SET007 Axioms: SET007+354.ax
%------------------------------------------------------------------------------
% File : SET007+354 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Lattice of Domains of an Extremally Disconnected Space
% 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 : tdlat_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 86 ( 2 unt; 0 def)
% Number of atoms : 558 ( 57 equ)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 542 ( 70 ~; 0 |; 244 &)
% ( 27 <=>; 201 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 1 con; 0-3 aty)
% Number of variables : 152 ( 141 !; 11 ?)
% 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_tdlat_3,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v1_tdlat_3(A)
& v2_tdlat_3(A) ) ).
fof(cc1_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_tdlat_3(A)
=> v2_pre_topc(A) ) ) ).
fof(cc2_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v2_tdlat_3(A)
=> v2_pre_topc(A) ) ) ).
fof(cc3_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_tdlat_3(A)
=> v3_tdlat_3(A) ) ) ).
fof(cc4_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v2_tdlat_3(A)
=> v3_tdlat_3(A) ) ) ).
fof(rc2_tdlat_3,axiom,
? [A] :
( l1_pre_topc(A)
& v1_pre_topc(A)
& v3_tdlat_3(A) ) ).
fof(rc3_tdlat_3,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& v2_tdlat_3(A)
& v3_tdlat_3(A) ) ).
fof(cc5_tdlat_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_pre_topc(B)
& v1_borsuk_1(B,A)
& v1_tsep_1(B,A)
& v1_tdlat_3(B)
& v3_tdlat_3(B) ) ) ) ).
fof(rc4_tdlat_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_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) ) ) ).
fof(cc6_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_pre_topc(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B) ) ) ) ).
fof(rc5_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& v2_pre_topc(B)
& v2_tdlat_3(B)
& v3_tdlat_3(B) ) ) ).
fof(rc6_tdlat_3,axiom,
? [A] :
( l1_pre_topc(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v3_tdlat_3(A) ) ).
fof(cc7_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v1_tdlat_3(A) )
=> ( v2_pre_topc(A)
& v3_tdlat_3(A) ) ) ) ).
fof(cc8_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v2_tdlat_3(A) )
=> ( v2_pre_topc(A)
& v3_tdlat_3(A) ) ) ) ).
fof(cc9_tdlat_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) ) ) ) ) ).
fof(cc10_tdlat_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_pre_topc(B)
& v1_borsuk_1(B,A) ) ) ) ) ).
fof(cc11_tdlat_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_borsuk_1(B,A)
=> ( v2_pre_topc(B)
& v1_tsep_1(B,A) ) ) ) ) ).
fof(rc7_tdlat_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) ) ) ).
fof(rc8_tdlat_3,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v4_tdlat_3(A) ) ).
fof(rc9_tdlat_3,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v5_tdlat_3(A) ) ).
fof(cc12_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v5_tdlat_3(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A) ) ) ) ).
fof(cc13_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_tdlat_3(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v5_tdlat_3(A) ) ) ) ).
fof(cc14_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(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)
& v4_tdlat_3(B) ) ) ) ) ).
fof(rc10_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_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)
& v4_tdlat_3(B) ) ) ).
fof(cc15_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v5_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)
& v4_tdlat_3(B)
& v5_tdlat_3(B) ) ) ) ) ).
fof(rc11_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v5_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)
& v4_tdlat_3(B)
& v5_tdlat_3(B) ) ) ).
fof(t1_tdlat_3,axiom,
$true ).
fof(t2_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,B) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,k3_subset_1(u1_struct_0(A),B))) ) ) ).
fof(t3_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,B)) ) ) ).
fof(t4_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)) ) ) ).
fof(t5_tdlat_3,axiom,
$true ).
fof(t6_tdlat_3,axiom,
! [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)))
=> ( k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A)
=> ( ( v4_pre_topc(B,A)
=> k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,C)) = u1_struct_0(A) )
& ( v4_pre_topc(C,A)
=> k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),C) = u1_struct_0(A) ) ) ) ) ) ) ).
fof(t7_tdlat_3,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) )
<=> k6_pre_topc(A,B) = k1_tops_1(A,B) ) ) ) ).
fof(t8_tdlat_3,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) )
=> k1_tops_1(A,k6_pre_topc(A,B)) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ).
