SET007 Axioms: SET007+638.ax


%------------------------------------------------------------------------------
% File     : SET007+638 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Meet Continuous Lattices Revisited
% 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    : waybel30 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   1 unit)
%            Number of atoms       : 1171 (  39 equality)
%            Maximal formula depth :   48 (  12 average)
%            Number of connectives : 1162 (  73 ~  ;   0  |; 894  &)
%                                         (  22 <=>; 173 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   83 (   0 propositional; 1-3 arity)
%            Number of functors    :   44 (   3 constant; 0-3 arity)
%            Number of variables   :  194 (   0 singleton; 174 !;  20 ?)
%            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(fc1_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
        & v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v24_waybel_0(k2_yellow_1(k8_waybel_0(A)))
        & ~ v1_yellow_3(k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(fc2_waybel30,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
        & v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_lattice3(k2_yellow_1(k8_waybel_0(A)))
        & v24_waybel_0(k2_yellow_1(k8_waybel_0(A)))
        & ~ v1_yellow_3(k2_yellow_1(k8_waybel_0(A)))
        & v1_waybel_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_waybel_2(k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(cc1_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( ~ v3_struct_0(B)
            & v6_group_1(B)
            & v3_realset2(B) ) ) ) )).

fof(fc3_waybel30,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) )
     => ~ v1_xboole_0(k2_waybel19(A)) ) )).

fof(fc4_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k5_waybel11(A)))
        & v1_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v2_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v3_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v4_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v1_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v2_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v3_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v1_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v2_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v3_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v24_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & v25_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & ~ v1_yellow_3(k2_yellow_1(k5_waybel11(A)))
        & ~ v3_realset2(k2_yellow_1(k5_waybel11(A))) ) ) )).

fof(fc5_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k5_waybel11(A)))
        & v1_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v2_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v3_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v4_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v1_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v2_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v3_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v1_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v2_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v3_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v24_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & v25_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & ~ v1_yellow_3(k2_yellow_1(k5_waybel11(A)))
        & ~ v3_realset2(k2_yellow_1(k5_waybel11(A))) ) ) )).

fof(fc6_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k2_waybel19(A)))
        & v1_orders_2(k2_yellow_1(k2_waybel19(A)))
        & v2_orders_2(k2_yellow_1(k2_waybel19(A)))
        & v3_orders_2(k2_yellow_1(k2_waybel19(A)))
        & v4_orders_2(k2_yellow_1(k2_waybel19(A)))
        & v1_lattice3(k2_yellow_1(k2_waybel19(A)))
        & v2_lattice3(k2_yellow_1(k2_waybel19(A)))
        & v3_lattice3(k2_yellow_1(k2_waybel19(A)))
        & v1_yellow_0(k2_yellow_1(k2_waybel19(A)))
        & v2_yellow_0(k2_yellow_1(k2_waybel19(A)))
        & v3_yellow_0(k2_yellow_1(k2_waybel19(A)))
        & v24_waybel_0(k2_yellow_1(k2_waybel19(A)))
        & v25_waybel_0(k2_yellow_1(k2_waybel19(A)))
        & ~ v1_yellow_3(k2_yellow_1(k2_waybel19(A)))
        & ~ v3_realset2(k2_yellow_1(k2_waybel19(A))) ) ) )).

fof(cc2_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & ~ v1_yellow_3(A)
          & v4_waybel11(A) ) ) ) )).

fof(cc3_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(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)
          & ~ v1_yellow_3(A)
          & v2_compts_1(A)
          & v2_waybel19(A)
          & v1_urysohn1(A) ) ) ) )).

fof(rc1_waybel30,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(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)
      & ~ v1_yellow_3(A)
      & v1_waybel_2(A)
      & v2_waybel_2(A)
      & v1_waybel_9(A)
      & v4_waybel11(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A) ) )).

fof(rc2_waybel30,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(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)
      & ~ v1_yellow_3(A)
      & v1_waybel_2(A)
      & v2_waybel_2(A)
      & v2_compts_1(A)
      & v3_compts_1(A)
      & v4_compts_1(A)
      & v5_compts_1(A)
      & v1_waybel_9(A)
      & v2_waybel19(A)
      & v1_urysohn1(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v6_waybel_3(A) ) )).

