TPTP Problem File: TOP048+1.p
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%------------------------------------------------------------------------------
% File : TOP048+1 : TPTP v8.2.0. Released v3.4.0.
% Domain : Topology
% Problem : Compactness of Lim-inf Topology T27
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [BE01] Bancerek & Endou (2001), Compactness of Lim-inf Topolo
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t27_waybel33 [Urb08]
% Status : Theorem
% Rating : 0.92 v8.2.0, 0.94 v7.5.0, 0.97 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.87 v7.0.0, 0.93 v6.4.0, 0.92 v6.3.0, 1.00 v6.0.0, 0.96 v5.5.0, 1.00 v3.7.0, 0.95 v3.5.0, 1.00 v3.4.0
% Syntax : Number of formulae : 184 ( 18 unt; 0 def)
% Number of atoms : 1147 ( 15 equ)
% Maximal formula atoms : 27 ( 6 avg)
% Number of connectives : 1124 ( 161 ~; 1 |; 742 &)
% ( 7 <=>; 213 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 80 ( 78 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-3 aty)
% Number of variables : 274 ( 220 !; 54 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Normal version: includes the axioms (which may be theorems from
% other articles) and background that are possibly necessary.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
fof(t27_waybel33,conjecture,
! [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_waybel33(A)
& l1_waybel_9(A) )
=> ( v2_compts_1(A)
& v1_urysohn1(A) ) ) ).
fof(abstractness_v1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_orders_2(A)
=> A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ) ).
fof(cc10_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ) ) ).
fof(cc10_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v3_compts_1(A) )
=> ( v2_pre_topc(A)
& v1_urysohn1(A) ) ) ) ).
fof(cc11_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_yellow_0(A) ) ) ) ).
fof(cc11_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v1_urysohn1(A) )
=> ( v2_pre_topc(A)
& v2_t_0topsp(A) ) ) ) ).
fof(cc12_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v24_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc13_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A) ) ) ) ).
fof(cc14_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc14_yellow13,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_pre_topc(A)
& v2_yellow13(A) ) ) ) ).
fof(cc1_finset_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_finset_1(A) ) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ) ).
fof(cc1_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc1_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_relat_1(A) ) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ) ).
fof(cc1_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> ( v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ) ) ).
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(cc1_waybel33,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( ~ v3_struct_0(A)
& v1_waybel33(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A) ) ) ) ).
fof(cc1_waybel_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v16_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel_0(B,A)
& v2_waybel_0(B,A) ) ) ) ).
fof(cc1_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A)
& v3_waybel_7(B,A) )
=> ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ) ) ).
fof(cc1_yellow11,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v1_yellow11(A) ) ) ) ).
fof(cc1_yellow13,axiom,
! [A] :
( v1_realset1(A)
=> v1_finset_1(A) ) ).
fof(cc1_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ~ v3_struct_0(B) ) ) ).
fof(cc2_finset_1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_finset_1(B) ) ) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ) ).
fof(cc2_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc2_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v2_tops_1(B,A) ) ) ) ).
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(cc2_waybel29,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( 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)
& ~ v1_yellow_3(B) ) ) ) ).
fof(cc2_waybel33,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_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)
& v1_waybel33(A) ) ) ) ).
fof(cc2_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ) ) ).
fof(cc2_yellow13,axiom,
! [A] :
( l1_struct_0(A)
=> ( v3_realset2(A)
=> v6_group_1(A) ) ) ).
fof(cc2_yellow_9,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v2_orders_2(B) ) ) ).
fof(cc3_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v3_tops_1(B,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(cc3_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v1_yellow_0(B)
& v25_waybel_0(B) ) ) ) ).
fof(cc3_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_realset2(A)
& v2_orders_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_waybel_3(A) ) ) ) ).
fof(cc3_yellow13,axiom,
! [A] :
( l1_struct_0(A)
=> ( ~ v3_realset2(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc3_yellow_9,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v3_orders_2(B) ) ) ).
fof(cc4_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
=> v2_tops_1(B,A) ) ) ) ).
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(cc4_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_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)
& v2_lattice3(B) ) ) ) ).
fof(cc4_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_waybel_3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v2_waybel_3(A) ) ) ) ).
fof(cc4_yellow11,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v6_group_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v1_yellow_0(A) ) ) ) ).
fof(cc4_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_finset_1(B)
=> v4_pre_topc(B,A) ) ) ) ).
fof(cc4_yellow_9,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v4_orders_2(B) ) ) ).
fof(cc5_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& v2_tops_1(B,A) )
=> ( v2_tops_1(B,A)
& v3_tops_1(B,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(cc5_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v16_waybel_0(A) ) ) ) ).
fof(cc5_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A) ) ) ) ).
fof(cc5_yellow11,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v6_group_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc5_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& v6_group_1(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A) ) ) ) ).
fof(cc5_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ) ).
fof(cc6_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& v3_tops_1(B,A) )
=> ( v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A)
& v3_tops_1(B,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(cc6_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& v16_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& v2_waybel_3(A) ) ) ) ).
