SET007 Axioms: SET007+832.ax
%------------------------------------------------------------------------------
% File : SET007+832 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Algebraic Properties of Homotopies
% 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_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 159 ( 23 unt; 0 def)
% Number of atoms : 949 ( 116 equ)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 872 ( 82 ~; 3 |; 405 &)
% ( 32 <=>; 350 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 1 prp; 0-6 aty)
% Number of functors : 88 ( 88 usr; 37 con; 0-6 aty)
% Number of variables : 367 ( 338 !; 29 ?)
% 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_6,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v3_struct_0(k15_euclid(A))
& v1_pre_topc(k15_euclid(A))
& v2_pre_topc(k15_euclid(A))
& v1_monoid_0(k15_euclid(A))
& v2_monoid_0(k15_euclid(A)) ) ) ).
fof(fc2_borsuk_6,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_compts_1(k22_borsuk_1)
& v3_compts_1(k22_borsuk_1)
& v3_yellow_8(k22_borsuk_1)
& v1_urysohn1(k22_borsuk_1)
& v1_borsuk_2(k22_borsuk_1)
& v2_t_0topsp(k22_borsuk_1)
& v1_borsuk_6(k22_borsuk_1) ) ).
fof(rc1_borsuk_6,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A)
& v1_borsuk_6(A) ) ).
fof(rc2_borsuk_6,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_6(A) ) ).
fof(cc1_borsuk_6,axiom,
! [A] :
( ( v1_borsuk_6(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B) ) ) ) ).
fof(cc2_borsuk_6,axiom,
! [A] :
( ( v1_borsuk_6(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> v1_borsuk_6(B) ) ) ).
fof(fc3_borsuk_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_6(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_6(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
=> ( v1_xcmplx_0(k1_mcart_1(C))
& v1_xreal_0(k1_mcart_1(C)) ) ) ).
fof(fc4_borsuk_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_6(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_6(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
=> ( v1_xcmplx_0(k2_mcart_1(C))
& v1_xreal_0(k2_mcart_1(C)) ) ) ).
fof(fc5_borsuk_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& m1_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr))
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_xcmplx_0(k1_mcart_1(B))
& v1_xreal_0(k1_mcart_1(B)) ) ) ).
fof(fc6_borsuk_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& m1_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr))
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_xcmplx_0(k2_mcart_1(B))
& v1_xreal_0(k2_mcart_1(B)) ) ) ).
fof(fc7_borsuk_6,axiom,
( ~ v3_struct_0(k3_topmetr)
& v1_pre_topc(k3_topmetr)
& v2_pre_topc(k3_topmetr)
& v1_connsp_1(k3_topmetr)
& v3_compts_1(k3_topmetr)
& v1_urysohn1(k3_topmetr)
& v1_borsuk_2(k3_topmetr)
& v2_t_0topsp(k3_topmetr)
& v1_borsuk_6(k3_topmetr) ) ).
fof(fc8_borsuk_6,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_funct_1(k1_pre_topc(A))
& v1_xboole_0(k1_pre_topc(A))
& v6_compts_1(k1_pre_topc(A),A)
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A)) ) ) ).
fof(rc3_borsuk_6,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(B)
& v1_xboole_0(B)
& v6_compts_1(B,A)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B) ) ) ).
fof(fc9_borsuk_6,axiom,
( v1_relat_1(k3_borsuk_6)
& v1_funct_1(k3_borsuk_6)
& v1_funct_2(k3_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(k3_borsuk_6,k5_topmetr,k5_topmetr) ) ).
fof(fc10_borsuk_6,axiom,
( v1_relat_1(k4_borsuk_6)
& v1_funct_1(k4_borsuk_6)
& v1_funct_2(k4_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(k4_borsuk_6,k5_topmetr,k5_topmetr) ) ).
fof(fc11_borsuk_6,axiom,
( v1_relat_1(k5_borsuk_6)
& v1_funct_1(k5_borsuk_6)
& v1_funct_2(k5_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(k5_borsuk_6,k5_topmetr,k5_topmetr) ) ).
fof(fc12_borsuk_6,axiom,
( ~ v1_xboole_0(k6_borsuk_6)
& v4_pre_topc(k6_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr)) ) ).
