SET007 Axioms: SET007+638.ax
%------------------------------------------------------------------------------
% File : SET007+638 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 1171 ( 39 equ)
% Maximal formula atoms : 47 ( 14 avg)
% Number of connectives : 1162 ( 73 ~; 0 |; 894 &)
% ( 22 <=>; 173 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 83 ( 82 usr; 0 prp; 1-3 aty)
% Number of functors : 44 ( 44 usr; 3 con; 0-3 aty)
% Number of variables : 194 ( 174 !; 20 ?)
% 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) ) ) ).
%------------------------------------------------------------------------------