fof(cc6_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v6_group_1(A) )
=> ( v2_pre_topc(A)
& v2_compts_1(A) ) ) ) ).
fof(cc7_waybel_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_compts_1(A)
& v3_compts_1(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_compts_1(A)
& v5_compts_1(A)
& v6_waybel_3(A) ) ) ) ).
fof(cc7_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A) )
=> ( v2_pre_topc(A)
& v1_urysohn1(A)
& v3_compts_1(A)
& v4_compts_1(A)
& v5_compts_1(A) ) ) ) ).
fof(cc8_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& v5_compts_1(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_compts_1(A) ) ) ) ).
fof(cc9_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v1_lattice3(A)
& v24_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc9_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v1_urysohn1(A)
& v4_compts_1(A) )
=> ( v2_pre_topc(A)
& v3_compts_1(A) ) ) ) ).
fof(d1_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> k1_waybel33(A,B,C) = k1_yellow_0(A,a_3_0_waybel33(A,B,C)) ) ) ) ).
fof(d3_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> k2_pre_topc(A) = u1_struct_0(A) ) ).
fof(d4_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_waybel_9(B)
=> ( m1_yellow_9(B,A)
<=> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ) ).
fof(dt_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ( v1_orders_2(g1_orders_2(A,B))
& l1_orders_2(g1_orders_2(A,B)) ) ) ).
fof(dt_k1_struct_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k1_tarski,axiom,
$true ).
fof(dt_k1_waybel33,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_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(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> m1_subset_1(k1_waybel33(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_yellow_0,axiom,
! [A,B] :
( l1_orders_2(A)
=> m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k2_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_yellow_0,axiom,
! [A,B] :
( l1_orders_2(A)
=> m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_zfmisc_1,axiom,
$true ).
fof(dt_k3_yellow_1,axiom,
! [A] :
( v1_orders_2(k3_yellow_1(A))
& l1_orders_2(k3_yellow_1(A)) ) ).
fof(dt_k6_pre_topc,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_l1_waybel_9,axiom,
! [A] :
( l1_waybel_9(A)
=> ( l1_pre_topc(A)
& l1_orders_2(A) ) ) ).
fof(dt_m1_relset_1,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_m1_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_9(B,A)
=> l1_waybel_9(B) ) ) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ).
fof(dt_m2_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m2_yellow_9(B,A)
=> ( v2_pre_topc(B)
& l1_pre_topc(B) ) ) ) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_u1_struct_0,axiom,
$true ).
fof(existence_l1_orders_2,axiom,
? [A] : l1_orders_2(A) ).
fof(existence_l1_pre_topc,axiom,
? [A] : l1_pre_topc(A) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A) ).
fof(existence_l1_waybel_9,axiom,
? [A] : l1_waybel_9(A) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A) ).
fof(existence_m1_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] : m1_yellow_9(B,A) ) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B) ).
fof(existence_m2_yellow_9,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] : m2_yellow_9(B,A) ) ).
fof(fc12_relat_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0) ) ).
fof(fc14_finset_1,axiom,
! [A,B] :
( ( v1_finset_1(A)
& v1_finset_1(B) )
=> v1_finset_1(k2_zfmisc_1(A,B)) ) ).
fof(fc15_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v12_waybel_0(k2_pre_topc(A),A)
& v13_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc1_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(k1_tarski(A))
& v1_finset_1(k1_tarski(A)) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ).
fof(fc1_waybel_7,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& ~ v1_yellow_3(k3_yellow_1(A))
& v2_waybel_1(k3_yellow_1(A))
& v9_waybel_1(k3_yellow_1(A))
& v10_waybel_1(k3_yellow_1(A))
& v11_waybel_1(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A)) ) ).
fof(fc1_yellow13,axiom,
! [A] :
( ( v6_group_1(A)
& l1_struct_0(A) )
=> v1_finset_1(u1_struct_0(A)) ) ).
fof(fc2_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_tarski(A)) ).
fof(fc2_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v4_pre_topc(k6_pre_topc(A,B),A) ) ).
fof(fc2_waybel_0,axiom,
! [A] :
( ( v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v1_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc2_waybel_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k3_yellow_1(A))
& ~ v3_realset2(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& ~ v1_yellow_3(k3_yellow_1(A))
& v2_waybel_1(k3_yellow_1(A))
& v9_waybel_1(k3_yellow_1(A))
& v10_waybel_1(k3_yellow_1(A))
& v11_waybel_1(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A)) ) ) ).
fof(fc2_yellow13,axiom,
! [A] :
( ( v3_realset2(A)
& l1_struct_0(A) )
=> v1_realset1(u1_struct_0(A)) ) ).
fof(fc3_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v1_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc3_yellow13,axiom,
! [A] :
( ( v2_compts_1(A)
& l1_pre_topc(A) )
=> ( v1_tops_1(k2_pre_topc(A),A)
& v6_compts_1(k2_pre_topc(A),A) ) ) ).
fof(fc4_relat_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0) ) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ).