fof(fc13_borsuk_6,axiom,
( ~ v1_xboole_0(k7_borsuk_6)
& v4_pre_topc(k7_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr)) ) ).
fof(fc14_borsuk_6,axiom,
( ~ v1_xboole_0(k8_borsuk_6)
& v4_pre_topc(k8_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr)) ) ).
fof(t1_borsuk_6,axiom,
u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)) = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,np__1),k1_rcomp_1(np__0,np__1)) ).
fof(t2_borsuk_6,axiom,
$true ).
fof(t3_borsuk_6,axiom,
$true ).
fof(t4_borsuk_6,axiom,
$true ).
fof(t5_borsuk_6,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) )
=> r2_hidden(k7_xcmplx_0(k6_xcmplx_0(C,A),k6_xcmplx_0(B,A)),u1_struct_0(k4_topmetr(np__0,np__1))) ) ) ) ) ).
fof(t6_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ( r1_xreal_0(A,k6_real_1(np__1,np__2))
=> m1_subset_1(k3_xcmplx_0(np__2,A),u1_struct_0(k5_topmetr)) ) ) ).
fof(t7_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ( r1_xreal_0(k6_real_1(np__1,np__2),A)
=> m1_subset_1(k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1),u1_struct_0(k5_topmetr)) ) ) ).
fof(t8_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> m1_subset_1(k3_xcmplx_0(A,B),u1_struct_0(k5_topmetr)) ) ) ).
fof(t9_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> m1_subset_1(k3_xcmplx_0(k6_real_1(np__1,np__2),A),u1_struct_0(k5_topmetr)) ) ).
fof(t10_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ( r1_xreal_0(k6_real_1(np__1,np__2),A)
=> m1_subset_1(k6_xcmplx_0(A,k6_real_1(np__1,np__4)),u1_struct_0(k5_topmetr)) ) ) ).
fof(t11_borsuk_6,axiom,
$true ).
fof(t12_borsuk_6,axiom,
m1_borsuk_2(k7_grcat_1(k5_topmetr),k22_borsuk_1,k23_borsuk_1,k24_borsuk_1) ).
fof(t13_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,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(A,B)
& r1_xreal_0(C,D) )
=> ( ~ v1_xboole_0(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)))
& v6_compts_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k6_borsuk_1(k5_topmetr,k5_topmetr))
& m1_subset_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ) ) ) ) ) ) ).
fof(d1_borsuk_6,axiom,
! [A] :
( l1_struct_0(A)
=> ( v1_borsuk_6(A)
<=> v2_membered(u1_struct_0(A)) ) ) ).
fof(t18_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ( v1_borsuk_6(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v1_xreal_0(B) ) ) ) ).
fof(t24_borsuk_6,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(np__2)))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k1_funct_1(A,k4_tarski(B,C)) = k10_finseq_1(B,C) ) ) ) ).
fof(t31_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B)))
=> ( m1_subset_1(k1_mcart_1(C),u1_struct_0(A))
& m1_subset_1(k2_mcart_1(C),u1_struct_0(B)) ) ) ) ) ).
fof(t32_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
=> ( ( A = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)),k1_rcomp_1(np__0,np__1))
& B = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(k6_real_1(np__1,np__2),np__1),k1_rcomp_1(np__0,np__1)) )
=> k2_xboole_0(k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),A)),k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),B))) = k2_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr)) ) ) ) ).
fof(t33_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
=> ( ( A = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)),k1_rcomp_1(np__0,np__1))
& B = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(k6_real_1(np__1,np__2),np__1),k1_rcomp_1(np__0,np__1)) )
=> k3_xboole_0(k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),A)),k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),B))) = k2_zfmisc_1(k1_tarski(k6_real_1(np__1,np__2)),k1_rcomp_1(np__0,np__1)) ) ) ) ).
fof(t34_borsuk_6,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_xboole_0(k1_xboole_0)
& v6_compts_1(k1_xboole_0,A)
& m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(t35_borsuk_6,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(B,C)
=> ( v1_xboole_0(k1_rcomp_1(B,C))
& v6_compts_1(k1_rcomp_1(B,C),A)
& m1_subset_1(k1_rcomp_1(B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(t36_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,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))
=> ( v6_compts_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k6_borsuk_1(k5_topmetr,k5_topmetr))
& m1_subset_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ) ) ) ) ) ).
