SET007 Axioms: SET007+698.ax


%------------------------------------------------------------------------------
% File     : SET007+698 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Categorial Background for Duality Theory
% 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    : yellow21 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   77 (   2 unit)
%            Number of atoms       : 1555 (  73 equality)
%            Maximal formula depth :   27 (  12 average)
%            Number of connectives : 1601 ( 123 ~  ;   0  |;1096  &)
%                                         (  43 <=>; 339 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   95 (   1 propositional; 0-4 arity)
%            Number of functors    :   63 (  16 constant; 0-6 arity)
%            Number of variables   :  323 (   0 singleton; 306 !;  17 ?)
%            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_yellow21,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_yellow21(A)) ) )).

fof(fc2_yellow21,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => v4_orders_3(k2_yellow21(A)) ) )).

fof(cc1_yellow21,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v3_yellow21(A) )
       => ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v1_altcat_2(A)
          & v2_yellow21(A) ) ) ) )).

fof(cc2_yellow21,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v11_altcat_1(A)
          & v12_altcat_1(A)
          & v2_yellow21(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)
          & v4_yellow18(A)
          & v1_yellow21(A) ) ) ) )).

fof(rc1_yellow21,axiom,(
    ? [A] :
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v2_altcat_1(A)
      & v6_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)
      & v4_yellow18(A)
      & v1_yellow21(A)
      & v2_yellow21(A)
      & v3_yellow21(A) ) )).

fof(rc2_yellow21,axiom,(
    ? [A] :
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v2_altcat_1(A)
      & v6_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)
      & v4_yellow18(A)
      & v1_yellow21(A)
      & v2_yellow21(A)
      & v4_yellow21(A) ) )).

fof(cc3_yellow21,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_wellord1(A) )
     => ( v1_relat_1(A)
        & v1_wellord1(A)
        & v1_relat_2(A)
        & v4_relat_2(A)
        & v6_relat_2(A)
        & v8_relat_2(A) ) ) )).

fof(rc3_yellow21,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_wellord1(A)
      & v2_wellord1(A)
      & v1_relat_2(A)
      & v4_relat_2(A)
      & v6_relat_2(A)
      & v8_relat_2(A) ) )).

fof(fc3_yellow21,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_relat_1(B)
        & v1_relat_2(B) )
     => ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
        & v1_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) )).

fof(fc4_yellow21,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_relat_1(B)
        & v4_relat_2(B) )
     => ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
        & v4_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) )).

fof(fc5_yellow21,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_relat_1(B)
        & v8_relat_2(B) )
     => ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
        & v8_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) )).

fof(rc4_yellow21,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_relset_1(B,A,A)
          & v1_relat_1(B)
          & v1_wellord1(B)
          & v2_wellord1(B)
          & v1_relat_2(B)
          & v4_relat_2(B)
          & v6_relat_2(B)
          & v8_relat_2(B)
          & v1_partfun1(B,A,A)
          & v5_yellow21(B) ) ) )).

fof(fc6_yellow21,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_wellord1(B)
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & v5_yellow21(B)
        & m1_relset_1(B,A,A) )
     => ( ~ v3_struct_0(g1_orders_2(A,B))
        & v1_orders_2(g1_orders_2(A,B))
        & v2_orders_2(g1_orders_2(A,B))
        & v3_orders_2(g1_orders_2(A,B))
        & v4_orders_2(g1_orders_2(A,B))
        & v1_yellow_0(g1_orders_2(A,B))
        & v2_yellow_0(g1_orders_2(A,B))
        & v3_yellow_0(g1_orders_2(A,B))
        & v16_waybel_0(g1_orders_2(A,B))
        & v24_waybel_0(g1_orders_2(A,B))
        & v25_waybel_0(g1_orders_2(A,B))
        & v1_waybel_8(g1_orders_2(A,B))
        & v2_waybel_8(g1_orders_2(A,B))
        & v1_lattice3(g1_orders_2(A,B))
        & v2_lattice3(g1_orders_2(A,B))
        & v3_lattice3(g1_orders_2(A,B))
        & v2_waybel_3(g1_orders_2(A,B))
        & v3_waybel_3(g1_orders_2(A,B)) ) ) )).

fof(cc4_yellow21,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ( ~ v1_xboole_0(A)
        & ~ v2_setfam_1(A) ) ) )).

fof(fc7_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ( ~ v3_struct_0(k6_yellow21(A))
        & v2_altcat_1(k6_yellow21(A))
        & v6_altcat_1(k6_yellow21(A))
        & v9_altcat_1(k6_yellow21(A))
        & v11_altcat_1(k6_yellow21(A))
        & v12_altcat_1(k6_yellow21(A))
        & v1_altcat_2(k6_yellow21(A))
        & v2_yellow18(k6_yellow21(A))
        & v3_yellow18(k6_yellow21(A))
        & v4_yellow18(k6_yellow21(A))
        & v1_yellow21(k6_yellow21(A))
        & v2_yellow21(k6_yellow21(A))
        & v3_yellow21(k6_yellow21(A))
        & v4_yellow21(k6_yellow21(A)) ) ) )).

fof(fc8_yellow21,axiom,(
    ! [A,B,C] :
      ( ( ~ v2_setfam_1(A)
        & m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
        & m1_subset_1(C,u1_struct_0(k6_yellow21(A))) )
     => ~ v1_xboole_0(k1_altcat_1(k6_yellow21(A),B,C)) ) )).

fof(cc5_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v3_yellow18(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v11_altcat_1(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B)
              & v3_altcat_2(B,A)
              & v3_yellow18(B) ) ) ) ) )).

