_1(F,u1_struct_0(B))
                               => ( k1_altcat_1(B,E,F) != k1_xboole_0
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_altcat_1(B,E,F))
                                     => k6_functor0(A,B,C,k3_functor0(B,A,D,E),k3_functor0(B,A,D,F),k6_functor0(B,A,D,E,F,G)) = G ) ) ) ) )
                     => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).

fof(t7_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( ( v16_functor0(D,B,A)
                      & m2_functor0(D,B,A) )
                   => ( ( ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => k3_functor0(A,B,C,k3_functor0(B,A,D,E)) = E )
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => ! [F] :
                                ( m1_subset_1(F,u1_struct_0(B))
                               => ( k1_altcat_1(B,E,F) != k1_xboole_0
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_altcat_1(B,E,F))
                                     => k8_functor0(A,B,C,k3_functor0(B,A,D,F),k3_functor0(B,A,D,E),k8_functor0(B,A,D,E,F,G)) = G ) ) ) ) )
                     => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).

fof(t8_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( ( v15_functor0(D,B,A)
                      & m2_functor0(D,B,A) )
                   => ( ( ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => k3_functor0(B,A,D,k3_functor0(A,B,C,E)) = E )
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ( k1_altcat_1(A,E,F) != k1_xboole_0
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_altcat_1(A,E,F))
                                     => k6_functor0(B,A,D,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),k6_functor0(A,B,C,E,F,G)) = G ) ) ) ) )
                     => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).

fof(t9_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( ( v16_functor0(D,B,A)
                      & m2_functor0(D,B,A) )
                   => ( ( ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => k3_functor0(B,A,D,k3_functor0(A,B,C,E)) = E )
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ( k1_altcat_1(A,E,F) != k1_xboole_0
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_altcat_1(A,E,F))
                                     => k8_functor0(B,A,D,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),k8_functor0(A,B,C,E,F,G)) = G ) ) ) ) )
                     => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).

fof(d1_yellow20,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( l2_altcat_1(B)
         => ( r1_yellow20(A,B)
          <=> ! [C,D,E] : r1_partfun1(k1_funct_1(u2_altcat_1(A),k3_mcart_1(C,D,E)),k1_funct_1(u2_altcat_1(B),k3_mcart_1(C,D,E))) ) ) ) )).

fof(t10_yellow20,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( l2_altcat_1(B)
         => ( r1_yellow20(A,B)
          <=> ! [C,D,E,F] :
                ( ( r2_hidden(F,k1_relat_1(k1_funct_1(u2_altcat_1(A),k3_mcart_1(C,D,E))))
                  & r2_hidden(F,k1_relat_1(k1_funct_1(u2_altcat_1(B),k3_mcart_1(C,D,E)))) )
               => k1_funct_1(k1_funct_1(u2_altcat_1(A),k3_mcart_1(C,D,E)),F) = k1_funct_1(k1_funct_1(u2_altcat_1(B),k3_mcart_1(C,D,E)),F) ) ) ) ) )).

fof(t11_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & l2_altcat_1(B) )
         => ( r1_yellow20(A,B)
          <=> ! [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))
                       => ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
                            & k1_altcat_1(A,D,E) != k1_xboole_0
                            & ? [F] :
                                ( m1_subset_1(F,u1_struct_0(B))
                                & ? [G] :
                                    ( m1_subset_1(G,u1_struct_0(B))
                                    & ? [H] :
                                        ( m1_subset_1(H,u1_struct_0(B))
                                        & k1_altcat_1(B,F,G) != k1_xboole_0
                                        & k1_altcat_1(B,G,H) != k1_xboole_0
                                        & F = C
                                        & G = D
                                        & H = E
                                        & ? [I] :
                                            ( m1_subset_1(I,k1_altcat_1(A,C,D))
                                            & ? [J] :
                                                ( m1_subset_1(J,k1_altcat_1(B,F,G))
                                                & J = I
                                                & ? [K] :
                                                    ( m1_subset_1(K,k1_altcat_1(A,D,E))
                                                    & ? [L] :
                                                        ( m1_subset_1(L,k1_altcat_1(B,G,H))
                                                        & L = K
                                                        & k5_altcat_1(A,C,D,E,I,K) != k5_altcat_1(B,F,G,H,J,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v9_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v9_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & v2_yellow18(B)
            & l2_altcat_1(B) )
         => r1_yellow20(A,B) ) ) )).