fof(d2_borsuk_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k1_borsuk_6(A,B,C,D) = k7_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(np__0,np__1)),u1_struct_0(k4_topmetr(C,D)),k4_treal_1(A,B,k1_treal_1(np__0,np__1),k2_treal_1(np__0,np__1)),k3_treal_1(C,D,k1_treal_1(C,D),k2_treal_1(C,D))) ) ) ) ) ).
fof(t37_borsuk_6,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,A)
& ~ r1_xreal_0(D,C)
& ~ ( k1_funct_1(k1_borsuk_6(A,B,C,D),A) = C
& k1_funct_1(k1_borsuk_6(A,B,C,D),B) = D ) ) ) ) ) ) ).
fof(t38_borsuk_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(C,D)
=> ( r1_xreal_0(B,A)
| ( v1_funct_1(k1_borsuk_6(A,B,C,D))
& v1_funct_2(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& v5_pre_topc(k1_borsuk_6(A,B,C,D),k4_topmetr(A,B),k4_topmetr(C,D))
& m2_relset_1(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) ) ) ) ) ) ) ) ).
fof(t39_borsuk_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(C,D)
=> ( r1_xreal_0(B,A)
| ! [E] :
( v1_xreal_0(E)
=> ( ( r1_xreal_0(A,E)
& r1_xreal_0(E,B) )
=> k1_funct_1(k1_borsuk_6(A,B,C,D),E) = k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(D,C),k6_xcmplx_0(B,A)),k6_xcmplx_0(E,A)),C) ) ) ) ) ) ) ) ) ).
fof(t40_borsuk_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ~ ( v5_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
& v5_pre_topc(B,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
& ! [C] :
( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> m1_subset_1(k3_xcmplx_0(k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,C),k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,C)),u1_struct_0(k5_topmetr)) )
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ~ ( ! [D] :
( m1_subset_1(D,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,D) = E
& k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,D) = F )
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),C,D) = k3_xcmplx_0(E,F) ) ) ) )
& v5_pre_topc(C,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr) ) ) ) ) ) ).
fof(t41_borsuk_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ~ ( v5_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
& v5_pre_topc(B,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
& ! [C] :
( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> m1_subset_1(k2_xcmplx_0(k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,C),k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,C)),u1_struct_0(k5_topmetr)) )
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ~ ( ! [D] :
( m1_subset_1(D,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,D) = E
& k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,D) = F )
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),C,D) = k2_xcmplx_0(E,F) ) ) ) )
& v5_pre_topc(C,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr) ) ) ) ) ) ).
fof(t42_borsuk_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ~ ( v5_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
& v5_pre_topc(B,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
& ! [C] :
( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> m1_subset_1(k6_xcmplx_0(k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,C),k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,C)),u1_struct_0(k5_topmetr)) )
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
& m2_relset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
=> ~ ( ! [D] :
( m1_subset_1(D,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,D) = E
& k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,D) = F )
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),C,D) = k6_xcmplx_0(E,F) ) ) ) )
& v5_pre_topc(C,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr) ) ) ) ) ) ).
fof(t43_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ( v5_pre_topc(D,k5_topmetr,A)
=> ( v1_funct_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D))
& v1_funct_2(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),u1_struct_0(k5_topmetr),u1_struct_0(A))
& v5_pre_topc(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),k5_topmetr,A)
& m2_relset_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),u1_struct_0(k5_topmetr),u1_struct_0(A)) ) ) ) ) ) ) ).
fof(t44_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( ( k1_funct_1(D,np__0) = B
& k1_funct_1(D,np__1) = C )
=> ( k1_funct_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),np__0) = C
& k1_funct_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),np__1) = B ) ) ) ) ) ) ).
fof(t45_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ( ( v5_pre_topc(D,k5_topmetr,A)
& k1_funct_1(D,np__0) = B
& k1_funct_1(D,np__1) = C )
=> ( v5_pre_topc(k2_borsuk_2(A,B,C,D),k5_topmetr,A)
& k1_funct_1(k2_borsuk_2(A,B,C,D),np__0) = C
& k1_funct_1(k2_borsuk_2(A,B,C,D),np__1) = B ) ) ) ) ) ) ).