fof(cc6_yellow21,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_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v11_altcat_1(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B)
              & v3_altcat_2(B,A)
              & v2_yellow18(B) ) ) ) ) )).

fof(cc7_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v9_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B) )
           => ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v9_altcat_1(B)
              & v11_altcat_1(B) ) ) ) ) )).

fof(cc8_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v1_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v11_altcat_1(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B)
              & v3_altcat_2(B,A)
              & v1_yellow21(B) ) ) ) ) )).

fof(cc9_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v9_altcat_1(B)
              & v11_altcat_1(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B)
              & v3_altcat_2(B,A)
              & v2_yellow18(B)
              & v3_yellow18(B)
              & v4_yellow18(B)
              & v1_yellow21(B)
              & v2_yellow21(B) ) ) ) ) )).

fof(cc10_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & v4_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v2_altcat_2(B,A)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v9_altcat_1(B)
              & v11_altcat_1(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B)
              & v3_altcat_2(B,A)
              & v2_yellow18(B)
              & v3_yellow18(B)
              & v4_yellow18(B)
              & v1_yellow21(B)
              & v2_yellow21(B)
              & v4_yellow21(B) ) ) ) ) )).

fof(cc11_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v3_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v9_altcat_1(B)
              & v11_altcat_1(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B)
              & v3_altcat_2(B,A)
              & v2_yellow18(B)
              & v3_yellow18(B)
              & v4_yellow18(B)
              & v1_yellow21(B)
              & v2_yellow21(B)
              & v3_yellow21(B) ) ) ) ) )).

fof(fc9_yellow21,axiom,(
    ! [A,B,C] :
      ( ( ~ v2_setfam_1(A)
        & m1_subset_1(B,u1_struct_0(k7_yellow21(A)))
        & m1_subset_1(C,u1_struct_0(k7_yellow21(A))) )
     => ~ v1_xboole_0(k1_altcat_1(k7_yellow21(A),B,C)) ) )).

fof(fc10_yellow21,axiom,(
    ! [A,B,C] :
      ( ( ~ v2_setfam_1(A)
        & m1_subset_1(B,u1_struct_0(k8_yellow21(A)))
        & m1_subset_1(C,u1_struct_0(k8_yellow21(A))) )
     => ~ v1_xboole_0(k1_altcat_1(k8_yellow21(A),B,C)) ) )).

fof(d1_yellow21,axiom,(
    ! [A] :
      ( ( l1_struct_0(A)
       => k1_yellow21(A) = A )
      & ( ~ l1_struct_0(A)
       => k1_yellow21(A) = g1_struct_0(A) ) ) )).

fof(d2_yellow21,axiom,(
    ! [A,B] :
      ( B = k2_yellow21(A)
    <=> ! [C] :
          ( r2_hidden(C,B)
        <=> ( v1_orders_2(C)
            & v2_orders_2(C)
            & v3_orders_2(C)
            & v4_orders_2(C)
            & l1_orders_2(C)
            & r2_hidden(u1_struct_0(k1_yellow21(C)),A) ) ) ) )).

fof(d3_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v1_yellow21(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( l1_struct_0(C)
                & B = C
                & k3_yellow18(A,B) = u1_struct_0(C) ) ) ) ) )).

fof(d4_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v2_yellow21(A)
      <=> ( v9_altcat_1(A)
          & v3_yellow18(A)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( ( v2_orders_2(D)
                        & v3_orders_2(D)
                        & v4_orders_2(D)
                        & v1_lattice3(D)
                        & v2_lattice3(D)
                        & l1_orders_2(D) )
                     => ! [E] :
                          ( ( v2_orders_2(E)
                            & v3_orders_2(E)
                            & v4_orders_2(E)
                            & v1_lattice3(E)
                            & v2_lattice3(E)
                            & l1_orders_2(E) )
                         => ( ( D = B
                              & E = C )
                           => r1_tarski(k1_altcat_1(A,B,C),k1_orders_3(D,E)) ) ) ) ) ) ) ) ) )).

fof(d5_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v3_yellow21(A)
      <=> ( v2_yellow21(A)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & v3_lattice3(B)
                & l1_orders_2(B) ) ) ) ) ) )).

fof(t1_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v1_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_yellow18(A,B) = u1_struct_0(k1_yellow21(B)) ) ) )).

fof(t2_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v3_yellow18(A)
        & v1_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_altcat_1(A,B) = k7_grcat_1(k1_yellow21(B)) ) ) )).

fof(d6_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_yellow21(A,B) = B ) ) )).

fof(d7_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(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))
                   => k5_yellow21(A,B,C,D) = D ) ) ) ) ) )).

fof(t3_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(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) = k7_funct_2(u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D)),k5_yellow21(A,B,C,E),k5_yellow21(A,C,D,F)) ) ) ) ) ) ) ) )).

fof(d8_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A) )
     => ( v4_yellow21(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
                      & m2_relset_1(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) )
                   => ( v23_waybel_0(D,k3_yellow21(A,B),k3_yellow21(A,C))
                     => r2_hidden(D,k1_altcat_1(A,B,C)) ) ) ) ) ) ) )).

fof(t4_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & v4_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v23_waybel_0(k5_yellow21(A,B,C,D),k3_yellow21(A,B),k3_yellow21(A,C))
                   => v3_altcat_3(D,A,B,C) ) ) ) ) ) )).

fof(t5_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(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)
                      & ~ v23_waybel_0(k5_yellow21(A,B,C,D),k3_yellow21(A,B),k3_yellow21(A,C)) ) ) ) ) ) )).

fof(d9_yellow21,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v5_yellow21(A)
      <=> ? [B] :
          ! [C] :
            ( r2_hidden(C,k3_relat_1(A))
           => r2_hidden(k4_tarski(C,B),A) ) ) ) )).