fof(d2_yellow20,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_yellow20(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] :
                      ( r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => k1_funct_1(C,D) = k3_xboole_0(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(t13_yellow20,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => k1_yellow20(B,C) = k3_pboole(A,B,C) ) ) )).

fof(t14_yellow20,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,A)
     => ! [D] :
          ( m1_pboole(D,B)
         => m1_pboole(k1_yellow20(C,D),k3_xboole_0(A,B)) ) ) )).

fof(t15_yellow20,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,A)
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ! [E] :
              ( m1_pboole(E,B)
             => ( E = k1_yellow20(C,D)
               => r2_altcat_2(B,A,E,C) ) ) ) ) )).

fof(t16_yellow20,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m2_relset_1(E,A,B) )
     => ! [F] :
          ( ( v1_funct_1(F)
            & v1_funct_2(F,C,D)
            & m2_relset_1(F,C,D) )
         => ( r1_partfun1(E,F)
           => ( v1_funct_1(k3_xboole_0(E,F))
              & v1_funct_2(k3_xboole_0(E,F),k3_xboole_0(A,C),k3_xboole_0(B,D))
              & m2_relset_1(k3_xboole_0(E,F),k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ) ) ) )).

fof(t17_yellow20,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,A)
     => ! [D] :
          ( m1_pboole(D,A)
         => ! [E] :
              ( m1_pboole(E,B)
             => ! [F] :
                  ( m1_pboole(F,B)
                 => ! [G] :
                      ( m1_pboole(G,k3_xboole_0(A,B))
                     => ! [H] :
                          ( m1_pboole(H,k3_xboole_0(A,B))
                         => ( ( G = k1_yellow20(C,E)
                              & H = k1_yellow20(D,F) )
                           => ! [I] :
                                ( m3_pboole(I,A,C,D)
                               => ! [J] :
                                    ( m3_pboole(J,B,E,F)
                                   => ( ! [K] :
                                          ( ( r2_hidden(K,k1_relat_1(I))
                                            & r2_hidden(K,k1_relat_1(J)) )
                                         => r1_partfun1(k1_funct_1(I,K),k1_funct_1(J,K)) )
                                     => m3_pboole(k1_yellow20(I,J),k3_xboole_0(A,B),G,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_yellow20,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,k2_zfmisc_1(A,A))
     => ! [D] :
          ( m1_pboole(D,k2_zfmisc_1(B,B))
         => ? [E] :
              ( m1_pboole(E,k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(A,B)))
              & E = k1_yellow20(C,D)
              & k1_yellow20(k2_altcat_1(A,C),k2_altcat_1(B,D)) = k2_altcat_1(k3_xboole_0(A,B),E) ) ) ) )).

fof(t19_yellow20,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,k2_zfmisc_1(A,A))
     => ! [D] :
          ( m1_pboole(D,k2_zfmisc_1(A,A))
         => ! [E] :
              ( m1_pboole(E,k2_zfmisc_1(B,B))
             => ! [F] :
                  ( m1_pboole(F,k2_zfmisc_1(B,B))
                 => ? [G] :
                      ( m1_pboole(G,k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(A,B)))
                      & ? [H] :
                          ( m1_pboole(H,k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(A,B)))
                          & G = k1_yellow20(C,E)
                          & H = k1_yellow20(D,F)
                          & k1_yellow20(k3_altcat_1(A,C,D),k3_altcat_1(B,E,F)) = k3_altcat_1(k3_xboole_0(A,B),G,H) ) ) ) ) ) ) )).

fof(d3_yellow20,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( l2_altcat_1(B)
         => ( r1_yellow20(A,B)
           => ! [C] :
                ( ( v6_altcat_1(C)
                  & l2_altcat_1(C) )
               => ( C = k2_yellow20(A,B)
                <=> ( u1_struct_0(C) = k3_xboole_0(u1_struct_0(A),u1_struct_0(B))
                    & u1_altcat_1(C) = k1_yellow20(u1_altcat_1(A),u1_altcat_1(B))
                    & u2_altcat_1(C) = k1_yellow20(u2_altcat_1(A),u2_altcat_1(B)) ) ) ) ) ) ) )).

