SET007 Axioms: SET007+729.ax
%------------------------------------------------------------------------------
% File : SET007+729 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Decompositions of Intervals and Simple Closed Curves
% 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 91 ( 1 unt; 0 def)
% Number of atoms : 605 ( 79 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 635 ( 121 ~; 14 |; 195 &)
% ( 4 <=>; 301 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 44 ( 43 usr; 0 prp; 1-4 aty)
% Number of functors : 43 ( 43 usr; 8 con; 0-4 aty)
% Number of variables : 271 ( 258 !; 13 ?)
% 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_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> ( ~ v1_xboole_0(A)
& ~ v1_realset1(A)
& v1_topreal2(A)
& v2_connsp_1(A,k15_euclid(np__2))
& v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A) ) ) ) ).
fof(rc1_borsuk_4,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_xboole_0(B)
& v2_connsp_1(B,A)
& v6_compts_1(B,A) ) ) ).
fof(rc2_borsuk_4,axiom,
! [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) ) ) ).
fof(rc3_borsuk_4,axiom,
! [A] :
( ~ v1_realset1(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& ~ v1_realset1(B) ) ) ).
fof(fc1_borsuk_4,axiom,
( ~ v1_xboole_0(u1_struct_0(k5_topmetr))
& v1_membered(u1_struct_0(k5_topmetr))
& v2_membered(u1_struct_0(k5_topmetr)) ) ).
fof(t1_borsuk_4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ~ ( r2_xboole_0(B,C)
& ! [D] :
( m1_subset_1(D,A)
=> ~ ( r2_hidden(D,C)
& r1_tarski(B,k4_xboole_0(C,k1_tarski(D))) ) ) ) ) ) ) ).
fof(t2_borsuk_4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ( v1_realset1(B)
<=> ? [C] :
( m1_subset_1(C,A)
& B = k1_tarski(C) ) ) ) ) ).
fof(t3_borsuk_4,axiom,
! [A] :
( ~ v1_realset1(A)
=> ! [B] :
~ ! [C] :
( m1_subset_1(C,A)
=> C = B ) ) ).
fof(t4_borsuk_4,axiom,
! [A] :
( ~ v1_realset1(A)
=> ! [B] :
( ( ~ v1_realset1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
? [D] :
( m1_subset_1(D,A)
& r2_hidden(D,B)
& D != C ) ) ) ).
fof(t5_borsuk_4,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v2_funct_1(A)
& v2_funct_1(B)
& k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_tarski(C)
& k3_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k1_tarski(k1_funct_1(A,C)) )
=> v2_funct_1(k1_funct_4(A,B)) ) ) ) ).
fof(t6_borsuk_4,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v2_funct_1(A)
& v2_funct_1(B)
& k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_tarski(C)
& k3_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k1_tarski(k1_funct_1(A,C))
& k1_funct_1(A,C) = k1_funct_1(B,C) )
=> k2_funct_1(k1_funct_4(A,B)) = k1_funct_4(k2_funct_1(A),k2_funct_1(B)) ) ) ) ).
fof(t7_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,B)
& v1_xboole_0(k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C))) ) ) ) ) ) ).
fof(t8_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> v1_jordan1(k3_topreal1(A,B,C),A) ) ) ) ).
fof(t9_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(np__0,D)
& r1_xreal_0(D,np__1) )
=> ( r1_xreal_0(C,A)
| r1_xreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,D),B),k3_xcmplx_0(D,C))) ) ) ) ) ) ) ).
fof(t10_borsuk_4,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( r2_hidden(A,k1_rcomp_1(B,C))
& ~ r2_hidden(A,k2_rcomp_1(B,C))
& A != B
& A != C ) ) ) ).
fof(t11_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xboole_0(k2_rcomp_1(A,B),k1_rcomp_1(C,D))
& r1_xreal_0(B,C) ) ) ) ) ) ).
fof(t12_borsuk_4,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_xboole_0(k1_rcomp_1(A,B),k2_rcomp_1(C,D)) ) ) ) ) ) ).
