SET007 Axioms: SET007+388.ax
%------------------------------------------------------------------------------
% File : SET007+388 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Nowhere and Everywhere Dense Subspaces of Topological Spaces
% 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 : tex_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 124 ( 0 unt; 0 def)
% Number of atoms : 1344 ( 30 equ)
% Maximal formula atoms : 21 ( 10 avg)
% Number of connectives : 1613 ( 393 ~; 6 |; 823 &)
% ( 26 <=>; 365 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 32 usr; 0 prp; 1-3 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-3 aty)
% Number of variables : 323 ( 289 !; 34 ?)
% 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_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_borsuk_1(B,A)
& v1_tex_3(B,A) )
=> ( v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& ~ v2_tex_2(B,A) ) ) ) ) ).
fof(cc2_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v2_tex_2(B,A)
& v1_tex_3(B,A) )
=> ( v2_pre_topc(B)
& ~ v1_borsuk_1(B,A)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc3_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_borsuk_1(B,A)
& v2_tex_2(B,A) )
=> ( v2_pre_topc(B)
& ~ v1_tex_3(B,A) ) ) ) ) ).
fof(rc1_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_tex_3(B,A) ) ) ).
fof(cc4_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_3(B,A)
=> ( v2_pre_topc(B)
& v1_tex_3(B,A) ) ) ) ) ).
fof(cc5_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v1_tex_3(B,A)
=> ( v2_pre_topc(B)
& ~ v2_tex_3(B,A) ) ) ) ) ).
fof(cc6_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v2_tex_2(B,A)
=> ( v2_pre_topc(B)
& v2_tex_3(B,A) ) ) ) ) ).
fof(cc7_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v2_tex_3(B,A)
=> ( v2_pre_topc(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(rc2_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_tex_3(B,A)
& v2_tex_3(B,A) ) ) ).
fof(cc8_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_tsep_1(B,A)
& v1_tex_3(B,A) )
=> ( v2_pre_topc(B)
& v1_tex_3(B,A)
& v2_tex_3(B,A) ) ) ) ) ).
fof(cc9_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_tex_3(B,A)
& ~ v2_tex_3(B,A) )
=> ( v2_pre_topc(B)
& ~ v1_tsep_1(B,A)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc10_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_tsep_1(B,A)
& ~ v2_tex_3(B,A) )
=> ( v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A) ) ) ) ) ).
fof(rc3_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_tsep_1(B,A)
& v1_tex_3(B,A)
& v2_tex_3(B,A) ) ) ).
fof(cc11_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v1_tsep_1(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& ~ v3_tex_3(B,A) ) ) ) ) ).
fof(cc12_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v3_tex_3(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& ~ v1_tsep_1(B,A)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc13_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_3(B,A)
=> ( v2_pre_topc(B)
& ~ v3_tex_3(B,A) ) ) ) ) ).
fof(cc14_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v3_tex_3(B,A)
=> ( v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v2_tex_3(B,A) ) ) ) ) ).
fof(cc15_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v4_tex_3(B,A)
=> ( v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v2_tex_3(B,A)
& v3_tex_3(B,A) ) ) ) ) ).
fof(cc16_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_tex_3(B,A)
=> ( v2_pre_topc(B)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc17_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v4_tex_3(B,A)
=> ( v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A) ) ) ) ) ).
fof(cc18_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v1_tex_3(B,A)
=> ( v2_pre_topc(B)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc19_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_borsuk_1(B,A)
& v3_tex_3(B,A) )
=> ( v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A)
& v3_tex_3(B,A)
& v4_tex_3(B,A) ) ) ) ) ).
fof(cc20_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v3_tex_3(B,A)
& ~ v4_tex_3(B,A) )
=> ( v2_pre_topc(B)
& ~ v1_borsuk_1(B,A)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc21_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_borsuk_1(B,A)
& ~ v4_tex_3(B,A) )
=> ( v2_pre_topc(B)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc22_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_struct_0(B)
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc23_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_2(B,A)
=> ( v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v2_tex_2(B,A)
& ~ v5_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A) ) ) ) ) ).
fof(cc24_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v1_tex_3(B,A)
=> ( v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& ~ v2_tex_2(B,A)
& v5_tex_2(B,A)
& v1_tex_3(B,A)
& v2_tex_3(B,A)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(rc4_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ).
fof(rc5_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v2_tex_2(B,A)
& ~ v5_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A) ) ) ).
