SET007 Axioms: SET007+779.ax
%------------------------------------------------------------------------------
% File : SET007+779 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Subcontinua of a Real Line
% 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 : borsuk_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 150 ( 19 unt; 0 def)
% Number of atoms : 705 ( 155 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 722 ( 167 ~; 22 |; 232 &)
% ( 12 <=>; 289 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 1 prp; 0-7 aty)
% Number of functors : 56 ( 56 usr; 16 con; 0-7 aty)
% Number of variables : 318 ( 310 !; 8 ?)
% 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(fc1_borsuk_5,axiom,
( ~ v3_struct_0(k3_topmetr)
& v1_pre_topc(k3_topmetr)
& v2_pre_topc(k3_topmetr)
& v1_connsp_1(k3_topmetr)
& v2_t_0topsp(k3_topmetr)
& v3_compts_1(k3_topmetr)
& v1_borsuk_2(k3_topmetr)
& v1_urysohn1(k3_topmetr) ) ).
fof(rc1_borsuk_5,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_connsp_1(A) ) ).
fof(cc1_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> ( v1_xreal_0(A)
& v1_xcmplx_0(A)
& v1_rat_1(A) ) ) ).
fof(cc2_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k8_metric_1))
=> ( v1_xreal_0(A)
& v1_xcmplx_0(A) ) ) ).
fof(fc2_borsuk_5,axiom,
( v1_xreal_0(k7_power)
& v1_xcmplx_0(k7_power)
& ~ v1_rat_1(k7_power) ) ).
fof(rc2_borsuk_5,axiom,
? [A] :
( v1_xreal_0(A)
& v1_xcmplx_0(A)
& ~ v1_rat_1(A) ) ).
fof(fc3_borsuk_5,axiom,
( ~ v1_xboole_0(k1_borsuk_5)
& v1_membered(k1_borsuk_5)
& v2_membered(k1_borsuk_5) ) ).
fof(cc3_borsuk_5,axiom,
! [A] :
( ( v1_xreal_0(A)
& ~ v1_rat_1(A) )
=> ( ~ v1_xboole_0(A)
& v1_xreal_0(A)
& v1_xcmplx_0(A) ) ) ).
fof(fc4_borsuk_5,axiom,
! [A] :
( ( v1_xreal_0(A)
& ~ v1_rat_1(A) )
=> ( ~ v1_xboole_0(k3_int_1(A))
& v1_xreal_0(k3_int_1(A))
& v1_xcmplx_0(k3_int_1(A))
& ~ v1_rat_1(k3_int_1(A)) ) ) ).
fof(fc5_borsuk_5,axiom,
! [A] :
( ( v1_xreal_0(A)
& ~ v1_rat_1(A) )
=> ( ~ v1_xboole_0(k4_xcmplx_0(A))
& v1_xreal_0(k4_xcmplx_0(A))
& v1_xcmplx_0(k4_xcmplx_0(A))
& ~ v1_rat_1(k4_xcmplx_0(A)) ) ) ).
fof(fc6_borsuk_5,axiom,
! [A,B] :
( ( v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
& v1_xreal_0(k2_xcmplx_0(A,B))
& v1_xcmplx_0(k2_xcmplx_0(A,B))
& ~ v1_rat_1(k2_xcmplx_0(A,B)) ) ) ).
fof(fc7_borsuk_5,axiom,
! [A,B] :
( ( v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
& v1_xreal_0(k2_xcmplx_0(B,A))
& v1_xcmplx_0(k2_xcmplx_0(B,A))
& ~ v1_rat_1(k2_xcmplx_0(B,A)) ) ) ).
fof(fc8_borsuk_5,axiom,
! [A,B] :
( ( v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
& v1_xreal_0(k6_xcmplx_0(A,B))
& v1_xcmplx_0(k6_xcmplx_0(A,B))
& ~ v1_rat_1(k6_xcmplx_0(A,B)) ) ) ).
fof(fc9_borsuk_5,axiom,
! [A,B] :
( ( v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
& v1_xreal_0(k6_xcmplx_0(B,A))
& v1_xcmplx_0(k6_xcmplx_0(B,A))
& ~ v1_rat_1(k6_xcmplx_0(B,A)) ) ) ).