fof(t6_yellow21,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v2_funct_1(C) )
     => ! [D] :
          ( v1_relat_1(D)
         => ( r2_hidden(k4_tarski(A,B),k5_relat_1(k5_relat_1(C,D),k2_funct_1(C)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(B,k1_relat_1(C))
              & r2_hidden(k4_tarski(k1_funct_1(C,A),k1_funct_1(C,B)),D) ) ) ) ) )).

fof(t7_yellow21,axiom,(
    ! [A,B] :
      ( v3_ordinal1(B)
     => ~ ( r2_wellord2(A,B)
          & ! [C] :
              ( ( v1_relat_2(C)
                & v4_relat_2(C)
                & v8_relat_2(C)
                & v1_partfun1(C,A,A)
                & m2_relset_1(C,A,A) )
             => ~ ( r2_wellord1(C,A)
                  & k2_wellord2(C) = B ) ) ) ) )).

fof(t8_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_yellow_0(A)
      <=> v5_yellow21(u1_orders_2(A)) ) ) )).

fof(t9_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ( v2_wellord1(u1_orders_2(A))
       => ( v16_waybel_0(A)
          & v3_lattice3(A)
          & v3_waybel_3(A) ) ) ) )).

fof(t10_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ( v2_wellord1(u1_orders_2(A))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_orders_2(A,C,B)
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ~ ( v1_waybel_3(D,A)
                            & r3_orders_2(A,C,D)
                            & r3_orders_2(A,D,B) ) ) ) ) ) ) ) )).

fof(t11_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ( v2_wellord1(u1_orders_2(A))
       => v2_waybel_8(A) ) ) )).

fof(d10_yellow21,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ ! [B] :
              ( m1_subset_1(B,A)
             => v1_xboole_0(B) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v6_altcat_1(B)
              & v11_altcat_1(B)
              & v12_altcat_1(B)
              & v2_yellow21(B)
              & l2_altcat_1(B) )
           => ( B = k6_yellow21(A)
            <=> ( ! [C] :
                    ( ( v2_orders_2(C)
                      & v3_orders_2(C)
                      & v4_orders_2(C)
                      & v1_lattice3(C)
                      & v2_lattice3(C)
                      & l1_orders_2(C) )
                   => ( m1_subset_1(C,u1_struct_0(B))
                    <=> ( v1_orders_2(C)
                        & v3_lattice3(C)
                        & r2_hidden(u1_struct_0(C),A) ) ) )
                & ! [C] :
                    ( m1_subset_1(C,u1_struct_0(B))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(B))
                       => ! [E] :
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D)))
                              & v5_orders_3(E,k3_yellow21(B,C),k3_yellow21(B,D))
                              & m2_relset_1(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D))) )
                           => ( r2_hidden(E,k1_altcat_1(B,C,D))
                            <=> v22_waybel_0(E,k3_yellow21(B,C),k3_yellow21(B,D)) ) ) ) ) ) ) ) ) ) )).

fof(t12_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => r1_tarski(u1_struct_0(k6_yellow21(A)),k2_yellow21(A)) ) )).

fof(t13_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
        <=> ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B)
            & r2_hidden(B,k2_yellow21(A)) ) ) ) )).

fof(t14_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( r2_hidden(u1_struct_0(B),A)
           => ( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
            <=> ( v1_orders_2(B)
                & v3_lattice3(B) ) ) ) ) ) )).

fof(t15_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_yellow21(A)))
             => ! [D] :
                  ( r2_hidden(D,k1_altcat_1(k6_yellow21(A),B,C))
                <=> ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k4_yellow21(k6_yellow21(A),B)),u1_struct_0(k4_yellow21(k6_yellow21(A),C)))
                    & v22_waybel_0(D,k4_yellow21(k6_yellow21(A),B),k4_yellow21(k6_yellow21(A),C))
                    & m2_relset_1(D,u1_struct_0(k4_yellow21(k6_yellow21(A),B)),u1_struct_0(k4_yellow21(k6_yellow21(A),C))) ) ) ) ) ) )).

fof(t16_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( D = C
                   => k3_yellow18(B,D) = k3_yellow18(A,C) ) ) ) ) ) )).

fof(d11_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & v2_altcat_2(B,k6_yellow21(A))
            & v3_altcat_2(B,k6_yellow21(A))
            & m1_altcat_2(B,k6_yellow21(A)) )
         => ( B = k7_yellow21(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(k6_yellow21(A)))
               => ( m1_subset_1(C,u1_struct_0(B))
                <=> v3_waybel_3(k4_yellow21(k6_yellow21(A),C)) ) ) ) ) ) )).

fof(d12_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & v2_altcat_2(B,k7_yellow21(A))
            & v3_altcat_2(B,k7_yellow21(A))
            & m1_altcat_2(B,k7_yellow21(A)) )
         => ( B = k8_yellow21(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(k7_yellow21(A)))
               => ( m1_subset_1(C,u1_struct_0(B))
                <=> v2_waybel_8(k4_yellow21(k7_yellow21(A),C)) ) ) ) ) ) )).

fof(t17_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( r2_hidden(u1_struct_0(B),A)
           => ( m1_subset_1(B,u1_struct_0(k7_yellow21(A)))
            <=> ( v1_orders_2(B)
                & v3_lattice3(B)
                & v3_waybel_3(B) ) ) ) ) ) )).

fof(t18_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( r2_hidden(u1_struct_0(B),A)
           => ( m1_subset_1(B,u1_struct_0(k8_yellow21(A)))
            <=> ( v1_orders_2(B)
                & v3_lattice3(B)
                & v2_waybel_8(B) ) ) ) ) ) )).

