SET007 Axioms: SET007+682.ax


%------------------------------------------------------------------------------
% File     : SET007+682 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Concrete Categories
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : yellow18 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  107 (   1 unit)
%            Number of atoms       : 1827 ( 281 equality)
%            Maximal formula depth :   35 (  14 average)
%            Number of connectives : 2004 ( 284 ~  ;   3  |;1032  &)
%                                         (  39 <=>; 646 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   67 (   1 propositional; 0-5 arity)
%            Number of functors    :  124 (  41 constant; 0-6 arity)
%            Number of variables   :  643 (   0 singleton; 558 !;  85 ?)
%            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_yellow18,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_multop_1(A,B,C,D))
        & v1_funct_1(k1_multop_1(A,B,C,D)) ) ) )).

fof(fc2_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k1_yellow18(A))
        & v2_altcat_1(k1_yellow18(A))
        & v6_altcat_1(k1_yellow18(A))
        & v11_altcat_1(k1_yellow18(A)) ) ) )).

fof(fc3_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k1_yellow18(A))
        & v2_altcat_1(k1_yellow18(A))
        & v6_altcat_1(k1_yellow18(A))
        & v12_altcat_1(k1_yellow18(A))
        & v1_altcat_2(k1_yellow18(A)) ) ) )).

fof(fc4_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v6_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
        & v8_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
        & v9_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
        & v11_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
        & v12_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
        & v14_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
        & v16_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
        & v21_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A)) ) ) )).

fof(fc5_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v6_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
        & v8_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
        & v9_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
        & v11_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
        & v12_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
        & v14_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
        & v16_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
        & v21_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A) ) ) )).

fof(cc1_yellow18,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v8_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v1_altcat_2(A)
          & v2_yellow18(A) ) ) ) )).

fof(fc6_yellow18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k7_altcat_1(A))
        & v2_altcat_1(k7_altcat_1(A))
        & v6_altcat_1(k7_altcat_1(A))
        & v8_altcat_1(k7_altcat_1(A))
        & v9_altcat_1(k7_altcat_1(A))
        & v10_altcat_1(k7_altcat_1(A))
        & v11_altcat_1(k7_altcat_1(A))
        & v12_altcat_1(k7_altcat_1(A))
        & v1_altcat_2(k7_altcat_1(A))
        & v2_yellow18(k7_altcat_1(A))
        & v3_yellow18(k7_altcat_1(A)) ) ) )).

fof(cc2_yellow18,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v4_yellow18(A) )
       => ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v9_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v1_altcat_2(A)
          & v2_yellow18(A)
          & v3_yellow18(A) ) ) ) )).

fof(cc3_yellow18,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v9_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v2_yellow18(A)
          & v3_yellow18(A) )
       => ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v1_altcat_2(A)
          & v4_yellow18(A) ) ) ) )).

fof(rc1_yellow18,axiom,(
    ? [A] :
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v2_altcat_1(A)
      & v6_altcat_1(A)
      & v8_altcat_1(A)
      & v9_altcat_1(A)
      & v10_altcat_1(A)
      & v11_altcat_1(A)
      & v12_altcat_1(A)
      & v1_altcat_2(A)
      & v2_yellow18(A)
      & v3_yellow18(A)
      & v4_yellow18(A) ) )).

fof(cc4_yellow18,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow18(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ! [D] :
          ( m1_subset_1(D,k1_altcat_1(A,B,C))
         => ( v1_relat_1(D)
            & v1_funct_1(D) ) ) ) )).

fof(fc7_yellow18,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k3_yellow18(k4_yellow18(A),B)) ) )).

fof(fc8_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v6_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v8_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v9_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v10_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v12_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v13_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v15_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v21_functor0(k5_yellow18(A),A,k4_yellow18(A)) ) ) )).

fof(t1_yellow18,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_subset_1(E,u1_struct_0(A))
                         => k3_functor0(A,B,C,E) = k3_functor0(A,B,D,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(A,B,C,E,F,G) = k6_functor0(A,B,D,E,F,G) ) ) ) ) )
                   => g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) = g2_functor0(A,B,u1_functor0(A,B,D),u2_functor0(A,B,D)) ) ) ) ) ) )).

fof(t2_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] :
                  ( ( v16_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ( ( ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => k3_functor0(A,B,C,E) = k3_functor0(A,B,D,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(A,B,C,E,F,G) = k8_functor0(A,B,D,E,F,G) ) ) ) ) )
                   => g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) = g2_functor0(A,B,u1_functor0(A,B,D),u2_functor0(A,B,D)) ) ) ) ) ) )).

fof(d1_yellow18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,B),C)
                    & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
                 => ( v2_funct_1(D)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ! [G] :
                                ( m1_subset_1(G,B)
                               => ! [H] :
                                    ( m1_subset_1(H,B)
                                   => ( k2_binop_1(A,B,C,D,E,G) = k2_binop_1(A,B,C,D,F,H)
                                     => ( E = F
                                        & G = H ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_yellow18,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_yellow18(A,B)
          <=> ? [C] :
                ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B)
                & ? [D] :
                    ( v15_functor0(D,B,A)
                    & m2_functor0(D,B,A)
                    & r1_functor3(A,A,k1_functor3(A,B,A,C,D),k12_functor0(A))
                    & r1_functor3(B,B,k1_functor3(B,A,B,D,C),k12_functor0(B)) ) ) ) ) ) )).

fof(t3_yellow18,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] :
              ( ( ~ v3_struct_0(C)
                & v1_altcat_2(C)
                & l1_altcat_1(C) )
             => ! [D] :
                  ( ( v8_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( ( v8_functor0(E,A,B)
                        & l2_functor0(E,A,B) )
                     => ! [F] :
                          ( l2_functor0(F,B,C)
                         => ! [G] :
                              ( l2_functor0(G,B,C)
                             => ( ( g2_functor0(A,B,u1_functor0(A,B,D),u2_functor0(A,B,D)) = g2_functor0(A,B,u1_functor0(A,B,E),u2_functor0(A,B,E))
                                  & g2_functor0(B,C,u1_functor0(B,C,F),u2_functor0(B,C,F)) = g2_functor0(B,C,u1_functor0(B,C,G),u2_functor0(B,C,G)) )
                               => k13_functor0(A,B,C,D,F) = k13_functor0(A,B,C,E,G) ) ) ) ) ) ) ) ) )).

fof(t4_yellow18,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) )
             => ( ( r1_yellow18(A,B)
                  & r1_yellow18(B,C) )
               => r1_yellow18(A,C) ) ) ) ) )).

fof(t5_yellow18,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_functor0(A,B)
           => r1_yellow18(A,B) ) ) ) )).

fof(d3_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ( r2_yellow18(A,B)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & u1_altcat_1(B) = k1_altcat_2(u1_struct_0(A),u1_altcat_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [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))
                                     => ( ( F = C
                                          & G = D
                                          & H = E )
                                       => k4_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B),F,G,H) = k1_functor0(k1_binop_1(u1_altcat_1(A),D,C),k1_binop_1(u1_altcat_1(A),E,D),k1_binop_1(u1_altcat_1(A),E,C),k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),E,D,C)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ( r2_yellow18(A,B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => m1_subset_1(C,u1_struct_0(B)) ) ) ) ) )).

fof(t7_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ( r2_yellow18(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))
                           => ( ( E = C
                                & F = D )
                             => k1_altcat_1(A,C,D) = k1_altcat_1(B,F,E) ) ) ) ) ) ) ) ) )).

fof(t8_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ( r2_yellow18(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))
                           => ( ( E = C
                                & F = D )
                             => ! [G] :
                                  ( m1_subset_1(G,k1_altcat_1(A,C,D))
                                 => m1_subset_1(G,k1_altcat_1(B,F,E)) ) ) ) ) ) ) ) ) ) )).

