SET007 Axioms: SET007+573.ax


%------------------------------------------------------------------------------
% File     : SET007+573 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Bases of Continuous 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    : waybel23 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  127 (   1 unit)
%            Number of atoms       : 1197 (  39 equality)
%            Maximal formula depth :   20 (   9 average)
%            Number of connectives : 1198 ( 128 ~  ;   0  |; 738  &)
%                                         (  29 <=>; 303 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   65 (   1 propositional; 0-3 arity)
%            Number of functors    :   39 (   1 constant; 0-5 arity)
%            Number of variables   :  311 (   0 singleton; 300 !;  11 ?)
%            Maximal term depth    :    6 (   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(cc1_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_waybel23(B,A)
           => v1_waybel23(B,A) ) ) ) )).

fof(cc2_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel23(B,A)
           => v2_waybel23(B,A) ) ) ) )).

fof(rc1_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_waybel23(B,A)
          & v2_waybel23(B,A)
          & v3_waybel23(B,A)
          & v4_waybel23(B,A) ) ) )).

fof(fc1_waybel23,axiom,(
    ! [A,B] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_waybel23(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k5_yellow_0(A,B))
        & v1_orders_2(k5_yellow_0(A,B))
        & v3_orders_2(k5_yellow_0(A,B))
        & v4_orders_2(k5_yellow_0(A,B))
        & v2_lattice3(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A) ) ) )).

fof(fc2_waybel23,axiom,(
    ! [A,B] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v2_waybel23(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k5_yellow_0(A,B))
        & v1_orders_2(k5_yellow_0(A,B))
        & v3_orders_2(k5_yellow_0(A,B))
        & v4_orders_2(k5_yellow_0(A,B))
        & v1_lattice3(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A) ) ) )).

fof(cc3_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel23(B,A)
           => v2_waybel_0(B,A) ) ) ) )).

fof(cc4_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_waybel23(B,A)
           => v1_waybel_0(B,A) ) ) ) )).

fof(fc3_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k6_waybel_0(A,B))
        & v1_waybel_0(k6_waybel_0(A,B),A)
        & v12_waybel_0(k6_waybel_0(A,B),A)
        & v2_waybel23(k6_waybel_0(A,B),A) ) ) )).

fof(fc4_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k7_waybel_0(A,B))
        & v1_waybel_0(k7_waybel_0(A,B),A)
        & v2_waybel_0(k7_waybel_0(A,B),A)
        & v13_waybel_0(k7_waybel_0(A,B),A)
        & v2_waybel23(k7_waybel_0(A,B),A) ) ) )).

fof(fc5_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k6_waybel_0(A,B))
        & v1_waybel_0(k6_waybel_0(A,B),A)
        & v2_waybel_0(k6_waybel_0(A,B),A)
        & v12_waybel_0(k6_waybel_0(A,B),A)
        & v1_waybel23(k6_waybel_0(A,B),A) ) ) )).

fof(fc6_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k7_waybel_0(A,B))
        & v2_waybel_0(k7_waybel_0(A,B),A)
        & v13_waybel_0(k7_waybel_0(A,B),A)
        & v1_waybel23(k7_waybel_0(A,B),A) ) ) )).

fof(fc7_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_waybel_0(k1_waybel_3(A,B),A)
        & v12_waybel_0(k1_waybel_3(A,B),A)
        & v2_waybel23(k1_waybel_3(A,B),A) ) ) )).

fof(fc8_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_waybel_0(k2_waybel_3(A,B),A)
        & v13_waybel_0(k2_waybel_3(A,B),A)
        & v2_waybel23(k2_waybel_3(A,B),A) ) ) )).

fof(fc9_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v2_waybel_0(k1_waybel_3(A,B),A)
        & v12_waybel_0(k1_waybel_3(A,B),A)
        & v1_waybel23(k1_waybel_3(A,B),A) ) ) )).

