SET007 Axioms: SET007+387.ax
%------------------------------------------------------------------------------
% File : SET007+387 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Maximal Discrete Subspaces of Almost Discrete 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 164 ( 4 unt; 0 def)
% Number of atoms : 1356 ( 50 equ)
% Maximal formula atoms : 17 ( 8 avg)
% Number of connectives : 1553 ( 361 ~; 4 |; 717 &)
% ( 23 <=>; 448 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 2 con; 0-4 aty)
% Number of variables : 386 ( 356 !; 30 ?)
% 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(rc1_tex_2,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_realset1(A) ) ).
fof(rc2_tex_2,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ).
fof(cc1_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( ~ v1_tex_2(B,k1_zfmisc_1(A))
=> ~ v1_xboole_0(B) ) ) ) ).
fof(cc2_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_xboole_0(B)
=> v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ).
fof(cc3_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_realset1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_tex_2(B,k1_zfmisc_1(A))
=> ( v1_xboole_0(B)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ).
fof(cc4_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_realset1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( ~ v1_xboole_0(B)
=> ( ~ v1_xboole_0(B)
& ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ).
fof(rc3_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& v1_tex_2(B,k1_zfmisc_1(A)) ) ) ).
fof(rc4_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ).
fof(rc5_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_realset1(B) ) ) ).
fof(fc1_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(k1_tarski(A))
& v1_realset1(k1_tarski(A))
& v1_finset_1(k1_tarski(A)) ) ).
fof(cc5_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_realset1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( ( ~ v1_xboole_0(B)
& ~ v1_tex_2(B,k1_zfmisc_1(A)) )
=> ( ~ v1_xboole_0(B)
& v1_realset1(B)
& ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ).
fof(cc6_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_realset1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( ( ~ v1_xboole_0(B)
& v1_realset1(B) )
=> ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ).
fof(cc7_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_realset1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( ( ~ v1_xboole_0(B)
& ~ v1_tex_2(B,k1_zfmisc_1(A)) )
=> ( ~ v1_xboole_0(B)
& ~ v1_realset1(B) ) ) ) ) ).
fof(rc6_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_realset1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_realset1(B)
& v1_tex_2(B,k1_zfmisc_1(A)) ) ) ).
fof(rc7_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_realset1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& ~ v1_realset1(B)
& ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ).
fof(cc8_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ~ v1_xboole_0(B)
=> ( ~ v1_xboole_0(B)
& ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(cc9_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_struct_0(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))) )
=> ( ~ v1_xboole_0(B)
& v1_realset1(B) ) ) ) ) ).
fof(cc10_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ~ v1_xboole_0(B)
& v1_realset1(B) )
=> ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(cc11_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_struct_0(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))) )
=> ( ~ v1_xboole_0(B)
& ~ v1_realset1(B) ) ) ) ) ).
fof(rc8_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_realset1(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(rc9_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& ~ v1_realset1(B)
& ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(rc10_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_realset1(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(cc12_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_struct_0(B)
=> ( ~ v3_struct_0(B)
& ~ v2_tex_2(B,A) ) ) ) ) ).
fof(cc13_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v2_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v3_realset2(B) ) ) ) ) ).
fof(cc14_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc15_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v2_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& ~ v3_realset2(B) ) ) ) ) ).
fof(rc11_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& ~ v2_tex_2(B,A) ) ) ).
fof(cc16_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v1_tdlat_3(B)
=> v2_pre_topc(B) ) ) ) ).
fof(cc17_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tdlat_3(B)
=> v2_pre_topc(B) ) ) ) ).
fof(cc18_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v2_pre_topc(B)
=> ~ v1_tdlat_3(B) ) ) ) ).
fof(cc19_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v2_pre_topc(B)
=> ~ v2_tdlat_3(B) ) ) ) ).
fof(cc20_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v1_tdlat_3(B)
=> v3_tdlat_3(B) ) ) ) ).
fof(cc21_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_tdlat_3(B)
=> ~ v1_tdlat_3(B) ) ) ) ).
fof(cc22_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tdlat_3(B)
=> v3_tdlat_3(B) ) ) ) ).
fof(cc23_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_tdlat_3(B)
=> ~ v2_tdlat_3(B) ) ) ) ).
fof(cc24_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v1_tdlat_3(B)
& v2_tdlat_3(B) )
=> ( ~ v3_struct_0(B)
& v3_realset2(B) ) ) ) ) ).