fof(fc7_waybel30,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & l1_orders_2(A)
        & v3_waybel11(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v13_waybel_0(k5_waybel_0(A,B),A)
        & v3_waybel11(k5_waybel_0(A,B),A) ) ) )).

fof(fc8_waybel30,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k4_waybel_1(A,B))
        & v1_relat_1(k4_waybel_1(A,B))
        & v1_funct_1(k4_waybel_1(A,B))
        & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v5_pre_topc(k4_waybel_1(A,B),A,A)
        & v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v19_waybel_0(k4_waybel_1(A,B),A,A)
        & v22_waybel_0(k4_waybel_1(A,B),A,A)
        & v5_orders_3(k4_waybel_1(A,B),A,A) ) ) )).

fof(fc9_waybel30,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k1_waybel30(A,B))
        & v1_finset_1(k1_waybel30(A,B))
        & v1_membered(k1_waybel30(A,B))
        & v2_membered(k1_waybel30(A,B))
        & v3_membered(k1_waybel30(A,B))
        & v4_membered(k1_waybel30(A,B))
        & v5_membered(k1_waybel30(A,B)) ) ) )).

fof(cc4_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v2_waybel19(A)
          & v3_waybel_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(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)
          & ~ v1_yellow_3(A)
          & v3_compts_1(A)
          & v1_urysohn1(A) ) ) ) )).

fof(cc5_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v2_waybel_2(A)
          & v3_compts_1(A)
          & v2_waybel19(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(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)
          & ~ v1_yellow_3(A)
          & v1_waybel_2(A)
          & v2_waybel_2(A)
          & v2_waybel_3(A)
          & v3_waybel_3(A) ) ) ) )).

fof(cc6_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_waybel30(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_waybel30(A) ) ) ) )).

fof(cc7_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_waybel30(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_waybel30(A) ) ) ) )).

fof(cc8_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v1_waybel30(A)
          & v3_waybel30(A) ) ) ) )).

fof(cc9_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_waybel30(A) ) ) ) )).

fof(rc3_waybel30,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_tdlat_3(A)
      & v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(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)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v2_waybel_1(A)
      & v9_waybel_1(A)
      & v10_waybel_1(A)
      & v1_waybel_8(A)
      & v2_waybel_8(A)
      & v3_waybel_8(A)
      & ~ v1_yellow_3(A)
      & v1_waybel_2(A)
      & v2_waybel_2(A)
      & v2_compts_1(A)
      & v3_compts_1(A)
      & v4_compts_1(A)
      & v5_compts_1(A)
      & v1_waybel_9(A)
      & v1_waybel19(A)
      & v2_waybel19(A)
      & v1_urysohn1(A)
      & v2_yellow13(A)
      & v4_waybel11(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v6_waybel_3(A)
      & v6_group_1(A)
      & v3_realset2(A)
      & v1_waybel30(A)
      & v2_waybel30(A)
      & v3_waybel30(A) ) )).

fof(cc10_waybel30,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v2_waybel19(A)
          & v3_waybel_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(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)
          & ~ v1_yellow_3(A)
          & v2_compts_1(A)
          & v2_waybel19(A)
          & v1_urysohn1(A)
          & v1_waybel30(A)
          & v3_waybel30(A) ) ) ) )).

fof(fc10_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & v3_waybel_3(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k5_waybel11(A)))
        & v1_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v2_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v3_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v4_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v1_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v2_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v3_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v1_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v2_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v3_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v24_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & v25_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & ~ v1_yellow_3(k2_yellow_1(k5_waybel11(A)))
        & v1_waybel_2(k2_yellow_1(k5_waybel11(A)))
        & v2_waybel_2(k2_yellow_1(k5_waybel11(A)))
        & v2_waybel_3(k2_yellow_1(k5_waybel11(A)))
        & v3_waybel_3(k2_yellow_1(k5_waybel11(A)))
        & ~ v3_realset2(k2_yellow_1(k5_waybel11(A))) ) ) )).

fof(fc11_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_8(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k5_waybel11(A)))
        & v1_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v2_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v3_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v4_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v1_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v2_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v3_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v1_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v2_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v3_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v24_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & v25_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & v1_waybel_8(k2_yellow_1(k5_waybel11(A)))
        & v2_waybel_8(k2_yellow_1(k5_waybel11(A)))
        & ~ v1_yellow_3(k2_yellow_1(k5_waybel11(A)))
        & v1_waybel_2(k2_yellow_1(k5_waybel11(A)))
        & v2_waybel_2(k2_yellow_1(k5_waybel11(A)))
        & v2_waybel_3(k2_yellow_1(k5_waybel11(A)))
        & v3_waybel_3(k2_yellow_1(k5_waybel11(A)))
        & ~ v3_realset2(k2_yellow_1(k5_waybel11(A))) ) ) )).