fof(t20_yellow20,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( l2_altcat_1(B)
         => ( r1_yellow20(A,B)
           => k2_yellow20(A,B) = k2_yellow20(B,A) ) ) ) )).

fof(t21_yellow20,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( l2_altcat_1(B)
         => ( r1_yellow20(A,B)
           => m1_altcat_2(k2_yellow20(A,B),A) ) ) ) )).

fof(t22_yellow20,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( l2_altcat_1(B)
         => ( r1_yellow20(A,B)
           => ! [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,u1_struct_0(k2_yellow20(A,B)))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(k2_yellow20(A,B)))
                                   => ( ( G = C
                                        & G = E
                                        & H = D
                                        & H = F )
                                     => k1_altcat_1(k2_yellow20(A,B),G,H) = k3_xboole_0(k1_altcat_1(A,C,D),k1_altcat_1(B,E,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_yellow20,axiom,(
    ! [A] :
      ( ( v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( v2_altcat_1(B)
            & l2_altcat_1(B) )
         => ( r1_yellow20(A,B)
           => v2_altcat_1(k2_yellow20(A,B)) ) ) ) )).

fof(t24_yellow20,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( l2_altcat_1(B)
         => ( r1_yellow20(A,B)
           => ! [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,u1_struct_0(k2_yellow20(A,B)))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(k2_yellow20(A,B)))
                                   => ( ( G = C
                                        & G = E
                                        & H = D
                                        & H = F )
                                     => ( k1_altcat_1(A,C,D) = k1_xboole_0
                                        | k1_altcat_1(B,E,F) = k1_xboole_0
                                        | ! [I] :
                                            ( m1_subset_1(I,k1_altcat_1(A,C,D))
                                           => ! [J] :
                                                ( m1_subset_1(J,k1_altcat_1(B,E,F))
                                               => ( I = J
                                                 => r2_hidden(I,k1_altcat_1(k2_yellow20(A,B),G,H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ( r1_yellow20(A,B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k2_yellow20(A,B)))
                       => ( ( E = C
                            & E = D
                            & k8_altcat_1(A,C) = k8_altcat_1(B,D) )
                         => r2_hidden(k8_altcat_1(A,C),k1_altcat_1(k2_yellow20(A,B),E,E)) ) ) ) ) ) ) ) )).

fof(t26_yellow20,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) )
         => ( ( r1_yellow20(A,B)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ( C = D
                       => k8_altcat_1(A,C) = k8_altcat_1(B,D) ) ) ) )
           => ( v3_struct_0(k2_yellow20(A,B))
              | ( v2_altcat_1(k2_yellow20(A,B))
                & v3_altcat_2(k2_yellow20(A,B),A)
                & m1_altcat_2(k2_yellow20(A,B),A) ) ) ) ) ) )).

fof(t27_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_altcat_2(B,A) )
         => ( v2_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))
                           => ( ( E = C
                                & F = D )
                             => k1_altcat_1(B,E,F) = k1_altcat_1(A,C,D) ) ) ) ) ) ) ) ) )).

fof(t28_yellow20,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(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( k1_altcat_1(B,C,D) != k1_xboole_0
                   => ! [E] :
                        ( m1_subset_1(E,k1_altcat_1(B,C,D))
                       => k6_functor0(B,A,k10_functor0(A,B),C,D,E) = E ) ) ) ) ) ) )).

fof(t29_yellow20,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)
                & v3_altcat_2(C,A)
                & m1_altcat_2(C,A) )
             => ! [D] :
                  ( l2_functor0(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ( F = E
                           => k3_functor0(C,B,k14_functor0(A,B,C,D),F) = k3_functor0(A,B,D,E) ) ) ) ) ) ) ) )).