fof(t13_borsuk_4,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_xboole_0(k2_rcomp_1(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) ).
fof(t14_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_tarski(k1_rcomp_1(A,B),k1_rcomp_1(C,D)) )
=> ( r1_xreal_0(C,A)
& r1_xreal_0(B,D) ) ) ) ) ) ) ).
fof(t15_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_tarski(k2_rcomp_1(A,B),k1_rcomp_1(C,D))
=> ( r1_xreal_0(B,A)
| ( r1_xreal_0(C,A)
& r1_xreal_0(B,D) ) ) ) ) ) ) ) ).
fof(t16_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_tarski(k2_rcomp_1(A,B),k1_rcomp_1(C,D))
=> ( r1_xreal_0(B,A)
| r1_tarski(k1_rcomp_1(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) ) ).
fof(t17_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_rcomp_1(B,C)
=> ( r1_xreal_0(C,B)
| r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) ).
fof(t18_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_rcomp_2(B,C)
=> ( r1_xreal_0(C,B)
| r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) ).
fof(t19_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k1_rcomp_2(B,C)
=> ( r1_xreal_0(C,B)
| r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) ).
fof(t20_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( A != B
=> k7_pscomp_1(k2_rcomp_2(A,B)) = k1_rcomp_1(A,B) ) ) ) ).
fof(t21_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( A != B
=> k7_pscomp_1(k1_rcomp_2(A,B)) = k1_rcomp_1(A,B) ) ) ) ).
fof(t22_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_rcomp_1(B,C)
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k5_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(t23_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_rcomp_2(B,C)
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k5_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(t24_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k1_rcomp_2(B,C)
=> ( r1_xreal_0(C,B)
| k6_pre_topc(k5_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) ).
fof(t25_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& k1_rcomp_1(A,B) = k2_rcomp_2(A,B) ) ) ) ).
fof(t26_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xboole_0(k1_rcomp_2(A,B),k1_seq_4(B))
& r1_xboole_0(k2_rcomp_2(A,B),k1_seq_4(A)) ) ) ) ).
fof(t27_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> k6_subset_1(k1_numbers,k1_rcomp_1(A,B),k1_seq_4(A)) = k2_rcomp_2(A,B) ) ) ) ).
fof(t28_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> k6_subset_1(k1_numbers,k1_rcomp_1(A,B),k1_seq_4(B)) = k1_rcomp_2(A,B) ) ) ) ).
fof(t29_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,B)
& k5_subset_1(k1_numbers,k2_rcomp_2(A,B),k1_rcomp_2(B,C)) != k1_seq_4(B) ) ) ) ) ).
fof(t30_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xboole_0(k1_rcomp_2(A,B),k1_rcomp_1(B,C))
& r1_xboole_0(k1_rcomp_1(A,B),k2_rcomp_2(B,C)) ) ) ) ) ).
fof(t31_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(B,C) )
=> k6_subset_1(k1_numbers,k1_rcomp_1(A,C),k1_seq_4(B)) = k4_subset_1(k1_numbers,k1_rcomp_2(A,B),k2_rcomp_2(B,C)) ) ) ) ) ).
fof(t32_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(B,C)
& A = k1_rcomp_1(B,C) )
=> ( r1_xreal_0(np__0,B)
& r1_xreal_0(C,np__1) ) ) ) ) ) ).
fof(t33_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ( ( A = k1_rcomp_2(C,D)
& B = k2_rcomp_2(D,E) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(E,D)
| r1_connsp_1(k5_topmetr,A,B) ) ) ) ) ) ) ) ).
fof(t34_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> k1_rcomp_1(A,B) = k4_subset_1(k1_numbers,k1_rcomp_2(A,B),k1_seq_4(B)) ) ) ) ).
fof(t35_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> k1_rcomp_1(A,B) = k4_subset_1(k1_numbers,k1_seq_4(A),k2_rcomp_2(A,B)) ) ) ) ).