fof(t19_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_yellow21(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_yellow21(A)))
             => ! [D] :
                  ( r2_hidden(D,k1_altcat_1(k7_yellow21(A),B,C))
                <=> ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k4_yellow21(k7_yellow21(A),B)),u1_struct_0(k4_yellow21(k7_yellow21(A),C)))
                    & v22_waybel_0(D,k4_yellow21(k7_yellow21(A),B),k4_yellow21(k7_yellow21(A),C))
                    & m2_relset_1(D,u1_struct_0(k4_yellow21(k7_yellow21(A),B)),u1_struct_0(k4_yellow21(k7_yellow21(A),C))) ) ) ) ) ) )).

fof(t20_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k8_yellow21(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k8_yellow21(A)))
             => ! [D] :
                  ( r2_hidden(D,k1_altcat_1(k8_yellow21(A),B,C))
                <=> ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k4_yellow21(k8_yellow21(A),B)),u1_struct_0(k4_yellow21(k8_yellow21(A),C)))
                    & v22_waybel_0(D,k4_yellow21(k8_yellow21(A),B),k4_yellow21(k8_yellow21(A),C))
                    & m2_relset_1(D,u1_struct_0(k4_yellow21(k8_yellow21(A),B)),u1_struct_0(k4_yellow21(k8_yellow21(A),C))) ) ) ) ) ) )).

fof(s1_yellow21,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s1_yellow21)
         => ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & l1_orders_2(C) )
                 => ( ( r2_hidden(A,f1_s1_yellow21)
                      & r2_hidden(B,f1_s1_yellow21)
                      & r2_hidden(C,f1_s1_yellow21) )
                   => ! [D] :
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                          & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                       => ! [E] :
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                              & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                           => ( ( p1_s1_yellow21(A,B,D)
                                & p1_s1_yellow21(B,C,E) )
                             => p1_s1_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ( r2_hidden(A,f1_s1_yellow21)
           => p1_s1_yellow21(A,A,k7_grcat_1(A)) ) ) )
   => ? [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)
        & v2_yellow21(A)
        & u1_struct_0(A) = f1_s1_yellow21
        & ! [B] :
            ( ( v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & v2_lattice3(B)
              & l1_orders_2(B) )
           => ! [C] :
                ( ( v2_orders_2(C)
                  & v3_orders_2(C)
                  & v4_orders_2(C)
                  & v1_lattice3(C)
                  & v2_lattice3(C)
                  & l1_orders_2(C) )
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                      & v5_orders_3(D,B,C)
                      & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                   => ( r2_hidden(D,k1_binop_1(u1_altcat_1(A),B,C))
                    <=> ( r2_hidden(B,f1_s1_yellow21)
                        & r2_hidden(C,f1_s1_yellow21)
                        & p1_s1_yellow21(B,C,D) ) ) ) ) ) ) )).

fof(s2_yellow21,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s2_yellow21)
         => ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & l1_orders_2(C) )
                 => ( ( r2_hidden(A,f1_s2_yellow21)
                      & r2_hidden(B,f1_s2_yellow21)
                      & r2_hidden(C,f1_s2_yellow21) )
                   => ! [D] :
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                          & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                       => ! [E] :
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                              & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                           => ( ( p1_s2_yellow21(A,B,D)
                                & p1_s2_yellow21(B,C,E) )
                             => p1_s2_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ( r2_hidden(A,f1_s2_yellow21)
           => p1_s2_yellow21(A,A,k7_grcat_1(A)) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A)
        & u1_struct_0(A) = f1_s2_yellow21
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
                      & v5_orders_3(D,k3_yellow21(A,B),k3_yellow21(A,C))
                      & m2_relset_1(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) )
                   => ( r2_hidden(D,k1_altcat_1(A,B,C))
                    <=> p1_s2_yellow21(k3_yellow21(A,B),k3_yellow21(A,C),D) ) ) ) ) ) )).

fof(s3_yellow21,axiom,
    ( ( ? [A] :
          ( v1_orders_2(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & l1_orders_2(A)
          & p1_s3_yellow21(A)
          & r2_hidden(u1_struct_0(A),f1_s3_yellow21) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & l1_orders_2(C) )
                 => ( ( p1_s3_yellow21(A)
                      & p1_s3_yellow21(B)
                      & p1_s3_yellow21(C) )
                   => ! [D] :
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                          & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                       => ! [E] :
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                              & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                           => ( ( p2_s3_yellow21(A,B,D)
                                & p2_s3_yellow21(B,C,E) )
                             => p2_s3_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ( p1_s3_yellow21(A)
           => p2_s3_yellow21(A,A,k7_grcat_1(A)) ) ) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v6_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A)
        & ! [B] :
            ( ( v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & v2_lattice3(B)
              & l1_orders_2(B) )
           => ( m1_subset_1(B,u1_struct_0(A))
            <=> ( v1_orders_2(B)
                & p1_s3_yellow21(B)
                & r2_hidden(u1_struct_0(B),f1_s3_yellow21) ) ) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
                      & v5_orders_3(D,k3_yellow21(A,B),k3_yellow21(A,C))
                      & m2_relset_1(D,u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) )
                   => ( r2_hidden(D,k1_altcat_1(A,B,C))
                    <=> p2_s3_yellow21(k3_yellow21(A,B),k3_yellow21(A,C),D) ) ) ) ) ) )).

