SET007 Axioms: SET007+407.ax
%------------------------------------------------------------------------------
% File : SET007+407 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Maximal Kolmogorov Subspaces of a Topological Space
% Version : [Urb08] axioms.
% English : As Stone Retracts of the Ambient Space
% 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 : tsp_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 65 ( 0 unt; 0 def)
% Number of atoms : 606 ( 52 equ)
% Maximal formula atoms : 17 ( 9 avg)
% Number of connectives : 661 ( 120 ~; 4 |; 299 &)
% ( 17 <=>; 221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 0 prp; 1-3 aty)
% Number of functors : 19 ( 19 usr; 0 con; 1-4 aty)
% Number of variables : 196 ( 189 !; 7 ?)
% 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_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_t_0topsp(B) ) ) ) ) ).
fof(cc2_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v2_t_0topsp(B) )
=> ( ~ v3_struct_0(B)
& ~ v2_tsp_2(B,A) ) ) ) ) ).
fof(cc3_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_tsp_2(B,A)
=> ( v2_pre_topc(B)
& v1_tex_3(B,A) ) ) ) ) ).
fof(cc4_tsp_2,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_tsp_2(B,A) ) ) ) ) ).
fof(cc5_tsp_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_tsp_2(B,A) )
=> ( v2_pre_topc(B)
& ~ v2_tex_2(B,A) ) ) ) ) ).
fof(cc6_tsp_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_tex_2(B,A) )
=> ( v2_pre_topc(B)
& ~ v2_tsp_2(B,A) ) ) ) ) ).
fof(cc7_tsp_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_tsp_2(B,A) )
=> ( v2_pre_topc(B)
& ~ v1_tsep_1(B,A) ) ) ) ) ).
fof(cc8_tsp_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_tsp_2(B,A) )
=> ( v2_pre_topc(B)
& ~ v2_tex_2(B,A) ) ) ) ) ).
fof(cc9_tsp_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)
& v1_borsuk_1(B,A) )
=> ( v2_pre_topc(B)
& ~ v2_tsp_2(B,A) ) ) ) ) ).
fof(cc10_tsp_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_tsp_2(B,A) )
=> ( v2_pre_topc(B)
& ~ v1_borsuk_1(B,A) ) ) ) ) ).
fof(rc1_tsp_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_tex_3(B,A)
& v2_t_0topsp(B)
& v2_tsp_2(B,A) ) ) ).
fof(d1_tsp_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_tsp_1(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_subset_1(k4_tex_4(A,C),k4_tex_4(A,D)) ) ) ) ) ) ) ) ).
fof(d2_tsp_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_tsp_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C)) = k1_struct_0(A,C) ) ) ) ) ) ).
fof(d3_tsp_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_tsp_1(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_tex_4(D,A)
& k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) ) ) ) ) ) ) ) ).
fof(d4_tsp_2,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
<=> ( v1_tsp_1(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tsp_1(C,A)
& r1_tarski(B,C) )
=> B = C ) ) ) ) ) ) ).
fof(t1_tsp_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
& v1_tsp_2(C,A) )
=> v1_tsp_2(D,B) ) ) ) ) ) ).
fof(d5_tsp_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_tsp_2(B,A)
<=> ( v1_tsp_1(B,A)
& k3_tex_4(A,B) = u1_struct_0(A) ) ) ) ) ).
fof(t2_tsp_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_tsp_2(B,A)
=> v1_tops_1(B,A) ) ) ) ).
fof(t3_tsp_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_pre_topc(B,A) )
& v1_tsp_2(B,A)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t4_tsp_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))) )
=> ~ v1_tsp_2(B,A) ) ) ).
fof(t5_tsp_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_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(C,A)
=> C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ) ).
fof(t6_tsp_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_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(C,A)
=> C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ) ).
fof(t7_tsp_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_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) ) ) ) ) ).
fof(t8_tsp_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_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k1_tops_1(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,C))) ) ) ) ) ).
fof(d6_tsp_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_tsp_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,k4_tex_4(A,C)) = k1_struct_0(A,D) ) ) ) ) ) ).
fof(t9_tsp_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_tsp_1(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(B,C)
& v1_tsp_2(C,A) ) ) ) ) ) ).
fof(t10_tsp_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_tsp_2(B,A) ) ) ).
fof(d7_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_tsp_1(B,A)
=> ( v2_tsp_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> v1_tsp_2(C,A) ) ) ) ) ) ).
fof(t11_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_tsp_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> ( v1_tsp_2(C,A)
<=> v2_tsp_2(B,A) ) ) ) ) ) ).
fof(d8_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m2_tsp_1(B,A) )
=> ( v2_tsp_2(B,A)
<=> ( v2_t_0topsp(B)
& ! [C] :
( ( ~ v3_struct_0(C)
& v2_t_0topsp(C)
& m2_tsp_1(C,A) )
=> ( m2_tsp_1(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(t12_tsp_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))) )
=> ~ ( v1_tsp_2(B,A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v1_pre_topc(C)
& m2_tsp_1(C,A) )
=> ~ ( v2_tsp_2(C,A)
& B = u1_struct_0(C) ) ) ) ) ) ).
fof(t13_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_t_0topsp(B)
& m2_tsp_1(B,A) )
=> ? [C] :
( v1_pre_topc(C)
& m2_tsp_1(C,A)
& m2_tsp_1(B,C)
& v2_tsp_2(C,A) ) ) ) ).