fof(cc25_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_tdlat_3(B)
& ~ v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& ~ v1_tdlat_3(B) ) ) ) ) ).
fof(cc26_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v1_tdlat_3(B)
& ~ v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& ~ v2_tdlat_3(B) ) ) ) ) ).
fof(rc12_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v3_realset2(B) ) ) ).
fof(fc2_tex_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k1_tex_2(A,B))
& v1_pre_topc(k1_tex_2(A,B))
& v3_realset2(k1_tex_2(A,B)) ) ) ).
fof(rc13_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v3_realset2(B)
& v2_tex_2(B,A) ) ) ).
fof(cc27_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B) ) ) ) ) ).
fof(rc14_tex_2,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_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B) ) ) ).
fof(fc3_tex_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k1_tex_2(A,B))
& v1_pre_topc(k1_tex_2(A,B))
& v2_pre_topc(k1_tex_2(A,B))
& v1_tdlat_3(k1_tex_2(A,B))
& v2_tdlat_3(k1_tex_2(A,B))
& v3_tdlat_3(k1_tex_2(A,B))
& v4_tdlat_3(k1_tex_2(A,B))
& v5_tdlat_3(k1_tex_2(A,B))
& v3_realset2(k1_tex_2(A,B)) ) ) ).
fof(rc15_tex_2,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_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B) ) ) ).
fof(fc4_tex_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k1_tex_2(A,B))
& v1_pre_topc(k1_tex_2(A,B))
& v2_pre_topc(k1_tex_2(A,B))
& v1_tdlat_3(k1_tex_2(A,B))
& v2_tdlat_3(k1_tex_2(A,B))
& v3_tdlat_3(k1_tex_2(A,B))
& v4_tdlat_3(k1_tex_2(A,B))
& v5_tdlat_3(k1_tex_2(A,B))
& v3_realset2(k1_tex_2(A,B)) ) ) ).
fof(cc28_tex_2,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)
& v1_tsep_1(B,A)
& v1_borsuk_1(B,A) ) ) ) ) ).
fof(cc29_tex_2,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_pre_topc(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc30_tex_2,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_pre_topc(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(rc16_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v1_tsep_1(B,A)
& v1_borsuk_1(B,A) ) ) ).
fof(cc31_tex_2,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)
& v2_tdlat_3(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tsep_1(B,A)
& v1_borsuk_1(B,A)
& v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B) ) ) ) ) ).
fof(cc32_tex_2,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_realset2(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tsep_1(B,A)
& v1_borsuk_1(B,A)
& v1_tdlat_3(B)
& ~ v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v3_realset2(B) ) ) ) ) ).
fof(rc17_tex_2,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_tsep_1(B,A)
& v1_borsuk_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v2_tex_2(B,A) ) ) ).
fof(cc33_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v1_tdlat_3(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B) ) ) ) ) ).
fof(cc34_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& ~ v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v3_realset2(B) ) ) ) ) ).
fof(cc35_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& ~ v1_tsep_1(B,A)
& ~ v1_borsuk_1(B,A)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc36_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v1_tdlat_3(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(rc18_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_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_tsep_1(B,A)
& ~ v1_borsuk_1(B,A)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v2_tex_2(B,A) ) ) ).
fof(rc19_tex_2,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)
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v2_tex_2(B,A) ) ) ).
fof(cc37_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v5_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B) ) ) ) ) ).
fof(cc38_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v1_tdlat_3(B) )
=> ( ~ v3_struct_0(B)
& ~ v5_tex_2(B,A) ) ) ) ) ).
fof(cc39_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v5_tex_2(B,A)
=> ( v2_pre_topc(B)
& v1_tsep_1(B,A)
& v1_borsuk_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& ~ v2_tex_2(B,A) ) ) ) ) ).
fof(cc40_tex_2,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_tsep_1(B,A)
& v1_borsuk_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& ~ v5_tex_2(B,A) ) ) ) ) ).
fof(cc41_tex_2,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_tsep_1(B,A)
& v1_borsuk_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v5_tex_2(B,A) ) ) ) ) ).
fof(cc42_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v5_tex_2(B,A)
=> ( v2_pre_topc(B)
& v1_tsep_1(B,A)
& v1_borsuk_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc43_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v5_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B) ) ) ) ) ).
fof(cc44_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v5_tex_2(B,A) ) ) ) ) ).