fof(t36_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ( r1_xreal_0(C,B)
| k1_rcomp_1(A,D) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k1_rcomp_1(A,B),k2_rcomp_1(B,C)),k1_rcomp_1(C,D)) ) ) ) ) ) ) ).
fof(t37_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ( r1_xreal_0(C,B)
| k6_subset_1(k1_numbers,k1_rcomp_1(A,D),k4_subset_1(k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D))) = k2_rcomp_1(B,C) ) ) ) ) ) ) ).
fof(t38_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,B)
& k4_subset_1(k1_numbers,k2_rcomp_2(A,B),k2_rcomp_1(B,C)) != k2_rcomp_1(A,C) ) ) ) ) ).
fof(t39_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,B)
& ~ r1_tarski(k1_rcomp_2(B,C),k2_rcomp_1(A,C)) ) ) ) ) ).
fof(t40_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,B)
& k4_subset_1(k1_numbers,k2_rcomp_2(A,B),k1_rcomp_2(B,C)) != k2_rcomp_1(A,C) ) ) ) ) ).
fof(t41_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,B)
& k6_subset_1(k1_numbers,k2_rcomp_1(A,C),k2_rcomp_2(A,B)) != k2_rcomp_1(B,C) ) ) ) ) ).
fof(t42_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,B)
& k6_subset_1(k1_numbers,k2_rcomp_1(A,C),k1_rcomp_2(B,C)) != k2_rcomp_1(A,B) ) ) ) ) ).
fof(t43_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) ) ).
fof(t44_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> m1_subset_1(k2_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) ) ).
fof(t45_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( v1_integra1(k1_seq_4(A))
& m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)) ) ) ).
fof(t46_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k5_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
=> ( ( r1_xreal_0(B,C)
& r1_xreal_0(C,D)
& r2_hidden(B,A)
& r2_hidden(D,A) )
=> r2_hidden(C,A) ) ) ) ) ) ).
fof(t47_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k5_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_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(t48_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ( C = k1_rcomp_1(A,B)
=> v4_pre_topc(C,k5_topmetr) ) ) ) ) ).
fof(t49_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ( r1_xreal_0(A,B)
=> ( ~ v1_xboole_0(k1_rcomp_1(A,B))
& v2_connsp_1(k1_rcomp_1(A,B),k5_topmetr)
& v6_compts_1(k1_rcomp_1(A,B),k5_topmetr)
& m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) ) ) ) ).
fof(t50_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( B = A
=> ( v1_seq_4(B)
& v2_seq_4(B) ) ) ) ) ).
fof(t51_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_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(t52_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ( A = B
=> ( v2_rcomp_1(A)
<=> v4_pre_topc(B,k5_topmetr) ) ) ) ) ).
fof(t53_borsuk_4,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> r1_xreal_0(k4_pscomp_1(A),k3_pscomp_1(A)) ) ).
fof(t54_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k5_topmetr)
& v6_compts_1(A,k5_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_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(t55_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k5_topmetr)
& v6_compts_1(A,k5_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
=> ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) ) ).
fof(t56_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_connsp_1(A,k5_topmetr)
& v6_compts_1(A,k5_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
& ? [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
& r1_xreal_0(B,C)
& A = k1_rcomp_1(B,C) ) ) ) ).
fof(d1_borsuk_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_pre_topc(A)
& m1_pre_topc(A,k5_topmetr) )
=> ( A = k1_borsuk_4
<=> u1_struct_0(A) = k2_rcomp_1(np__0,np__1) ) ) ).
fof(t57_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ( A = u1_struct_0(k1_borsuk_4)
=> k1_borsuk_4 = k3_pre_topc(k5_topmetr,A) ) ) ).
fof(t58_borsuk_4,axiom,
u1_struct_0(k1_borsuk_4) = k4_xboole_0(u1_struct_0(k5_topmetr),k2_tarski(np__0,np__1)) ).
fof(t59_borsuk_4,axiom,
( v1_tsep_1(k1_borsuk_4,k5_topmetr)
& m1_pre_topc(k1_borsuk_4,k5_topmetr) ) ).