fof(t9_yellow18,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) )
         => ( r2_yellow18(A,B)
          <=> ( u1_struct_0(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,u1_struct_0(B))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(B))
                                     => ( ( F = C
                                          & G = D
                                          & H = E )
                                       => ( k1_altcat_1(A,C,D) = k1_altcat_1(B,G,F)
                                          & ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
                                              & k1_altcat_1(A,D,E) != k1_xboole_0
                                              & ? [I] :
                                                  ( m1_subset_1(I,k1_altcat_1(A,C,D))
                                                  & ? [J] :
                                                      ( m1_subset_1(J,k1_altcat_1(A,D,E))
                                                      & ? [K] :
                                                          ( m1_subset_1(K,k1_altcat_1(B,G,F))
                                                          & ? [L] :
                                                              ( m1_subset_1(L,k1_altcat_1(B,H,G))
                                                              & K = I
                                                              & L = J
                                                              & k5_altcat_1(B,H,G,F,L,K) != k5_altcat_1(A,C,D,E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t10_yellow18,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) )
         => ( r2_yellow18(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) ) ) ) ) ) ) )).

fof(t11_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ? [B] :
          ( ~ v3_struct_0(B)
          & v2_altcat_1(B)
          & v6_altcat_1(B)
          & l2_altcat_1(B)
          & r2_yellow18(A,B) ) ) )).

fof(t12_yellow18,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) )
         => ( ( r2_yellow18(A,B)
              & v11_altcat_1(A) )
           => v11_altcat_1(B) ) ) ) )).

fof(t13_yellow18,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) )
         => ( ( r2_yellow18(A,B)
              & v12_altcat_1(A) )
           => v12_altcat_1(B) ) ) ) )).

fof(t14_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_altcat_1(C) )
             => ( r2_yellow18(A,B)
               => ( r2_yellow18(A,C)
                <=> g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(C),u1_altcat_1(C),u2_altcat_1(C)) ) ) ) ) ) )).

fof(d4_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & l2_altcat_1(B) )
         => ( B = k1_yellow18(A)
          <=> r2_yellow18(A,B) ) ) ) )).

fof(d5_yellow18,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) )
         => ( r2_yellow18(A,B)
           => ! [C] :
                ( ( v9_functor0(C,A,B)
                  & v16_functor0(C,A,B)
                  & m2_functor0(C,A,B) )
               => ( C = k2_yellow18(A,B)
                <=> ( ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => k3_functor0(A,B,C,D) = D )
                    & ! [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))
                                 => k8_functor0(A,B,C,D,E,F) = F ) ) ) ) ) ) ) ) ) ) )).

fof(t15_yellow18,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) )
         => ( r2_yellow18(A,B)
           => k2_functor3(B,A,B,k2_yellow18(B,A),k2_yellow18(A,B)) = k12_functor0(B) ) ) ) )).

fof(t16_yellow18,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) )
         => ( r2_yellow18(A,B)
           => v21_functor0(k2_yellow18(A,B),A,B) ) ) ) )).

fof(t17_yellow18,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) )
         => ( r2_yellow18(A,B)
           => r2_functor0(A,B) ) ) ) )).

fof(t18_yellow18,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) )
             => ( r2_yellow18(A,B)
               => ( r1_functor0(A,C)
                <=> r2_functor0(B,C) ) ) ) ) ) )).

fof(t19_yellow18,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) )
                 => ( ( r2_yellow18(A,B)
                      & r2_yellow18(C,D)
                      & r1_functor0(A,C) )
                   => r1_functor0(B,D) ) ) ) ) ) )).

fof(t20_yellow18,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) )
                 => ( ( r2_yellow18(A,B)
                      & r2_yellow18(C,D)
                      & r2_functor0(A,C) )
                   => r2_functor0(B,D) ) ) ) ) ) )).

fof(t21_yellow18,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) )
         => ( r2_yellow18(A,B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
                        & k1_altcat_1(A,D,C) != k1_xboole_0
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                            & ? [F] :
                                ( m1_subset_1(F,u1_struct_0(B))
                                & E = C
                                & F = D
                                & ? [G] :
                                    ( m1_subset_1(G,k1_altcat_1(A,C,D))
                                    & ? [H] :
                                        ( m1_subset_1(H,k1_altcat_1(B,F,E))
                                        & H = G
                                        & ~ ( v1_altcat_3(G,A,C,D)
                                          <=> v2_altcat_3(H,B,F,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_yellow18,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) )
         => ( r2_yellow18(A,B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
                        & k1_altcat_1(A,D,C) != k1_xboole_0
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                            & ? [F] :
                                ( m1_subset_1(F,u1_struct_0(B))
                                & E = C
                                & F = D
                                & ? [G] :
                                    ( m1_subset_1(G,k1_altcat_1(A,C,D))
                                    & ? [H] :
                                        ( m1_subset_1(H,k1_altcat_1(B,F,E))
                                        & H = G
                                        & ~ ( v2_altcat_3(G,A,C,D)
                                          <=> v1_altcat_3(H,B,F,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_yellow18,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) )
         => ( r2_yellow18(A,B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
                        & k1_altcat_1(A,D,C) != k1_xboole_0
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                            & ? [F] :
                                ( m1_subset_1(F,u1_struct_0(B))
                                & E = C
                                & F = D
                                & ? [G] :
                                    ( m1_subset_1(G,k1_altcat_1(A,C,D))
                                    & ? [H] :
                                        ( m1_subset_1(H,k1_altcat_1(B,F,E))
                                        & H = G
                                        & v1_altcat_3(G,A,C,D)
                                        & v2_altcat_3(G,A,C,D)
                                        & k1_altcat_3(B,F,E,H) != k1_altcat_3(A,C,D,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_yellow18,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) )
         => ( r2_yellow18(A,B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
                        & k1_altcat_1(A,D,C) != k1_xboole_0
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                            & ? [F] :
                                ( m1_subset_1(F,u1_struct_0(B))
                                & E = C
                                & F = D
                                & ? [G] :
                                    ( m1_subset_1(G,k1_altcat_1(A,C,D))
                                    & ? [H] :
                                        ( m1_subset_1(H,k1_altcat_1(B,F,E))
                                        & H = G
                                        & ~ ( v3_altcat_3(G,A,C,D)
                                          <=> v3_altcat_3(H,B,F,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_yellow18,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) )
                 => ( ( r2_yellow18(A,B)
                      & r2_yellow18(C,D) )
                   => ! [E] :
                        ( ( v15_functor0(E,B,C)
                          & m2_functor0(E,B,C) )
                       => ! [F] :
                            ( ( v15_functor0(F,B,C)
                              & m2_functor0(F,B,C) )
                           => ( r1_functor3(B,C,E,F)
                             => r1_functor3(A,D,k2_functor3(A,B,D,k2_yellow18(A,B),k3_functor3(B,C,D,F,k2_yellow18(C,D))),k2_functor3(A,B,D,k2_yellow18(A,B),k3_functor3(B,C,D,E,k2_yellow18(C,D)))) ) ) ) ) ) ) ) ) )).

fof(t26_yellow18,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) )
                 => ( ( r2_yellow18(A,B)
                      & r2_yellow18(C,D)
                      & r1_yellow18(A,C) )
                   => r1_yellow18(B,D) ) ) ) ) ) )).

fof(d6_yellow18,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) )
         => ( r3_yellow18(A,B)
          <=> r1_yellow18(A,k1_yellow18(B)) ) ) ) )).

fof(t27_yellow18,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) )
         => ( r2_functor0(A,B)
           => r3_yellow18(A,B) ) ) ) )).

fof(t28_yellow18,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) )
             => ( r2_yellow18(A,B)
               => ( r1_yellow18(A,C)
                <=> r3_yellow18(B,C) ) ) ) ) ) )).