fof(cc5_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_waybel23(B,A)
           => ~ v1_xboole_0(B) ) ) ) )).

fof(cc6_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v7_waybel23(B,A)
           => ~ v1_xboole_0(B) ) ) ) )).

fof(rc2_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v6_waybel23(B,A) ) ) )).

fof(rc3_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v7_waybel23(B,A) ) ) )).

fof(rc4_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_waybel23(B,A)
          & ~ v1_xboole_0(B)
          & v6_waybel23(B,A) ) ) )).

fof(rc5_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_waybel23(B,A)
          & ~ v1_xboole_0(B)
          & v7_waybel23(B,A) ) ) )).

fof(fc10_waybel23,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A)
        & v6_waybel23(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k5_yellow_0(A,B))
        & v1_orders_2(k5_yellow_0(A,B))
        & v4_orders_2(k5_yellow_0(A,B))
        & v1_yellow_0(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A) ) ) )).

fof(cc7_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_waybel23(B,A)
         => ( v1_waybel_0(B,A)
            & v2_waybel23(B,A) ) ) ) )).

fof(rc6_waybel23,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & ~ v3_realset2(A) ) )).

fof(cc8_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & ~ v3_realset2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_waybel23(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & v2_waybel23(B,A) ) ) ) )).

fof(fc11_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_orders_2(k5_yellow_0(A,B))
        & v2_orders_2(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A) ) ) )).

fof(fc12_waybel23,axiom,(
    ! [A,B] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_orders_2(k5_yellow_0(A,B))
        & v3_orders_2(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A) ) ) )).

fof(fc13_waybel23,axiom,(
    ! [A,B] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_orders_2(k5_yellow_0(A,B))
        & v4_orders_2(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A) ) ) )).

fof(fc14_waybel23,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v4_yellow_0(B,A)
        & m1_yellow_0(B,A) )
     => ( v1_relat_1(k3_waybel23(A,B))
        & v1_funct_1(k3_waybel23(A,B))
        & v1_funct_2(k3_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A))
        & v5_orders_3(k3_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),A) ) ) )).

fof(fc15_waybel23,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v4_yellow_0(B,A)
        & m1_yellow_0(B,A) )
     => ( v1_relat_1(k4_waybel23(A,B))
        & v1_funct_1(k4_waybel23(A,B))
        & v1_funct_2(k4_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & v5_orders_3(k4_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(fc16_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A)
        & v6_waybel23(B,A)
        & m1_waybel23(B,A) )
     => ( v1_relat_1(k5_waybel23(A,B))
        & v1_funct_1(k5_waybel23(A,B))
        & v1_funct_2(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
        & v5_orders_3(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) )).

fof(fc17_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A)
        & v6_waybel23(B,A)
        & m1_waybel23(B,A) )
     => ( v1_relat_1(k3_waybel23(A,k5_yellow_0(A,B)))
        & v1_funct_1(k3_waybel23(A,k5_yellow_0(A,B)))
        & v1_funct_2(k3_waybel23(A,k5_yellow_0(A,B)),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))),u1_struct_0(A))
        & v5_orders_3(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
        & v17_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
        & v18_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
        & v19_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
        & v20_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
        & v21_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
        & v22_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) )).

fof(fc18_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A)
        & v6_waybel23(B,A)
        & m1_waybel23(B,A) )
     => ( v1_relat_1(k5_waybel23(A,B))
        & v1_funct_1(k5_waybel23(A,B))
        & v1_funct_2(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
        & v5_orders_3(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v18_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v20_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v22_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) )).

fof(t1_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_waybel_8(A,B) = k3_xboole_0(k1_waybel_3(A,B),u1_struct_0(k1_waybel_8(A))) ) ) )).

fof(t2_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k12_waybel_0(A,B),k12_waybel_0(A,C)) ) ) ) ) )).

