SET007 Axioms: SET007+559.ax


%------------------------------------------------------------------------------
% File     : SET007+559 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Kernel Projections and Quotient Lattices
% 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    : waybel20 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   58 (   1 unit)
%            Number of atoms       :  741 (  26 equality)
%            Maximal formula depth :   20 (  11 average)
%            Number of connectives :  763 (  80 ~  ;   1  |; 474  &)
%                                         (   6 <=>; 202 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   49 (   1 propositional; 0-3 arity)
%            Number of functors    :   41 (   1 constant; 0-6 arity)
%            Number of variables   :  184 (   0 singleton; 180 !;   4 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
          & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
          & v11_quantal1(B)
          & v5_orders_3(B,A,A)
          & v22_waybel_0(B,A,A)
          & v6_waybel_1(B,A)
          & v8_waybel_1(B,A) ) ) )).

fof(t1_waybel20,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k6_partfun1(A)))
     => k1_funct_5(B) = k2_funct_5(B) ) )).

fof(t2_waybel20,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v3_relat_2(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)))
                & v8_relat_2(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)))
                & v1_partfun1(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)),A,A)
                & m2_relset_1(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)),A,A) ) ) ) ) )).

fof(t3_waybel20,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( r1_tarski(k1_funct_5(k9_relat_1(k15_funct_3(A,B),C)),k9_relat_1(A,k1_funct_5(C)))
              & r1_tarski(k2_funct_5(k9_relat_1(k15_funct_3(A,B),C)),k9_relat_1(B,k2_funct_5(C))) ) ) ) )).

fof(t4_waybel20,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( r1_tarski(C,k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)))
             => ( k1_funct_5(k9_relat_1(k15_funct_3(A,B),C)) = k9_relat_1(A,k1_funct_5(C))
                & k2_funct_5(k9_relat_1(k15_funct_3(A,B),C)) = k9_relat_1(B,k2_funct_5(C)) ) ) ) ) )).

fof(t5_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( r2_yellow_0(A,k1_xboole_0)
       => v2_yellow_0(A) ) ) )).

fof(t6_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( r1_yellow_0(A,k1_xboole_0)
       => v1_yellow_0(A) ) ) )).

fof(t7_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
             => ( r2_yellow_0(k3_yellow_3(A,B),C)
               => k2_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k2_yellow_0(A,k4_yellow_3(A,B,C)),k2_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) )).

fof(t8_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
             => ( r1_yellow_0(k3_yellow_3(A,B),C)
               => k1_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k1_yellow_0(A,k4_yellow_3(A,B,C)),k1_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) )).

fof(t9_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_orders_2(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( v17_waybel_0(E,A,C)
                              & v17_waybel_0(F,B,D) )
                           => v17_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) )).

fof(t10_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_orders_2(D)
                    & v4_orders_2(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( v21_waybel_0(E,A,C)
                              & v21_waybel_0(F,B,D) )
                           => v21_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) )).

fof(t11_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_orders_2(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( v18_waybel_0(E,A,C)
                              & v18_waybel_0(F,B,D) )
                           => v18_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) )).

fof(t12_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_orders_2(D)
                    & v4_orders_2(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
                         => ( ( v22_waybel_0(E,A,C)
                              & v22_waybel_0(F,B,D) )
                           => v22_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) )).

fof(t13_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ( ( r1_tarski(B,k6_partfun1(u1_struct_0(A)))
              & r2_yellow_0(k3_yellow_3(A,A),B) )
           => r2_hidden(k2_yellow_0(k3_yellow_3(A,A),B),k6_partfun1(u1_struct_0(A))) ) ) ) )).

fof(t14_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ( ( r1_tarski(B,k6_partfun1(u1_struct_0(A)))
              & r1_yellow_0(k3_yellow_3(A,A),B) )
           => r2_hidden(k1_yellow_0(k3_yellow_3(A,A),B),k6_partfun1(u1_struct_0(A))) ) ) ) )).

fof(t15_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v2_orders_2(A) )
           => v2_orders_2(B) ) ) ) )).

fof(t16_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v3_orders_2(A) )
           => v3_orders_2(B) ) ) ) )).

fof(t17_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v4_orders_2(A) )
           => v4_orders_2(B) ) ) ) )).

fof(t18_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v3_lattice3(A) )
           => v3_lattice3(B) ) ) ) )).

fof(t19_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v17_waybel_0(B,A,A)
           => v17_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) )).