fof(t29_yellow18,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) )
             => ( ( r3_yellow18(A,B)
                  & r1_yellow18(B,C) )
               => r3_yellow18(A,C) ) ) ) ) )).

fof(t30_yellow18,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) )
             => ( ( r3_yellow18(A,B)
                  & r3_yellow18(B,C) )
               => r1_yellow18(A,C) ) ) ) ) )).

fof(t31_yellow18,axiom,(
    ! [A,B,C] :
      ( r2_hidden(C,k1_funct_2(A,B))
    <=> ( v1_relat_1(C)
        & v1_funct_1(C)
        & k1_funct_5(C) = A
        & r1_tarski(k2_funct_5(C),B) ) ) )).

fof(d7_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v2_yellow18(A)
      <=> ? [B] :
            ( m1_pboole(B,u1_struct_0(A))
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_tarski(k1_altcat_1(A,C,D),k1_funct_2(k1_funct_1(B,C),k1_funct_1(B,D))) ) ) ) ) ) )).

fof(d8_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B,C] :
          ( ( m1_subset_1(B,u1_struct_0(A))
           => ( C = k3_yellow18(A,B)
            <=> ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & D = B
                  & C = k1_funct_5(k8_altcat_1(A,D)) ) ) )
          & ( ~ m1_subset_1(B,u1_struct_0(A))
           => ( C = k3_yellow18(A,B)
            <=> C = k1_xboole_0 ) ) ) ) )).

fof(d9_yellow18,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))
         => k3_yellow18(A,B) = k1_funct_5(k8_altcat_1(A,B)) ) ) )).

fof(t32_yellow18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
         => k8_altcat_1(k7_altcat_1(A),B) = k6_partfun1(B) ) ) )).

fof(t33_yellow18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
         => k3_yellow18(k7_altcat_1(A),B) = B ) ) )).

fof(d10_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v3_yellow18(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k8_altcat_1(A,B) = k6_partfun1(k3_yellow18(A,B)) ) ) ) )).

fof(d11_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v4_yellow18(A)
      <=> ( v2_yellow18(A)
          & v9_altcat_1(A)
          & v3_yellow18(A) ) ) ) )).

fof(t34_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v2_yellow18(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_tarski(k1_altcat_1(A,B,C),k1_funct_2(k3_yellow18(A,B),k3_yellow18(A,C))) ) ) ) ) )).

fof(t35_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_altcat_1(A,B,C) != k1_xboole_0
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ( v1_funct_1(D)
                      & v1_funct_2(D,k3_yellow18(A,B),k3_yellow18(A,C))
                      & m2_relset_1(D,k3_yellow18(A,B),k3_yellow18(A,C)) ) ) ) ) ) ) )).

fof(t36_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_altcat_1(A,B,C) != k1_xboole_0
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ( k1_relat_1(D) = k3_yellow18(A,B)
                      & r1_tarski(k2_relat_1(D),k3_yellow18(A,C)) ) ) ) ) ) ) )).

fof(t37_yellow18,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] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_yellow18(A,B) = k1_relat_1(k8_altcat_1(A,B)) ) ) )).

fof(t38_yellow18,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] :
          ( 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))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & ~ ! [E] :
                            ( m1_subset_1(E,k1_altcat_1(A,B,C))
                           => ! [F] :
                                ( m1_subset_1(F,k1_altcat_1(A,C,D))
                               => k5_altcat_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ) ) ) ) ) ) )).

fof(t39_yellow18,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] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_hidden(k6_partfun1(k3_yellow18(A,B)),k1_altcat_1(A,B,B))
           => k8_altcat_1(A,B) = k6_partfun1(k3_yellow18(A,B)) ) ) ) )).

fof(t40_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v4_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] :
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v1_altcat_3(D,A,B,C)
                      & k2_relat_1(D) != k3_yellow18(A,C) ) ) ) ) ) )).

fof(t41_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v4_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] :
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v2_altcat_3(D,A,B,C)
                      & ~ v2_funct_1(D) ) ) ) ) ) )).

fof(t42_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v4_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] :
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v3_altcat_3(D,A,B,C)
                      & ~ ( v2_funct_1(D)
                          & k2_relat_1(D) = k3_yellow18(A,C) ) ) ) ) ) ) )).

fof(t43_yellow18,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] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_altcat_1(A,B,C) != k1_xboole_0
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ( ( v2_funct_1(D)
                        & r2_hidden(k2_funct_1(D),k1_altcat_1(A,C,B)) )
                     => v3_altcat_3(D,A,B,C) ) ) ) ) ) ) )).

fof(t44_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v4_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] :
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v3_altcat_3(D,A,B,C)
                      & k1_altcat_3(A,B,C,D) != k2_funct_1(D) ) ) ) ) ) )).

fof(d12_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & v4_yellow18(B)
            & l2_altcat_1(B) )
         => ( B = k4_yellow18(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( r2_hidden(D,k3_yellow18(B,C))
                    <=> ( r2_hidden(D,k3_card_3(k2_card_3(u1_altcat_1(A))))
                        & C = k20_mcart_1(D) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( r2_hidden(E,k1_funct_2(k3_yellow18(B,C),k3_yellow18(B,D)))
                              & ? [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))
                                          & F = C
                                          & G = D
                                          & k1_altcat_1(A,F,G) != k1_xboole_0
                                          & ! [I] :
                                              ( m1_subset_1(I,u1_struct_0(A))
                                             => ( k1_altcat_1(A,I,F) != k1_xboole_0
                                               => ! [J] :
                                                    ( m1_subset_1(J,k1_altcat_1(A,I,F))
                                                   => k1_funct_1(E,k4_tarski(J,k4_tarski(I,F))) = k4_tarski(k5_altcat_1(A,I,F,G,J,H),k4_tarski(I,G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t45_yellow18,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] :
              ( r2_hidden(C,k3_yellow18(k4_yellow18(A),B))
            <=> ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & ? [E] :
                      ( m1_subset_1(E,k1_altcat_1(A,D,B))
                      & k1_altcat_1(A,D,B) != k1_xboole_0
                      & C = k4_tarski(E,k4_tarski(D,B)) ) ) ) ) ) )).

fof(t46_yellow18,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))
             => ( k1_altcat_1(A,B,C) != k1_xboole_0
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => ? [E] :
                        ( v1_funct_1(E)
                        & v1_funct_2(E,k3_yellow18(k4_yellow18(A),B),k3_yellow18(k4_yellow18(A),C))
                        & m2_relset_1(E,k3_yellow18(k4_yellow18(A),B),k3_yellow18(k4_yellow18(A),C))
                        & r2_hidden(E,k1_binop_1(u1_altcat_1(k4_yellow18(A)),B,C))
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,k1_altcat_1(A,F,B))
                               => ( k1_altcat_1(A,F,B) != k1_xboole_0
                                 => k1_funct_1(E,k4_tarski(G,k4_tarski(F,B))) = k4_tarski(k5_altcat_1(A,F,B,C,G,D),k4_tarski(F,C)) ) ) ) ) ) ) ) ) ) )).

fof(t47_yellow18,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))
             => ( k1_altcat_1(A,B,C) != k1_xboole_0
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D) )
                   => ! [E] :
                        ( ( v1_relat_1(E)
                          & v1_funct_1(E) )
                       => ( ( r2_hidden(D,k1_binop_1(u1_altcat_1(k4_yellow18(A)),B,C))
                            & r2_hidden(E,k1_binop_1(u1_altcat_1(k4_yellow18(A)),B,C))
                            & k1_funct_1(D,k4_tarski(k8_altcat_1(A,B),k4_tarski(B,B))) = k1_funct_1(E,k4_tarski(k8_altcat_1(A,B),k4_tarski(B,B))) )
                         => D = E ) ) ) ) ) ) ) )).