fof(rc6_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& ~ v1_tsep_1(B,A)
& v2_tex_2(B,A)
& ~ v2_tex_3(B,A)
& v3_tex_3(B,A) ) ) ).
fof(rc7_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& ~ v1_borsuk_1(B,A)
& v2_tex_2(B,A)
& v1_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ).
fof(cc25_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_struct_0(B)
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc26_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_2(B,A)
=> ( v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v2_tex_3(B,A) ) ) ) ) ).
fof(cc27_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_3(B,A)
=> ( v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& ~ v2_tex_2(B,A)
& v1_tex_3(B,A)
& v2_tex_3(B,A)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc28_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v3_tex_3(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& ~ v1_borsuk_1(B,A)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc29_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v1_borsuk_1(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc30_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v2_tex_2(B,A)
& v1_tex_3(B,A) )
=> ( v2_pre_topc(B)
& ~ v1_tsep_1(B,A)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc31_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_tsep_1(B,A)
& v1_tex_3(B,A) )
=> ( v2_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& ~ v2_tex_2(B,A)
& v1_tex_3(B,A)
& v2_tex_3(B,A)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ) ) ).
fof(cc32_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_tsep_1(B,A)
& v2_tex_2(B,A) )
=> ( v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A) ) ) ) ) ).
fof(rc8_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v4_tex_3(B,A) ) ) ).
fof(rc9_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v2_tex_2(B,A)
& ~ v2_tex_3(B,A) ) ) ).
fof(rc10_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& ~ v1_tsep_1(B,A)
& v2_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A)
& v3_tex_3(B,A)
& v4_tex_3(B,A) ) ) ).
fof(rc11_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& ~ v1_borsuk_1(B,A)
& v2_tex_2(B,A)
& v1_tex_3(B,A)
& v2_tex_3(B,A)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ).
fof(rc12_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_borsuk_1(B,A)
& ~ v1_tsep_1(B,A)
& v2_tex_2(B,A)
& ~ v1_tex_3(B,A)
& ~ v2_tex_3(B,A)
& v3_tex_3(B,A)
& v4_tex_3(B,A) ) ) ).
fof(rc13_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& ~ v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& v2_tex_2(B,A)
& v1_tex_3(B,A)
& v2_tex_3(B,A)
& ~ v3_tex_3(B,A)
& ~ v4_tex_3(B,A) ) ) ).
fof(t1_tex_3,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)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_tsep_2(A,B,C)
=> ( ~ v1_xboole_0(B)
<=> v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(t2_tex_3,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)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_tsep_2(A,B,C)
=> ( v1_tops_1(B,A)
<=> v2_tops_1(C,A) ) ) ) ) ) ).
fof(t3_tex_3,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)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_tsep_2(A,B,C)
=> ( v2_tops_1(B,A)
<=> v1_tops_1(C,A) ) ) ) ) ) ).
fof(t4_tex_3,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)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_tsep_2(A,B,C)
=> ( v1_tops_3(B,A)
<=> v3_tops_1(C,A) ) ) ) ) ) ).
fof(t5_tex_3,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)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_tsep_2(A,B,C)
=> ( v3_tops_1(B,A)
<=> v1_tops_3(C,A) ) ) ) ) ) ).
fof(t6_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r4_tsep_2(A,B,C)
=> ( v2_tex_2(B,A)
& v2_tex_2(C,A) ) ) ) ) ) ).
fof(t7_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_tex_2(C,A)
& m1_pre_topc(C,A)
& B = u1_struct_0(C) ) ) ) ).
fof(t8_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tex_2(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_tex_2(C,A)
& m1_pre_topc(C,A)
& r4_tsep_2(A,B,C) ) ) ) ).
fof(d1_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v1_tex_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> v1_tops_1(C,A) ) ) ) ) ) ).
fof(t9_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> ( v1_tex_3(B,A)
<=> v1_tops_1(C,A) ) ) ) ) ) ).
fof(t10_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v1_tops_1(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t11_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tex_3(B,A)
& m1_pre_topc(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
=> ( v1_tops_1(D,B)
<=> v1_tops_1(C,A) ) ) ) ) ) ) ).
fof(t12_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_pre_topc(C,A)
=> ( m1_pre_topc(B,C)
=> v1_tex_3(C,A) ) ) ) ) ).
fof(t13_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( m1_pre_topc(B,C)
=> ( v1_tex_3(B,C)
& m1_pre_topc(B,C) ) ) ) ) ) ).