fof(t2_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k2_yellow_1(k8_waybel_0(A)))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
         => ( ~ v1_xboole_0(k3_tarski(B))
            & v1_waybel_0(k3_tarski(B),A)
            & v12_waybel_0(k3_tarski(B),A)
            & m1_subset_1(k3_tarski(B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t3_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k2_yellow_1(k8_waybel_0(A)))
            & 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) = k3_tarski(B) ) ) )).

fof(t5_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v4_waybel11(C)
                & m1_yellow_9(C,B) )
             => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
               => g1_waybel_9(u1_struct_0(C),u1_orders_2(C),u1_pre_topc(C)) = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ) ) ) )).

fof(t6_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & v2_waybel19(C)
                & m1_yellow_9(C,B) )
             => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
               => g1_waybel_9(u1_struct_0(C),u1_orders_2(C),u1_pre_topc(C)) = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ) ) ) )).

fof(t7_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(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
                      & v4_pre_topc(D,B) )
                   => v4_pre_topc(C,A) ) ) ) ) ) )).

fof(t9_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => k2_waybel19(A) = u1_pre_topc(A) ) )).

fof(t10_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => r1_tarski(k5_waybel11(A),k2_waybel19(A)) ) )).

fof(t11_waybel30,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] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => k2_waybel19(A) = k2_waybel19(B) ) ) ) )).

fof(t12_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,k2_waybel19(A))
          <=> v3_pre_topc(B,A) ) ) ) )).

fof(t13_waybel30,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_waybel11(B,A)
           => v3_waybel11(k5_waybel_0(A,B),A) ) ) ) )).

fof(t14_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(C,k2_waybel19(A))
               => r2_hidden(k5_waybel_0(A,C),k5_waybel11(B)) ) ) ) ) )).

fof(t15_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(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
                      & v3_pre_topc(C,A) )
                   => v3_pre_topc(k5_waybel_0(B,D),B) ) ) ) ) ) )).

fof(t17_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v13_waybel_0(C,A)
                & 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
                   => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) )).

fof(t18_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v12_waybel_0(C,A)
                & 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
                   => k6_pre_topc(A,C) = k6_pre_topc(B,D) ) ) ) ) ) )).

fof(t19_waybel30,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] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & v2_waybel19(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( ( v2_pre_topc(D)
                    & v2_waybel19(D)
                    & m1_yellow_9(D,B) )
                 => ( v3_waybel_3(k2_yellow_1(k5_waybel11(B)))
                   => u1_pre_topc(k6_borsuk_1(C,D)) = k2_waybel19(k3_yellow_3(A,B)) ) ) ) ) ) )).

fof(t20_waybel30,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] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & v2_waybel19(C)
                & m1_yellow_9(C,k3_yellow_3(A,B)) )
             => ! [D] :
                  ( ( v2_pre_topc(D)
                    & v2_waybel19(D)
                    & m1_yellow_9(D,A) )
                 => ! [E] :
                      ( ( v2_pre_topc(E)
                        & v2_waybel19(E)
                        & m1_yellow_9(E,B) )
                     => ( v3_waybel_3(k2_yellow_1(k5_waybel11(B)))
                       => g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k6_borsuk_1(D,E) ) ) ) ) ) ) )).

fof(t21_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) )).

fof(t22_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( v3_waybel_3(k2_yellow_1(k5_waybel11(A)))
       => v2_yellow13(A) ) ) )).

fof(t23_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( v3_waybel_3(k2_yellow_1(k5_waybel11(A)))
       => ( v3_compts_1(A)
        <=> ! [B] :
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,A))))
             => ( B = u1_orders_2(A)
               => v4_pre_topc(B,k6_borsuk_1(A,A)) ) ) ) ) ) )).

fof(t24_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(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(k1_waybel30(A,B),k1_waybel30(A,C)) ) ) ) ) )).

fof(t25_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_waybel30(A,k7_waybel_0(A,B)) = k2_waybel_3(A,B) ) ) )).