fof(cc45_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v3_realset2(B)
& v5_tex_2(B,A) ) ) ) ) ).
fof(cc46_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v5_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& ~ v1_tdlat_3(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v3_realset2(B)
& ~ v5_tex_2(B,A) ) ) ) ) ).
fof(cc47_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v5_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v2_tex_2(B,A) ) ) ) ) ).
fof(cc48_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v1_tdlat_3(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v2_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v5_tex_2(B,A) ) ) ) ) ).
fof(cc49_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v2_tdlat_3(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v5_tex_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v3_realset2(B) ) ) ) ) ).
fof(cc50_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& ~ v2_tdlat_3(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v3_realset2(B) )
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& ~ v5_tex_2(B,A) ) ) ) ) ).
fof(rc20_tex_2,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_tdlat_3(B)
& v3_tdlat_3(B)
& v4_tdlat_3(B)
& v5_tdlat_3(B)
& v5_tex_2(B,A) ) ) ).
fof(d1_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v1_realset1(A)
<=> ? [B] :
( m1_subset_1(B,A)
& A = k6_domain_1(A,B) ) ) ) ).
fof(t1_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_realset1(B) )
=> ( r1_tarski(A,B)
=> A = B ) ) ) ).
fof(t2_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_realset1(A) )
=> ! [B] :
( ~ v1_xboole_0(k3_xboole_0(A,B))
=> r1_tarski(A,B) ) ) ).
fof(t3_tex_2,axiom,
$true ).
fof(t4_tex_2,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& v3_realset2(A) )
=> v3_realset2(B) ) ) ) ).
fof(d2_tex_2,axiom,
! [A,B] :
( m1_subset_1(B,A)
=> ( v1_tex_2(B,A)
<=> B != k3_tarski(A) ) ) ).
fof(t5_tex_2,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_tex_2(B,k1_zfmisc_1(A))
<=> B != A ) ) ).
fof(t6_tex_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ~ ( v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A))
& v1_realset1(A) ) ) ) ).
fof(t7_tex_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_realset1(A) )
=> ! [B] :
( m1_subset_1(B,A)
=> v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ) ).
fof(t8_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A)))
& v3_realset2(A) ) ) ) ).
fof(t9_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(t10_tex_2,axiom,
$true ).
fof(t11_tex_2,axiom,
$true ).
fof(t12_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v2_pre_topc(A) )
=> v2_pre_topc(B) ) ) ) ).
fof(d3_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(t13_tex_2,axiom,
! [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_2(C,k1_zfmisc_1(u1_struct_0(A)))
<=> v2_tex_2(B,A) ) ) ) ) ) ).
fof(t14_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_pre_topc(C,A)
=> ( ( g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))
& v2_tex_2(B,A) )
=> v2_tex_2(C,A) ) ) ) ) ).
fof(t15_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_pre_topc(B,A)
=> ~ ( u1_struct_0(B) = u1_struct_0(A)
& v2_tex_2(B,A) ) ) ) ).
fof(t16_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v2_tex_2(B,A)
& m1_pre_topc(B,A) )
=> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ).
fof(t17_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v1_tdlat_3(A) )
=> v1_tdlat_3(B) ) ) ) ).
fof(t18_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v2_tdlat_3(A) )
=> v2_tdlat_3(B) ) ) ) ).
fof(t19_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v3_tdlat_3(A) )
=> v3_tdlat_3(B) ) ) ) ).
fof(d4_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& m1_pre_topc(C,A) )
=> ( C = k1_tex_2(A,B)
<=> u1_struct_0(C) = k1_struct_0(A,B) ) ) ) ) ).
fof(t20_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v2_tex_2(k1_tex_2(A,B),A)
<=> v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t21_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( v2_tex_2(k1_tex_2(A,B),A)
& v3_realset2(A) ) ) ) ).
fof(t22_tex_2,axiom,
$true ).
fof(t23_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_realset2(B)
& m1_pre_topc(B,A) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(k1_tex_2(A,C)),u1_pre_topc(k1_tex_2(A,C))) ) ) ) ).
fof(t24_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v2_pre_topc(k1_tex_2(A,B))
=> ( v1_tdlat_3(k1_tex_2(A,B))
& v2_tdlat_3(k1_tex_2(A,B)) ) ) ) ) ).
fof(d5_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(C,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(D,A)
& k5_subset_1(u1_struct_0(A),B,D) = C ) ) ) ) ) ) ) ).