fof(t30_yellow20,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)
                & v3_altcat_2(C,A)
                & m1_altcat_2(C,A) )
             => ! [D] :
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(C))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(C))
                                 => ( ( G = E
                                      & H = F )
                                   => ( k1_altcat_1(C,G,H) = k1_xboole_0
                                      | ! [I] :
                                          ( m1_subset_1(I,k1_altcat_1(A,E,F))
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_altcat_1(C,G,H))
                                             => ( J = I
                                               => k6_functor0(C,B,k4_yellow20(A,B,C,D),G,H,J) = k6_functor0(A,B,D,E,F,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t31_yellow20,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)
                & v3_altcat_2(C,A)
                & m1_altcat_2(C,A) )
             => ! [D] :
                  ( ( v16_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(C))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(C))
                                 => ( ( G = E
                                      & H = F )
                                   => ( k1_altcat_1(C,G,H) = k1_xboole_0
                                      | ! [I] :
                                          ( m1_subset_1(I,k1_altcat_1(A,E,F))
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_altcat_1(C,G,H))
                                             => ( J = I
                                               => k8_functor0(C,B,k5_yellow20(A,B,C,D),G,H,J) = k8_functor0(A,B,D,E,F,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t32_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( ( v10_functor0(C,A,B)
                  & v4_functor0(C,A,B) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k3_functor0(A,B,C,D) = k3_functor0(A,B,C,E)
                         => D = E ) ) ) ) ) ) ) )).

fof(t33_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_altcat_2(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & v10_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))
                       => ( k1_altcat_1(A,D,E) != k1_xboole_0
                         => ! [F] :
                              ( m1_subset_1(F,k1_altcat_1(A,D,E))
                             => ! [G] :
                                  ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                 => ( k6_functor0(A,B,C,D,E,F) = k6_functor0(A,B,C,D,E,G)
                                   => F = G ) ) ) ) ) ) ) ) ) ) )).

fof(t34_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v10_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v20_functor0(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( k1_altcat_1(B,D,E) != k1_xboole_0
                         => ! [F] :
                              ( m1_subset_1(F,k1_altcat_1(B,D,E))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                  & ? [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                      & ? [I] :
                                          ( m1_subset_1(I,k1_altcat_1(A,G,H))
                                          & D = k3_functor0(A,B,C,G)
                                          & E = k3_functor0(A,B,C,H)
                                          & k1_altcat_1(A,G,H) != k1_xboole_0
                                          & F = k6_functor0(A,B,C,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( ( v11_functor0(C,A,B)
                  & v4_functor0(C,A,B) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k3_functor0(A,B,C,D) = k3_functor0(A,B,C,E)
                         => D = E ) ) ) ) ) ) ) )).

fof(t36_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_altcat_2(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & 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))
                       => ( k1_altcat_1(A,D,E) != k1_xboole_0
                         => ! [F] :
                              ( m1_subset_1(F,k1_altcat_1(A,D,E))
                             => ! [G] :
                                  ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                 => ( k8_functor0(A,B,C,D,E,F) = k8_functor0(A,B,C,D,E,G)
                                   => F = G ) ) ) ) ) ) ) ) ) ) )).