fof(t3_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v8_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => r1_tarski(k12_waybel_0(A,C),k12_waybel_0(B,D)) ) ) ) ) ) )).

fof(t4_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v8_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => k12_waybel_0(A,C) = k12_waybel_0(B,D) ) ) ) ) ) )).

fof(t5_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v6_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( r2_hidden(k3_yellow_0(A),u1_struct_0(B))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( C = D
                     => r1_tarski(k12_waybel_0(B,D),k12_waybel_0(A,C)) ) ) ) ) ) ) )).

fof(t6_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))
         => k1_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) = k4_waybel_0(A,k12_waybel_0(A,k1_waybel23(A,B))) ) ) )).

fof(t7_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_waybel_0(A,k4_waybel_0(A,B)) = k4_waybel_0(A,B) ) ) )).

fof(t8_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_waybel_0(A,k5_waybel_0(A,B)) = k5_waybel_0(A,B) ) ) )).

fof(t9_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_waybel_0(A,k6_waybel_0(A,B)) = k6_waybel_0(A,B) ) ) )).

fof(t10_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_waybel_0(A,k7_waybel_0(A,B)) = k7_waybel_0(A,B) ) ) )).

fof(t11_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => r1_tarski(k4_waybel_0(B,D),k4_waybel_0(A,C)) ) ) ) ) ) )).

fof(t12_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => r1_tarski(k5_waybel_0(B,D),k5_waybel_0(A,C)) ) ) ) ) ) )).

fof(t13_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( C = D
                   => r1_tarski(k6_waybel_0(B,D),k6_waybel_0(A,C)) ) ) ) ) ) )).

fof(t14_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( C = D
                   => r1_tarski(k7_waybel_0(B,D),k7_waybel_0(A,C)) ) ) ) ) ) )).

fof(d1_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel23(B,A)
          <=> v5_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).

fof(d2_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_waybel23(B,A)
          <=> v6_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).

fof(d3_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_waybel23(B,A)
          <=> v7_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).

fof(d4_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel23(B,A)
          <=> v8_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).

fof(t15_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel23(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B)
                        & r2_yellow_0(A,k2_struct_0(A,C,D)) )
                     => r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) )).

fof(t16_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_waybel23(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B)
                        & r1_yellow_0(A,k2_struct_0(A,C,D)) )
                     => r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) )).

fof(t17_waybel23,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel23(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) )).

fof(t18_waybel23,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_waybel23(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),B) ) ) ) ) ) ) )).

fof(t19_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_waybel23(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(B))
               => ( r2_yellow_0(A,C)
                 => r2_hidden(k2_yellow_0(A,C),B) ) ) ) ) ) )).

fof(t20_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel23(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(B))
               => ( r1_yellow_0(A,C)
                 => r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) )).

fof(t21_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v3_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => ( r2_yellow_0(A,C)
               => ( r2_yellow_0(k5_yellow_0(A,B),C)
                  & k2_yellow_0(k5_yellow_0(A,B),C) = k2_yellow_0(A,C) ) ) ) ) ) )).

fof(t22_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => ( r1_yellow_0(A,C)
               => ( r1_yellow_0(k5_yellow_0(A,B),C)
                  & k1_yellow_0(k5_yellow_0(A,B),C) = k1_yellow_0(A,C) ) ) ) ) ) )).

fof(t23_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_struct_0(C,A,B)
             => ! [D] :
                  ( m1_struct_0(D,A,B)
                 => ( r2_yellow_0(A,k2_struct_0(A,C,D))
                   => ( r2_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D))
                      & k2_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D)) = k2_yellow_0(A,k2_struct_0(A,C,D)) ) ) ) ) ) ) )).

fof(t24_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_struct_0(C,A,B)
             => ! [D] :
                  ( m1_struct_0(D,A,B)
                 => ( r1_yellow_0(A,k2_struct_0(A,C,D))
                   => ( r1_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D))
                      & k1_yellow_0(k5_yellow_0(A,B),k2_struct_0(A,C,D)) = k1_yellow_0(A,k2_struct_0(A,C,D)) ) ) ) ) ) ) )).