fof(t20_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v21_waybel_0(B,A,A)
           => v21_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) )).

fof(t21_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v18_waybel_0(B,A,A)
           => v18_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) )).

fof(t22_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v22_waybel_0(B,A,A)
           => v22_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) )).

fof(t23_waybel20,axiom,(
    $true )).

fof(t24_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(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)) )
             => ( v21_waybel_0(C,A,B)
               => v5_orders_3(C,A,B) ) ) ) ) )).

fof(t25_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(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)) )
             => ( v5_orders_3(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( v2_waybel_0(D,A)
                     => v2_waybel_0(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) )).

fof(t26_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(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)) )
                     => ( ( v17_waybel_0(D,A,B)
                          & v17_waybel_0(E,B,C) )
                       => v17_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) )).

fof(t27_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v4_orders_2(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)) )
                     => ( ( v21_waybel_0(D,A,B)
                          & v21_waybel_0(E,B,C) )
                       => v21_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) )).

fof(t28_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(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)) )
                     => ( ( v18_waybel_0(D,A,B)
                          & v18_waybel_0(E,B,C) )
                       => v18_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) )).

fof(t29_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v4_orders_2(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)) )
                     => ( ( v22_waybel_0(D,A,B)
                          & v22_waybel_0(E,B,C) )
                       => v22_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) )).

fof(t30_waybel20,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_yellow_1(B)
            & v4_waybel_3(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( v4_orders_2(k3_waybel_3(A,B,C))
                  & v1_yellow_0(k3_waybel_3(A,B,C))
                  & l1_orders_2(k3_waybel_3(A,B,C)) ) )
           => v1_yellow_0(k5_yellow_1(A,B)) ) ) ) )).

fof(t31_waybel20,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_yellow_1(B)
            & v4_waybel_3(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( v4_orders_2(k3_waybel_3(A,B,C))
                  & v2_yellow_0(k3_waybel_3(A,B,C))
                  & l1_orders_2(k3_waybel_3(A,B,C)) ) )
           => v2_yellow_0(k5_yellow_1(A,B)) ) ) ) )).

fof(t32_waybel20,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_yellow_1(B)
            & v4_waybel_3(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( v4_orders_2(k3_waybel_3(A,B,C))
                  & v1_yellow_0(k3_waybel_3(A,B,C))
                  & l1_orders_2(k3_waybel_3(A,B,C)) ) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => k4_waybel_3(A,B,k3_yellow_0(k5_yellow_1(A,B)),C) = k3_yellow_0(k3_waybel_3(A,B,C)) ) ) ) ) )).

fof(t33_waybel20,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_yellow_1(B)
            & v4_waybel_3(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( v4_orders_2(k3_waybel_3(A,B,C))
                  & v2_yellow_0(k3_waybel_3(A,B,C))
                  & l1_orders_2(k3_waybel_3(A,B,C)) ) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => k4_waybel_3(A,B,k4_yellow_0(k5_yellow_1(A,B)),C) = k4_yellow_0(k3_waybel_3(A,B,C)) ) ) ) ) )).

fof(t34_waybel20,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_yellow_1(B)
            & v4_waybel_3(B)
            & v5_waybel_3(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( v2_orders_2(k6_waybel_3(A,B,C))
                  & v3_orders_2(k6_waybel_3(A,B,C))
                  & v4_orders_2(k6_waybel_3(A,B,C))
                  & v1_lattice3(k6_waybel_3(A,B,C))
                  & v2_lattice3(k6_waybel_3(A,B,C))
                  & v3_lattice3(k6_waybel_3(A,B,C))
                  & v3_waybel_3(k6_waybel_3(A,B,C))
                  & l1_orders_2(k6_waybel_3(A,B,C)) ) )
           => v3_waybel_3(k5_yellow_1(A,B)) ) ) ) )).

fof(t35_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v3_waybel_3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_waybel16(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
                 => ( D = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(B,B),k1_waybel20(A,A,B,B,C,C),k6_partfun1(u1_struct_0(B)))
                   => ( ~ v3_struct_0(k5_yellow_0(k3_yellow_3(A,A),D))
                      & v4_yellow_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A))
                      & v7_yellow_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A))
                      & v4_waybel_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A))
                      & m1_yellow_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A)) ) ) ) ) ) ) )).

fof(d1_waybel20,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ( ( v3_relat_2(B)
              & v8_relat_2(B)
              & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
           => k2_waybel20(A,B) = B ) ) ) )).