fof(t60_borsuk_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r2_hidden(A,u1_struct_0(k1_borsuk_4))
<=> ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A) ) ) ) ).
fof(t61_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ~ ( ~ r1_xreal_0(B,A)
& B != np__1
& ~ ( ~ v1_xboole_0(k2_rcomp_2(A,B))
& m1_subset_1(k2_rcomp_2(A,B),k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) ) ) ) ) ).
fof(t62_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ~ ( ~ r1_xreal_0(B,A)
& A != np__0
& ~ ( ~ v1_xboole_0(k1_rcomp_2(A,B))
& m1_subset_1(k1_rcomp_2(A,B),k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) ) ) ) ) ).
fof(t63_borsuk_4,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_borsuk_3(k3_pre_topc(k15_euclid(np__2),k2_topreal1),k3_pre_topc(k15_euclid(np__2),A)) ) ).
fof(t64_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ( r1_topreal1(k15_euclid(A),C,D,B)
=> r1_t_0topsp(k1_borsuk_4,k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),C,D)))) ) ) ) ) ) ).
fof(t65_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ( r1_topreal1(k15_euclid(A),C,D,B)
=> r1_t_0topsp(k5_topmetr,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ).
fof(t66_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ( B != C
=> r1_borsuk_3(k5_topmetr,k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))) ) ) ) ) ).
fof(t67_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
& ? [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
& ~ r1_xreal_0(C,B)
& A = k1_rcomp_1(B,C) ) )
=> r1_t_0topsp(k5_topmetr,k3_pre_topc(k1_borsuk_4,A)) ) ) ).
fof(t68_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_topmetr))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k5_topmetr))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,B)
& ~ r1_xreal_0(F,E)
& ! [G] :
( ( ~ v1_xboole_0(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k3_pre_topc(k5_topmetr,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
& m2_relset_1(H,u1_struct_0(k3_pre_topc(k5_topmetr,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
=> ~ ( G = k1_rcomp_1(E,F)
& v3_tops_2(H,k3_pre_topc(k5_topmetr,G),k3_pre_topc(k15_euclid(A),B))
& k1_funct_1(H,E) = C
& k1_funct_1(H,F) = D ) ) ) ) ) ) ) ) ) ) ).
fof(t69_borsuk_4,axiom,
! [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)) )
=> ! [D] :
( ( v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v5_pre_topc(C,A,B)
& m1_pre_topc(D,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k3_pre_topc(A,E)),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(k3_pre_topc(A,E)),u1_struct_0(D)) )
=> ( F = k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,E)
=> v5_pre_topc(F,k3_pre_topc(A,E),D) ) ) ) ) ) ) ) ) ).
fof(t70_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
=> ( A = k2_rcomp_1(B,C)
=> v3_pre_topc(A,k5_topmetr) ) ) ) ) ).
fof(t71_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
=> ( A = k2_rcomp_1(B,C)
=> v3_pre_topc(A,k1_borsuk_4) ) ) ) ) ).
fof(t72_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ( A = k2_rcomp_2(np__0,B)
=> v4_pre_topc(A,k1_borsuk_4) ) ) ) ).
fof(t73_borsuk_4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ( A = k1_rcomp_2(B,np__1)
=> v4_pre_topc(A,k1_borsuk_4) ) ) ) ).
fof(t74_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_topmetr))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k5_topmetr))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,B)
& ~ r1_xreal_0(F,E)
& F != np__1
& ! [G] :
( ( ~ v1_xboole_0(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C)))))
& m2_relset_1(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C))))) )
=> ~ ( G = k2_rcomp_2(E,F)
& v3_tops_2(H,k3_pre_topc(k1_borsuk_4,G),k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C))))
& k1_funct_1(H,F) = D ) ) ) ) ) ) ) ) ) ) ).