fof(s4_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & v2_yellow21(B)
            & l2_altcat_1(B) )
         => ( ( u1_struct_0(A) = f1_s4_yellow21
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D)))
                            & v5_orders_3(E,k3_yellow21(A,C),k3_yellow21(A,D))
                            & m2_relset_1(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D))) )
                         => ( r2_hidden(E,k1_altcat_1(A,C,D))
                          <=> p1_s4_yellow21(C,D,E) ) ) ) )
              & u1_struct_0(B) = f1_s4_yellow21
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D)))
                            & v5_orders_3(E,k3_yellow21(B,C),k3_yellow21(B,D))
                            & m2_relset_1(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D))) )
                         => ( r2_hidden(E,k1_altcat_1(B,C,D))
                          <=> p1_s4_yellow21(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(s5_yellow21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & v2_yellow21(B)
            & l2_altcat_1(B) )
         => ( ( ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & l1_orders_2(C) )
                 => ( m1_subset_1(C,u1_struct_0(A))
                  <=> ( v1_orders_2(C)
                      & p1_s5_yellow21(C)
                      & r2_hidden(u1_struct_0(C),f1_s5_yellow21) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D)))
                            & v5_orders_3(E,k3_yellow21(A,C),k3_yellow21(A,D))
                            & m2_relset_1(E,u1_struct_0(k3_yellow21(A,C)),u1_struct_0(k3_yellow21(A,D))) )
                         => ( r2_hidden(E,k1_altcat_1(A,C,D))
                          <=> p2_s5_yellow21(C,D,E) ) ) ) )
              & ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & l1_orders_2(C) )
                 => ( m1_subset_1(C,u1_struct_0(B))
                  <=> ( v1_orders_2(C)
                      & p1_s5_yellow21(C)
                      & r2_hidden(u1_struct_0(C),f1_s5_yellow21) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D)))
                            & v5_orders_3(E,k3_yellow21(B,C),k3_yellow21(B,D))
                            & m2_relset_1(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D))) )
                         => ( r2_hidden(E,k1_altcat_1(B,C,D))
                          <=> p2_s5_yellow21(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(s6_yellow21,axiom,
    ( ( ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s6_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f1_s6_yellow21))
                      & r2_hidden(B,u1_struct_0(f1_s6_yellow21))
                      & p1_s6_yellow21(A,B,C) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s6_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f2_s6_yellow21))
                      & r2_hidden(B,u1_struct_0(f2_s6_yellow21))
                      & p2_s6_yellow21(A,B,C) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ( r2_hidden(A,u1_struct_0(f1_s6_yellow21))
           => r2_hidden(f3_s6_yellow21(A),u1_struct_0(f2_s6_yellow21)) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( p1_s6_yellow21(A,B,C)
                   => ( v1_funct_1(f4_s6_yellow21(A,B,C))
                      & v1_funct_2(f4_s6_yellow21(A,B,C),u1_struct_0(f3_s6_yellow21(A)),u1_struct_0(f3_s6_yellow21(B)))
                      & m2_relset_1(f4_s6_yellow21(A,B,C),u1_struct_0(f3_s6_yellow21(A)),u1_struct_0(f3_s6_yellow21(B)))
                      & p2_s6_yellow21(f3_s6_yellow21(A),f3_s6_yellow21(B),f4_s6_yellow21(A,B,C)) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ( r2_hidden(A,u1_struct_0(f1_s6_yellow21))
           => f4_s6_yellow21(A,A,k7_grcat_1(A)) = k7_grcat_1(f3_s6_yellow21(A)) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & l1_orders_2(C) )
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                            & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                         => ( ( p1_s6_yellow21(A,B,D)
                              & p1_s6_yellow21(B,C,E) )
                           => f4_s6_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) = k5_relat_1(f4_s6_yellow21(A,B,D),f4_s6_yellow21(B,C,E)) ) ) ) ) ) ) )
   => ? [A] :
        ( v9_functor0(A,f1_s6_yellow21,f2_s6_yellow21)
        & v15_functor0(A,f1_s6_yellow21,f2_s6_yellow21)
        & m2_functor0(A,f1_s6_yellow21,f2_s6_yellow21)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s6_yellow21))
           => k3_functor0(f1_s6_yellow21,f2_s6_yellow21,A,B) = f3_s6_yellow21(k3_yellow21(f1_s6_yellow21,B)) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s6_yellow21))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(f1_s6_yellow21))
               => ( k1_altcat_1(f1_s6_yellow21,B,C) != k1_xboole_0
                 => ! [D] :
                      ( m1_subset_1(D,k1_altcat_1(f1_s6_yellow21,B,C))
                     => k6_functor0(f1_s6_yellow21,f2_s6_yellow21,A,B,C,D) = f4_s6_yellow21(k3_yellow21(f1_s6_yellow21,B),k3_yellow21(f1_s6_yellow21,C),k5_yellow21(f1_s6_yellow21,B,C,D)) ) ) ) ) ) )).