fof(d2_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ( v1_waybel20(B,A)
          <=> ( v3_relat_2(B)
              & v8_relat_2(B)
              & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
              & ~ v3_struct_0(k5_yellow_0(k3_yellow_3(A,A),B))
              & v4_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
              & v7_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
              & v4_waybel_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
              & m1_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A)) ) ) ) ) )).

fof(t36_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => ( v1_waybel20(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_hidden(k7_yellow_3(A,A,k2_yellow_0(A,k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),C)),C),B) ) ) ) ) )).

fof(d3_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => ( v1_waybel20(B,A)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                  & v8_waybel_1(C,A)
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
               => ( C = k3_waybel20(A,B)
                <=> ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k1_waybel_0(A,A,C,D) = k2_yellow_0(A,k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),D)) ) ) ) ) ) ) )).

fof(t37_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => ( v1_waybel20(B,A)
           => ( v22_waybel_0(k3_waybel20(A,B),A,A)
              & B = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(A,A),k1_waybel20(A,A,A,A,k3_waybel20(A,B),k3_waybel20(A,B)),k6_partfun1(u1_struct_0(A))) ) ) ) ) )).

fof(t39_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ( ( v3_relat_2(B)
              & v8_relat_2(B)
              & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
           => ( ! [C] :
                  ( ( v2_orders_2(C)
                    & v3_orders_2(C)
                    & v4_orders_2(C)
                    & v1_lattice3(C)
                    & v2_lattice3(C)
                    & v3_lattice3(C)
                    & v3_waybel_3(C)
                    & l1_orders_2(C) )
                 => ~ ( u1_struct_0(C) = k8_eqrel_1(u1_struct_0(A),k2_waybel20(A,B))
                      & ! [D] :
                          ( ( v1_funct_1(D)
                            & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
                            & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
                         => ( ! [E] :
                                ( m1_subset_1(E,u1_struct_0(A))
                               => k1_waybel_0(A,C,D,E) = k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),E) )
                           => m1_waybel16(D,A,C) ) ) ) )
              | ( ~ v3_struct_0(k5_yellow_0(k3_yellow_3(A,A),B))
                & v4_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
                & v7_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
                & v4_waybel_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
                & m1_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A)) ) ) ) ) ) )).

fof(d4_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v8_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => k4_waybel20(A,B) = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(A,A),k1_waybel20(A,A,A,A,B,B),k6_partfun1(u1_struct_0(A))) ) ) )).

fof(t40_waybel20,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v8_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v3_relat_2(k4_waybel20(A,B))
            & v8_relat_2(k4_waybel20(A,B))
            & v1_partfun1(k4_waybel20(A,B),u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(k4_waybel20(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(t41_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v22_waybel_0(B,A,A)
            & v8_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => v1_waybel20(k4_waybel20(A,B),A) ) ) )).

fof(d5_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => ( v1_waybel20(B,A)
           => ! [C] :
                ( ( v1_orders_2(C)
                  & v2_orders_2(C)
                  & v3_orders_2(C)
                  & v4_orders_2(C)
                  & v1_lattice3(C)
                  & v2_lattice3(C)
                  & v3_lattice3(C)
                  & v3_waybel_3(C)
                  & l1_orders_2(C) )
               => ( C = k5_waybel20(A,B)
                <=> ( u1_struct_0(C) = k8_eqrel_1(u1_struct_0(A),k2_waybel20(A,B))
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(C))
                       => ! [E] :
                            ( m1_subset_1(E,u1_struct_0(C))
                           => ( r3_orders_2(C,D,E)
                            <=> r3_orders_2(A,k2_yellow_0(A,D),k2_yellow_0(A,E)) ) ) ) ) ) ) ) ) ) )).

fof(t42_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => ( v1_waybel20(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k5_waybel20(A,B)))
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C = k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),D) ) ) ) ) ) )).

fof(t43_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => ( v1_waybel20(B,A)
           => B = k4_waybel20(A,k3_waybel20(A,B)) ) ) ) )).

fof(t44_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v22_waybel_0(B,A,A)
            & v8_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => B = k3_waybel20(A,k4_waybel20(A,B)) ) ) )).