fof(t46_borsuk_6,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] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D) )
=> r1_borsuk_6(A,B,D) ) ) ) ) ) ).
fof(t47_borsuk_6,axiom,
$true ).
fof(t48_borsuk_6,axiom,
$true ).
fof(t49_borsuk_6,axiom,
$true ).
fof(t50_borsuk_6,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))
=> ( r1_borsuk_6(A,B,C)
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> D = k2_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) ) ).
fof(t51_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> D = k2_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) ).
fof(d3_borsuk_6,axiom,
$true ).
fof(d4_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,C,D)
=> ! [G] :
( m1_borsuk_2(G,A,B,D)
=> ( G = k1_borsuk_2(A,B,C,D,E,F)
<=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( r1_xreal_0(H,k6_real_1(np__1,np__2))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),G,H) = k1_funct_1(E,k3_xcmplx_0(np__2,H)) )
& ( r1_xreal_0(k6_real_1(np__1,np__2),H)
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),G,H) = k1_funct_1(F,k6_xcmplx_0(k3_xcmplx_0(np__2,H),np__1)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( m1_borsuk_2(E,A,C,B)
=> ( E = k2_borsuk_2(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k5_topmetr))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),E,F) = k1_funct_1(D,k6_xcmplx_0(np__1,F)) ) ) ) ) ) ) ) ).
fof(d6_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(E,k5_topmetr,k5_topmetr)
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> ( ( k1_funct_1(E,np__0) = np__0
& k1_funct_1(E,np__1) = np__1
& r1_borsuk_6(A,B,C) )
=> k2_borsuk_6(A,B,C,D,E) = k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),u1_struct_0(A),E,D) ) ) ) ) ) ) ).
fof(t52_borsuk_6,axiom,
$true ).
fof(t53_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(E,k5_topmetr,k5_topmetr)
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> ( ( k1_funct_1(E,np__0) = np__0
& k1_funct_1(E,np__1) = np__1
& r1_borsuk_6(A,B,C) )
=> r3_borsuk_2(A,B,C,k2_borsuk_6(A,B,C,D,E),D) ) ) ) ) ) ) ).
fof(t54_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(E,k5_topmetr,k5_topmetr)
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> ( ( k1_funct_1(E,np__0) = np__0
& k1_funct_1(E,np__1) = np__1 )
=> r4_borsuk_2(A,B,C,k2_borsuk_6(A,B,C,D,E),D) ) ) ) ) ) ) ).
fof(d7_borsuk_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> ( A = k3_borsuk_6
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ( ( r1_xreal_0(B,k6_real_1(np__1,np__2))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k3_xcmplx_0(np__2,B) )
& ( ~ r1_xreal_0(B,k6_real_1(np__1,np__2))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = np__1 ) ) ) ) ) ).
fof(t55_borsuk_6,axiom,
( k1_funct_1(k3_borsuk_6,np__0) = np__0
& k1_funct_1(k3_borsuk_6,np__1) = np__1 ) ).
fof(d8_borsuk_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> ( A = k4_borsuk_6
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ( ( r1_xreal_0(B,k6_real_1(np__1,np__2))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = np__0 )
& ( ~ r1_xreal_0(B,k6_real_1(np__1,np__2))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(k3_xcmplx_0(np__2,B),np__1) ) ) ) ) ) ).
fof(t56_borsuk_6,axiom,
( k1_funct_1(k4_borsuk_6,np__0) = np__0
& k1_funct_1(k4_borsuk_6,np__1) = np__1 ) ).
fof(d9_borsuk_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> ( A = k5_borsuk_6
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ( ( r1_xreal_0(B,k6_real_1(np__1,np__2))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k3_xcmplx_0(k6_real_1(np__1,np__2),B) )
& ( r1_xreal_0(B,k6_real_1(np__3,np__4))
=> ( r1_xreal_0(B,k6_real_1(np__1,np__2))
| k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(B,k6_real_1(np__1,np__4)) ) )
& ( ~ r1_xreal_0(B,k6_real_1(np__3,np__4))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(k3_xcmplx_0(np__2,B),np__1) ) ) ) ) ) ).