fof(t37_yellow20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v20_functor0(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( k1_altcat_1(B,D,E) != k1_xboole_0
                         => ! [F] :
                              ( m1_subset_1(F,k1_altcat_1(B,D,E))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                  & ? [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                      & ? [I] :
                                          ( m1_subset_1(I,k1_altcat_1(A,G,H))
                                          & E = k3_functor0(A,B,C,G)
                                          & D = k3_functor0(A,B,C,H)
                                          & k1_altcat_1(A,G,H) != k1_xboole_0
                                          & F = k8_functor0(A,B,C,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_yellow20,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] :
              ( l2_functor0(C,A,B)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_altcat_1(D)
                    & v11_altcat_1(D)
                    & v12_altcat_1(D)
                    & l2_altcat_1(D) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v2_altcat_1(E)
                        & v11_altcat_1(E)
                        & v12_altcat_1(E)
                        & l2_altcat_1(E) )
                     => ( r2_yellow20(A,B,C,D,E)
                      <=> ( v2_altcat_1(D)
                          & v3_altcat_2(D,A)
                          & m1_altcat_2(D,A)
                          & v2_altcat_1(E)
                          & v3_altcat_2(E,B)
                          & m1_altcat_2(E,B)
                          & ? [F] :
                              ( v15_functor0(F,D,E)
                              & m2_functor0(F,D,E)
                              & v21_functor0(F,D,E)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(D))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ( G = H
                                       => k3_functor0(D,E,F,G) = k3_functor0(A,B,C,H) ) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(D))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(D))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ( ( G = I
                                                  & H = J )
                                               => ( k1_altcat_1(D,G,H) = k1_xboole_0
                                                  | ! [K] :
                                                      ( m1_subset_1(K,k1_altcat_1(D,G,H))
                                                     => ! [L] :
                                                          ( m1_subset_1(L,k1_altcat_1(A,I,J))
                                                         => ( K = L
                                                           => k6_functor0(D,E,F,G,H,K) = k1_funct_1(k4_functor0(A,B,C,I,J),L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_yellow20,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] :
              ( l2_functor0(C,A,B)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_altcat_1(D)
                    & v11_altcat_1(D)
                    & v12_altcat_1(D)
                    & l2_altcat_1(D) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v2_altcat_1(E)
                        & v11_altcat_1(E)
                        & v12_altcat_1(E)
                        & l2_altcat_1(E) )
                     => ( r3_yellow20(A,B,C,D,E)
                      <=> ( v2_altcat_1(D)
                          & v3_altcat_2(D,A)
                          & m1_altcat_2(D,A)
                          & v2_altcat_1(E)
                          & v3_altcat_2(E,B)
                          & m1_altcat_2(E,B)
                          & ? [F] :
                              ( v16_functor0(F,D,E)
                              & m2_functor0(F,D,E)
                              & v21_functor0(F,D,E)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(D))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ( G = H
                                       => k3_functor0(D,E,F,G) = k3_functor0(A,B,C,H) ) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(D))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(D))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ( ( G = I
                                                  & H = J )
                                               => ( k1_altcat_1(D,G,H) = k1_xboole_0
                                                  | ! [K] :
                                                      ( m1_subset_1(K,k1_altcat_1(D,G,H))
                                                     => ! [L] :
                                                          ( m1_subset_1(L,k1_altcat_1(A,I,J))
                                                         => ( K = L
                                                           => k8_functor0(D,E,F,G,H,K) = k1_funct_1(k4_functor0(A,B,C,I,J),L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_yellow20,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] :
                      ( l2_functor0(E,A,B)
                     => ( r2_yellow20(A,B,E,C,D)
                       => r1_functor0(C,D) ) ) ) ) ) ) )).

fof(t39_yellow20,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] :
                      ( l2_functor0(E,A,B)
                     => ( r3_yellow20(A,B,E,C,D)
                       => r2_functor0(C,D) ) ) ) ) ) ) )).

fof(t40_yellow20,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) )
             => ( r2_yellow20(A,B,C,A,B)
               => v21_functor0(C,A,B) ) ) ) ) )).

fof(t41_yellow20,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) )
             => ( r3_yellow20(A,B,C,A,B)
               => v21_functor0(C,A,B) ) ) ) ) )).

fof(t42_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => r2_yellow20(A,B,C,A,B) ) ) ) ) )).

fof(t43_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => r3_yellow20(A,B,C,A,B) ) ) ) ) )).

fof(t44_yellow20,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) )
         => r2_yellow20(A,A,k12_functor0(A),B,B) ) ) )).

fof(t45_yellow20,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k2_funct_4(A),k2_funct_4(B)) ) ) ) )).

fof(t46_yellow20,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v1_relat_1(k1_relat_1(A))
              & r1_tarski(k2_funct_4(A),k2_funct_4(B)) )
           => r1_tarski(A,B) ) ) ) )).

fof(t47_yellow20,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,k2_zfmisc_1(A,A))
     => ! [D] :
          ( m1_pboole(D,k2_zfmisc_1(B,B))
         => ( r2_altcat_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),C,D)
           => r2_altcat_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k1_altcat_2(A,C),k1_altcat_2(B,D)) ) ) ) )).

fof(t48_yellow20,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) )
         => m1_altcat_2(k1_yellow18(B),k1_yellow18(A)) ) ) )).

fof(t49_yellow20,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) )
         => ( v2_altcat_1(k1_yellow18(B))
            & v3_altcat_2(k1_yellow18(B),k1_yellow18(A))
            & m1_altcat_2(k1_yellow18(B),k1_yellow18(A)) ) ) ) )).