fof(d13_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( v9_functor0(B,A,k4_yellow18(A))
            & v15_functor0(B,A,k4_yellow18(A))
            & m2_functor0(B,A,k4_yellow18(A)) )
         => ( B = k5_yellow18(A)
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k3_functor0(A,k4_yellow18(A),B,C) = C )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( k1_altcat_1(A,C,D) != k1_xboole_0
                       => ! [E] :
                            ( m1_subset_1(E,k1_altcat_1(A,C,D))
                           => k1_funct_1(k6_functor0(A,k4_yellow18(A),B,C,D,E),k4_tarski(k8_altcat_1(A,C),k4_tarski(C,C))) = k4_tarski(E,k4_tarski(C,D)) ) ) ) ) ) ) ) ) )).

fof(t48_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => r1_functor0(A,k4_yellow18(A)) ) )).

fof(s1_yellow18,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s1_yellow18)
       => ! [B] :
            ( m1_subset_1(B,f1_s1_yellow18)
           => ! [C] :
                ( m1_subset_1(C,f1_s1_yellow18)
               => ! [D,E] :
                    ( ( r2_hidden(D,f2_s1_yellow18(A,B))
                      & r2_hidden(E,f2_s1_yellow18(B,C)) )
                   => r2_hidden(f3_s1_yellow18(A,B,C,D,E),f2_s1_yellow18(A,C)) ) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & l2_altcat_1(A)
        & u1_struct_0(A) = f1_s1_yellow18
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_altcat_1(A,B,C) = f2_s1_yellow18(B,C) ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,D) != k1_xboole_0
                        & ~ ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(A,B,C))
                             => ! [F] :
                                  ( m1_subset_1(F,k1_altcat_1(A,C,D))
                                 => k5_altcat_1(A,B,C,D,E,F) = f3_s1_yellow18(B,C,D,E,F) ) ) ) ) ) ) ) )).

fof(s2_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s2_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s2_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s2_yellow18))
                 => ~ ( k1_altcat_1(f1_s2_yellow18,A,B) != k1_xboole_0
                      & k1_altcat_1(f1_s2_yellow18,B,C) != k1_xboole_0
                      & ~ ! [D] :
                            ( m1_subset_1(D,k1_altcat_1(f1_s2_yellow18,A,B))
                           => ! [E] :
                                ( m1_subset_1(E,k1_altcat_1(f1_s2_yellow18,B,C))
                               => k5_altcat_1(f1_s2_yellow18,A,B,C,D,E) = f2_s2_yellow18(A,B,C,D,E) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s2_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s2_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s2_yellow18))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(f1_s2_yellow18))
                     => ! [E,F,G] :
                          ( ( r2_hidden(E,k1_altcat_1(f1_s2_yellow18,A,B))
                            & r2_hidden(F,k1_altcat_1(f1_s2_yellow18,B,C))
                            & r2_hidden(G,k1_altcat_1(f1_s2_yellow18,C,D)) )
                         => f2_s2_yellow18(A,C,D,f2_s2_yellow18(A,B,C,E,F),G) = f2_s2_yellow18(A,B,D,E,f2_s2_yellow18(B,C,D,F,G)) ) ) ) ) ) )
   => v11_altcat_1(f1_s2_yellow18) )).

fof(s3_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s3_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s3_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s3_yellow18))
                 => ~ ( k1_altcat_1(f1_s3_yellow18,A,B) != k1_xboole_0
                      & k1_altcat_1(f1_s3_yellow18,B,C) != k1_xboole_0
                      & ~ ! [D] :
                            ( m1_subset_1(D,k1_altcat_1(f1_s3_yellow18,A,B))
                           => ! [E] :
                                ( m1_subset_1(E,k1_altcat_1(f1_s3_yellow18,B,C))
                               => k5_altcat_1(f1_s3_yellow18,A,B,C,D,E) = f2_s3_yellow18(A,B,C,D,E) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s3_yellow18))
         => ? [B] :
              ( r2_hidden(B,k1_altcat_1(f1_s3_yellow18,A,A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s3_yellow18))
                 => ! [D] :
                      ( r2_hidden(D,k1_altcat_1(f1_s3_yellow18,A,C))
                     => f2_s3_yellow18(A,A,C,B,D) = D ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s3_yellow18))
         => ? [B] :
              ( r2_hidden(B,k1_altcat_1(f1_s3_yellow18,A,A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s3_yellow18))
                 => ! [D] :
                      ( r2_hidden(D,k1_altcat_1(f1_s3_yellow18,C,A))
                     => f2_s3_yellow18(C,A,A,D,B) = D ) ) ) ) )
   => v12_altcat_1(f1_s3_yellow18) )).

fof(s4_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s4_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s4_yellow18)
             => ! [C] :
                  ( m1_subset_1(C,f1_s4_yellow18)
                 => ! [D,E] :
                      ( ( r2_hidden(D,f2_s4_yellow18(A,B))
                        & r2_hidden(E,f2_s4_yellow18(B,C)) )
                     => r2_hidden(f3_s4_yellow18(A,B,C,D,E),f2_s4_yellow18(A,C)) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s4_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s4_yellow18)
             => ! [C] :
                  ( m1_subset_1(C,f1_s4_yellow18)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s4_yellow18)
                     => ! [E,F,G] :
                          ( ( r2_hidden(E,f2_s4_yellow18(A,B))
                            & r2_hidden(F,f2_s4_yellow18(B,C))
                            & r2_hidden(G,f2_s4_yellow18(C,D)) )
                         => f3_s4_yellow18(A,C,D,f3_s4_yellow18(A,B,C,E,F),G) = f3_s4_yellow18(A,B,D,E,f3_s4_yellow18(B,C,D,F,G)) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s4_yellow18)
         => ? [B] :
              ( r2_hidden(B,f2_s4_yellow18(A,A))
              & ! [C] :
                  ( m1_subset_1(C,f1_s4_yellow18)
                 => ! [D] :
                      ( r2_hidden(D,f2_s4_yellow18(A,C))
                     => f3_s4_yellow18(A,A,C,B,D) = D ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s4_yellow18)
         => ? [B] :
              ( r2_hidden(B,f2_s4_yellow18(A,A))
              & ! [C] :
                  ( m1_subset_1(C,f1_s4_yellow18)
                 => ! [D] :
                      ( r2_hidden(D,f2_s4_yellow18(C,A))
                     => f3_s4_yellow18(C,A,A,D,B) = D ) ) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & u1_struct_0(A) = f1_s4_yellow18
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_altcat_1(A,B,C) = f2_s4_yellow18(B,C) ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,D) != k1_xboole_0
                        & ~ ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(A,B,C))
                             => ! [F] :
                                  ( m1_subset_1(F,k1_altcat_1(A,C,D))
                                 => k5_altcat_1(A,B,C,D,E,F) = f3_s4_yellow18(B,C,D,E,F) ) ) ) ) ) ) ) )).

fof(s5_yellow18,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) )
         => ( ( u1_struct_0(A) = f1_s5_yellow18
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k1_altcat_1(A,C,D) = f2_s5_yellow18(C,D) ) )
              & ! [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,k1_altcat_1(A,C,D))
                                   => ! [G] :
                                        ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                       => k5_altcat_1(A,C,D,E,F,G) = f3_s5_yellow18(C,D,E,F,G) ) ) ) ) ) )
              & u1_struct_0(B) = f1_s5_yellow18
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => k1_altcat_1(B,C,D) = f2_s5_yellow18(C,D) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ~ ( k1_altcat_1(B,C,D) != k1_xboole_0
                              & k1_altcat_1(B,D,E) != k1_xboole_0
                              & ~ ! [F] :
                                    ( m1_subset_1(F,k1_altcat_1(B,C,D))
                                   => ! [G] :
                                        ( m1_subset_1(G,k1_altcat_1(B,D,E))
                                       => k5_altcat_1(B,C,D,E,F,G) = f3_s5_yellow18(C,D,E,F,G) ) ) ) ) ) ) )
           => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) )).