fof(t25_waybel23,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v2_lattice3(k5_yellow_0(A,B)) ) ) )).

fof(t26_waybel23,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v1_lattice3(k5_yellow_0(A,B)) ) ) )).

fof(t27_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v3_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => k2_yellow_0(k5_yellow_0(A,B),C) = k2_yellow_0(A,C) ) ) ) )).

fof(t28_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => k1_yellow_0(k5_yellow_0(A,B),C) = k1_yellow_0(A,C) ) ) ) )).

fof(t29_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v2_waybel_0(B,A) ) ) )).

fof(t30_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v1_waybel_0(B,A) ) ) )).

fof(t31_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( ~ v1_xboole_0(B)
              & v2_waybel_0(B,A)
              & v13_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
          <=> v1_waybel23(B,A) ) ) ) )).

fof(t32_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
          <=> v2_waybel23(B,A) ) ) ) )).

fof(t33_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v2_waybel23(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => v2_waybel23(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) )).

fof(t34_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_waybel23(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => v1_waybel23(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) )).

fof(t35_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_waybel23(k6_waybel_0(A,B),A) ) ) )).

fof(t36_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_waybel23(k6_waybel_0(A,B),A) ) ) )).

fof(t37_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_waybel23(k7_waybel_0(A,B),A) ) ) )).

fof(t38_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_waybel23(k7_waybel_0(A,B),A) ) ) )).

fof(t39_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_waybel23(k1_waybel_3(A,B),A) ) ) )).

fof(t40_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_waybel23(k1_waybel_3(A,B),A) ) ) )).

fof(t41_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_waybel23(k2_waybel_3(A,B),A) ) ) )).

fof(d6_waybel23,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v5_waybel23(A)
      <=> r1_tarski(k2_waybel23(A),k5_ordinal2) ) ) )).

fof(d7_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( m1_waybel23(B,A)
          <=> ( v2_waybel23(B,A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => C = k1_yellow_0(A,k5_subset_1(u1_struct_0(A),k1_waybel_3(A,C),B)) ) ) ) ) ) )).

fof(d8_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_waybel23(B,A)
          <=> r2_hidden(k3_yellow_0(A),B) ) ) ) )).

fof(d9_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v7_waybel23(B,A)
          <=> r2_hidden(k4_yellow_0(A),B) ) ) ) )).

fof(t42_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v1_yellow_0(k5_yellow_0(A,B)) ) ) )).

fof(t43_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel23(u1_struct_0(k1_waybel_8(A)),A)
        & m1_subset_1(u1_struct_0(k1_waybel_8(A)),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(t44_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ( v6_waybel23(u1_struct_0(k1_waybel_8(A)),A)
        & m1_waybel23(u1_struct_0(k1_waybel_8(A)),A) ) ) )).

fof(t45_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( m1_waybel23(u1_struct_0(k1_waybel_8(A)),A)
       => v2_waybel_8(A) ) ) )).

fof(t46_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( m1_waybel23(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( ~ r3_orders_2(A,D,C)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,B)
                                & ~ r3_orders_2(A,E,C)
                                & r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) )).

fof(t47_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( r2_hidden(k3_yellow_0(A),B)
           => ( m1_waybel23(B,A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r1_waybel_3(A,C,D)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ~ ( r2_hidden(E,B)
                                  & r3_orders_2(A,C,E)
                                  & r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) ) )).