fof(t50_yellow20,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) )
         => r3_yellow20(A,k1_yellow18(A),k2_yellow18(A,k1_yellow18(A)),B,k1_yellow18(B)) ) ) )).

fof(t51_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & v2_altcat_1(D)
                      & v3_altcat_2(D,A)
                      & m1_altcat_2(D,A) )
                   => ! [E] :
                        ( ( ~ v3_struct_0(E)
                          & v2_altcat_1(E)
                          & v3_altcat_2(E,B)
                          & m1_altcat_2(E,B) )
                       => ( r2_yellow20(A,B,C,D,E)
                         => r2_yellow20(B,A,k15_functor0(A,B,C),E,D) ) ) ) ) ) ) ) )).

fof(t52_yellow20,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) )
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & v2_altcat_1(D)
                      & v3_altcat_2(D,A)
                      & m1_altcat_2(D,A) )
                   => ! [E] :
                        ( ( ~ v3_struct_0(E)
                          & v2_altcat_1(E)
                          & v3_altcat_2(E,B)
                          & m1_altcat_2(E,B) )
                       => ( r3_yellow20(A,B,C,D,E)
                         => r3_yellow20(B,A,k15_functor0(A,B,C),E,D) ) ) ) ) ) ) ) )).

fof(t53_yellow20,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] :
                          ( ( ~ v3_struct_0(F)
                            & v2_altcat_1(F)
                            & v3_altcat_2(F,A)
                            & m1_altcat_2(F,A) )
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v2_altcat_1(G)
                                & v3_altcat_2(G,B)
                                & m1_altcat_2(G,B) )
                             => ! [H] :
                                  ( ( ~ v3_struct_0(H)
                                    & v2_altcat_1(H)
                                    & v3_altcat_2(H,C)
                                    & m1_altcat_2(H,C) )
                                 => ( ( r2_yellow20(A,B,D,F,G)
                                      & r2_yellow20(B,C,E,G,H) )
                                   => r2_yellow20(A,C,k1_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) )).

fof(t54_yellow20,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] :
                  ( ( v16_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( ~ v3_struct_0(F)
                            & v2_altcat_1(F)
                            & v3_altcat_2(F,A)
                            & m1_altcat_2(F,A) )
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v2_altcat_1(G)
                                & v3_altcat_2(G,B)
                                & m1_altcat_2(G,B) )
                             => ! [H] :
                                  ( ( ~ v3_struct_0(H)
                                    & v2_altcat_1(H)
                                    & v3_altcat_2(H,C)
                                    & m1_altcat_2(H,C) )
                                 => ( ( r3_yellow20(A,B,D,F,G)
                                      & r2_yellow20(B,C,E,G,H) )
                                   => r3_yellow20(A,C,k4_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) )).

fof(t55_yellow20,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] :
                      ( ( v16_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( ~ v3_struct_0(F)
                            & v2_altcat_1(F)
                            & v3_altcat_2(F,A)
                            & m1_altcat_2(F,A) )
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v2_altcat_1(G)
                                & v3_altcat_2(G,B)
                                & m1_altcat_2(G,B) )
                             => ! [H] :
                                  ( ( ~ v3_struct_0(H)
                                    & v2_altcat_1(H)
                                    & v3_altcat_2(H,C)
                                    & m1_altcat_2(H,C) )
                                 => ( ( r2_yellow20(A,B,D,F,G)
                                      & r3_yellow20(B,C,E,G,H) )
                                   => r3_yellow20(A,C,k3_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) )).

fof(t56_yellow20,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] :
                  ( ( v16_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v16_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] :
                          ( ( ~ v3_struct_0(F)
                            & v2_altcat_1(F)
                            & v3_altcat_2(F,A)
                            & m1_altcat_2(F,A) )
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v2_altcat_1(G)
                                & v3_altcat_2(G,B)
                                & m1_altcat_2(G,B) )
                             => ! [H] :
                                  ( ( ~ v3_struct_0(H)
                                    & v2_altcat_1(H)
                                    & v3_altcat_2(H,C)
                                    & m1_altcat_2(H,C) )
                                 => ( ( r3_yellow20(A,B,D,F,G)
                                      & r3_yellow20(B,C,E,G,H) )
                                   => r2_yellow20(A,C,k2_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) )).