fof(t57_borsuk_6,axiom,
( k1_funct_1(k5_borsuk_6,np__0) = np__0
& k1_funct_1(k5_borsuk_6,np__1) = np__1 ) ).
fof(t58_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,C,C) )
=> ( r1_borsuk_6(A,B,C)
=> k2_borsuk_6(A,B,C,D,k3_borsuk_6) = k1_borsuk_2(A,B,C,C,D,E) ) ) ) ) ) ) ).
fof(t59_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,B,B) )
=> ( r1_borsuk_6(A,B,C)
=> k2_borsuk_6(A,B,C,D,k4_borsuk_6) = k1_borsuk_2(A,B,B,C,E,D) ) ) ) ) ) ) ).
fof(t60_borsuk_6,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] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,A,D,E)
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,D,E) )
=> k2_borsuk_6(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k5_borsuk_6) = k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(d10_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
=> ( A = k6_borsuk_6
<=> ! [B] :
( r2_hidden(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
& ? [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
& B = k8_borsuk_1(k5_topmetr,k5_topmetr,C,D)
& r1_xreal_0(D,k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,C))) ) ) ) ) ) ).
fof(d11_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
=> ( A = k7_borsuk_6
<=> ! [B] :
( r2_hidden(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
& ? [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
& B = k8_borsuk_1(k5_topmetr,k5_topmetr,C,D)
& r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,C)),D)
& r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,C),np__1),D) ) ) ) ) ) ).
fof(d12_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
=> ( A = k8_borsuk_6
<=> ! [B] :
( r2_hidden(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
& ? [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
& B = k8_borsuk_1(k5_topmetr,k5_topmetr,C,D)
& r1_xreal_0(D,k6_xcmplx_0(k3_xcmplx_0(np__2,C),np__1)) ) ) ) ) ) ).
fof(t64_borsuk_6,axiom,
k4_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k4_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k7_borsuk_6),k8_borsuk_6) = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,np__1),k1_rcomp_1(np__0,np__1)) ).
fof(t67_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> ( r2_hidden(A,k6_borsuk_6)
=> r1_xreal_0(k1_mcart_1(A),k6_real_1(np__1,np__2)) ) ) ).
fof(t68_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
=> ( r2_hidden(A,k8_borsuk_6)
=> r1_xreal_0(k6_real_1(np__1,np__2),k1_mcart_1(A)) ) ) ).
fof(t69_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> r2_hidden(k4_tarski(np__0,A),k6_borsuk_6) ) ).
fof(t70_borsuk_6,axiom,
! [A] :
( r2_hidden(k4_tarski(np__0,A),k7_borsuk_6)
=> A = np__1 ) ).
fof(t71_borsuk_6,axiom,
! [A] :
( r2_hidden(k4_tarski(A,np__1),k8_borsuk_6)
=> A = np__1 ) ).
fof(t72_borsuk_6,axiom,
r2_hidden(k4_tarski(np__0,np__1),k7_borsuk_6) ).
fof(t73_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> r2_hidden(k4_tarski(A,np__1),k7_borsuk_6) ) ).
fof(t74_borsuk_6,axiom,
( r2_hidden(k4_tarski(k6_real_1(np__1,np__2),np__0),k8_borsuk_6)
& r2_hidden(k4_tarski(np__1,np__1),k8_borsuk_6) ) ).
fof(t75_borsuk_6,axiom,
r2_hidden(k4_tarski(k6_real_1(np__1,np__2),np__0),k7_borsuk_6) ).
fof(t76_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> r2_hidden(k4_tarski(np__1,A),k8_borsuk_6) ) ).
fof(t77_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ( r1_xreal_0(k6_real_1(np__1,np__2),A)
=> r2_hidden(k4_tarski(A,np__0),k8_borsuk_6) ) ) ).
fof(t78_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ( r1_xreal_0(A,k6_real_1(np__1,np__2))
=> r2_hidden(k4_tarski(A,np__0),k6_borsuk_6) ) ) ).
fof(t79_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_topmetr))
=> ( ~ r1_xreal_0(k6_real_1(np__1,np__2),A)
=> ( ~ r2_hidden(k4_tarski(A,np__0),k7_borsuk_6)
& ~ r2_hidden(k4_tarski(A,np__0),k8_borsuk_6) ) ) ) ).