fof(t48_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( r2_hidden(k3_yellow_0(A),B)
           => ( m1_waybel23(B,A)
            <=> ( r1_tarski(u1_struct_0(k1_waybel_8(A)),B)
                & ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ~ ( ~ r3_orders_2(A,D,C)
                            & ! [E] :
                                ( m1_subset_1(E,u1_struct_0(A))
                               => ~ ( r2_hidden(E,B)
                                    & ~ r3_orders_2(A,E,C)
                                    & r3_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t49_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel23(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( r2_hidden(k3_yellow_0(A),B)
           => ( m1_waybel23(B,A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( ~ r3_orders_2(A,D,C)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ~ ( r2_hidden(E,B)
                                  & ~ r3_orders_2(A,E,C)
                                  & r3_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) )).

fof(t50_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( ( r2_hidden(k3_yellow_0(A),u1_struct_0(B))
              & v2_waybel23(u1_struct_0(B),A)
              & m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ~ v1_xboole_0(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)))
                  & v1_waybel_0(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)),B)
                  & v12_waybel_0(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)),B)
                  & m1_subset_1(k3_xboole_0(k1_waybel_3(A,C),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) )).

fof(d10_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A)) )
             => ( C = k3_waybel23(A,B)
              <=> ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,B)
                      & v12_waybel_0(D,B)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                   => k1_funct_1(C,D) = k1_yellow_0(A,D) ) ) ) ) ) )).

fof(d11_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                & m2_relset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
             => ( C = k4_waybel23(A,B)
              <=> ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,B)
                      & v12_waybel_0(D,B)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                   => ? [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                        & D = E
                        & k1_funct_1(C,D) = k4_waybel_0(A,E) ) ) ) ) ) ) )).

fof(d12_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))) )
             => ( C = k5_waybel23(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),C,D) = k5_subset_1(u1_struct_0(A),k1_waybel_3(A,D),B) ) ) ) ) ) )).

fof(t51_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( k1_relat_1(k3_waybel23(A,B)) = k8_waybel_0(B)
            & m1_subset_1(k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),A,k3_waybel23(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t52_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( r2_hidden(C,k1_relat_1(k3_waybel23(A,B)))
            <=> ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,B)
                & v12_waybel_0(C,B)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) )).

fof(t53_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( k1_relat_1(k4_waybel23(A,B)) = k8_waybel_0(B)
            & m1_subset_1(k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),k2_yellow_1(k8_waybel_0(A)),k4_waybel23(A,B)),k1_zfmisc_1(k8_waybel_0(A))) ) ) ) )).

fof(t54_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( r2_hidden(C,k1_relat_1(k4_waybel23(A,B)))
            <=> ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,B)
                & v12_waybel_0(C,B)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) )).

fof(t55_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( r2_hidden(C,k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),k2_yellow_1(k8_waybel_0(A)),k4_waybel23(A,B)))
             => ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,A)
                & v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t56_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ( k1_relat_1(k5_waybel23(A,B)) = u1_struct_0(A)
            & m1_subset_1(k8_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),k5_waybel23(A,B)),k1_zfmisc_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ) )).

fof(t57_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ! [C] :
              ( r2_hidden(C,k8_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),k5_waybel23(A,B)))
             => ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,k5_yellow_0(A,B))
                & v12_waybel_0(C,k5_yellow_0(A,B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_0(A,B)))) ) ) ) ) )).

fof(t58_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => v5_orders_3(k3_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),A) ) ) )).

fof(t59_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => v5_orders_3(k4_waybel23(A,B),k2_yellow_1(k8_waybel_0(B)),k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(t60_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => v5_orders_3(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) )).

fof(t61_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => v18_waybel_0(k4_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(t62_waybel23,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => k3_waybel23(A,B) = k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),k4_waybel23(A,B),k3_yellow_2(A)) ) ) )).

fof(t63_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => v3_waybel_1(k1_waybel_1(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A,k3_waybel23(A,k5_yellow_0(A,B)),k5_waybel23(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) )).

fof(t64_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ( v4_waybel_1(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
            & v5_waybel_1(k5_waybel23(A,B),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) ) )).

fof(t65_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => k8_yellow_2(u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))),A,k3_waybel23(A,k5_yellow_0(A,B))) = u1_struct_0(A) ) ) )).