fof(t14_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_tsp_2(B,A)
& m2_tsp_1(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)))
=> ( D = C
=> ( v3_pre_topc(D,B)
<=> ( v3_pre_topc(k3_tex_4(A,C),A)
& D = k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t15_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(C,A)
<=> ( C = k3_tex_4(A,C)
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& v3_pre_topc(D,B)
& D = k3_xboole_0(C,u1_struct_0(B)) ) ) ) ) ) ) ).
fof(t16_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_tsp_2(B,A)
& m2_tsp_1(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)))
=> ( D = C
=> ( v4_pre_topc(D,B)
<=> ( v4_pre_topc(k3_tex_4(A,C),A)
& D = k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t17_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(C,A)
<=> ( C = k3_tex_4(A,C)
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& v4_pre_topc(D,B)
& D = k3_xboole_0(C,u1_struct_0(B)) ) ) ) ) ) ) ).
fof(t18_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( D = u1_struct_0(B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) )
=> ( 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)) ) ) ) ) ) ) ).
fof(t19_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)) )
=> ( 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)) ) ) ) ) ) ).
fof(t20_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( D = u1_struct_0(B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) )
=> v3_borsuk_1(C,A,B) ) ) ) ) ) ).
fof(t21_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)) )
=> v3_borsuk_1(C,A,B) ) ) ) ) ).
fof(t22_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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(t23_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> r1_borsuk_1(A,B) ) ) ).
fof(d9_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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)) )
=> ( C = k1_tsp_2(A,B)
<=> v3_borsuk_1(C,A,B) ) ) ) ) ).
fof(t24_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> k5_pre_topc(A,B,k1_tsp_2(A,B),k6_pre_topc(B,k1_struct_0(B,D))) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ) ).
fof(t25_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> k5_pre_topc(A,B,k1_tsp_2(A,B),k1_struct_0(B,D)) = k4_tex_4(A,C) ) ) ) ) ) ).
fof(t26_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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)))
=> ( D = C
=> k5_pre_topc(A,B,k1_tsp_2(A,B),D) = k3_tex_4(A,C) ) ) ) ) ) ).
fof(d10_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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)) )
=> ( C = k2_tsp_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = u1_struct_0(B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ).
fof(d11_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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)) )
=> ( C = k3_tsp_2(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)) ) ) ) ) ) ).
fof(t27_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_pre_topc(A,B,k3_tsp_2(A,B),k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),k3_tsp_2(A,B),C))) = k4_tex_4(A,C) ) ) ) ).
fof(t28_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_pre_topc(A,B,k3_tsp_2(A,B),k1_struct_0(A,C)) = k4_pre_topc(A,B,k3_tsp_2(A,B),k4_tex_4(A,C)) ) ) ) ).
fof(d12_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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)) )
=> ( C = k4_tsp_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = u1_struct_0(B)
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> k5_subset_1(u1_struct_0(A),D,k3_tex_4(A,E)) = k4_pre_topc(A,B,C,E) ) ) ) ) ) ) ) ).
fof(t29_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k5_pre_topc(A,B,k4_tsp_2(A,B),k4_pre_topc(A,B,k4_tsp_2(A,B),C)) = k3_tex_4(A,C) ) ) ) ).
fof(t30_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k4_pre_topc(A,B,k4_tsp_2(A,B),C) = k4_pre_topc(A,B,k4_tsp_2(A,B),k3_tex_4(A,C)) ) ) ) ).
fof(t31_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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(A)))
=> k4_pre_topc(A,B,k4_tsp_2(A,B),k4_subset_1(u1_struct_0(A),C,D)) = k4_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D)) ) ) ) ) ).
fof(t32_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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(A)))
=> ( ( v3_pre_topc(C,A)
| v3_pre_topc(D,A) )
=> k4_pre_topc(A,B,k4_tsp_2(A,B),k5_subset_1(u1_struct_0(A),C,D)) = k5_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D)) ) ) ) ) ) ).
fof(t33_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(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(A)))
=> ( ( v4_pre_topc(C,A)
| v4_pre_topc(D,A) )
=> k4_pre_topc(A,B,k4_tsp_2(A,B),k5_subset_1(u1_struct_0(A),C,D)) = k5_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D)) ) ) ) ) ) ).
fof(t34_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(C,A)
=> v3_pre_topc(k4_pre_topc(A,B,k4_tsp_2(A,B),C),B) ) ) ) ) ).
fof(t35_tsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m2_tsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(C,A)
=> v4_pre_topc(k4_pre_topc(A,B,k4_tsp_2(A,B),C),B) ) ) ) ) ).
fof(dt_k1_tsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k1_tsp_2(A,B))
& v1_funct_2(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k1_tsp_2(A,B),A,B)
& m2_relset_1(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(dt_k2_tsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k2_tsp_2(A,B))
& v1_funct_2(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k2_tsp_2(A,B),A,B)
& m2_relset_1(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(redefinition_k2_tsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m1_pre_topc(B,A) )
=> k2_tsp_2(A,B) = k1_tsp_2(A,B) ) ).
fof(dt_k3_tsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k3_tsp_2(A,B))
& v1_funct_2(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k3_tsp_2(A,B),A,B)
& m2_relset_1(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(redefinition_k3_tsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m1_pre_topc(B,A) )
=> k3_tsp_2(A,B) = k1_tsp_2(A,B) ) ).
fof(dt_k4_tsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k4_tsp_2(A,B))
& v1_funct_2(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k4_tsp_2(A,B),A,B)
& m2_relset_1(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(redefinition_k4_tsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_tsp_2(B,A)
& m1_pre_topc(B,A) )
=> k4_tsp_2(A,B) = k1_tsp_2(A,B) ) ).
%------------------------------------------------------------------------------