fof(s6_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s6_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s6_yellow18)
             => ! [C] :
                  ( m1_subset_1(C,f1_s6_yellow18)
                 => ! [D,E] :
                      ( ( r2_hidden(D,f2_s6_yellow18(A,B))
                        & p1_s6_yellow18(A,B,D)
                        & r2_hidden(E,f2_s6_yellow18(B,C))
                        & p1_s6_yellow18(B,C,E) )
                     => ( r2_hidden(f3_s6_yellow18(A,B,C,D,E),f2_s6_yellow18(A,C))
                        & p1_s6_yellow18(A,C,f3_s6_yellow18(A,B,C,D,E)) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s6_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s6_yellow18)
             => ! [C] :
                  ( m1_subset_1(C,f1_s6_yellow18)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s6_yellow18)
                     => ! [E,F,G] :
                          ( ( r2_hidden(E,f2_s6_yellow18(A,B))
                            & p1_s6_yellow18(A,B,E)
                            & r2_hidden(F,f2_s6_yellow18(B,C))
                            & p1_s6_yellow18(B,C,F)
                            & r2_hidden(G,f2_s6_yellow18(C,D))
                            & p1_s6_yellow18(C,D,G) )
                         => f3_s6_yellow18(A,C,D,f3_s6_yellow18(A,B,C,E,F),G) = f3_s6_yellow18(A,B,D,E,f3_s6_yellow18(B,C,D,F,G)) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s6_yellow18)
         => ? [B] :
              ( r2_hidden(B,f2_s6_yellow18(A,A))
              & p1_s6_yellow18(A,A,B)
              & ! [C] :
                  ( m1_subset_1(C,f1_s6_yellow18)
                 => ! [D] :
                      ( ( r2_hidden(D,f2_s6_yellow18(A,C))
                        & p1_s6_yellow18(A,C,D) )
                     => f3_s6_yellow18(A,A,C,B,D) = D ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s6_yellow18)
         => ? [B] :
              ( r2_hidden(B,f2_s6_yellow18(A,A))
              & p1_s6_yellow18(A,A,B)
              & ! [C] :
                  ( m1_subset_1(C,f1_s6_yellow18)
                 => ! [D] :
                      ( ( r2_hidden(D,f2_s6_yellow18(C,A))
                        & p1_s6_yellow18(C,A,D) )
                     => f3_s6_yellow18(C,A,A,D,B) = D ) ) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & u1_struct_0(A) = f1_s6_yellow18
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( r2_hidden(D,k1_altcat_1(A,B,C))
                  <=> ( r2_hidden(D,f2_s6_yellow18(B,C))
                      & p1_s6_yellow18(B,C,D) ) ) ) )
        & ! [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))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,D) != k1_xboole_0
                        & ~ ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(A,B,C))
                             => ! [F] :
                                  ( m1_subset_1(F,k1_altcat_1(A,C,D))
                                 => k5_altcat_1(A,B,C,D,E,F) = f3_s6_yellow18(B,C,D,E,F) ) ) ) ) ) ) ) )).

fof(s7_yellow18,axiom,
    ( ( ? [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s7_yellow18))
          & p1_s7_yellow18(A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s7_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s7_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s7_yellow18))
                 => ( ( p1_s7_yellow18(A)
                      & p1_s7_yellow18(B)
                      & p1_s7_yellow18(C) )
                   => ( k1_altcat_1(f1_s7_yellow18,A,B) = k1_xboole_0
                      | k1_altcat_1(f1_s7_yellow18,B,C) = k1_xboole_0
                      | ! [D] :
                          ( m1_subset_1(D,k1_altcat_1(f1_s7_yellow18,A,B))
                         => ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(f1_s7_yellow18,B,C))
                             => ( ( p2_s7_yellow18(A,B,D)
                                  & p2_s7_yellow18(B,C,E) )
                               => p2_s7_yellow18(A,C,k5_altcat_1(f1_s7_yellow18,A,B,C,D,E)) ) ) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s7_yellow18))
         => ( p1_s7_yellow18(A)
           => p2_s7_yellow18(A,A,k8_altcat_1(f1_s7_yellow18,A)) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v3_altcat_2(A,f1_s7_yellow18)
        & m1_altcat_2(A,f1_s7_yellow18)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s7_yellow18))
           => ( m1_subset_1(B,u1_struct_0(A))
            <=> p1_s7_yellow18(B) ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s7_yellow18))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(f1_s7_yellow18))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( D = B
                            & E = C )
                         => ( k1_altcat_1(f1_s7_yellow18,B,C) = k1_xboole_0
                            | ! [F] :
                                ( m1_subset_1(F,k1_altcat_1(f1_s7_yellow18,B,C))
                               => ( r2_hidden(F,k1_altcat_1(A,D,E))
                                <=> p2_s7_yellow18(B,C,F) ) ) ) ) ) ) ) ) ) )).

fof(s8_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
         => m1_subset_1(f3_s8_yellow18(A),u1_struct_0(f2_s8_yellow18)) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
             => ( k1_altcat_1(f1_s8_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s8_yellow18,A,B))
                   => r2_hidden(f4_s8_yellow18(A,B,C),k1_binop_1(u1_altcat_1(f2_s8_yellow18),f3_s8_yellow18(A),f3_s8_yellow18(B))) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s8_yellow18))
                 => ~ ( k1_altcat_1(f1_s8_yellow18,A,B) != k1_xboole_0
                      & k1_altcat_1(f1_s8_yellow18,B,C) != k1_xboole_0
                      & ? [D] :
                          ( m1_subset_1(D,k1_altcat_1(f1_s8_yellow18,A,B))
                          & ? [E] :
                              ( m1_subset_1(E,k1_altcat_1(f1_s8_yellow18,B,C))
                              & ? [F] :
                                  ( m1_subset_1(F,u1_struct_0(f2_s8_yellow18))
                                  & ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(f2_s8_yellow18))
                                      & ? [H] :
                                          ( m1_subset_1(H,u1_struct_0(f2_s8_yellow18))
                                          & F = f3_s8_yellow18(A)
                                          & G = f3_s8_yellow18(B)
                                          & H = f3_s8_yellow18(C)
                                          & ? [I] :
                                              ( m1_subset_1(I,k1_altcat_1(f2_s8_yellow18,F,G))
                                              & ? [J] :
                                                  ( m1_subset_1(J,k1_altcat_1(f2_s8_yellow18,G,H))
                                                  & I = f4_s8_yellow18(A,B,D)
                                                  & J = f4_s8_yellow18(B,C,E)
                                                  & f4_s8_yellow18(A,C,k5_altcat_1(f1_s8_yellow18,A,B,C,D,E)) != k5_altcat_1(f2_s8_yellow18,F,G,H,I,J) ) ) ) ) ) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s8_yellow18))
             => ( B = f3_s8_yellow18(A)
               => f4_s8_yellow18(A,A,k8_altcat_1(f1_s8_yellow18,A)) = k8_altcat_1(f2_s8_yellow18,B) ) ) ) )
   => ? [A] :
        ( v9_functor0(A,f1_s8_yellow18,f2_s8_yellow18)
        & v15_functor0(A,f1_s8_yellow18,f2_s8_yellow18)
        & m2_functor0(A,f1_s8_yellow18,f2_s8_yellow18)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
           => k3_functor0(f1_s8_yellow18,f2_s8_yellow18,A,B) = f3_s8_yellow18(B) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(f1_s8_yellow18))
               => ( k1_altcat_1(f1_s8_yellow18,B,C) != k1_xboole_0
                 => ! [D] :
                      ( m1_subset_1(D,k1_altcat_1(f1_s8_yellow18,B,C))
                     => k6_functor0(f1_s8_yellow18,f2_s8_yellow18,A,B,C,D) = f4_s8_yellow18(B,C,D) ) ) ) ) ) )).