fof(fc4_waybel_0,axiom,
! [A] :
( ( v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v2_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc5_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v2_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc8_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_pre_topc(k2_pre_topc(A),A)
& v4_pre_topc(k2_pre_topc(A),A) ) ) ).
fof(fc8_yellow_6,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v7_waybel_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& ~ v1_yellow_3(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A)) ) ).
fof(fc9_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> v1_tops_1(k2_pre_topc(A),A) ) ).
fof(fraenkel_a_3_0_waybel33,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& ~ v1_xboole_0(D)
& v2_waybel_0(D,k3_yellow_1(C))
& v13_waybel_0(D,k3_yellow_1(C))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) )
=> ( r2_hidden(A,a_3_0_waybel33(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& A = k2_yellow_0(B,E)
& r2_hidden(E,D) ) ) ) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ! [C,D] :
( g1_orders_2(A,B) = g1_orders_2(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(rc10_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc11_waybel_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v2_waybel_0(B,A)
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc12_waybel_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A) ) ).
fof(rc13_waybel_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(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) ) ).
fof(rc1_finset_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_finset_1(A) ) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A) ) ).
fof(rc1_lattice3,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A) ) ).
fof(rc1_relat_1,axiom,
? [A] :
( v1_xboole_0(A)
& v1_relat_1(A) ) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) ) ) ).
fof(rc1_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(B,A) ) ) ).
fof(rc1_waybel33,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_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel33(A) ) ).
fof(rc1_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_waybel_0(B,A)
& v2_waybel_0(B,A) ) ) ).
fof(rc1_waybel_3,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ).
fof(rc1_waybel_7,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_orders_2(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)
& ~ v1_yellow_3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ).
fof(rc1_yellow11,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v6_group_1(A) ) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) ) ).
fof(rc2_lattice3,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A) ) ).
fof(rc2_relat_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A) ) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& v1_xboole_0(B) ) ).
fof(rc2_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ).
fof(rc2_waybel_0,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)))
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_waybel_0(B,A)
& v2_waybel_0(B,A) ) ) ).
fof(rc2_waybel_3,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A) ) ).
fof(rc2_waybel_7,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ).
fof(rc2_yellow13,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v6_group_1(A)
& v3_realset2(A) ) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc3_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ).
fof(rc3_relat_1,axiom,
? [A] :
( v1_relat_1(A)
& v3_relat_1(A) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A) ) ).
fof(rc3_tops_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ).
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(rc3_waybel_7,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc4_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v3_relat_1(A)
& v1_funct_1(A) ) ).
fof(rc4_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_xboole_0(B)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A) ) ) ).
fof(rc4_waybel_3,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_compts_1(A)
& v3_compts_1(A)
& v4_compts_1(A)
& v5_compts_1(A)
& v6_waybel_3(A) ) ).
fof(rc4_waybel_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc4_yellow_6,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v3_orders_2(A)
& v7_waybel_0(A) ) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(rc5_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A)
& v3_tops_1(B,A) ) ) ).
fof(rc7_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc7_waybel_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
& ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
& v2_waybel_0(B,k3_yellow_1(A))
& v13_waybel_0(B,k3_yellow_1(A))
& v3_waybel_7(B,k3_yellow_1(A)) ) ) ).
fof(rc8_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc9_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A) ) ) ).
fof(redefinition_k1_struct_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k1_struct_0(A,B) = k1_tarski(B) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ) ).
fof(t23_waybel33,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_yellow_9(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(C,A)
=> ( v3_pre_topc(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) )
& ( v4_pre_topc(C,A)
=> ( v4_pre_topc(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ) ).
fof(t25_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel33(B)
& m1_yellow_9(B,A) )
=> ! [C] :
( ( v2_pre_topc(C)
& v2_waybel19(C)
& m1_yellow_9(C,A) )
=> m2_yellow_9(B,C) ) ) ) ).
fof(t26_waybel33,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)
& v1_waybel33(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> r2_waybel_7(A,B,k1_waybel33(A,k2_pre_topc(A),B)) ) ) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( v1_xboole_0(B)
| r2_hidden(A,B) ) ) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
<=> r2_hidden(C,B) )
=> A = B ) ).
fof(t33_yellow19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A)))
& v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_waybel_7(A,B,C) ) ) ) ) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ) ).
fof(t44_yellow_9,axiom,
! [A] :
( l1_waybel_9(A)
=> m1_yellow_9(A,A) ) ).
fof(t47_frechet2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_urysohn1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_pre_topc(A,k1_struct_0(A,B)) = k1_struct_0(A,B) ) ) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C)) )
=> m1_subset_1(A,C) ) ).
fof(t52_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
=> k6_pre_topc(A,B) = B )
& ( ( v2_pre_topc(A)
& k6_pre_topc(A,B) = B )
=> v4_pre_topc(B,A) ) ) ) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C))
& v1_xboole_0(C) ) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( r2_hidden(A,B)
& v1_xboole_0(B) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(A)
& A != B
& v1_xboole_0(B) ) ).
%------------------------------------------------------------------------------