fof(s7_yellow21,axiom,
    ( ( ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s7_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f1_s7_yellow21))
                      & r2_hidden(B,u1_struct_0(f1_s7_yellow21))
                      & p1_s7_yellow21(A,B,C) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s7_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f2_s7_yellow21))
                      & r2_hidden(B,u1_struct_0(f2_s7_yellow21))
                      & p2_s7_yellow21(A,B,C) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ( r2_hidden(A,u1_struct_0(f1_s7_yellow21))
           => r2_hidden(f3_s7_yellow21(A),u1_struct_0(f2_s7_yellow21)) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( p1_s7_yellow21(A,B,C)
                   => ( v1_funct_1(f4_s7_yellow21(A,B,C))
                      & v1_funct_2(f4_s7_yellow21(A,B,C),u1_struct_0(f3_s7_yellow21(B)),u1_struct_0(f3_s7_yellow21(A)))
                      & m2_relset_1(f4_s7_yellow21(A,B,C),u1_struct_0(f3_s7_yellow21(B)),u1_struct_0(f3_s7_yellow21(A)))
                      & p2_s7_yellow21(f3_s7_yellow21(B),f3_s7_yellow21(A),f4_s7_yellow21(A,B,C)) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ( r2_hidden(A,u1_struct_0(f1_s7_yellow21))
           => f4_s7_yellow21(A,A,k7_grcat_1(A)) = k7_grcat_1(f3_s7_yellow21(A)) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & l1_orders_2(C) )
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                            & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                         => ( ( p1_s7_yellow21(A,B,D)
                              & p1_s7_yellow21(B,C,E) )
                           => f4_s7_yellow21(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) = k5_relat_1(f4_s7_yellow21(B,C,E),f4_s7_yellow21(A,B,D)) ) ) ) ) ) ) )
   => ? [A] :
        ( v9_functor0(A,f1_s7_yellow21,f2_s7_yellow21)
        & v16_functor0(A,f1_s7_yellow21,f2_s7_yellow21)
        & m2_functor0(A,f1_s7_yellow21,f2_s7_yellow21)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s7_yellow21))
           => k3_functor0(f1_s7_yellow21,f2_s7_yellow21,A,B) = f3_s7_yellow21(k3_yellow21(f1_s7_yellow21,B)) )
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s7_yellow21))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(f1_s7_yellow21))
               => ( k1_altcat_1(f1_s7_yellow21,B,C) != k1_xboole_0
                 => ! [D] :
                      ( m1_subset_1(D,k1_altcat_1(f1_s7_yellow21,B,C))
                     => k8_functor0(f1_s7_yellow21,f2_s7_yellow21,A,B,C,D) = f4_s7_yellow21(k3_yellow21(f1_s7_yellow21,B),k3_yellow21(f1_s7_yellow21,C),k5_yellow21(f1_s7_yellow21,B,C,D)) ) ) ) ) ) )).

fof(s8_yellow21,axiom,
    ( ( ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s8_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f1_s8_yellow21))
                      & r2_hidden(B,u1_struct_0(f1_s8_yellow21))
                      & p1_s8_yellow21(A,B,C) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s8_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f2_s8_yellow21))
                      & r2_hidden(B,u1_struct_0(f2_s8_yellow21))
                      & p2_s8_yellow21(A,B,C) ) ) ) ) )
      & ? [A] :
          ( v15_functor0(A,f1_s8_yellow21,f2_s8_yellow21)
          & m2_functor0(A,f1_s8_yellow21,f2_s8_yellow21)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s8_yellow21))
             => k3_functor0(f1_s8_yellow21,f2_s8_yellow21,A,B) = f3_s8_yellow21(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s8_yellow21))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s8_yellow21))
                 => ( k1_altcat_1(f1_s8_yellow21,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s8_yellow21,B,C))
                       => k6_functor0(f1_s8_yellow21,f2_s8_yellow21,A,B,C,D) = f4_s8_yellow21(B,C,D) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ( ( r2_hidden(A,u1_struct_0(f1_s8_yellow21))
                  & r2_hidden(B,u1_struct_0(f1_s8_yellow21))
                  & f3_s8_yellow21(A) = f3_s8_yellow21(B) )
               => A = B ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                     => ( ( p1_s8_yellow21(A,B,C)
                          & p1_s8_yellow21(A,B,D)
                          & f4_s8_yellow21(A,B,C) = f4_s8_yellow21(A,B,D) )
                       => C = D ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ~ ( p2_s8_yellow21(A,B,C)
                      & ! [D] :
                          ( ( v2_orders_2(D)
                            & v3_orders_2(D)
                            & v4_orders_2(D)
                            & v1_lattice3(D)
                            & v2_lattice3(D)
                            & l1_orders_2(D) )
                         => ! [E] :
                              ( ( v2_orders_2(E)
                                & v3_orders_2(E)
                                & v4_orders_2(E)
                                & v1_lattice3(E)
                                & v2_lattice3(E)
                                & l1_orders_2(E) )
                             => ! [F] :
                                  ( ( v1_funct_1(F)
                                    & v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
                                    & m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
                                 => ~ ( r2_hidden(D,u1_struct_0(f1_s8_yellow21))
                                      & r2_hidden(E,u1_struct_0(f1_s8_yellow21))
                                      & p1_s8_yellow21(D,E,F)
                                      & A = f3_s8_yellow21(D)
                                      & B = f3_s8_yellow21(E)
                                      & C = f4_s8_yellow21(D,E,F) ) ) ) ) ) ) ) ) )
   => r1_functor0(f1_s8_yellow21,f2_s8_yellow21) )).