fof(t75_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_topmetr))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k5_topmetr))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,B)
& ~ r1_xreal_0(F,E)
& E != np__0
& ! [G] :
( ( ~ v1_xboole_0(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D)))))
& m2_relset_1(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D))))) )
=> ~ ( G = k1_rcomp_2(E,F)
& v3_tops_2(H,k3_pre_topc(k1_borsuk_4,G),k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D))))
& k1_funct_1(H,E) = C ) ) ) ) ) ) ) ) ) ) ).
fof(t76_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ( ( r1_topreal1(k15_euclid(A),D,E,B)
& r1_topreal1(k15_euclid(A),E,D,C)
& k5_subset_1(u1_struct_0(k15_euclid(A)),B,C) = k2_struct_0(k15_euclid(A),D,E) )
=> ( D = E
| r1_t_0topsp(k1_borsuk_4,k3_pre_topc(k15_euclid(A),k4_subset_1(u1_struct_0(k15_euclid(A)),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D)),k6_subset_1(u1_struct_0(k15_euclid(A)),C,k1_struct_0(k15_euclid(A),D))))) ) ) ) ) ) ) ) ).
fof(t77_borsuk_4,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,A)
=> r1_t_0topsp(k3_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k1_struct_0(k15_euclid(np__2),B))),k1_borsuk_4) ) ) ) ).
fof(t78_borsuk_4,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r1_t_0topsp(k3_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k1_struct_0(k15_euclid(np__2),B))),k3_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k1_struct_0(k15_euclid(np__2),C)))) ) ) ) ) ).
fof(t79_borsuk_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
=> ~ ( ? [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
& ? [E] :
( m1_subset_1(E,u1_struct_0(k5_topmetr))
& ~ r1_xreal_0(E,D)
& C = k1_rcomp_1(D,E) ) )
& r1_t_0topsp(k3_pre_topc(k1_borsuk_4,C),k3_pre_topc(k15_euclid(A),B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ r1_topreal1(k15_euclid(A),D,E,B) ) ) ) ) ) ) ).
fof(t80_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k1_borsuk_4))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k1_borsuk_4)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( v3_tops_2(B,k3_pre_topc(k15_euclid(np__2),A),k1_borsuk_4)
& r1_tarski(C,A)
& ? [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
& ? [E] :
( m1_subset_1(E,u1_struct_0(k5_topmetr))
& ~ r1_xreal_0(E,D)
& k4_pre_topc(k3_pre_topc(k15_euclid(np__2),A),k1_borsuk_4,B,C) = k1_rcomp_1(D,E) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ r1_topreal1(k15_euclid(np__2),D,E,C) ) ) ) ) ) ) ).
fof(t81_borsuk_4,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_tarski(B,A)
& B != A
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ r1_topreal1(k15_euclid(np__2),C,D,B) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> B != k1_struct_0(k15_euclid(np__2),C) ) ) ) ) ).
fof(t82_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k5_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
=> ~ ( r1_tarski(A,k2_rcomp_1(np__0,np__1))
& ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ~ ( r1_tarski(A,B)
& r1_tarski(B,k2_rcomp_1(np__0,np__1))
& k3_seq_4(A) = k4_pscomp_1(B)
& k2_seq_4(A) = k3_pscomp_1(B) ) ) ) ) ).
fof(t83_borsuk_4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k5_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
=> ~ ( r1_tarski(A,k2_rcomp_1(np__0,np__1))
& ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
=> ~ ( r1_xreal_0(B,C)
& r1_tarski(A,k1_rcomp_1(B,C))
& r1_tarski(k1_rcomp_1(B,C),k2_rcomp_1(np__0,np__1)) ) ) ) ) ) ).
fof(t84_borsuk_4,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v4_pre_topc(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_tarski(B,A)
& B != A
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( r1_topreal1(k15_euclid(np__2),C,D,E)
& r1_tarski(B,E)
& r1_tarski(E,A) ) ) ) ) ) ) ) ).
fof(dt_k1_borsuk_4,axiom,
( ~ v3_struct_0(k1_borsuk_4)
& v1_pre_topc(k1_borsuk_4)
& m1_pre_topc(k1_borsuk_4,k5_topmetr) ) ).
%------------------------------------------------------------------------------