fof(t26_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r1_tarski(k1_tops_1(A,B),k1_waybel30(A,B)) ) ) )).

fof(t27_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(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(k4_subset_1(u1_struct_0(A),k1_waybel30(A,B),k1_waybel30(A,C)),k1_waybel30(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) )).

fof(t28_waybel30,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v13_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k4_subset_1(u1_struct_0(A),k1_waybel30(A,B),k1_waybel30(A,C)) = k1_waybel30(A,k4_subset_1(u1_struct_0(A),B,C)) ) ) ) )).

fof(t30_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( v3_waybel_3(A)
      <=> ( v2_waybel_2(A)
          & v3_compts_1(A) ) ) ) )).

fof(d2_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ( v1_waybel30(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_yellow13(C,A,B)
                & ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                     => v5_yellow_0(k5_yellow_0(A,D),A) ) ) ) ) ) ) )).

fof(d3_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ( v2_waybel30(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_yellow13(C,A,B)
                & ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                     => ( v5_yellow_0(k5_yellow_0(A,D),A)
                        & v6_compts_1(D,A) ) ) ) ) ) ) ) )).

fof(d4_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ( v3_waybel30(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_yellow_8(C,A,B)
                & ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                     => v5_yellow_0(k5_yellow_0(A,D),A) ) ) ) ) ) ) )).

fof(t31_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v2_yellow13(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_yellow_0(k5_yellow_0(A,B),A)
           => v5_yellow_0(k5_yellow_0(A,k6_pre_topc(A,B)),A) ) ) ) )).

fof(t32_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(B))
               => ? [D] :
                    ( m1_yellow_8(D,B,C)
                    & ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                       => ( r2_hidden(E,D)
                         => ( ~ v1_xboole_0(E)
                            & v2_waybel_0(E,B)
                            & v13_waybel_0(E,B)
                            & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) )
          <=> v3_waybel30(A) ) ) ) )).

fof(t35_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( v3_waybel_3(A)
      <=> ( v3_waybel30(A)
          & v3_waybel_3(k2_yellow_1(k5_waybel11(A))) ) ) ) )).

fof(t36_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & v3_waybel_3(A)
        & l1_waybel_9(A) )
     => ( v2_compts_1(A)
        & v3_compts_1(A)
        & v2_yellow13(A)
        & v3_waybel30(A) ) ) )).

fof(t37_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_compts_1(A)
        & v2_waybel19(A)
        & v2_yellow13(A)
        & v3_waybel30(A)
        & l1_waybel_9(A) )
     => v2_waybel30(A) ) )).

fof(t40_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( v2_waybel_8(A)
      <=> ( v3_waybel30(A)
          & v2_waybel_8(k2_yellow_1(k5_waybel11(A))) ) ) ) )).

fof(dt_k1_waybel30,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_waybel30(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(t1_waybel30,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => k3_xboole_0(A,k3_tarski(B)) = k3_tarski(a_2_0_waybel30(A,B)) ) )).

fof(t4_waybel30,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)
            & v1_waybel_0(B,k2_yellow_1(k8_waybel_0(A)))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
             => k1_yellow_0(k2_yellow_1(k8_waybel_0(A)),k4_yellow_4(k2_yellow_1(k8_waybel_0(A)),k1_struct_0(k2_yellow_1(k8_waybel_0(A)),C),B)) = k3_tarski(a_3_0_waybel30(A,B,C)) ) ) ) )).

fof(t8_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => r1_tarski(k5_waybel11(A),a_1_0_waybel30(A)) ) )).

fof(t16_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_yellow_8(E,A,D)
                     => ( C = D
                       => m1_yellow_8(a_3_1_waybel30(A,D,E),B,C) ) ) ) ) ) ) )).

fof(d1_waybel30,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_waybel30(A,B) = a_2_1_waybel30(A,B) ) ) )).

fof(t29_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r1_tarski(k1_tops_1(A,k5_waybel_0(A,B)),k3_tarski(a_2_2_waybel30(A,B))) ) ) )).

fof(t33_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_tarski(a_3_2_waybel30(A,B,C),a_2_3_waybel30(A,C)) ) ) ) )).

fof(t34_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => a_3_3_waybel30(A,B,C) = a_2_4_waybel30(A,C) ) ) ) )).