fof(rc3_borsuk_5,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_xreal_0(A)
& v1_xcmplx_0(A)
& v1_rat_1(A) ) ).
fof(fc10_borsuk_5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k3_xcmplx_0(A,B))
& v1_xreal_0(k3_xcmplx_0(A,B))
& v1_xcmplx_0(k3_xcmplx_0(A,B))
& ~ v1_rat_1(k3_xcmplx_0(A,B)) ) ) ).
fof(fc11_borsuk_5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k3_xcmplx_0(B,A))
& v1_xreal_0(k3_xcmplx_0(B,A))
& v1_xcmplx_0(k3_xcmplx_0(B,A))
& ~ v1_rat_1(k3_xcmplx_0(B,A)) ) ) ).
fof(fc12_borsuk_5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k7_xcmplx_0(A,B))
& v1_xreal_0(k7_xcmplx_0(A,B))
& v1_xcmplx_0(k7_xcmplx_0(A,B))
& ~ v1_rat_1(k7_xcmplx_0(A,B)) ) ) ).
fof(fc13_borsuk_5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_rat_1(A)
& v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ( ~ v1_xboole_0(k7_xcmplx_0(B,A))
& v1_xreal_0(k7_xcmplx_0(B,A))
& v1_xcmplx_0(k7_xcmplx_0(B,A))
& ~ v1_rat_1(k7_xcmplx_0(B,A)) ) ) ).
fof(fc14_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ v1_xboole_0(k4_limfunc1(A))
& v1_membered(k4_limfunc1(A))
& v2_membered(k4_limfunc1(A)) ) ) ).
fof(fc15_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ v1_xboole_0(k2_limfunc1(A))
& v1_membered(k2_limfunc1(A))
& v2_membered(k2_limfunc1(A)) ) ) ).
fof(fc16_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ v1_xboole_0(k12_prob_1(A))
& v1_membered(k12_prob_1(A))
& v2_membered(k12_prob_1(A)) ) ) ).
fof(fc17_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ v1_xboole_0(k3_limfunc1(A))
& v1_membered(k3_limfunc1(A))
& v2_membered(k3_limfunc1(A)) ) ) ).
fof(fc18_borsuk_5,axiom,
( ~ v3_struct_0(k22_borsuk_1)
& v1_pre_topc(k22_borsuk_1)
& v2_pre_topc(k22_borsuk_1)
& v1_connsp_1(k22_borsuk_1)
& v2_t_0topsp(k22_borsuk_1)
& v2_compts_1(k22_borsuk_1)
& v3_compts_1(k22_borsuk_1)
& v3_yellow_8(k22_borsuk_1)
& v1_borsuk_2(k22_borsuk_1)
& v1_urysohn1(k22_borsuk_1) ) ).
fof(rc4_borsuk_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& v1_borsuk_5(B,A) ) ) ).
fof(rc5_borsuk_5,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& ~ v1_xboole_0(B)
& v1_tops_2(B,A)
& v2_tops_2(B,A) ) ) ).
fof(t1_borsuk_5,axiom,
$true ).
fof(t2_borsuk_5,axiom,
! [A,B,C] :
~ ( r1_tarski(A,B)
& r1_tarski(B,k2_xboole_0(A,k1_tarski(C)))
& k2_xboole_0(A,k1_tarski(C)) != B
& A != B ) ).
fof(t3_borsuk_5,axiom,
! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,C,F),k1_enumset1(B,D,E)) ).
fof(d1_borsuk_5,axiom,
! [A,B,C,D,E,F] :
( r1_borsuk_5(A,B,C,D,E,F)
<=> ( A != B
& A != C
& A != D
& A != E
& A != F
& B != C
& B != D
& B != E
& B != F
& C != D
& C != E
& C != F
& D != E
& D != F
& E != F ) ) ).
fof(d2_borsuk_5,axiom,
! [A,B,C,D,E,F,G] :
( r2_borsuk_5(A,B,C,D,E,F,G)
<=> ( A != B
& A != C
& A != D
& A != E
& A != F
& A != G
& B != C
& B != D
& B != E
& B != F
& B != G
& C != D
& C != E
& C != F
& C != G
& D != E
& D != F
& D != G
& E != F
& E != G
& F != G ) ) ).
