SET007 Axioms: SET007+558.ax
%------------------------------------------------------------------------------
% File : SET007+558 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Lawson Topology
% 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 : waybel19 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 66 ( 0 unt; 0 def)
% Number of atoms : 857 ( 33 equ)
% Maximal formula atoms : 28 ( 12 avg)
% Number of connectives : 859 ( 68 ~; 1 |; 584 &)
% ( 12 <=>; 194 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 59 ( 58 usr; 0 prp; 1-4 aty)
% Number of functors : 41 ( 41 usr; 1 con; 0-4 aty)
% Number of variables : 175 ( 161 !; 14 ?)
% 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_waybel19,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_pre_topc(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_pre_topc(A)
& ~ v1_yellow_3(A)
& v1_waybel19(A) ) ) ) ).
fof(rc1_waybel19,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(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_pre_topc(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& ~ v1_yellow_3(A)
& v1_waybel_9(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_realset2(A)
& v1_waybel19(A) ) ).
fof(rc2_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_waybel_9(B)
& v1_waybel19(B) ) ) ).
fof(cc2_waybel19,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_waybel19(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& ~ v1_yellow_3(A) ) ) ) ).
fof(cc3_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v1_yellow_0(B) ) ) ) ).
fof(cc4_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v2_waybel_3(B)
& v3_waybel_3(B)
& ~ v1_yellow_3(B) ) ) ) ).
fof(rc3_waybel19,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] :
( m1_yellow_9(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v2_pre_topc(B)
& ~ v1_yellow_3(B)
& v1_waybel_9(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel19(B) ) ) ).
fof(rc4_waybel19,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& ~ v1_yellow_3(A)
& v1_waybel_9(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A) ) ).
fof(rc5_waybel19,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& ~ v1_yellow_3(A)
& v1_waybel_9(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A) ) ).
fof(cc5_waybel19,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& ~ v1_yellow_3(A)
& v2_compts_1(A)
& v1_urysohn1(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A) ) ) ) ).
fof(cc6_waybel19,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_pre_topc(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& ~ v1_yellow_3(A)
& v3_compts_1(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A) ) ) ) ).
fof(t1_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( v2_pre_topc(B)
& v1_waybel_9(B)
& m1_yellow_9(B,A)
& v1_waybel19(B) ) ) ).
fof(t2_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_waybel19(B)
& l1_waybel_9(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> u1_pre_topc(A) = u1_pre_topc(B) ) ) ) ).
fof(d2_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( B = k1_waybel19(A)
<=> ! [C] :
( ( v2_pre_topc(C)
& v1_waybel19(C)
& m1_yellow_9(C,A) )
=> B = u1_pre_topc(C) ) ) ) ) ).
fof(t3_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(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))
=> k1_waybel19(A) = k1_waybel19(B) ) ) ) ).
fof(t4_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_pre_topc(k3_subset_1(u1_struct_0(A),k7_waybel_0(A,B)),A)
& v4_pre_topc(k7_waybel_0(A,B),A) ) ) ) ).
fof(t5_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> v12_waybel_0(B,A) ) ) ) ).
fof(t6_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> v13_waybel_0(B,A) ) ) ) ).
fof(t8_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v1_waybel19(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) )
=> v5_pre_topc(C,A,B) ) ) ) ) ).
fof(t9_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v1_waybel19(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v17_waybel_0(C,A,B)
=> v5_pre_topc(C,A,B) ) ) ) ) ).
fof(t10_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m2_cantor_1(B,A)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_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(A)))
=> ~ ( r2_hidden(D,B)
& r2_hidden(k2_yellow_0(A,C),D)
& r1_xboole_0(C,D) ) )
=> r2_hidden(k2_yellow_0(A,C),k6_pre_topc(A,C)) ) ) ) ) ).
fof(t11_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v1_waybel19(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(C,A,B)
=> v21_waybel_0(C,A,B) ) ) ) ) ).
fof(t12_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v1_waybel19(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v5_pre_topc(C,A,B)
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) ) )
=> v17_waybel_0(C,A,B) ) ) ) ) ).
fof(t13_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v2_pre_topc(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_pre_topc(A,k1_struct_0(A,B)) = k7_waybel_0(A,B) ) ) ).
fof(t14_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k3_subset_1(u1_struct_0(k3_yellow_3(A,B)),k7_waybel_0(k3_yellow_3(A,B),k7_yellow_3(A,B,C,D))) = k2_xboole_0(k2_zfmisc_1(k3_subset_1(u1_struct_0(A),k7_waybel_0(A,C)),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),k3_subset_1(u1_struct_0(B),k7_waybel_0(B,D)))) ) ) ) ) ).