fof(d6_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(C,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v4_pre_topc(D,A)
& k5_subset_1(u1_struct_0(A),B,D) = C ) ) ) ) ) ) ) ).
fof(t25_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& C = D
& v3_tex_2(C,A) )
=> v3_tex_2(D,B) ) ) ) ) ) ).
fof(t26_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(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_2(C,A)
<=> v1_tdlat_3(B) ) ) ) ) ) ).
fof(t27_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = u1_struct_0(A)
=> ( v3_tex_2(B,A)
<=> v1_tdlat_3(A) ) ) ) ) ).
fof(t28_tex_2,axiom,
! [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)))
=> ( ( r1_tarski(C,B)
& v3_tex_2(B,A) )
=> v3_tex_2(C,A) ) ) ) ) ).
fof(t29_tex_2,axiom,
! [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)))
=> ( ( v3_tex_2(B,A)
| v3_tex_2(C,A) )
=> v3_tex_2(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t30_tex_2,axiom,
! [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)))
=> ( ( v3_pre_topc(B,A)
& v3_pre_topc(C,A) )
=> ( v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)
& v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),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)))
=> ( ( v3_pre_topc(B,A)
& v3_pre_topc(C,A)
& v3_tex_2(B,A)
& v3_tex_2(C,A) )
=> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(t31_tex_2,axiom,
! [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)))
=> ( ( v4_pre_topc(B,A)
& v4_pre_topc(C,A) )
=> ( v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)
& v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),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)))
=> ( ( v4_pre_topc(B,A)
& v4_pre_topc(C,A)
& v3_tex_2(B,A)
& v3_tex_2(C,A) )
=> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(t32_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tex_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(D,A)
& k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C) ) ) ) ) ) ) ) ).
fof(t33_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tex_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v4_pre_topc(D,A)
& k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C) ) ) ) ) ) ) ) ).
fof(t34_tex_2,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_tex_2(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& v1_tdlat_3(C)
& m1_pre_topc(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(t35_tex_2,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_tex_2(B,A) ) ) ).
fof(t36_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v3_tex_2(k1_struct_0(A,B),A) ) ) ).
fof(t37_tex_2,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,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(D,A)
& k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) ) ) ) )
=> v3_tex_2(B,A) ) ) ) ).
fof(t38_tex_2,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)))
=> ( ( v3_pre_topc(B,A)
& v3_pre_topc(C,A)
& v3_tex_2(B,A)
& v3_tex_2(C,A) )
=> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t39_tex_2,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)))
=> ( ( v4_pre_topc(B,A)
& v4_pre_topc(C,A)
& v3_tex_2(B,A)
& v3_tex_2(C,A) )
=> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t40_tex_2,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_tops_3(B,A)
& v3_tex_2(B,A) )
=> v3_pre_topc(B,A) ) ) ) ).
fof(t41_tex_2,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)))
=> ( v3_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,B)
=> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)) = C ) ) ) ) ) ).
fof(t42_tex_2,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)))
=> ( v3_tex_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,C) ) ) ) ) ) ).
fof(t43_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v3_tex_2(B,A) ) ) ).
fof(t44_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_tex_2(B,A)
<=> v1_realset1(B) ) ) ) ).
fof(d7_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tex_2(B,A)
<=> ( v3_tex_2(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_tex_2(C,A)
& r1_tarski(B,C) )
=> B = C ) ) ) ) ) ) ).
fof(t45_tex_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& C = D
& v4_tex_2(C,A) )
=> v4_tex_2(D,B) ) ) ) ) ) ).
fof(t46_tex_2,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))) )
=> ~ v4_tex_2(B,A) ) ) ).
fof(t47_tex_2,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)))
=> ( ( v3_pre_topc(B,A)
& v4_tex_2(B,A) )
=> v1_tops_1(B,A) ) ) ) ).
fof(t48_tex_2,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_tops_1(B,A)
& v3_tex_2(B,A) )
=> v4_tex_2(B,A) ) ) ) ).
fof(t49_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tex_2(B,A)
<=> ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t50_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v4_tex_2(B,A)
<=> v1_realset1(B) ) ) ) ).
fof(d8_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v5_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> v4_tex_2(C,A) ) ) ) ) ) ).
fof(t51_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(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_2(C,A)
<=> v5_tex_2(B,A) ) ) ) ) ) ).