fof(t4_borsuk_5,axiom,
! [A,B,C,D,E,F] :
( r1_borsuk_5(A,B,C,D,E,F)
=> k4_card_1(k4_enumset1(A,B,C,D,E,F)) = np__6 ) ).
fof(t5_borsuk_5,axiom,
! [A,B,C,D,E,F,G] :
( r2_borsuk_5(A,B,C,D,E,F,G)
=> k4_card_1(k5_enumset1(A,B,C,D,E,F,G)) = np__7 ) ).
fof(t6_borsuk_5,axiom,
! [A,B,C,D,E,F] :
( r1_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F))
=> ( A != D
& A != E
& A != F
& B != D
& B != E
& B != F
& C != D
& C != E
& C != F ) ) ).
fof(t7_borsuk_5,axiom,
! [A,B,C,D,E,F] :
( ( r1_incproj(A,B,C)
& r1_incproj(D,E,F)
& r1_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) )
=> r1_borsuk_5(A,B,C,D,E,F) ) ).
fof(t8_borsuk_5,axiom,
! [A,B,C,D,E,F,G] :
( ( r1_borsuk_5(A,B,C,D,E,F)
& r1_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) )
=> r2_borsuk_5(A,B,C,D,E,F,G) ) ).
fof(t9_borsuk_5,axiom,
! [A,B,C,D,E,F,G] :
( r2_borsuk_5(A,B,C,D,E,F,G)
=> r2_borsuk_5(G,A,B,C,D,E,F) ) ).
fof(t10_borsuk_5,axiom,
! [A,B,C,D,E,F,G] :
( r2_borsuk_5(A,B,C,D,E,F,G)
=> r2_borsuk_5(A,B,E,C,F,G,D) ) ).
fof(t11_borsuk_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(A))
& v5_pre_topc(D,k5_topmetr,A)
& k1_funct_1(D,np__0) = B
& k1_funct_1(D,np__1) = C )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
=> ~ ( v5_pre_topc(D,k5_topmetr,A)
& k1_funct_1(D,np__0) = C
& k1_funct_1(D,np__1) = B ) ) ) ) ) ) ).
fof(t12_borsuk_5,axiom,
$true ).
fof(t13_borsuk_5,axiom,
k2_pre_topc(k3_topmetr) = k1_numbers ).
fof(t14_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,k4_limfunc1(B))
<=> ~ r1_xreal_0(A,B) ) ) ) ).
fof(t15_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,k3_limfunc1(B))
<=> r1_xreal_0(B,A) ) ) ) ).
fof(t16_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,k2_limfunc1(B))
<=> r1_xreal_0(A,B) ) ) ) ).
fof(t17_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,k12_prob_1(B))
<=> ~ r1_xreal_0(B,A) ) ) ) ).
fof(t18_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k4_xboole_0(k1_numbers,k1_seq_4(A)) = k4_subset_1(k1_numbers,k12_prob_1(A),k4_limfunc1(A)) ) ).
fof(t19_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(B,C)
=> ( r1_xreal_0(B,A)
| r1_xboole_0(k1_rcomp_1(A,B),k2_rcomp_2(C,D)) ) ) ) ) ) ) ).
fof(t20_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(B,C)
=> ( r1_xreal_0(B,A)
| r1_xboole_0(k1_rcomp_2(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) ) ).
fof(t21_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( r1_xreal_0(D,E)
& A = k1_rcomp_2(C,D)
& B = k2_rcomp_2(E,F) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_connsp_1(k3_topmetr,A,B) ) ) ) ) ) ) ) ) ).
fof(t22_borsuk_5,axiom,
$true ).
fof(t23_borsuk_5,axiom,
$true ).
fof(t24_borsuk_5,axiom,
$true ).
fof(t25_borsuk_5,axiom,
$true ).
fof(t26_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xboole_0(k2_limfunc1(A),k4_limfunc1(A)) ) ).
fof(t27_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xboole_0(k12_prob_1(A),k3_limfunc1(A)) ) ).