fof(t45_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v6_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v17_waybel_0(B,A,A)
           => ( v2_orders_2(k2_yellow_2(A,A,B))
              & v3_orders_2(k2_yellow_2(A,A,B))
              & v4_orders_2(k2_yellow_2(A,A,B))
              & v1_lattice3(k2_yellow_2(A,A,B))
              & v2_lattice3(k2_yellow_2(A,A,B))
              & v3_waybel_3(k2_yellow_2(A,A,B))
              & l1_orders_2(k2_yellow_2(A,A,B))
              & v7_yellow_0(k2_yellow_2(A,A,B),A) ) ) ) ) )).

fof(dt_k1_waybel20,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & l1_orders_2(C)
        & l1_orders_2(D)
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
        & m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
        & v1_funct_1(F)
        & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
        & m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
     => ( v1_funct_1(k1_waybel20(A,B,C,D,E,F))
        & v1_funct_2(k1_waybel20(A,B,C,D,E,F),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(k3_yellow_3(C,D)))
        & m2_relset_1(k1_waybel20(A,B,C,D,E,F),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(k3_yellow_3(C,D))) ) ) )).

fof(redefinition_k1_waybel20,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & l1_orders_2(C)
        & l1_orders_2(D)
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
        & m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
        & v1_funct_1(F)
        & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
        & m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
     => k1_waybel20(A,B,C,D,E,F) = k15_funct_3(E,F) ) )).

fof(dt_k2_waybel20,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
     => ( v3_relat_2(k2_waybel20(A,B))
        & v8_relat_2(k2_waybel20(A,B))
        & v1_partfun1(k2_waybel20(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k2_waybel20(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k3_waybel20,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
     => ( v1_funct_1(k3_waybel20(A,B))
        & v1_funct_2(k3_waybel20(A,B),u1_struct_0(A),u1_struct_0(A))
        & v8_waybel_1(k3_waybel20(A,B),A)
        & m2_relset_1(k3_waybel20(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k4_waybel20,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & v8_waybel_1(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k4_waybel20(A,B))
        & m1_subset_1(k4_waybel20(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) ) ) )).

fof(dt_k5_waybel20,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
     => ( v1_orders_2(k5_waybel20(A,B))
        & v2_orders_2(k5_waybel20(A,B))
        & v3_orders_2(k5_waybel20(A,B))
        & v4_orders_2(k5_waybel20(A,B))
        & v1_lattice3(k5_waybel20(A,B))
        & v2_lattice3(k5_waybel20(A,B))
        & v3_lattice3(k5_waybel20(A,B))
        & v3_waybel_3(k5_waybel20(A,B))
        & l1_orders_2(k5_waybel20(A,B)) ) ) )).

fof(t38_waybel20,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v8_waybel_1(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ~ ( v22_waybel_0(C,A,A)
                  & B = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(A,A),k1_waybel20(A,A,A,A,C,C),k6_partfun1(u1_struct_0(A)))
                  & ! [D] :
                      ( ( v1_orders_2(D)
                        & v2_orders_2(D)
                        & v3_orders_2(D)
                        & v4_orders_2(D)
                        & v1_lattice3(D)
                        & v2_lattice3(D)
                        & v3_lattice3(D)
                        & v3_waybel_3(D)
                        & l1_orders_2(D) )
                     => ~ ( u1_struct_0(D) = k8_eqrel_1(u1_struct_0(A),k2_waybel20(A,B))
                          & u1_orders_2(D) = a_3_0_waybel20(A,B,C)
                          & ! [E] :
                              ( ( v1_funct_1(E)
                                & v1_funct_2(E,u1_struct_0(A),u1_struct_0(D))
                                & m2_relset_1(E,u1_struct_0(A),u1_struct_0(D)) )
                             => ( ! [F] :
                                    ( m1_subset_1(F,u1_struct_0(A))
                                   => k1_waybel_0(A,D,E,F) = k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),F) )
                               => m1_waybel16(E,A,D) ) ) ) ) ) ) ) ) )).

fof(fraenkel_a_3_0_waybel20,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v3_waybel_3(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B))))
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(B))
        & v8_waybel_1(D,B)
        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_waybel20(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k1_domain_1(k1_zfmisc_1(u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)),k6_eqrel_1(u1_struct_0(B),k2_waybel20(B,C),E),k6_eqrel_1(u1_struct_0(B),k2_waybel20(B,C),F))
            & r3_orders_2(B,k1_waybel_0(B,B,D,E),k1_waybel_0(B,B,D,F)) ) ) ) )).
%------------------------------------------------------------------------------