fof(t14_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_tex_3(C,B)
& m1_pre_topc(C,B) )
=> ( ~ v3_struct_0(C)
& v1_tex_3(C,A)
& m1_pre_topc(C,A) ) ) ) ) ).
fof(t15_tex_3,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) )
=> ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> ( ( v1_tex_3(B,A)
& m1_pre_topc(B,A) )
<=> ( v1_tex_3(C,A)
& m1_pre_topc(C,A) ) ) ) ) ) ) ).
fof(d2_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> v1_tops_3(C,A) ) ) ) ) ) ).
fof(t16_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> ( v2_tex_3(B,A)
<=> v1_tops_3(C,A) ) ) ) ) ) ).
fof(t17_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v1_tops_3(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t18_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tex_3(B,A)
& m1_pre_topc(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
=> ( v1_tops_3(D,B)
<=> v1_tops_3(C,A) ) ) ) ) ) ) ).
fof(t19_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_pre_topc(C,A)
=> ( m1_pre_topc(B,C)
=> v2_tex_3(C,A) ) ) ) ) ).
fof(t20_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( m1_pre_topc(B,C)
=> ( v2_tex_3(B,C)
& m1_pre_topc(B,C) ) ) ) ) ) ).
fof(t21_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_tex_3(C,B)
& m1_pre_topc(C,B) )
=> ( v2_tex_3(C,A)
& m1_pre_topc(C,A) ) ) ) ) ).
fof(t22_tex_3,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) )
=> ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> ( ( v2_tex_3(B,A)
& m1_pre_topc(B,A) )
<=> ( v2_tex_3(C,A)
& m1_pre_topc(C,A) ) ) ) ) ) ) ).
fof(t23_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v1_tops_1(B,A)
& v3_pre_topc(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_tsep_1(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t24_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_3(B,A)
<=> ? [C] :
( v1_pre_topc(C)
& v1_tsep_1(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A)
& m1_pre_topc(C,B) ) ) ) ) ).
fof(t25_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ( v1_tex_3(B,A)
| v1_tex_3(C,A) )
=> ( v1_tex_3(k1_tsep_1(A,B,C),A)
& m1_pre_topc(k1_tsep_1(A,B,C),A) ) ) ) ) ) ).
fof(t26_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ( v2_tex_3(B,A)
| v2_tex_3(C,A) )
=> ( v2_tex_3(k1_tsep_1(A,B,C),A)
& m1_pre_topc(k1_tsep_1(A,B,C),A) ) ) ) ) ) ).
fof(t27_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ( v2_tex_3(B,A)
& v2_tex_3(C,A) )
=> ( v2_tex_3(k2_tsep_1(A,B,C),A)
& m1_pre_topc(k2_tsep_1(A,B,C),A) ) ) ) ) ) ).
fof(t28_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ( ( v2_tex_3(B,A)
& v1_tex_3(C,A) )
| ( v1_tex_3(B,A)
& v2_tex_3(C,A) ) )
=> ( v1_tex_3(k2_tsep_1(A,B,C),A)
& m1_pre_topc(k2_tsep_1(A,B,C),A) ) ) ) ) ) ).
fof(d3_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v3_tex_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> v2_tops_1(C,A) ) ) ) ) ) ).
fof(t29_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> ( v3_tex_3(B,A)
<=> v2_tops_1(C,A) ) ) ) ) ) ).
fof(t30_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v2_tops_1(B,A)
& ! [C] :
( ( v1_pre_topc(C)
& m1_pre_topc(C,A) )
=> ~ ( v3_tex_3(C,A)
& B = u1_struct_0(C) ) ) ) ) ) ).
fof(t31_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_pre_topc(C,A)
=> ( r3_tsep_2(A,B,C)
=> ( v1_tex_3(B,A)
<=> v3_tex_3(C,A) ) ) ) ) ) ).
fof(t32_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r4_tsep_2(A,B,C)
=> ( v3_tex_3(B,A)
<=> v1_tex_3(C,A) ) ) ) ) ) ).
fof(t33_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v3_tex_3(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,u1_struct_0(B))
=> v2_tops_1(C,A) ) ) ) ) ) ).
fof(t34_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_pre_topc(C,A)
=> ( ( v3_tex_3(B,A)
& m1_pre_topc(C,B) )
=> v3_tex_3(C,A) ) ) ) ) ).
fof(d4_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v4_tex_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> v3_tops_1(C,A) ) ) ) ) ) ).
fof(t35_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> ( v4_tex_3(B,A)
<=> v3_tops_1(C,A) ) ) ) ) ) ).