fof(t28_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,C)
& r1_xreal_0(C,B) )
=> k4_subset_1(k1_numbers,k1_rcomp_1(A,B),k3_limfunc1(C)) = k3_limfunc1(A) ) ) ) ) ).
fof(t29_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,C)
& r1_xreal_0(C,B) )
=> k4_subset_1(k1_numbers,k2_limfunc1(C),k1_rcomp_1(A,B)) = k2_limfunc1(B) ) ) ) ) ).
fof(t30_borsuk_5,axiom,
$true ).
fof(t31_borsuk_5,axiom,
$true ).
fof(t32_borsuk_5,axiom,
$true ).
fof(t33_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_metric_1))
=> ( r2_hidden(B,k6_pre_topc(k3_topmetr,A))
<=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,np__0)
& r1_xboole_0(k9_metric_1(k8_metric_1,B,C),A) ) ) ) ) ) ).
fof(t34_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k8_metric_1))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_metric_1))
=> ( r1_xreal_0(A,B)
=> k4_metric_1(k8_metric_1,A,B) = k6_xcmplx_0(B,A) ) ) ) ).
fof(t35_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( A = k3_numbers
=> k6_pre_topc(k3_topmetr,A) = u1_struct_0(k3_topmetr) ) ) ).
fof(t36_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_rcomp_1(B,C)
=> ( B = C
| k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(d3_borsuk_5,axiom,
k1_borsuk_5 = k4_xboole_0(k1_numbers,k3_numbers) ).
fof(d4_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k2_borsuk_5(A,B) = k3_xboole_0(k3_numbers,k2_rcomp_1(A,B)) ) ) ).
fof(d5_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k3_borsuk_5(A,B) = k5_subset_1(k1_numbers,k1_borsuk_5,k2_rcomp_1(A,B)) ) ) ).
fof(t37_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ v1_rat_1(A)
<=> r2_hidden(A,k1_borsuk_5) ) ) ).
fof(t38_borsuk_5,axiom,
! [A] :
( v1_rat_1(A)
=> ! [B] :
( ( v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ~ v1_rat_1(k2_xcmplx_0(A,B)) ) ) ).
fof(t39_borsuk_5,axiom,
! [A] :
( ( v1_xreal_0(A)
& ~ v1_rat_1(A) )
=> ~ v1_rat_1(k4_xcmplx_0(A)) ) ).
fof(t40_borsuk_5,axiom,
! [A] :
( v1_rat_1(A)
=> ! [B] :
( ( v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ~ v1_rat_1(k6_xcmplx_0(A,B)) ) ) ).
fof(t41_borsuk_5,axiom,
! [A] :
( v1_rat_1(A)
=> ! [B] :
( ( v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ~ v1_rat_1(k6_xcmplx_0(B,A)) ) ) ).
fof(t42_borsuk_5,axiom,
! [A] :
( v1_rat_1(A)
=> ! [B] :
( ( v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ~ ( A != np__0
& v1_rat_1(k3_xcmplx_0(A,B)) ) ) ) ).
fof(t43_borsuk_5,axiom,
! [A] :
( v1_rat_1(A)
=> ! [B] :
( ( v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ~ ( A != np__0
& v1_rat_1(k7_xcmplx_0(B,A)) ) ) ) ).
fof(t44_borsuk_5,axiom,
! [A] :
( v1_rat_1(A)
=> ! [B] :
( ( v1_xreal_0(B)
& ~ v1_rat_1(B) )
=> ~ ( A != np__0
& v1_rat_1(k7_xcmplx_0(A,B)) ) ) ) ).
fof(t45_borsuk_5,axiom,
! [A] :
( ( v1_xreal_0(A)
& ~ v1_rat_1(A) )
=> ~ v1_rat_1(k4_int_1(A)) ) ).
fof(t46_borsuk_5,axiom,
$true ).
fof(t47_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& ! [C] :
( v1_rat_1(C)
=> ! [D] :
( v1_rat_1(D)
=> ~ ( ~ r1_xreal_0(C,A)
& ~ r1_xreal_0(D,C)
& ~ r1_xreal_0(B,D) ) ) ) ) ) ) ).
fof(t48_borsuk_5,axiom,
$true ).