fof(s1_yellow20,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
         => ( m1_subset_1(A,u1_struct_0(f2_s1_yellow20))
          <=> p1_s1_yellow20(A) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s1_yellow20))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f2_s1_yellow20))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(f2_s1_yellow20))
                     => ( ( C = A
                          & D = B )
                       => ( k1_altcat_1(f1_s1_yellow20,A,B) = k1_xboole_0
                          | ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(f1_s1_yellow20,A,B))
                             => ( r2_hidden(E,k1_altcat_1(f2_s1_yellow20,C,D))
                              <=> p2_s1_yellow20(A,B,E) ) ) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
         => ( m1_subset_1(A,u1_struct_0(f3_s1_yellow20))
          <=> p1_s1_yellow20(A) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s1_yellow20))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f3_s1_yellow20))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(f3_s1_yellow20))
                     => ( ( C = A
                          & D = B )
                       => ( k1_altcat_1(f1_s1_yellow20,A,B) = k1_xboole_0
                          | ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(f1_s1_yellow20,A,B))
                             => ( r2_hidden(E,k1_altcat_1(f3_s1_yellow20,C,D))
                              <=> p2_s1_yellow20(A,B,E) ) ) ) ) ) ) ) ) )
   => g2_altcat_1(u1_struct_0(f2_s1_yellow20),u1_altcat_1(f2_s1_yellow20),u2_altcat_1(f2_s1_yellow20)) = g2_altcat_1(u1_struct_0(f3_s1_yellow20),u1_altcat_1(f3_s1_yellow20),u2_altcat_1(f3_s1_yellow20)) )).

fof(s2_yellow20,axiom,
    ( ? [A] :
        ( m1_subset_1(A,u1_struct_0(f1_s2_yellow20))
        & p1_s2_yellow20(A) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v2_altcat_2(A,f1_s2_yellow20)
        & v3_altcat_2(A,f1_s2_yellow20)
        & m1_altcat_2(A,f1_s2_yellow20)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s2_yellow20))
           => ( m1_subset_1(B,u1_struct_0(A))
            <=> p1_s2_yellow20(B) ) ) ) )).

fof(s3_yellow20,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s3_yellow20))
         => ( m1_subset_1(A,u1_struct_0(f2_s3_yellow20))
          <=> p1_s3_yellow20(A) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s3_yellow20))
         => ( m1_subset_1(A,u1_struct_0(f3_s3_yellow20))
          <=> p1_s3_yellow20(A) ) ) )
   => g2_altcat_1(u1_struct_0(f2_s3_yellow20),u1_altcat_1(f2_s3_yellow20),u2_altcat_1(f2_s3_yellow20)) = g2_altcat_1(u1_struct_0(f3_s3_yellow20),u1_altcat_1(f3_s3_yellow20),u2_altcat_1(f3_s3_yellow20)) )).

fof(s4_yellow20,axiom,
    ( ( v21_functor0(f3_s4_yellow20,f1_s4_yellow20,f2_s4_yellow20)
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s4_yellow20))
         => ( m1_subset_1(A,u1_struct_0(f4_s4_yellow20))
          <=> m1_subset_1(k3_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,A),u1_struct_0(f5_s4_yellow20)) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s4_yellow20))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s4_yellow20))
             => ( k1_altcat_1(f1_s4_yellow20,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(f4_s4_yellow20))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(f4_s4_yellow20))
                       => ( ( C = A
                            & D = B )
                         => ! [E] :
                              ( m1_subset_1(E,u1_struct_0(f5_s4_yellow20))
                             => ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(f5_s4_yellow20))
                                 => ( ( E = k3_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,A)
                                      & F = k3_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,B) )
                                   => ! [G] :
                                        ( m1_subset_1(G,k1_altcat_1(f1_s4_yellow20,A,B))
                                       => ( r2_hidden(G,k1_altcat_1(f4_s4_yellow20,C,D))
                                        <=> r2_hidden(k6_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,A,B,G),k1_altcat_1(f5_s4_yellow20,E,F)) ) ) ) ) ) ) ) ) ) ) ) )
   => r2_yellow20(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,f4_s4_yellow20,f5_s4_yellow20) )).