fof(s9_yellow21,axiom,
    ( ( ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f1_s9_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f1_s9_yellow21))
                      & r2_hidden(B,u1_struct_0(f1_s9_yellow21))
                      & p1_s9_yellow21(A,B,C) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ( r2_hidden(C,k1_binop_1(u1_altcat_1(f2_s9_yellow21),A,B))
                  <=> ( r2_hidden(A,u1_struct_0(f2_s9_yellow21))
                      & r2_hidden(B,u1_struct_0(f2_s9_yellow21))
                      & p2_s9_yellow21(A,B,C) ) ) ) ) )
      & ? [A] :
          ( v16_functor0(A,f1_s9_yellow21,f2_s9_yellow21)
          & m2_functor0(A,f1_s9_yellow21,f2_s9_yellow21)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s9_yellow21))
             => k3_functor0(f1_s9_yellow21,f2_s9_yellow21,A,B) = f3_s9_yellow21(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s9_yellow21))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s9_yellow21))
                 => ( k1_altcat_1(f1_s9_yellow21,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s9_yellow21,B,C))
                       => k8_functor0(f1_s9_yellow21,f2_s9_yellow21,A,B,C,D) = f4_s9_yellow21(B,C,D) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ( ( r2_hidden(A,u1_struct_0(f1_s9_yellow21))
                  & r2_hidden(B,u1_struct_0(f1_s9_yellow21))
                  & f3_s9_yellow21(A) = f3_s9_yellow21(B) )
               => A = B ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                     => ( f4_s9_yellow21(A,B,C) = f4_s9_yellow21(A,B,D)
                       => C = D ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ! [B] :
              ( ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
                 => ~ ( p2_s9_yellow21(A,B,C)
                      & ! [D] :
                          ( ( v2_orders_2(D)
                            & v3_orders_2(D)
                            & v4_orders_2(D)
                            & v1_lattice3(D)
                            & v2_lattice3(D)
                            & l1_orders_2(D) )
                         => ! [E] :
                              ( ( v2_orders_2(E)
                                & v3_orders_2(E)
                                & v4_orders_2(E)
                                & v1_lattice3(E)
                                & v2_lattice3(E)
                                & l1_orders_2(E) )
                             => ! [F] :
                                  ( ( v1_funct_1(F)
                                    & v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
                                    & m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
                                 => ~ ( r2_hidden(D,u1_struct_0(f1_s9_yellow21))
                                      & r2_hidden(E,u1_struct_0(f1_s9_yellow21))
                                      & p1_s9_yellow21(D,E,F)
                                      & B = f3_s9_yellow21(D)
                                      & A = f3_s9_yellow21(E)
                                      & C = f4_s9_yellow21(D,E,F) ) ) ) ) ) ) ) ) )
   => r2_functor0(f1_s9_yellow21,f2_s9_yellow21) )).

fof(s10_yellow21,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s10_yellow21))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k3_yellow21(f1_s10_yellow21,A)),u1_struct_0(k3_yellow21(f1_s10_yellow21,B)))
                    & v5_orders_3(C,k3_yellow21(f1_s10_yellow21,A),k3_yellow21(f1_s10_yellow21,B))
                    & m2_relset_1(C,u1_struct_0(k3_yellow21(f1_s10_yellow21,A)),u1_struct_0(k3_yellow21(f1_s10_yellow21,B))) )
                 => ( r2_hidden(C,k1_altcat_1(f1_s10_yellow21,A,B))
                  <=> p1_s10_yellow21(k3_yellow21(f1_s10_yellow21,A),k3_yellow21(f1_s10_yellow21,B),C) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s10_yellow21))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k3_yellow21(f2_s10_yellow21,A)),u1_struct_0(k3_yellow21(f2_s10_yellow21,B)))
                    & v5_orders_3(C,k3_yellow21(f2_s10_yellow21,A),k3_yellow21(f2_s10_yellow21,B))
                    & m2_relset_1(C,u1_struct_0(k3_yellow21(f2_s10_yellow21,A)),u1_struct_0(k3_yellow21(f2_s10_yellow21,B))) )
                 => ( r2_hidden(C,k1_altcat_1(f2_s10_yellow21,A,B))
                  <=> p2_s10_yellow21(k3_yellow21(f2_s10_yellow21,A),k3_yellow21(f2_s10_yellow21,B),C) ) ) ) )
      & ? [A] :
          ( v15_functor0(A,f1_s10_yellow21,f2_s10_yellow21)
          & m2_functor0(A,f1_s10_yellow21,f2_s10_yellow21)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
             => k3_functor0(f1_s10_yellow21,f2_s10_yellow21,A,B) = f3_s10_yellow21(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f1_s10_yellow21))
                 => ( k1_altcat_1(f1_s10_yellow21,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f1_s10_yellow21,B,C))
                       => k6_functor0(f1_s10_yellow21,f2_s10_yellow21,A,B,C,D) = f5_s10_yellow21(B,C,D) ) ) ) ) )
      & ? [A] :
          ( v15_functor0(A,f2_s10_yellow21,f1_s10_yellow21)
          & m2_functor0(A,f2_s10_yellow21,f1_s10_yellow21)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
             => k3_functor0(f2_s10_yellow21,f1_s10_yellow21,A,B) = f4_s10_yellow21(B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(f2_s10_yellow21))
                 => ( k1_altcat_1(f2_s10_yellow21,B,C) != k1_xboole_0
                   => ! [D] :
                        ( m1_subset_1(D,k1_altcat_1(f2_s10_yellow21,B,C))
                       => k6_functor0(f2_s10_yellow21,f1_s10_yellow21,A,B,C,D) = f6_s10_yellow21(B,C,D) ) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ~ ( r2_hidden(A,u1_struct_0(f1_s10_yellow21))
              & ! [B] :
                  ( ( v1_funct_1(B)
                    & v1_funct_2(B,u1_struct_0(f4_s10_yellow21(f3_s10_yellow21(A))),u1_struct_0(A))
                    & v5_orders_3(B,f4_s10_yellow21(f3_s10_yellow21(A)),A)
                    & m2_relset_1(B,u1_struct_0(f4_s10_yellow21(f3_s10_yellow21(A))),u1_struct_0(A)) )
                 => ~ ( B = f7_s10_yellow21(A)
                      & v23_waybel_0(B,f4_s10_yellow21(f3_s10_yellow21(A)),A)
                      & p1_s10_yellow21(f4_s10_yellow21(f3_s10_yellow21(A)),A,B)
                      & p1_s10_yellow21(A,f4_s10_yellow21(f3_s10_yellow21(A)),k2_funct_1(B)) ) ) ) )
      & ! [A] :
          ( ( v2_orders_2(A)
            & v3_orders_2(A)
            & v4_orders_2(A)
            & v1_lattice3(A)
            & v2_lattice3(A)
            & l1_orders_2(A) )
         => ~ ( r2_hidden(A,u1_struct_0(f2_s10_yellow21))
              & ! [B] :
                  ( ( v1_funct_1(B)
                    & v1_funct_2(B,u1_struct_0(A),u1_struct_0(f3_s10_yellow21(f4_s10_yellow21(A))))
                    & v5_orders_3(B,A,f3_s10_yellow21(f4_s10_yellow21(A)))
                    & m2_relset_1(B,u1_struct_0(A),u1_struct_0(f3_s10_yellow21(f4_s10_yellow21(A)))) )
                 => ~ ( B = f8_s10_yellow21(A)
                      & v23_waybel_0(B,A,f3_s10_yellow21(f4_s10_yellow21(A)))
                      & p2_s10_yellow21(A,f3_s10_yellow21(f4_s10_yellow21(A)),B)
                      & p2_s10_yellow21(f3_s10_yellow21(f4_s10_yellow21(A)),A,k2_funct_1(B)) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s10_yellow21))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s10_yellow21))
             => ( k1_altcat_1(f1_s10_yellow21,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f1_s10_yellow21,A,B))
                   => k5_relat_1(f6_s10_yellow21(f3_s10_yellow21(A),f3_s10_yellow21(B),f5_s10_yellow21(A,B,C)),f7_s10_yellow21(B)) = k5_relat_1(f7_s10_yellow21(A),k5_yellow21(f1_s10_yellow21,A,B,C)) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s10_yellow21))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s10_yellow21))
             => ( k1_altcat_1(f2_s10_yellow21,A,B) != k1_xboole_0
               => ! [C] :
                    ( m1_subset_1(C,k1_altcat_1(f2_s10_yellow21,A,B))
                   => k5_relat_1(f8_s10_yellow21(A),f5_s10_yellow21(f4_s10_yellow21(A),f4_s10_yellow21(B),f6_s10_yellow21(A,B,C))) = k5_relat_1(k5_yellow21(f2_s10_yellow21,A,B,C),f8_s10_yellow21(B)) ) ) ) ) )
   => r1_yellow18(f1_s10_yellow21,f2_s10_yellow21) )).