fof(t9_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_tops_1(B,A)
& r1_tarski(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) )
=> ( v6_tops_1(B,A)
& v5_tops_1(B,A) ) ) ) ) ).
fof(t10_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_tops_1(B,A)
& r1_tarski(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) )
=> ( v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ) ) ).
fof(t11_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> ( k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,B)
& k6_pre_topc(A,B) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) ).
fof(d1_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_tdlat_3(A)
<=> u1_pre_topc(A) = k1_pcomps_1(u1_struct_0(A)) ) ) ).
fof(d2_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v2_tdlat_3(A)
<=> u1_pre_topc(A) = k2_tarski(k1_xboole_0,u1_struct_0(A)) ) ) ).
fof(t12_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v1_tdlat_3(A)
& v2_tdlat_3(A) )
=> k1_pcomps_1(u1_struct_0(A)) = k2_tarski(k1_xboole_0,u1_struct_0(A)) ) ) ).
fof(t13_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( r2_hidden(k1_xboole_0,u1_pre_topc(A))
& r2_hidden(u1_struct_0(A),u1_pre_topc(A))
& k1_pcomps_1(u1_struct_0(A)) = k2_tarski(k1_xboole_0,u1_struct_0(A)) )
=> ( v1_tdlat_3(A)
& v2_tdlat_3(A) ) ) ) ).
fof(t14_tdlat_3,axiom,
! [A] :
( ( v1_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A)) ) ) ).
fof(t15_tdlat_3,axiom,
! [A] :
( ( v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,u1_pre_topc(A))
=> r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A)) ) ) ) ).
fof(t16_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( k1_pcomps_1(u1_struct_0(A)) = k2_tarski(k1_xboole_0,u1_struct_0(A))
=> ( v1_tdlat_3(A)
& v2_tdlat_3(A) ) ) ) ).
fof(d3_tdlat_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v3_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,u1_pre_topc(A))
=> r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A)) ) ) ) ) ).
fof(t17_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v3_pre_topc(B,A) ) ) ) ).
fof(t18_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v4_pre_topc(B,A) ) ) ) ).
fof(t19_tdlat_3,axiom,
! [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))
=> ( B = k1_tarski(C)
=> v3_pre_topc(B,A) ) ) )
=> v1_tdlat_3(A) ) ) ).
fof(t20_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(B,A)
& B != k1_xboole_0
& B != u1_struct_0(A) ) ) ) ) ).
fof(t21_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v4_pre_topc(B,A)
& B != k1_xboole_0
& B != u1_struct_0(A) ) ) ) ) ).
fof(t22_tdlat_3,axiom,
! [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))
=> ( B = k1_tarski(C)
=> k6_pre_topc(A,B) = u1_struct_0(A) ) ) )
=> v2_tdlat_3(A) ) ) ).
fof(t23_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> v4_pre_topc(B,A) ) ) ) ) ).
fof(t24_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> v3_pre_topc(B,A) ) ) ) ) ).
fof(t25_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> k6_pre_topc(A,B) = B ) ) ) ) ).
fof(t26_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> k1_tops_1(A,B) = B ) ) ) ) ).
fof(t27_tdlat_3,axiom,
! [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))
=> ( B = k1_tarski(C)
=> v3_pre_topc(k6_pre_topc(A,B),A) ) ) )
=> v3_tdlat_3(A) ) ) ).
fof(t28_tdlat_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_tdlat_3(A)
<=> ( v3_tdlat_3(A)
& ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B = k1_tarski(C)
=> v4_pre_topc(B,A) ) ) ) ) ) ) ).
fof(d4_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> v3_pre_topc(k6_pre_topc(A,B),A) ) ) ) ) ).
fof(t29_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> v4_pre_topc(k1_tops_1(A,B),A) ) ) ) ) ).
fof(t30_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(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)
& r1_xboole_0(B,C) )
=> r1_xboole_0(k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ) ) ).
fof(t31_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(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)
& k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) )
=> k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = u1_struct_0(A) ) ) ) ) ) ).
fof(t32_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> k6_pre_topc(A,B) = k1_tops_1(A,k6_pre_topc(A,B)) ) ) ) ) ).
fof(t33_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> k1_tops_1(A,B) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) ).