fof(s5_yellow20,axiom,
    ( ( v21_functor0(f3_s5_yellow20,f1_s5_yellow20,f2_s5_yellow20)
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s5_yellow20))
         => ( m1_subset_1(A,u1_struct_0(f4_s5_yellow20))
          <=> m1_subset_1(k3_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,A),u1_struct_0(f5_s5_yellow20)) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s5_yellow20))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s5_yellow20))
             => ( k1_altcat_1(f1_s5_yellow20,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(f4_s5_yellow20))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(f4_s5_yellow20))
                       => ( ( C = A
                            & D = B )
                         => ! [E] :
                              ( m1_subset_1(E,u1_struct_0(f5_s5_yellow20))
                             => ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(f5_s5_yellow20))
                                 => ( ( E = k3_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,A)
                                      & F = k3_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,B) )
                                   => ! [G] :
                                        ( m1_subset_1(G,k1_altcat_1(f1_s5_yellow20,A,B))
                                       => ( r2_hidden(G,k1_altcat_1(f4_s5_yellow20,C,D))
                                        <=> r2_hidden(k8_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,A,B,G),k1_altcat_1(f5_s5_yellow20,F,E)) ) ) ) ) ) ) ) ) ) ) ) )
   => r3_yellow20(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,f4_s5_yellow20,f5_s5_yellow20) )).

fof(symmetry_r1_yellow20,axiom,(
    ! [A,B] :
      ( ( l2_altcat_1(A)
        & l2_altcat_1(B) )
     => ( r1_yellow20(A,B)
       => r1_yellow20(B,A) ) ) )).

fof(dt_k1_yellow20,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_yellow20(A,B))
        & v1_funct_1(k1_yellow20(A,B)) ) ) )).

fof(commutativity_k1_yellow20,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_yellow20(A,B) = k1_yellow20(B,A) ) )).

fof(dt_k2_yellow20,axiom,(
    ! [A,B] :
      ( ( l2_altcat_1(A)
        & l2_altcat_1(B) )
     => ( v6_altcat_1(k2_yellow20(A,B))
        & l2_altcat_1(k2_yellow20(A,B)) ) ) )).

fof(dt_k3_yellow20,axiom,(
    ! [A,B] :
      ( ( ~ 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)
        & v3_altcat_2(B,A)
        & m1_altcat_2(B,A) )
     => ( v9_functor0(k3_yellow20(A,B),B,A)
        & v15_functor0(k3_yellow20(A,B),B,A)
        & m2_functor0(k3_yellow20(A,B),B,A) ) ) )).

fof(redefinition_k3_yellow20,axiom,(
    ! [A,B] :
      ( ( ~ 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)
        & v3_altcat_2(B,A)
        & m1_altcat_2(B,A) )
     => k3_yellow20(A,B) = k10_functor0(A,B) ) )).

fof(dt_k4_yellow20,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)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v3_altcat_2(C,A)
        & m1_altcat_2(C,A)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => ( v9_functor0(k4_yellow20(A,B,C,D),C,B)
        & v15_functor0(k4_yellow20(A,B,C,D),C,B)
        & m2_functor0(k4_yellow20(A,B,C,D),C,B) ) ) )).

fof(redefinition_k4_yellow20,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)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v3_altcat_2(C,A)
        & m1_altcat_2(C,A)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => k4_yellow20(A,B,C,D) = k14_functor0(A,B,C,D) ) )).

fof(dt_k5_yellow20,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)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v3_altcat_2(C,A)
        & m1_altcat_2(C,A)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => ( v9_functor0(k5_yellow20(A,B,C,D),C,B)
        & v16_functor0(k5_yellow20(A,B,C,D),C,B)
        & m2_functor0(k5_yellow20(A,B,C,D),C,B) ) ) )).

fof(redefinition_k5_yellow20,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)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v3_altcat_2(C,A)
        & m1_altcat_2(C,A)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => k5_yellow20(A,B,C,D) = k14_functor0(A,B,C,D) ) )).
%------------------------------------------------------------------------------