fof(s9_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
         => m1_subset_1(f3_s9_yellow18(A),u1_struct_0(f2_s9_yellow18)) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
             => ( k1_altcat_1(f1_s9_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s9_yellow18,A,B))
                   => r2_hidden(f4_s9_yellow18(A,B,C),k1_binop_1(u1_altcat_1(f2_s9_yellow18),f3_s9_yellow18(B),f3_s9_yellow18(A))) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s9_yellow18))
                 => ~ ( k1_altcat_1(f1_s9_yellow18,A,B) != k1_xboole_0
                      & k1_altcat_1(f1_s9_yellow18,B,C) != k1_xboole_0
                      & ? [D] :
                          ( m1_subset_1(D,k1_altcat_1(f1_s9_yellow18,A,B))
                          & ? [E] :
                              ( m1_subset_1(E,k1_altcat_1(f1_s9_yellow18,B,C))
                              & ? [F] :
                                  ( m1_subset_1(F,u1_struct_0(f2_s9_yellow18))
                                  & ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(f2_s9_yellow18))
                                      & ? [H] :
                                          ( m1_subset_1(H,u1_struct_0(f2_s9_yellow18))
                                          & F = f3_s9_yellow18(A)
                                          & G = f3_s9_yellow18(B)
                                          & H = f3_s9_yellow18(C)
                                          & ? [I] :
                                              ( m1_subset_1(I,k1_altcat_1(f2_s9_yellow18,G,F))
                                              & ? [J] :
                                                  ( m1_subset_1(J,k1_altcat_1(f2_s9_yellow18,H,G))
                                                  & I = f4_s9_yellow18(A,B,D)
                                                  & J = f4_s9_yellow18(B,C,E)
                                                  & f4_s9_yellow18(A,C,k5_altcat_1(f1_s9_yellow18,A,B,C,D,E)) != k5_altcat_1(f2_s9_yellow18,H,G,F,J,I) ) ) ) ) ) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s9_yellow18))
             => ( B = f3_s9_yellow18(A)
               => f4_s9_yellow18(A,A,k8_altcat_1(f1_s9_yellow18,A)) = k8_altcat_1(f2_s9_yellow18,B) ) ) ) )
   => ? [A] :
        ( v9_functor0(A,f1_s9_yellow18,f2_s9_yellow18)
        & v16_functor0(A,f1_s9_yellow18,f2_s9_yellow18)
        & m2_functor0(A,f1_s9_yellow18,f2_s9_yellow18)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
           => k3_functor0(f1_s9_yellow18,f2_s9_yellow18,A,B) = f3_s9_yellow18(B) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(f1_s9_yellow18))
               => ( k1_altcat_1(f1_s9_yellow18,B,C) != k1_xboole_0
                 => ! [D] :
                      ( m1_subset_1(D,k1_altcat_1(f1_s9_yellow18,B,C))
                     => k8_functor0(f1_s9_yellow18,f2_s9_yellow18,A,B,C,D) = f4_s9_yellow18(B,C,D) ) ) ) ) ) )).

fof(s10_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
         => k3_functor0(f1_s10_yellow18,f2_s10_yellow18,f3_s10_yellow18,A) = f4_s10_yellow18(A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s10_yellow18))
             => ( k1_altcat_1(f1_s10_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s10_yellow18,A,B))
                   => k6_functor0(f1_s10_yellow18,f2_s10_yellow18,f3_s10_yellow18,A,B,C) = f5_s10_yellow18(A,B,C) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s10_yellow18))
             => ( f4_s10_yellow18(A) = f4_s10_yellow18(B)
               => A = B ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s10_yellow18))
             => ( k1_altcat_1(f1_s10_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s10_yellow18,A,B))
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s10_yellow18,A,B))
                       => ( f5_s10_yellow18(A,B,C) = f5_s10_yellow18(A,B,D)
                         => C = D ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s10_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s10_yellow18))
             => ( k1_altcat_1(f2_s10_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f2_s10_yellow18,A,B))
                   => ? [D] :
                        ( m1_subset_1(D,u1_struct_0(f1_s10_yellow18))
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(f1_s10_yellow18))
                            & ? [F] :
                                ( m1_subset_1(F,k1_altcat_1(f1_s10_yellow18,D,E))
                                & A = f4_s10_yellow18(D)
                                & B = f4_s10_yellow18(E)
                                & k1_altcat_1(f1_s10_yellow18,D,E) != k1_xboole_0
                                & C = f5_s10_yellow18(D,E,F) ) ) ) ) ) ) ) )
   => v21_functor0(f3_s10_yellow18,f1_s10_yellow18,f2_s10_yellow18) )).

fof(s11_yellow18,axiom,
    ( ( ? [A] :
          ( v15_functor0(A,f1_s11_yellow18,f2_s11_yellow18)
          & m2_functor0(A,f1_s11_yellow18,f2_s11_yellow18)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
             => k3_functor0(f1_s11_yellow18,f2_s11_yellow18,A,B) = f3_s11_yellow18(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s11_yellow18))
                 => ( k1_altcat_1(f1_s11_yellow18,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s11_yellow18,B,C))
                       => k6_functor0(f1_s11_yellow18,f2_s11_yellow18,A,B,C,D) = f4_s11_yellow18(B,C,D) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s11_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
             => ( f3_s11_yellow18(A) = f3_s11_yellow18(B)
               => A = B ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s11_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
             => ( k1_altcat_1(f1_s11_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s11_yellow18,A,B))
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s11_yellow18,A,B))
                       => ( f4_s11_yellow18(A,B,C) = f4_s11_yellow18(A,B,D)
                         => C = D ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s11_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s11_yellow18))
             => ( k1_altcat_1(f2_s11_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f2_s11_yellow18,A,B))
                   => ? [D] :
                        ( m1_subset_1(D,u1_struct_0(f1_s11_yellow18))
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(f1_s11_yellow18))
                            & ? [F] :
                                ( m1_subset_1(F,k1_altcat_1(f1_s11_yellow18,D,E))
                                & A = f3_s11_yellow18(D)
                                & B = f3_s11_yellow18(E)
                                & k1_altcat_1(f1_s11_yellow18,D,E) != k1_xboole_0
                                & C = f4_s11_yellow18(D,E,F) ) ) ) ) ) ) ) )
   => r1_functor0(f1_s11_yellow18,f2_s11_yellow18) )).

fof(s12_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
         => k3_functor0(f1_s12_yellow18,f2_s12_yellow18,f3_s12_yellow18,A) = f4_s12_yellow18(A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s12_yellow18))
             => ( k1_altcat_1(f1_s12_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s12_yellow18,A,B))
                   => k8_functor0(f1_s12_yellow18,f2_s12_yellow18,f3_s12_yellow18,A,B,C) = f5_s12_yellow18(A,B,C) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s12_yellow18))
             => ( f4_s12_yellow18(A) = f4_s12_yellow18(B)
               => A = B ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s12_yellow18))
             => ( k1_altcat_1(f1_s12_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s12_yellow18,A,B))
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s12_yellow18,A,B))
                       => ( f5_s12_yellow18(A,B,C) = f5_s12_yellow18(A,B,D)
                         => C = D ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s12_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s12_yellow18))
             => ( k1_altcat_1(f2_s12_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f2_s12_yellow18,A,B))
                   => ? [D] :
                        ( m1_subset_1(D,u1_struct_0(f1_s12_yellow18))
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(f1_s12_yellow18))
                            & ? [F] :
                                ( m1_subset_1(F,k1_altcat_1(f1_s12_yellow18,D,E))
                                & B = f4_s12_yellow18(D)
                                & A = f4_s12_yellow18(E)
                                & k1_altcat_1(f1_s12_yellow18,D,E) != k1_xboole_0
                                & C = f5_s12_yellow18(D,E,F) ) ) ) ) ) ) ) )
   => v21_functor0(f3_s12_yellow18,f1_s12_yellow18,f2_s12_yellow18) )).