fof(t66_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ( v17_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A)
            & v18_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))),A) ) ) ) )).

fof(t67_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => v18_waybel_0(k5_waybel23(A,B),A,k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) )).

fof(t68_waybel23,axiom,(
    $true )).

fof(t70_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => r5_waybel_1(k1_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))),k5_yellow_0(A,B)) ) ) )).

fof(t71_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ( ! [C] :
                ( ( v6_waybel23(C,A)
                  & m1_waybel23(C,A) )
               => r1_tarski(B,C) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
               => C = k5_subset_1(u1_struct_0(A),k1_waybel_3(A,k1_yellow_0(A,C)),B) ) ) ) ) )).

fof(t72_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_8(A)
      <=> ( v6_waybel23(u1_struct_0(k1_waybel_8(A)),A)
          & m1_waybel23(u1_struct_0(k1_waybel_8(A)),A)
          & ! [B] :
              ( ( v6_waybel23(B,A)
                & m1_waybel23(B,A) )
             => r1_tarski(u1_struct_0(k1_waybel_8(A)),B) ) ) ) ) )).

fof(t73_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_8(A)
      <=> ? [B] :
            ( v6_waybel23(B,A)
            & m1_waybel23(B,A)
            & ! [C] :
                ( ( v6_waybel23(C,A)
                  & m1_waybel23(C,A) )
               => r1_tarski(B,C) ) ) ) ) )).

fof(dt_m1_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_waybel23(B,A)
         => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m1_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ? [B] : m1_waybel23(B,A) ) )).

fof(dt_k1_waybel23,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
     => m1_subset_1(k1_waybel23(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(redefinition_k1_waybel23,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
     => k1_waybel23(A,B) = k3_tarski(B) ) )).

fof(dt_k2_waybel23,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => v1_card_1(k2_waybel23(A)) ) )).

fof(dt_k3_waybel23,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v4_yellow_0(B,A)
        & m1_yellow_0(B,A) )
     => ( v1_funct_1(k3_waybel23(A,B))
        & v1_funct_2(k3_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A))
        & m2_relset_1(k3_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(A)) ) ) )).

fof(dt_k4_waybel23,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v4_yellow_0(B,A)
        & m1_yellow_0(B,A) )
     => ( v1_funct_1(k4_waybel23(A,B))
        & v1_funct_2(k4_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & m2_relset_1(k4_waybel23(A,B),u1_struct_0(k2_yellow_1(k8_waybel_0(B))),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) )).

fof(dt_k5_waybel23,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A)
        & v6_waybel23(B,A)
        & m1_waybel23(B,A) )
     => ( v1_funct_1(k5_waybel23(A,B))
        & v1_funct_2(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))))
        & m2_relset_1(k5_waybel23(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))) ) ) )).

fof(d5_waybel23,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => k2_waybel23(A) = k1_setfam_1(a_1_0_waybel23(A)) ) )).

fof(t69_waybel23,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => u1_struct_0(k1_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))) = a_2_0_waybel23(A,B) ) ) )).

fof(fraenkel_a_1_0_waybel23,axiom,(
    ! [A,B] :
      ( l1_pre_topc(B)
     => ( r2_hidden(A,a_1_0_waybel23(B))
      <=> ? [C] :
            ( m1_cantor_1(C,B)
            & A = k1_card_1(C) ) ) ) )).

fof(fraenkel_a_2_0_waybel23,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v1_yellow_0(B)
        & v3_waybel_3(B)
        & l1_orders_2(B)
        & v6_waybel23(C,B)
        & m1_waybel23(C,B) )
     => ( r2_hidden(A,a_2_0_waybel23(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k5_yellow_0(B,C)))
            & A = k6_waybel_0(k5_yellow_0(B,C),D) ) ) ) )).
%------------------------------------------------------------------------------