fof(dt_k1_yellow21,axiom,(
    ! [A] : l1_struct_0(k1_yellow21(A)) )).

fof(dt_k2_yellow21,axiom,(
    $true )).

fof(dt_k3_yellow21,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v2_orders_2(k3_yellow21(A,B))
        & v3_orders_2(k3_yellow21(A,B))
        & v4_orders_2(k3_yellow21(A,B))
        & v1_lattice3(k3_yellow21(A,B))
        & v2_lattice3(k3_yellow21(A,B))
        & l1_orders_2(k3_yellow21(A,B)) ) ) )).

fof(redefinition_k3_yellow21,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k3_yellow21(A,B) = k1_yellow21(B) ) )).

fof(dt_k4_yellow21,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v3_yellow21(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v2_orders_2(k4_yellow21(A,B))
        & v3_orders_2(k4_yellow21(A,B))
        & v4_orders_2(k4_yellow21(A,B))
        & v1_lattice3(k4_yellow21(A,B))
        & v2_lattice3(k4_yellow21(A,B))
        & v3_lattice3(k4_yellow21(A,B))
        & l1_orders_2(k4_yellow21(A,B)) ) ) )).

fof(redefinition_k4_yellow21,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v3_yellow21(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k4_yellow21(A,B) = k1_yellow21(B) ) )).

fof(dt_k5_yellow21,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & v2_yellow21(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,k1_altcat_1(A,B,C)) )
     => ( v1_funct_1(k5_yellow21(A,B,C,D))
        & v1_funct_2(k5_yellow21(A,B,C,D),u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C)))
        & v5_orders_3(k5_yellow21(A,B,C,D),k3_yellow21(A,B),k3_yellow21(A,C))
        & m2_relset_1(k5_yellow21(A,B,C,D),u1_struct_0(k3_yellow21(A,B)),u1_struct_0(k3_yellow21(A,C))) ) ) )).

fof(dt_k6_yellow21,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k6_yellow21(A))
        & v2_altcat_1(k6_yellow21(A))
        & v6_altcat_1(k6_yellow21(A))
        & v11_altcat_1(k6_yellow21(A))
        & v12_altcat_1(k6_yellow21(A))
        & v2_yellow21(k6_yellow21(A))
        & l2_altcat_1(k6_yellow21(A)) ) ) )).

fof(dt_k7_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ( ~ v3_struct_0(k7_yellow21(A))
        & v2_altcat_1(k7_yellow21(A))
        & v6_altcat_1(k7_yellow21(A))
        & v2_altcat_2(k7_yellow21(A),k6_yellow21(A))
        & v3_altcat_2(k7_yellow21(A),k6_yellow21(A))
        & m1_altcat_2(k7_yellow21(A),k6_yellow21(A)) ) ) )).

fof(dt_k8_yellow21,axiom,(
    ! [A] :
      ( ~ v2_setfam_1(A)
     => ( ~ v3_struct_0(k8_yellow21(A))
        & v2_altcat_1(k8_yellow21(A))
        & v6_altcat_1(k8_yellow21(A))
        & v2_altcat_2(k8_yellow21(A),k7_yellow21(A))
        & v3_altcat_2(k8_yellow21(A),k7_yellow21(A))
        & m1_altcat_2(k8_yellow21(A),k7_yellow21(A)) ) ) )).
%------------------------------------------------------------------------------