fof(t49_borsuk_5,axiom,
$true ).
fof(t50_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& ! [C] :
( ( v1_xreal_0(C)
& ~ v1_rat_1(C) )
=> ~ ( ~ r1_xreal_0(C,A)
& ~ r1_xreal_0(B,C) ) ) ) ) ) ).
fof(t51_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( A = k1_borsuk_5
=> k6_pre_topc(k3_topmetr,A) = u1_struct_0(k3_topmetr) ) ) ).
fof(t52_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(B,A)
=> ( r2_hidden(C,k2_borsuk_5(A,B))
<=> ( v1_rat_1(C)
& ~ r1_xreal_0(C,A)
& ~ r1_xreal_0(B,C) ) ) ) ) ) ) ).
fof(t53_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(B,A)
=> ( r2_hidden(C,k3_borsuk_5(A,B))
<=> ( ~ v1_rat_1(C)
& ~ r1_xreal_0(C,A)
& ~ r1_xreal_0(B,C) ) ) ) ) ) ) ).
fof(t54_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_borsuk_5(B,C)
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(t55_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k3_borsuk_5(B,C)
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(t56_borsuk_5,axiom,
! [A] :
( ( v2_pre_topc(A)
& v1_connsp_1(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v3_pre_topc(B,A)
& v4_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = k1_xboole_0
| B = k2_pre_topc(A) ) ) ) ).
fof(t57_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ~ ( v4_pre_topc(A,k3_topmetr)
& v3_pre_topc(A,k3_topmetr)
& A != k1_xboole_0
& A != k1_numbers ) ) ).
fof(t58_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k1_rcomp_2(B,C)
=> ( B = C
| k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(t59_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_rcomp_2(B,C)
=> ( B = C
| k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(t60_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( A = k4_subset_1(k1_numbers,k1_rcomp_2(B,C),k2_rcomp_2(C,D))
=> ( r1_xreal_0(C,B)
| r1_xreal_0(D,C)
| k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,D) ) ) ) ) ) ) ).
fof(t61_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k1_seq_4(B)
=> k6_pre_topc(k3_topmetr,A) = k1_seq_4(B) ) ) ) ).
fof(t62_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( A = B
=> ( v3_rcomp_1(A)
<=> v3_pre_topc(B,k3_topmetr) ) ) ) ) ).
fof(t63_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k4_limfunc1(B)
=> v3_pre_topc(A,k3_topmetr) ) ) ) ).
fof(t64_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k12_prob_1(B)
=> v3_pre_topc(A,k3_topmetr) ) ) ) ).
fof(t65_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k2_limfunc1(B)
=> v4_pre_topc(A,k3_topmetr) ) ) ) ).
fof(t66_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k3_limfunc1(B)
=> v4_pre_topc(A,k3_topmetr) ) ) ) ).
fof(t67_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k3_limfunc1(A) = k4_subset_1(k1_numbers,k1_seq_4(A),k4_limfunc1(A)) ) ).
fof(t68_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k2_limfunc1(A) = k4_subset_1(k1_numbers,k1_seq_4(A),k12_prob_1(A)) ) ).
fof(t69_borsuk_5,axiom,
$true ).
fof(t70_borsuk_5,axiom,
$true ).
fof(t71_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k4_limfunc1(A) != k1_numbers ) ).
fof(t72_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k3_limfunc1(A) != k1_numbers ) ).
fof(t73_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k2_limfunc1(A) != k1_numbers ) ).
fof(t74_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k12_prob_1(A) != k1_numbers ) ).
fof(t75_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k4_limfunc1(B)
=> k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) ).
fof(t76_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k7_pscomp_1(k4_limfunc1(A)) = k3_limfunc1(A) ) ).
fof(t77_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k12_prob_1(B)
=> k6_pre_topc(k3_topmetr,A) = k2_limfunc1(B) ) ) ) ).
fof(t78_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> k7_pscomp_1(k12_prob_1(A)) = k2_limfunc1(A) ) ).
fof(t79_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [C] :
( v1_xreal_0(C)
=> ( ( A = k12_prob_1(C)
& B = k4_limfunc1(C) )
=> r1_connsp_1(k3_topmetr,A,B) ) ) ) ) ).