fof(t15_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_pre_topc(C)
& v1_waybel19(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( ( v2_pre_topc(D)
& v1_waybel19(D)
& m1_yellow_9(D,B) )
=> k1_waybel19(k3_yellow_3(A,B)) = u1_pre_topc(k6_borsuk_1(C,D)) ) ) ) ) ).
fof(t16_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_pre_topc(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_pre_topc(B)
& v1_waybel19(B)
& l1_waybel_9(B) )
=> k1_waybel19(k3_yellow_3(A,B)) = u1_pre_topc(k6_borsuk_1(A,B)) ) ) ).
fof(t17_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v1_waybel19(B)
& l1_waybel_9(B) )
=> ( m1_yellow_9(B,k3_yellow_3(A,A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( C = k4_waybel_2(A)
=> v5_pre_topc(C,B,A) ) ) ) ) ) ).
fof(t18_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(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))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( v1_waybel_0(k1_waybel_3(A,C),A)
& ~ v1_xboole_0(k1_waybel_3(A,C)) ) )
& v2_waybel_3(A) )
=> v2_waybel_3(B) ) ) ) ).
fof(t19_waybel19,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
=> ( ( r2_hidden(D,u1_pre_topc(A))
| r2_hidden(D,u1_pre_topc(B)) )
=> v3_pre_topc(D,C) ) ) ) ) ) ).
fof(t20_waybel19,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
=> ( ( E = D
& v3_pre_topc(D,A) )
=> v3_pre_topc(E,C) ) ) ) ) ) ) ).
fof(t21_waybel19,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
=> ( ( E = D
& v4_pre_topc(D,A) )
=> v4_pre_topc(E,C) ) ) ) ) ) ) ) ).
fof(t22_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B,C] :
( ( r1_tarski(B,C)
& r1_tarski(C,u1_pre_topc(A)) )
=> ( ( m1_cantor_1(B,A)
=> m1_cantor_1(C,A) )
& ( m2_cantor_1(B,A)
=> m2_cantor_1(C,A) ) ) ) ) ).
fof(t23_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( m3_yellow_9(C,A,B)
=> ! [D] :
( m2_cantor_1(D,A)
=> ! [E] :
( m2_cantor_1(E,B)
=> m2_cantor_1(k2_xboole_0(D,E),C) ) ) ) ) ) ) ).
fof(t24_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( m3_yellow_9(E,A,B)
=> ! [F] :
( m3_yellow_9(F,C,D)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(G,u1_struct_0(A),u1_struct_0(C)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(H,u1_struct_0(B),u1_struct_0(D)) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(E),u1_struct_0(F))
& m2_relset_1(I,u1_struct_0(E),u1_struct_0(F)) )
=> ( ( I = G
& I = H
& v5_pre_topc(G,A,C)
& v5_pre_topc(H,B,D) )
=> v5_pre_topc(I,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_cantor_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_hidden(D,E)
& r2_hidden(E,B) )
=> r1_waybel_0(A,C,E) ) )
=> r2_hidden(D,k11_yellow_6(A,C)) ) ) ) ) ) ).
fof(t26_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_waybel_0(A,B,C)
=> r1_tarski(k11_yellow_6(A,B),k6_pre_topc(A,C)) ) ) ) ) ).
fof(t27_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( u1_waybel_0(A,k2_yellow_9(A,B)) = k6_relat_1(B)
& u1_waybel_0(A,k3_yellow_9(A,B)) = k6_relat_1(B) ) ) ) ).
fof(t28_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k6_waybel_0(A,B)) = k1_struct_0(A,B) ) ) ).
fof(d3_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_waybel_9(A) )
=> ( v2_waybel19(A)
<=> m2_cantor_1(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k1_waybel19(A),k5_waybel11(A)),A) ) ) ).
fof(t29_waybel19,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_pre_topc(B)
& v1_waybel19(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v4_waybel11(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( ( v2_pre_topc(D)
& m1_yellow_9(D,A) )
=> ( v2_waybel19(D)
<=> m3_yellow_9(D,C,B) ) ) ) ) ) ).
fof(d4_waybel19,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] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( B = k2_waybel19(A)
<=> ! [C] :
( ( v2_pre_topc(C)
& v2_waybel19(C)
& m1_yellow_9(C,A) )
=> B = u1_pre_topc(C) ) ) ) ) ).
fof(t33_waybel19,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) )
=> k2_waybel19(A) = k1_cantor_1(u1_struct_0(A),k2_cantor_1(u1_struct_0(A),k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k5_waybel11(A),k1_waybel19(A)))) ) ).
fof(t34_waybel19,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_pre_topc(B)
& v1_waybel19(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v2_pre_topc(C)
& v4_waybel11(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( m3_yellow_9(D,C,B)
=> k2_waybel19(A) = u1_pre_topc(D) ) ) ) ) ).