fof(s13_yellow18,axiom,
    ( ( ? [A] :
          ( v16_functor0(A,f1_s13_yellow18,f2_s13_yellow18)
          & m2_functor0(A,f1_s13_yellow18,f2_s13_yellow18)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
             => k3_functor0(f1_s13_yellow18,f2_s13_yellow18,A,B) = f3_s13_yellow18(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s13_yellow18))
                 => ( k1_altcat_1(f1_s13_yellow18,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s13_yellow18,B,C))
                       => k8_functor0(f1_s13_yellow18,f2_s13_yellow18,A,B,C,D) = f4_s13_yellow18(B,C,D) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s13_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
             => ( f3_s13_yellow18(A) = f3_s13_yellow18(B)
               => A = B ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s13_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
             => ( k1_altcat_1(f1_s13_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s13_yellow18,A,B))
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s13_yellow18,A,B))
                       => ( f4_s13_yellow18(A,B,C) = f4_s13_yellow18(A,B,D)
                         => C = D ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s13_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s13_yellow18))
             => ( k1_altcat_1(f2_s13_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f2_s13_yellow18,A,B))
                   => ? [D] :
                        ( m1_subset_1(D,u1_struct_0(f1_s13_yellow18))
                        & ? [E] :
                            ( m1_subset_1(E,u1_struct_0(f1_s13_yellow18))
                            & ? [F] :
                                ( m1_subset_1(F,k1_altcat_1(f1_s13_yellow18,D,E))
                                & B = f3_s13_yellow18(D)
                                & A = f3_s13_yellow18(E)
                                & k1_altcat_1(f1_s13_yellow18,D,E) != k1_xboole_0
                                & C = f4_s13_yellow18(D,E,F) ) ) ) ) ) ) ) )
   => r2_functor0(f1_s13_yellow18,f2_s13_yellow18) )).

fof(s14_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s14_yellow18))
         => r2_hidden(f5_s14_yellow18(A),k1_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A))) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s14_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s14_yellow18))
             => ( k1_altcat_1(f1_s14_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s14_yellow18,A,B))
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A)))
                       => ( D = f5_s14_yellow18(A)
                         => ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,B),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,B)))
                             => ( E = f5_s14_yellow18(B)
                               => k5_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,B),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,B),k6_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A,B,C),E) = k5_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,B),D,k6_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A,B,C)) ) ) ) ) ) ) ) ) )
   => ? [A] :
        ( m2_functor2(A,f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,f4_s14_yellow18)
        & r2_functor2(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,f4_s14_yellow18)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s14_yellow18))
           => k2_functor2(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,f4_s14_yellow18,A,B) = f5_s14_yellow18(B) ) ) )).

fof(s15_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s15_yellow18))
         => ( r2_hidden(f5_s15_yellow18(A),k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)))
            & k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A)) != k1_xboole_0
            & ! [B] :
                ( m1_subset_1(B,k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)))
               => ( B = f5_s15_yellow18(A)
                 => v3_altcat_3(B,f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s15_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s15_yellow18))
             => ( k1_altcat_1(f1_s15_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s15_yellow18,A,B))
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)))
                       => ( D = f5_s15_yellow18(A)
                         => ! [E] :
                              ( m1_subset_1(E,k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,B),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,B)))
                             => ( E = f5_s15_yellow18(B)
                               => k5_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,B),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,B),k6_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A,B,C),E) = k5_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,B),D,k6_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A,B,C)) ) ) ) ) ) ) ) ) )
   => ? [A] :
        ( m1_functor3(A,f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,f4_s15_yellow18)
        & r1_functor3(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,f4_s15_yellow18)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s15_yellow18))
           => k2_functor2(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,f4_s15_yellow18,A,B) = f5_s15_yellow18(B) ) ) )).

fof(s16_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s16_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s16_yellow18)
             => ! [C] :
                  ( m1_subset_1(C,f1_s16_yellow18)
                 => ! [D] :
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D) )
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( ( r2_hidden(D,f2_s16_yellow18(A,B))
                              & r2_hidden(E,f2_s16_yellow18(B,C)) )
                           => r2_hidden(k5_relat_1(D,E),f2_s16_yellow18(A,C)) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s16_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s16_yellow18)
             => r1_tarski(f2_s16_yellow18(A,B),k1_funct_2(f3_s16_yellow18(A),f3_s16_yellow18(B))) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s16_yellow18)
         => r2_hidden(k6_partfun1(f3_s16_yellow18(A)),f2_s16_yellow18(A,A)) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v4_yellow18(A)
        & l2_altcat_1(A)
        & u1_struct_0(A) = f1_s16_yellow18
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k3_yellow18(A,B) = f3_s16_yellow18(B) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_altcat_1(A,B,C) = f2_s16_yellow18(B,C) ) ) ) )).

fof(s17_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s17_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s17_yellow18)
             => ! [C] :
                  ( m1_subset_1(C,f1_s17_yellow18)
                 => ! [D] :
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D) )
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( ( p1_s17_yellow18(A,B,D)
                              & p1_s17_yellow18(B,C,E) )
                           => p1_s17_yellow18(A,C,k5_relat_1(D,E)) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s17_yellow18)
         => p1_s17_yellow18(A,A,k6_partfun1(f2_s17_yellow18(A))) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v4_yellow18(A)
        & l2_altcat_1(A)
        & u1_struct_0(A) = f1_s17_yellow18
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k3_yellow18(A,B) = f2_s17_yellow18(B) )
        & ! [B] :
            ( m1_subset_1(B,f1_s17_yellow18)
           => ! [C] :
                ( m1_subset_1(C,f1_s17_yellow18)
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D) )
                   => ( r2_hidden(D,k1_binop_1(u1_altcat_1(A),B,C))
                    <=> ( r2_hidden(D,k1_funct_2(f2_s17_yellow18(B),f2_s17_yellow18(C)))
                        & p1_s17_yellow18(B,C,D) ) ) ) ) ) ) )).

fof(s18_yellow18,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s18_yellow18)
         => ! [B] :
              ( m1_subset_1(B,f1_s18_yellow18)
             => ! [C] :
                  ( m1_subset_1(C,f1_s18_yellow18)
                 => ! [D] :
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D) )
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( ( p2_s18_yellow18(A,B,D)
                              & p2_s18_yellow18(B,C,E) )
                           => p2_s18_yellow18(A,C,k5_relat_1(D,E)) ) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s18_yellow18)
         => ! [B] :
              ( ! [C] :
                  ( r2_hidden(C,B)
                <=> ( r2_hidden(C,f2_s18_yellow18(A))
                    & p1_s18_yellow18(A,C) ) )
             => p2_s18_yellow18(A,A,k6_partfun1(B)) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v4_yellow18(A)
        & l2_altcat_1(A)
        & u1_struct_0(A) = f1_s18_yellow18
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( r2_hidden(C,k3_yellow18(A,B))
              <=> ( r2_hidden(C,f2_s18_yellow18(B))
                  & p1_s18_yellow18(B,C) ) ) )
        & ! [B] :
            ( m1_subset_1(B,f1_s18_yellow18)
           => ! [C] :
                ( m1_subset_1(C,f1_s18_yellow18)
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D) )
                   => ( r2_hidden(D,k1_binop_1(u1_altcat_1(A),B,C))
                    <=> ( r2_hidden(D,k1_funct_2(k3_yellow18(A,B),k3_yellow18(A,C)))
                        & p2_s18_yellow18(B,C,D) ) ) ) ) ) ) )).

fof(s19_yellow18,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) )
         => ( ( u1_struct_0(A) = f1_s19_yellow18
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k1_altcat_1(A,C,D) = f2_s19_yellow18(C,D) ) )
              & u1_struct_0(B) = f1_s19_yellow18
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => k1_altcat_1(B,C,D) = f2_s19_yellow18(C,D) ) ) )
           => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) )).