fof(t80_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k4_subset_1(k1_numbers,k1_rcomp_2(B,C),k4_limfunc1(C))
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) ) ) ).
fof(t81_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k4_subset_1(k1_numbers,k2_rcomp_1(B,C),k4_limfunc1(C))
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) ) ) ).
fof(t82_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_borsuk_5(B,C),k2_rcomp_1(C,D)),k4_limfunc1(D))
=> ( r1_xreal_0(C,B)
| r1_xreal_0(D,C)
| k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) ) ) ) ).
fof(t83_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_xboole_0(k1_numbers,A) ) ).
fof(t84_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ~ r1_xreal_0(B,A)
=> r1_xboole_0(k3_borsuk_5(A,B),k2_borsuk_5(A,B)) ) ) ) ).
fof(t85_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k4_xboole_0(k1_numbers,k2_borsuk_5(A,B)) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(A),k3_borsuk_5(A,B)),k3_limfunc1(B)) ) ) ).
fof(t86_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( r1_xreal_0(A,B)
& ~ r1_xreal_0(C,B)
& r2_hidden(A,k4_subset_1(k1_numbers,k2_rcomp_1(B,C),k4_limfunc1(C))) ) ) ) ) ).
fof(t87_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& r2_hidden(B,k4_subset_1(k1_numbers,k2_rcomp_1(A,B),k4_limfunc1(B))) ) ) ) ).
fof(t88_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ~ r1_xreal_0(B,A)
=> k6_subset_1(k1_numbers,k3_limfunc1(A),k4_subset_1(k1_numbers,k2_rcomp_1(A,B),k4_limfunc1(B))) = k4_subset_1(k1_numbers,k1_seq_4(A),k1_seq_4(B)) ) ) ) ).
fof(t89_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_borsuk_5(np__2,np__4),k2_rcomp_1(np__4,np__5)),k4_limfunc1(np__5))
=> k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(np__2),k3_borsuk_5(np__2,np__4)),k1_seq_4(np__4)),k1_seq_4(np__5)) ) ) ).
fof(t90_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k1_seq_4(B)
=> k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k12_prob_1(B),k4_limfunc1(B)) ) ) ) ).
fof(t91_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ~ r1_xreal_0(B,A)
=> k5_subset_1(k1_numbers,k4_limfunc1(A),k2_limfunc1(B)) = k2_rcomp_2(A,B) ) ) ) ).
fof(t92_borsuk_5,axiom,
k5_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(np__1),k4_limfunc1(np__1)),k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(np__2),k3_borsuk_5(np__2,np__4)),k1_seq_4(np__4)),k1_seq_4(np__5))) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(np__1),k2_rcomp_2(np__1,np__2)),k3_borsuk_5(np__2,np__4)),k1_seq_4(np__4)),k1_seq_4(np__5)) ).
fof(t93_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> k6_subset_1(k1_numbers,k12_prob_1(B),k1_seq_4(A)) = k4_subset_1(k1_numbers,k12_prob_1(A),k2_rcomp_1(A,B)) ) ) ) ).
fof(t94_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> k6_subset_1(k1_numbers,k4_limfunc1(A),k1_seq_4(B)) = k4_subset_1(k1_numbers,k2_rcomp_1(A,B),k4_limfunc1(B)) ) ) ) ).
fof(t95_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(B,C)
& A = k4_subset_1(k1_numbers,k1_seq_4(B),k3_limfunc1(C)) )
=> k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(B,C)) ) ) ) ) ).
fof(t96_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(B,C))
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k3_topmetr,A) = k2_limfunc1(C) ) ) ) ) ) ).
fof(t97_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_2(B,C))
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k3_topmetr,A) = k2_limfunc1(C) ) ) ) ) ) ).
fof(t98_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k2_limfunc1(B)
=> k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_limfunc1(B) ) ) ) ).
fof(t99_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k3_limfunc1(B)
=> k3_subset_1(u1_struct_0(k3_topmetr),A) = k12_prob_1(B) ) ) ) ).