fof(t36_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v3_tops_1(B,A)
& ! [C] :
( ( v1_pre_topc(C)
& m1_pre_topc(C,A) )
=> ~ ( v4_tex_3(C,A)
& B = u1_struct_0(C) ) ) ) ) ) ).
fof(t37_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_pre_topc(C,A)
=> ( r3_tsep_2(A,B,C)
=> ( v2_tex_3(B,A)
<=> v4_tex_3(C,A) ) ) ) ) ) ).
fof(t38_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r4_tsep_2(A,B,C)
=> ( v4_tex_3(B,A)
<=> v2_tex_3(C,A) ) ) ) ) ) ).
fof(t39_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v4_tex_3(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,u1_struct_0(B))
=> v3_tops_1(C,A) ) ) ) ) ) ).
fof(t40_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_pre_topc(C,A)
=> ( ( v4_tex_3(B,A)
& m1_pre_topc(C,B) )
=> v4_tex_3(C,A) ) ) ) ) ).
fof(t41_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v2_tops_1(B,A)
& v4_pre_topc(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_borsuk_1(C,A)
& m1_pre_topc(C,A) )
=> ~ ( v3_tex_3(C,A)
& B = u1_struct_0(C) ) ) ) ) ) ).
fof(t42_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( v4_tex_3(B,A)
<=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_borsuk_1(C,A)
& m1_pre_topc(C,A)
& v3_tex_3(C,A)
& m1_pre_topc(B,C) ) ) ) ) ).
fof(t43_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ~ ( ( v3_tex_3(B,A)
| v3_tex_3(C,A) )
& ~ r1_tsep_1(A,B,C)
& ~ v3_tex_3(k2_tsep_1(A,B,C),A) ) ) ) ) ).
fof(t44_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ( v4_tex_3(B,A)
& v4_tex_3(C,A) )
=> v4_tex_3(k1_tsep_1(A,B,C),A) ) ) ) ) ).
fof(t45_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ( ( v4_tex_3(B,A)
& v3_tex_3(C,A) )
| ( v3_tex_3(B,A)
& v4_tex_3(C,A) ) )
=> v3_tex_3(k1_tsep_1(A,B,C),A) ) ) ) ) ).
fof(t46_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ~ ( ( v4_tex_3(B,A)
| v4_tex_3(C,A) )
& ~ r1_tsep_1(A,B,C)
& ~ v4_tex_3(k2_tsep_1(A,B,C),A) ) ) ) ) ).
fof(t47_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( m1_pre_topc(B,A)
=> ~ v3_tex_3(B,A) )
=> v1_tdlat_3(A) ) ) ).
fof(t48_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( ( v2_tex_2(B,A)
& m1_pre_topc(B,A) )
=> ~ v1_tex_3(B,A) )
=> v1_tdlat_3(A) ) ) ).
fof(t49_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ ( ? [B] :
( ~ v3_struct_0(B)
& m1_pre_topc(B,A)
& v3_tex_3(B,A) )
& v1_tdlat_3(A) ) ) ).
fof(t50_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ ( ? [B] :
( ~ v3_struct_0(B)
& m1_pre_topc(B,A)
& v1_tex_3(B,A)
& v2_tex_2(B,A) )
& v1_tdlat_3(A) ) ) ).
fof(t51_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v2_tops_1(B,A)
& ! [C] :
( ( v1_pre_topc(C)
& v3_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t52_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v1_tops_1(B,A)
& ! [C] :
( ( v1_pre_topc(C)
& v2_tex_2(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t53_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_tex_2(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A)
& r4_tsep_2(A,B,C) ) ) ) ).
fof(t54_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tex_2(B,A)
& v1_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v3_tex_3(C,A)
& m1_pre_topc(C,A)
& r4_tsep_2(A,B,C) ) ) ) ).
fof(t55_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(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) )
=> ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> ( ( v3_tex_3(B,A)
& m1_pre_topc(B,A) )
<=> ( v3_tex_3(C,A)
& m1_pre_topc(C,A) ) ) ) ) ) ) ).
fof(t56_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( m1_pre_topc(B,A)
=> ~ v4_tex_3(B,A) )
=> v3_tdlat_3(A) ) ) ).
fof(t57_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( ( v2_tex_2(B,A)
& m1_pre_topc(B,A) )
=> ~ v2_tex_3(B,A) )
=> v3_tdlat_3(A) ) ) ).