fof(t80_borsuk_6,axiom,
k5_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k8_borsuk_6) = k1_tarski(k4_tarski(k6_real_1(np__1,np__2),np__0)) ).
fof(t81_borsuk_6,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] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,A,D,E)
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,D,E) )
=> r3_borsuk_2(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H))) ) ) ) ) ) ) ) ) ) ).
fof(t82_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,A,D,E)
=> r4_borsuk_2(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H))) ) ) ) ) ) ) ) ) ).
fof(t83_borsuk_6,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] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r3_borsuk_2(A,B,C,E,F)
& r3_borsuk_2(A,C,D,G,H) )
=> r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t84_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ( ( r4_borsuk_2(A,B,C,E,F)
& r4_borsuk_2(A,C,D,G,H) )
=> r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t85_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ( ( r1_borsuk_6(A,B,C)
& r3_borsuk_2(A,B,C,D,E) )
=> r3_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D),k2_borsuk_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t86_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ( r4_borsuk_2(A,B,C,D,E)
=> r4_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D),k2_borsuk_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t87_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ( ( r3_borsuk_2(A,B,C,D,E)
& r3_borsuk_2(A,B,C,E,F) )
=> r3_borsuk_2(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t88_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,C,C) )
=> ( r1_borsuk_6(A,B,C)
=> r3_borsuk_2(A,B,C,k1_borsuk_2(A,B,C,C,D,E),D) ) ) ) ) ) ) ).
fof(t89_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,C,C) )
=> r4_borsuk_2(A,B,C,k1_borsuk_2(A,B,C,C,D,E),D) ) ) ) ) ) ).
fof(t90_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,B,B) )
=> ( r1_borsuk_6(A,B,C)
=> r3_borsuk_2(A,B,C,k1_borsuk_2(A,B,B,C,E,D),D) ) ) ) ) ) ) ).
fof(t91_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,B,B) )
=> r4_borsuk_2(A,B,C,k1_borsuk_2(A,B,B,C,E,D),D) ) ) ) ) ) ).
fof(t92_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,B,B) )
=> ( r1_borsuk_6(A,B,C)
=> r3_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,D,k2_borsuk_2(A,B,C,D)),E) ) ) ) ) ) ) ).
fof(t93_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,B,B) )
=> r4_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,D,k2_borsuk_2(A,B,C,D)),E) ) ) ) ) ) ).
fof(t94_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,C,C) )
=> ( r1_borsuk_6(A,B,C)
=> r3_borsuk_2(A,C,C,k1_borsuk_2(A,C,B,C,k2_borsuk_2(A,B,C,D),D),E) ) ) ) ) ) ) ).
fof(t95_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( ( v5_seqm_3(E)
& m1_borsuk_2(E,A,C,C) )
=> r4_borsuk_2(A,C,C,k1_borsuk_2(A,C,B,C,k2_borsuk_2(A,B,C,D),D),E) ) ) ) ) ) ).
fof(t96_borsuk_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v5_seqm_3(C)
& m1_borsuk_2(C,A,B,B) )
=> ! [D] :
( ( v5_seqm_3(D)
& m1_borsuk_2(D,A,B,B) )
=> r3_borsuk_2(A,B,B,C,D) ) ) ) ) ).
fof(d13_borsuk_6,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] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ( r3_borsuk_2(A,B,C,D,E)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
& m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) )
=> ( m1_borsuk_6(F,A,B,C,D,E)
<=> ( v5_pre_topc(F,k6_borsuk_1(k5_topmetr,k5_topmetr),A)
& ! [G] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ( k1_binop_1(F,G,np__0) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),D,G)
& k1_binop_1(F,G,np__1) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),E,G)
& ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( k1_binop_1(F,np__0,H) = B
& k1_binop_1(F,np__1,H) = C ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_borsuk_6,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s1_borsuk_6)
=> ( ~ ( p1_s1_borsuk_6(A)
& p2_s1_borsuk_6(A) )
& ~ ( p1_s1_borsuk_6(A)
& p3_s1_borsuk_6(A) )
& ~ ( p2_s1_borsuk_6(A)
& p3_s1_borsuk_6(A) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s1_borsuk_6)
=> ~ ( ~ p1_s1_borsuk_6(A)
& ~ p2_s1_borsuk_6(A)
& ~ p3_s1_borsuk_6(A) ) ) )
=> ? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& k1_relat_1(A) = f1_s1_borsuk_6
& ! [B] :
( m1_subset_1(B,f1_s1_borsuk_6)
=> ( ( p1_s1_borsuk_6(B)
=> k1_funct_1(A,B) = f2_s1_borsuk_6(B) )
& ( p2_s1_borsuk_6(B)
=> k1_funct_1(A,B) = f3_s1_borsuk_6(B) )
& ( p3_s1_borsuk_6(B)
=> k1_funct_1(A,B) = f4_s1_borsuk_6(B) ) ) ) ) ) ).