fof(t100_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_2(B,C)),k3_borsuk_5(C,D)),k1_seq_4(D))
=> ( r1_xreal_0(C,B)
| r1_xreal_0(D,C)
| k6_pre_topc(k3_topmetr,A) = k2_limfunc1(D) ) ) ) ) ) ) ).
fof(t101_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_2(B,C)),k3_borsuk_5(C,D)),k1_seq_4(D)),k1_seq_4(E))
=> ( r1_xreal_0(C,B)
| r1_xreal_0(D,C)
| k6_pre_topc(k3_topmetr,A) = k4_subset_1(k1_numbers,k2_limfunc1(D),k1_seq_4(E)) ) ) ) ) ) ) ) ).
fof(t102_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(B,C)
& A = k4_subset_1(k1_numbers,k2_limfunc1(B),k1_seq_4(C)) )
=> k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k2_rcomp_1(B,C),k4_limfunc1(C)) ) ) ) ) ).
fof(t103_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k4_subset_1(k1_numbers,k3_limfunc1(A),k1_seq_4(B)) != k1_numbers ) ) ).
fof(t104_borsuk_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k4_subset_1(k1_numbers,k2_limfunc1(A),k1_seq_4(B)) != k1_numbers ) ) ).
fof(t105_borsuk_5,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)))
=> ~ ( B != C
& k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C) ) ) ) ) ).
fof(t106_borsuk_5,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( k1_numbers = k3_subset_1(u1_struct_0(k3_topmetr),A)
=> A = k1_xboole_0 ) ) ).
fof(t107_borsuk_5,axiom,
! [A] :
( ( v6_compts_1(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( B = A
=> ( v1_seq_4(B)
& v2_seq_4(B) ) ) ) ) ).
fof(t108_borsuk_5,axiom,
! [A] :
( ( v6_compts_1(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r2_hidden(C,B)
& B = A )
=> ( r1_xreal_0(k4_pscomp_1(B),C)
& r1_xreal_0(C,k3_pscomp_1(B)) ) ) ) ) ) ).
fof(t109_borsuk_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k3_topmetr)
& v6_compts_1(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( ( A = B
& r1_tarski(k1_rcomp_1(k4_pscomp_1(B),k3_pscomp_1(B)),B) )
=> k1_rcomp_1(k4_pscomp_1(B),k3_pscomp_1(B)) = B ) ) ) ).
fof(t110_borsuk_5,axiom,
! [A] :
( ( v2_connsp_1(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(B,C)
& r1_xreal_0(C,D)
& r2_hidden(B,A)
& r2_hidden(D,A) )
=> r2_hidden(C,A) ) ) ) ) ) ).
fof(t111_borsuk_5,axiom,
! [A] :
( ( v2_connsp_1(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r1_tarski(k1_rcomp_1(B,C),A) ) ) ) ) ).
fof(t112_borsuk_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k3_topmetr)
& v6_compts_1(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
=> ( ~ v1_xboole_0(A)
& v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) ) ).
fof(t113_borsuk_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k3_topmetr)
& v6_compts_1(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
=> ? [B] :
( v1_xreal_0(B)
& ? [C] :
( v1_xreal_0(C)
& r1_xreal_0(B,C)
& A = k1_rcomp_1(B,C) ) ) ) ).
fof(d6_borsuk_5,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_borsuk_5(B,A)
<=> ~ r2_hidden(u1_struct_0(A),B) ) ) ) ).
fof(t114_borsuk_5,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ( v1_borsuk_5(B,A)
& r1_tarski(C,B) )
=> v1_borsuk_5(C,A) ) ) ) ) ).
fof(t115_borsuk_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_borsuk_5(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> ! [C] :
( ( v1_borsuk_5(C,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> v1_borsuk_5(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A) ) ) ) ).
fof(dt_k1_borsuk_5,axiom,
m1_subset_1(k1_borsuk_5,k1_zfmisc_1(k1_numbers)) ).
fof(dt_k2_borsuk_5,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B) )
=> m1_subset_1(k2_borsuk_5(A,B),k1_zfmisc_1(k1_numbers)) ) ).
fof(dt_k3_borsuk_5,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B) )
=> m1_subset_1(k3_borsuk_5(A,B),k1_zfmisc_1(k1_numbers)) ) ).
%------------------------------------------------------------------------------