fof(t35_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> v3_waybel11(B,A) ) ) ) ).
fof(t36_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(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)))
=> ( v3_pre_topc(B,A)
=> v3_waybel11(B,A) ) ) ) ).
fof(t37_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_waybel19(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(C,A)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( D = C
=> v3_pre_topc(D,B) ) ) ) ) ) ) ).
fof(t38_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_pre_topc(k7_waybel_0(A,B),A)
& v4_pre_topc(k6_waybel_0(A,B),A)
& v4_pre_topc(k1_struct_0(A,B),A) ) ) ) ).
fof(t39_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_pre_topc(k3_subset_1(u1_struct_0(A),k7_waybel_0(A,B)),A)
& v3_pre_topc(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A)
& v3_pre_topc(k3_subset_1(u1_struct_0(A),k1_struct_0(A,B)),A) ) ) ) ).
fof(t40_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_pre_topc(k2_waybel_3(A,B),A)
& v4_pre_topc(k3_subset_1(u1_struct_0(A),k2_waybel_3(A,B)),A) ) ) ) ).
fof(t41_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& v2_waybel19(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v13_waybel_0(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( v3_pre_topc(C,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = C
=> v3_pre_topc(D,A) ) ) ) ) ) ) ).
fof(t42_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v4_pre_topc(B,A)
<=> v2_waybel11(B,A) ) ) ) ).
fof(t43_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k11_yellow_6(A,k3_yellow_9(A,B)) = k1_struct_0(A,k2_yellow_0(A,B)) ) ) ).
fof(s1_waybel19,axiom,
( ( ? [A] :
( m2_cantor_1(A,f1_s1_waybel19)
& ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
=> ( r2_hidden(B,A)
=> p1_s1_waybel19(B) ) ) )
& ! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(f1_s1_waybel19))))
=> ( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
=> ( r2_hidden(B,A)
=> p1_s1_waybel19(B) ) )
=> p1_s1_waybel19(k5_setfam_1(u1_struct_0(f1_s1_waybel19),A)) ) )
& ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
=> ( ( p1_s1_waybel19(A)
& p1_s1_waybel19(B) )
=> p1_s1_waybel19(k5_subset_1(u1_struct_0(f1_s1_waybel19),A,B)) ) ) )
& p1_s1_waybel19(k2_pre_topc(f1_s1_waybel19)) )
=> ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_waybel19)))
=> ( v3_pre_topc(A,f1_s1_waybel19)
=> p1_s1_waybel19(A) ) ) ) ).
fof(dt_k1_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> m1_subset_1(k1_waybel19(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_waybel19,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) )
=> m1_subset_1(k2_waybel19(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(d1_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_waybel_9(A) )
=> ( v1_waybel19(A)
<=> m2_cantor_1(a_1_0_waybel19(A),A) ) ) ).
fof(t7_waybel19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_waybel_9(A) )
=> ( v1_waybel19(A)
<=> m1_cantor_1(a_1_1_waybel19(A),A) ) ) ).
fof(t30_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> m2_cantor_1(k2_xboole_0(k5_waybel11(A),a_1_2_waybel19(A)),A) ) ).
fof(t31_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> m2_cantor_1(k2_xboole_0(k5_waybel11(A),a_1_3_waybel19(A)),A) ) ).
fof(t32_waybel19,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> m1_cantor_1(a_1_4_waybel19(A),A) ) ).
fof(fraenkel_a_1_0_waybel19,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_0_waybel19(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = k3_subset_1(u1_struct_0(B),k7_waybel_0(B,C)) ) ) ) ).
fof(fraenkel_a_1_1_waybel19,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_1_waybel19(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = k3_subset_1(u1_struct_0(B),k5_waybel_0(B,C))
& v1_finset_1(C) ) ) ) ).
fof(fraenkel_a_1_2_waybel19,axiom,
! [A,B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel19(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_2_waybel19(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = k3_subset_1(u1_struct_0(B),k7_waybel_0(B,C)) ) ) ) ).
fof(fraenkel_a_1_3_waybel19,axiom,
! [A,B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel19(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_3_waybel19(B))
<=> ? [C,D] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,u1_struct_0(B))
& A = k6_subset_1(u1_struct_0(B),C,k7_waybel_0(B,D))
& r2_hidden(C,k5_waybel11(B)) ) ) ) ).
fof(fraenkel_a_1_4_waybel19,axiom,
! [A,B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel19(B)
& l1_waybel_9(B) )
=> ( r2_hidden(A,a_1_4_waybel19(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) ) ) ) ).
%------------------------------------------------------------------------------