fof(t52_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( v5_tex_2(B,A)
<=> ( v1_tdlat_3(B)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_tdlat_3(C)
& m1_pre_topc(C,A) )
=> ( m1_pre_topc(B,C)
=> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) ) ) ) ) ) ) ).
fof(t53_tex_2,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))) )
=> ~ ( v4_tex_2(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& m1_pre_topc(C,A) )
=> ~ ( v5_tex_2(C,A)
& B = u1_struct_0(C) ) ) ) ) ) ).
fof(t55_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C)))
=> k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ).
fof(t56_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C)))
| k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ).
fof(t57_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v4_pre_topc(D,A)
& k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) ) ) ) )
=> v3_tex_2(B,A) ) ) ) ).
fof(t58_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,C) ) )
=> v3_tex_2(B,A) ) ) ) ).
fof(t59_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> ( C = D
| r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,D))) ) ) ) ) ) ) ) ).
fof(t60_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,k6_pre_topc(A,B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,D) ) ) ) ) ) ) ) ).
fof(t61_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(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) )
& v4_tex_2(B,A)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t62_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tex_2(B,A)
=> v1_tops_1(B,A) ) ) ) ).
fof(t64_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tex_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_hidden(D,B)
& k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,D) ) ) ) ) ) ).
fof(t65_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_tex_2(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(B,C)
& v4_tex_2(C,A) ) ) ) ) ) ).
fof(t66_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v4_tex_2(B,A) ) ) ).
fof(t67_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tdlat_3(B)
& m1_pre_topc(B,A) )
=> ? [C] :
( ~ v3_struct_0(C)
& v1_pre_topc(C)
& m1_pre_topc(C,A)
& m1_pre_topc(B,C)
& v5_tex_2(C,A) ) ) ) ).
fof(t68_tex_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(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) ) ) ) ).
fof(t69_tex_2,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] :
( ( 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) ) )
=> v1_tdlat_3(A) ) ) ).
fof(t70_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_tdlat_3(B)
& l1_pre_topc(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) ) ) ) ).
fof(t71_tex_2,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] :
( ( 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)) )
=> v5_pre_topc(C,B,A) ) )
=> v2_tdlat_3(A) ) ) ).
fof(t72_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v3_borsuk_1(C,A,B) ) ) ) ).
fof(t73_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> r1_borsuk_1(A,B) ) ) ).
fof(t74_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_tex_2(B,A)
& m1_pre_topc(B,A) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v3_borsuk_1(C,A,B) ) ) ) ).
fof(t75_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_tex_2(B,A)
& m1_pre_topc(B,A) )
=> r1_borsuk_1(A,B) ) ) ).
fof(t76_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_tex_2(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_borsuk_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = E
=> k5_pre_topc(A,B,C,D) = k6_pre_topc(A,E) ) ) ) ) ) ) ) ).
fof(t77_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_tex_2(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_borsuk_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( D = E
=> k5_pre_topc(A,B,C,k1_struct_0(B,D)) = k6_pre_topc(A,k1_struct_0(A,E)) ) ) ) ) ) ) ) ).
fof(t78_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tdlat_3(B)
& m1_pre_topc(B,A) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v3_borsuk_1(C,A,B) ) ) ) ).
fof(t79_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tdlat_3(B)
& m1_pre_topc(B,A) )
=> r1_borsuk_1(A,B) ) ) ).
fof(s1_tex_2,axiom,
( ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2)))
=> ~ ( r2_hidden(A,f2_s1_tex_2)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_tex_2))
=> ~ p1_s1_tex_2(A,B) ) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2))
& m2_relset_1(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2))
& ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2)))
=> ( r2_hidden(B,f2_s1_tex_2)
=> p1_s1_tex_2(B,k1_funct_1(A,B)) ) ) ) ) ).
fof(dt_k1_tex_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k1_tex_2(A,B))
& v1_pre_topc(k1_tex_2(A,B))
& m1_pre_topc(k1_tex_2(A,B),A) ) ) ).
fof(t54_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,B) = k3_tarski(a_2_0_tex_2(A,B)) ) ) ).
fof(t63_tex_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tex_2(B,A)
=> k3_tarski(a_2_0_tex_2(A,B)) = u1_struct_0(A) ) ) ) ).
fof(fraenkel_a_2_0_tex_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_tdlat_3(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_tex_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k6_pre_topc(B,k1_struct_0(B,D))
& r2_hidden(D,C) ) ) ) ).
%------------------------------------------------------------------------------