fof(dt_m1_borsuk_6,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_borsuk_2(D,A,B,C)
& m1_borsuk_2(E,A,B,C) )
=> ! [F] :
( m1_borsuk_6(F,A,B,C,D,E)
=> ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
& m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) ) ) ) ).
fof(existence_m1_borsuk_6,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_borsuk_2(D,A,B,C)
& m1_borsuk_2(E,A,B,C) )
=> ? [F] : m1_borsuk_6(F,A,B,C,D,E) ) ).
fof(symmetry_r1_borsuk_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_borsuk_6(A,B,C)
=> r1_borsuk_6(A,C,B) ) ) ).
fof(reflexivity_r1_borsuk_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r1_borsuk_6(A,B,B) ) ).
fof(redefinition_r1_borsuk_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_borsuk_6(A,B,C)
<=> r1_borsuk_2(A,B,C) ) ) ).
fof(dt_k1_borsuk_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( v1_funct_1(k1_borsuk_6(A,B,C,D))
& v1_funct_2(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) ) ) ).
fof(dt_k2_borsuk_6,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_borsuk_2(D,A,B,C)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(E,k5_topmetr,k5_topmetr)
& m1_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> m1_borsuk_2(k2_borsuk_6(A,B,C,D,E),A,B,C) ) ).
fof(dt_k3_borsuk_6,axiom,
( v1_funct_1(k3_borsuk_6)
& v1_funct_2(k3_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& m2_relset_1(k3_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) ) ).
fof(dt_k4_borsuk_6,axiom,
( v1_funct_1(k4_borsuk_6)
& v1_funct_2(k4_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& m2_relset_1(k4_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) ) ).
fof(dt_k5_borsuk_6,axiom,
( v1_funct_1(k5_borsuk_6)
& v1_funct_2(k5_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& m2_relset_1(k5_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) ) ).
fof(dt_k6_borsuk_6,axiom,
m1_subset_1(k6_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ).
fof(dt_k7_borsuk_6,axiom,
m1_subset_1(k7_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ).
fof(dt_k8_borsuk_6,axiom,
m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ).
fof(t14_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( A = a_0_0_borsuk_6
& B = a_0_1_borsuk_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k6_real_1(np__1,np__2)),A) = B ) ) ) ).
fof(t15_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( A = a_0_2_borsuk_6
& B = a_0_3_borsuk_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k6_real_1(np__1,np__2)),A) = B ) ) ) ).
fof(t16_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( A = a_0_4_borsuk_6
& B = a_0_5_borsuk_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k1_real_1(k6_real_1(np__1,np__2))),A) = B ) ) ) ).
fof(t17_borsuk_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( A = a_0_6_borsuk_6
& B = a_0_7_borsuk_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k1_real_1(k6_real_1(np__1,np__2))),A) = B ) ) ) ).
fof(t19_borsuk_6,axiom,
( v4_pre_topc(a_0_0_borsuk_6,k15_euclid(np__2))
& m1_subset_1(a_0_0_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t20_borsuk_6,axiom,
( v4_pre_topc(a_0_2_borsuk_6,k15_euclid(np__2))
& m1_subset_1(a_0_2_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t21_borsuk_6,axiom,
( v4_pre_topc(a_0_6_borsuk_6,k15_euclid(np__2))
& m1_subset_1(a_0_6_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t22_borsuk_6,axiom,
( v4_pre_topc(a_0_4_borsuk_6,k15_euclid(np__2))
& m1_subset_1(a_0_4_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t23_borsuk_6,axiom,
( v4_pre_topc(a_0_8_borsuk_6,k15_euclid(np__2))
& m1_subset_1(a_0_8_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t25_borsuk_6,axiom,
( v4_pre_topc(a_0_9_borsuk_6,k6_borsuk_1(k3_topmetr,k3_topmetr))
& m1_subset_1(a_0_9_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))) ) ).