fof(t58_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ ( ? [B] :
( ~ v3_struct_0(B)
& m1_pre_topc(B,A)
& v4_tex_3(B,A) )
& v3_tdlat_3(A) ) ) ).
fof(t59_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ ( ? [B] :
( ~ v3_struct_0(B)
& m1_pre_topc(B,A)
& v3_tex_3(B,A)
& v1_borsuk_1(B,A) )
& v3_tdlat_3(A) ) ) ).
fof(t60_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ ( ? [B] :
( ~ v3_struct_0(B)
& m1_pre_topc(B,A)
& v2_tex_3(B,A)
& v2_tex_2(B,A) )
& v3_tdlat_3(A) ) ) ).
fof(t61_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ ( ? [B] :
( ~ v3_struct_0(B)
& m1_pre_topc(B,A)
& v1_tex_3(B,A)
& v1_tsep_1(B,A)
& v2_tex_2(B,A) )
& v3_tdlat_3(A) ) ) ).
fof(t62_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v3_tops_1(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v4_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t63_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v1_tops_3(B,A)
& ! [C] :
( ( v1_pre_topc(C)
& v2_tex_2(C,A)
& v2_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t64_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_tex_2(C,A)
& v2_tex_3(C,A)
& m1_pre_topc(C,A)
& r4_tsep_2(A,B,C) ) ) ) ).
fof(t65_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tex_2(B,A)
& v2_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v4_tex_3(C,A)
& m1_pre_topc(C,A)
& r4_tsep_2(A,B,C) ) ) ) ).
fof(t66_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(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) )
=> ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> ( ( v4_tex_3(B,A)
& m1_pre_topc(B,A) )
<=> ( v4_tex_3(C,A)
& m1_pre_topc(C,A) ) ) ) ) ) ) ).
fof(t67_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v2_tops_1(B,A)
& v4_pre_topc(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_borsuk_1(C,A)
& v3_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t68_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( v1_tops_1(B,A)
& v3_pre_topc(B,A)
& ! [C] :
( ( v1_pre_topc(C)
& v1_tsep_1(C,A)
& v2_tex_2(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t69_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_borsuk_1(B,A)
& v3_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_tsep_1(C,A)
& v2_tex_2(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A)
& r4_tsep_2(A,B,C) ) ) ) ).
fof(t70_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tsep_1(B,A)
& v2_tex_2(B,A)
& v1_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_borsuk_1(C,A)
& v3_tex_3(C,A)
& m1_pre_topc(C,A)
& r4_tsep_2(A,B,C) ) ) ) ).
fof(t71_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( v4_tex_3(B,A)
<=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_borsuk_1(C,A)
& v3_tex_3(C,A)
& m1_pre_topc(C,A)
& m1_pre_topc(B,C) ) ) ) ) ).
fof(t72_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ~ ( ~ ( v3_tex_3(B,A)
& v1_borsuk_1(B,A) )
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_tex_2(C,A)
& v2_tex_3(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_pre_topc(D)
& v1_borsuk_1(D,A)
& v3_tex_3(D,A)
& m1_pre_topc(D,A) )
=> ~ ( k2_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& k1_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ) ) ) ) ).
fof(t73_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ~ ( ~ ( v1_tex_3(B,A)
& v1_tsep_1(B,A) )
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_tsep_1(C,A)
& v2_tex_2(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_pre_topc(D)
& v4_tex_3(D,A)
& m1_pre_topc(D,A) )
=> ~ ( r1_tsep_1(A,C,D)
& k1_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ) ) ) ).
fof(t74_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_tsep_1(C,A)
& v2_tex_2(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A)
& ? [D] :
( ~ v3_struct_0(D)
& v1_pre_topc(D)
& v1_borsuk_1(D,A)
& v3_tex_3(D,A)
& m1_pre_topc(D,A)
& r4_tsep_2(A,C,D)
& m1_pre_topc(B,D) ) ) ) ) ).
fof(t75_tex_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_tex_2(B,A)
& v2_tex_3(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( v1_pre_topc(C)
& v1_tsep_1(C,A)
& v2_tex_2(C,A)
& v1_tex_3(C,A)
& m1_pre_topc(C,A)
& ? [D] :
( v1_pre_topc(D)
& v1_borsuk_1(D,A)
& v3_tex_3(D,A)
& m1_pre_topc(D,A)
& r3_tsep_2(A,C,D)
& m1_pre_topc(C,B) ) ) ) ) ).
%------------------------------------------------------------------------------