fof(t38_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v3_compts_1(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => B = k1_yellow_0(A,a_2_5_waybel30(A,B)) ) ) )).

fof(t39_waybel30,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_2(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ( v3_waybel_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => B = k1_yellow_0(A,a_2_4_waybel30(A,B)) ) ) ) )).

fof(s1_waybel30,axiom,(
    a_0_0_waybel30 = k1_xboole_0 )).

fof(fraenkel_a_2_0_waybel30,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ( r2_hidden(A,a_2_0_waybel30(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,C)
            & A = k3_xboole_0(B,D) ) ) ) )).

fof(fraenkel_a_3_0_waybel30,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & ~ v1_xboole_0(C)
        & v1_waybel_0(C,k2_yellow_1(k8_waybel_0(B)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(B)))))
        & m1_subset_1(D,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) )
     => ( r2_hidden(A,a_3_0_waybel30(B,C,D))
      <=> ? [E] :
            ( m1_struct_0(E,k2_yellow_1(k8_waybel_0(B)),C)
            & A = k3_xboole_0(D,E) ) ) ) )).

fof(fraenkel_a_1_0_waybel30,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B) )
     => ( r2_hidden(A,a_1_0_waybel30(B))
      <=> ? [C,D] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k6_subset_1(u1_struct_0(B),C,k5_waybel_0(B,D))
            & r2_hidden(C,k5_waybel11(B))
            & v1_finset_1(D) ) ) ) )).

fof(fraenkel_a_3_1_waybel30,axiom,(
    ! [A,B,C,D] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel_2(B)
        & v2_waybel19(B)
        & l1_waybel_9(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_yellow_8(D,B,C) )
     => ( r2_hidden(A,a_3_1_waybel30(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & A = k5_waybel_0(B,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_2_1_waybel30,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_1_waybel30(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ! [E] :
                ( ( ~ v1_xboole_0(E)
                  & v1_waybel_0(E,B)
                  & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
               => ~ ( r3_orders_2(B,D,k1_yellow_0(B,E))
                    & r1_xboole_0(C,E) ) ) ) ) ) )).

fof(fraenkel_a_2_2_waybel30,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v2_waybel_2(B)
        & v4_waybel11(B)
        & l1_waybel_9(B)
        & v1_finset_1(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_2_waybel30(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k2_waybel_3(B,D)
            & r2_hidden(D,C) ) ) ) )).

fof(fraenkel_a_3_2_waybel30,axiom,(
    ! [A,B,C,D] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel19(B)
        & l1_waybel_9(B)
        & v4_waybel11(C)
        & m1_yellow_9(C,B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_2_waybel30(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
            & A = k2_yellow_0(C,E)
            & r2_hidden(D,E)
            & r2_hidden(E,k5_waybel11(C)) ) ) ) )).

fof(fraenkel_a_2_3_waybel30,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel19(B)
        & l1_waybel_9(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_3_waybel30(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k2_yellow_0(B,D)
            & r2_hidden(C,D)
            & r2_hidden(D,k2_waybel19(B)) ) ) ) )).

fof(fraenkel_a_3_3_waybel30,axiom,(
    ! [A,B,C,D] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel_2(B)
        & v2_waybel19(B)
        & l1_waybel_9(B)
        & v4_waybel11(C)
        & m1_yellow_9(C,B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_3_waybel30(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
            & A = k2_yellow_0(C,E)
            & r2_hidden(D,E)
            & r2_hidden(E,k5_waybel11(C)) ) ) ) )).

fof(fraenkel_a_2_4_waybel30,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel_2(B)
        & v2_waybel19(B)
        & l1_waybel_9(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_4_waybel30(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k2_yellow_0(B,D)
            & r2_hidden(C,D)
            & r2_hidden(D,k2_waybel19(B)) ) ) ) )).

fof(fraenkel_a_2_5_waybel30,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & v2_waybel_2(B)
        & v3_compts_1(B)
        & v2_waybel19(B)
        & l1_waybel_9(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_5_waybel30(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k2_yellow_0(B,D)
            & r2_hidden(C,D)
            & r2_hidden(D,k2_waybel19(B)) ) ) ) )).

fof(fraenkel_a_0_0_waybel30,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_waybel30)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(f1_s1_waybel30))
          & A = f3_s1_waybel30(B)
          & r2_hidden(B,k1_xboole_0) ) ) )).
%------------------------------------------------------------------------------