fof(s20_yellow18,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) )
         => ( ( u1_struct_0(A) = f1_s20_yellow18
              & ! [C] :
                  ( m1_subset_1(C,f1_s20_yellow18)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s20_yellow18)
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(A),C,D))
                          <=> ( r2_hidden(E,k1_funct_2(f2_s20_yellow18(C),f2_s20_yellow18(D)))
                              & p1_s20_yellow18(C,D,E) ) ) ) ) )
              & u1_struct_0(B) = f1_s20_yellow18
              & ! [C] :
                  ( m1_subset_1(C,f1_s20_yellow18)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s20_yellow18)
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( r2_hidden(E,k1_funct_2(f2_s20_yellow18(C),f2_s20_yellow18(D)))
                              & p1_s20_yellow18(C,D,E) ) ) ) ) ) )
           => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) )).

fof(s21_yellow18,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) )
         => ( ( u1_struct_0(A) = f1_s21_yellow18
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( r2_hidden(D,k3_yellow18(A,C))
                    <=> ( r2_hidden(D,f2_s21_yellow18(C))
                        & p1_s21_yellow18(C,D) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,f1_s21_yellow18)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s21_yellow18)
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(A),C,D))
                          <=> ( r2_hidden(E,k1_funct_2(k3_yellow18(A,C),k3_yellow18(A,D)))
                              & p2_s21_yellow18(C,D,E) ) ) ) ) )
              & u1_struct_0(B) = f1_s21_yellow18
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( r2_hidden(D,k3_yellow18(B,C))
                    <=> ( r2_hidden(D,f2_s21_yellow18(C))
                        & p1_s21_yellow18(C,D) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,f1_s21_yellow18)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s21_yellow18)
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( r2_hidden(E,k1_funct_2(k3_yellow18(B,C),k3_yellow18(B,D)))
                              & p2_s21_yellow18(C,D,E) ) ) ) ) ) )
           => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) )).

fof(s22_yellow18,axiom,
    ( ( ? [A] :
          ( v15_functor0(A,f1_s22_yellow18,f2_s22_yellow18)
          & m2_functor0(A,f1_s22_yellow18,f2_s22_yellow18)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
             => k3_functor0(f1_s22_yellow18,f2_s22_yellow18,A,B) = f3_s22_yellow18(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s22_yellow18))
                 => ( k1_altcat_1(f1_s22_yellow18,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s22_yellow18,B,C))
                       => k6_functor0(f1_s22_yellow18,f2_s22_yellow18,A,B,C,D) = f5_s22_yellow18(B,C,D) ) ) ) ) )
      & ? [A] :
          ( v15_functor0(A,f2_s22_yellow18,f1_s22_yellow18)
          & m2_functor0(A,f2_s22_yellow18,f1_s22_yellow18)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
             => k3_functor0(f2_s22_yellow18,f1_s22_yellow18,A,B) = f4_s22_yellow18(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f2_s22_yellow18))
                 => ( k1_altcat_1(f2_s22_yellow18,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f2_s22_yellow18,B,C))
                       => k6_functor0(f2_s22_yellow18,f1_s22_yellow18,A,B,C,D) = f6_s22_yellow18(B,C,D) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s22_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
             => ( A = f4_s22_yellow18(f3_s22_yellow18(B))
               => ( r2_hidden(f7_s22_yellow18(B),k1_altcat_1(f1_s22_yellow18,A,B))
                  & r2_hidden(k2_funct_1(f7_s22_yellow18(B)),k1_altcat_1(f1_s22_yellow18,B,A))
                  & v2_funct_1(f7_s22_yellow18(B)) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s22_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
             => ( B = f3_s22_yellow18(f4_s22_yellow18(A))
               => ( r2_hidden(f8_s22_yellow18(A),k1_altcat_1(f2_s22_yellow18,A,B))
                  & r2_hidden(k2_funct_1(f8_s22_yellow18(A)),k1_altcat_1(f2_s22_yellow18,B,A))
                  & v2_funct_1(f8_s22_yellow18(A)) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s22_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
             => ( k1_altcat_1(f1_s22_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s22_yellow18,A,B))
                   => k5_relat_1(f6_s22_yellow18(f3_s22_yellow18(A),f3_s22_yellow18(B),f5_s22_yellow18(A,B,C)),f7_s22_yellow18(B)) = k5_relat_1(f7_s22_yellow18(A),C) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s22_yellow18))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
             => ( k1_altcat_1(f2_s22_yellow18,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f2_s22_yellow18,A,B))
                   => k5_relat_1(f8_s22_yellow18(A),f5_s22_yellow18(f4_s22_yellow18(A),f4_s22_yellow18(B),f6_s22_yellow18(A,B,C))) = k5_relat_1(C,f8_s22_yellow18(B)) ) ) ) ) )
   => r1_yellow18(f1_s22_yellow18,f2_s22_yellow18) )).

fof(s23_yellow18,axiom,
    ( ! [A,B] :
        ~ ( r2_hidden(A,f1_s23_yellow18)
          & r2_hidden(B,k1_funct_1(f2_s23_yellow18,A))
          & ! [C] :
              ~ ( r2_hidden(C,k1_funct_1(f3_s23_yellow18,A))
                & p1_s23_yellow18(A,B,C) ) )
   => ? [A] :
        ( m3_pboole(A,f1_s23_yellow18,f2_s23_yellow18,f3_s23_yellow18)
        & ! [B,C] :
            ( ( r2_hidden(B,f1_s23_yellow18)
              & r2_hidden(C,k1_funct_1(f2_s23_yellow18,B)) )
           => ( r2_hidden(k1_funct_1(k1_funct_1(A,B),C),k1_funct_1(f3_s23_yellow18,B))
              & p1_s23_yellow18(B,C,k1_funct_1(k1_funct_1(A,B),C)) ) ) ) )).

fof(redefinition_v1_yellow18,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_yellow18(D,A,B,C)
      <=> v2_funct_1(D) ) ) )).

fof(symmetry_r1_yellow18,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)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ( r1_yellow18(A,B)
       => r1_yellow18(B,A) ) ) )).

fof(reflexivity_r1_yellow18,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)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => r1_yellow18(A,A) ) )).

fof(symmetry_r2_yellow18,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & l2_altcat_1(B) )
     => ( r2_yellow18(A,B)
       => r2_yellow18(B,A) ) ) )).

fof(symmetry_r3_yellow18,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)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ( r3_yellow18(A,B)
       => r3_yellow18(B,A) ) ) )).

fof(dt_k1_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k1_yellow18(A))
        & v2_altcat_1(k1_yellow18(A))
        & v6_altcat_1(k1_yellow18(A))
        & l2_altcat_1(k1_yellow18(A)) ) ) )).

fof(dt_k2_yellow18,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)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ( v9_functor0(k2_yellow18(A,B),A,B)
        & v16_functor0(k2_yellow18(A,B),A,B)
        & m2_functor0(k2_yellow18(A,B),A,B) ) ) )).

fof(dt_k3_yellow18,axiom,(
    $true )).

fof(dt_k4_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k4_yellow18(A))
        & v2_altcat_1(k4_yellow18(A))
        & v6_altcat_1(k4_yellow18(A))
        & v11_altcat_1(k4_yellow18(A))
        & v12_altcat_1(k4_yellow18(A))
        & v4_yellow18(k4_yellow18(A))
        & l2_altcat_1(k4_yellow18(A)) ) ) )).

fof(dt_k5_yellow18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v9_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & v15_functor0(k5_yellow18(A),A,k4_yellow18(A))
        & m2_functor0(k5_yellow18(A),A,k4_yellow18(A)) ) ) )).
%------------------------------------------------------------------------------