fof(t34_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> ( v4_pre_topc(B,A)
& v3_pre_topc(B,A) ) ) ) ) ) ).
fof(t35_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> ( v5_tops_1(B,A)
& v6_tops_1(B,A) ) ) ) ) ) ).
fof(t36_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> k1_tops_1(A,k6_pre_topc(A,B)) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) ).
fof(t37_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> k1_tops_1(A,B) = k6_pre_topc(A,B) ) ) ) ) ).
fof(t38_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v6_tops_1(B,A)
=> v5_tops_1(B,A) )
& ( v5_tops_1(B,A)
=> v6_tops_1(B,A) ) ) ) ) ) ).
fof(d5_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v5_tdlat_3(A)
<=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> v4_tdlat_3(B) ) ) ) ).
fof(t39_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(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)
& v1_tops_1(C,A) )
=> v4_tdlat_3(B) ) ) ) ) ).
fof(t40_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( ( ~ v3_struct_0(B)
& v1_borsuk_1(B,A)
& m1_pre_topc(B,A) )
=> v4_tdlat_3(B) )
=> v5_tdlat_3(A) ) ) ).
fof(t41_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> k1_tdlat_1(A) = k5_tdlat_1(A) ) ).
fof(t42_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> ( k2_tdlat_1(A) = k6_tdlat_1(A)
& k3_tdlat_1(A) = k7_tdlat_1(A) ) ) ).
fof(t43_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> k4_tdlat_1(A) = k8_tdlat_1(A) ) ).
fof(t44_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> k1_tdlat_1(A) = k9_tdlat_1(A) ) ).
fof(t45_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> ( k2_tdlat_1(A) = k10_tdlat_1(A)
& k3_tdlat_1(A) = k11_tdlat_1(A) ) ) ).
fof(t46_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> k4_tdlat_1(A) = k12_tdlat_1(A) ) ).
fof(t47_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_tdlat_1(A))
=> ! [C] :
( m1_subset_1(C,k1_tdlat_1(A))
=> ( k1_binop_1(k2_tdlat_1(A),B,C) = k2_xboole_0(B,C)
& k1_binop_1(k3_tdlat_1(A),B,C) = k3_xboole_0(B,C) ) ) ) ) ).
fof(t48_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A)))
=> ! [D] :
( m1_subset_1(D,k1_tdlat_1(A))
=> ! [E] :
( m1_subset_1(E,k1_tdlat_1(A))
=> ( ( B = D
& C = E )
=> ( k3_lattices(k4_tdlat_1(A),B,C) = k2_xboole_0(D,E)
& k4_lattices(k4_tdlat_1(A),B,C) = k3_xboole_0(D,E) ) ) ) ) ) ) ) ).
fof(t49_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
=> ( C = B
=> k15_lattice3(k4_tdlat_1(A),C) = k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) ) ) ) ) ) ).
fof(t50_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
=> ( C = B
=> ( ( C != k1_xboole_0
=> k16_lattice3(k4_tdlat_1(A),C) = k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)) )
& ( C = k1_xboole_0
=> k16_lattice3(k4_tdlat_1(A),C) = k2_pre_topc(A) ) ) ) ) ) ) ) ).
fof(t51_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ( ~ v3_struct_0(k4_tdlat_1(A))
& v10_lattices(k4_tdlat_1(A))
& v12_lattices(k4_tdlat_1(A))
& l3_lattices(k4_tdlat_1(A)) ) ) ) ).
fof(t52_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( k4_tdlat_1(A) = k8_tdlat_1(A)
=> v4_tdlat_3(A) ) ) ).
fof(t53_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( k4_tdlat_1(A) = k12_tdlat_1(A)
=> v4_tdlat_3(A) ) ) ).
fof(t54_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( k8_tdlat_1(A) = k12_tdlat_1(A)
=> v4_tdlat_3(A) ) ) ).
fof(t55_tdlat_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v4_tdlat_3(A)
<=> ( ~ v3_struct_0(k4_tdlat_1(A))
& v10_lattices(k4_tdlat_1(A))
& v17_lattices(k4_tdlat_1(A))
& l3_lattices(k4_tdlat_1(A)) ) ) ) ).
%------------------------------------------------------------------------------