fof(t26_borsuk_6,axiom,
( v4_pre_topc(a_0_10_borsuk_6,k6_borsuk_1(k3_topmetr,k3_topmetr))
& m1_subset_1(a_0_10_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))) ) ).
fof(t27_borsuk_6,axiom,
( v4_pre_topc(a_0_11_borsuk_6,k6_borsuk_1(k3_topmetr,k3_topmetr))
& m1_subset_1(a_0_11_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))) ) ).
fof(t28_borsuk_6,axiom,
( ~ v1_xboole_0(a_0_12_borsuk_6)
& v4_pre_topc(a_0_12_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr))
& m1_subset_1(a_0_12_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ) ).
fof(t29_borsuk_6,axiom,
( ~ v1_xboole_0(a_0_13_borsuk_6)
& v4_pre_topc(a_0_13_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr))
& m1_subset_1(a_0_13_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ) ).
fof(t30_borsuk_6,axiom,
( ~ v1_xboole_0(a_0_14_borsuk_6)
& v4_pre_topc(a_0_14_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr))
& m1_subset_1(a_0_14_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ) ).
fof(t61_borsuk_6,axiom,
k6_borsuk_6 = a_0_12_borsuk_6 ).
fof(t62_borsuk_6,axiom,
k7_borsuk_6 = a_0_13_borsuk_6 ).
fof(t63_borsuk_6,axiom,
k8_borsuk_6 = a_0_14_borsuk_6 ).
fof(t65_borsuk_6,axiom,
k5_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k7_borsuk_6) = a_0_15_borsuk_6 ).
fof(t66_borsuk_6,axiom,
k5_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k8_borsuk_6,k7_borsuk_6) = a_0_16_borsuk_6 ).
fof(fraenkel_a_0_0_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_0_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k22_euclid(B),k5_real_1(k4_real_1(np__2,k21_euclid(B)),np__1)) ) ) ).
fof(fraenkel_a_0_1_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_1_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k22_euclid(B),k21_euclid(B)) ) ) ).
fof(fraenkel_a_0_2_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_2_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k5_real_1(k4_real_1(np__2,k21_euclid(B)),np__1),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_3_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_3_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k21_euclid(B),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_4_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_4_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k5_real_1(np__1,k4_real_1(np__2,k21_euclid(B))),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_5_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_5_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_6_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_6_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k22_euclid(B),k5_real_1(np__1,k4_real_1(np__2,k21_euclid(B)))) ) ) ).
fof(fraenkel_a_0_7_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_7_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ).
fof(fraenkel_a_0_8_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_8_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k5_real_1(np__1,k4_real_1(np__2,k21_euclid(B))),k22_euclid(B))
& r1_xreal_0(k5_real_1(k4_real_1(np__2,k21_euclid(B)),np__1),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_9_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_9_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))
& A = B
& r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B)))) ) ) ).
fof(fraenkel_a_0_10_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_10_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))
& A = B
& r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1)) ) ) ).
fof(fraenkel_a_0_11_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_11_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))
& A = B
& r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B))),k2_mcart_1(B))
& r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1),k2_mcart_1(B)) ) ) ).
fof(fraenkel_a_0_12_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_12_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
& A = B
& r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B)))) ) ) ).
fof(fraenkel_a_0_13_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_13_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
& A = B
& r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B))),k2_mcart_1(B))
& r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1),k2_mcart_1(B)) ) ) ).
fof(fraenkel_a_0_14_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_14_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
& A = B
& r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1)) ) ) ).
fof(fraenkel_a_0_15_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_15_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
& A = B
& k2_mcart_1(B) = k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B))) ) ) ).
fof(fraenkel_a_0_16_borsuk_6,axiom,
! [A] :
( r2_hidden(A,a_0_16_borsuk_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
& A = B
& k2_mcart_1(B) = k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1) ) ) ).
%------------------------------------------------------------------------------