SET007 Axioms: SET007+780.ax
%------------------------------------------------------------------------------
% File : SET007+780 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Kuratowski Closure-Complement Problem
% 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 : kurato_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 105 ( 56 unt; 0 def)
% Number of atoms : 310 ( 53 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 269 ( 64 ~; 0 |; 136 &)
% ( 2 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-7 aty)
% Number of functors : 37 ( 37 usr; 10 con; 0-7 aty)
% Number of variables : 82 ( 79 !; 3 ?)
% 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_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_finset_1(k1_kurato_1(A,B)) ) ).
fof(fc2_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_finset_1(k2_kurato_1(A,B)) ) ).
fof(fc3_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_finset_1(k5_kurato_1(A,B)) ) ).
fof(fc4_kurato_1,axiom,
( ~ v3_pre_topc(k6_kurato_1,k3_topmetr)
& ~ v4_pre_topc(k6_kurato_1,k3_topmetr) ) ).
fof(fc5_kurato_1,axiom,
v1_borsuk_5(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) ).
fof(fc6_kurato_1,axiom,
v1_borsuk_5(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) ).
fof(fc7_kurato_1,axiom,
( v1_finset_1(k2_kurato_1(k3_topmetr,k6_kurato_1))
& v1_borsuk_5(k2_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) ) ).
fof(fc8_kurato_1,axiom,
( v1_finset_1(k2_kurato_1(k3_topmetr,k6_kurato_1))
& v1_borsuk_5(k2_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
& v1_setfam_1(k2_kurato_1(k3_topmetr,k6_kurato_1)) ) ).
fof(fc9_kurato_1,axiom,
( v1_borsuk_5(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
& v1_setfam_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) ) ).
fof(fc10_kurato_1,axiom,
( v1_borsuk_5(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
& v1_setfam_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) ) ).
fof(rc1_kurato_1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr))))
& v1_borsuk_5(A,k3_topmetr)
& v1_setfam_1(A) ) ).
fof(fc11_kurato_1,axiom,
( v1_borsuk_5(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
& v2_tops_2(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
& v1_setfam_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) ) ).
fof(fc12_kurato_1,axiom,
( v1_borsuk_5(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
& v1_tops_2(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr)
& v1_setfam_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) ) ).
fof(fc13_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_finset_1(k3_kurato_1(A,B)) ) ).
fof(fc14_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_finset_1(k4_kurato_1(A,B)) ) ).
fof(fc15_kurato_1,axiom,
( ~ v1_xboole_0(k6_kurato_1)
& ~ v3_pre_topc(k6_kurato_1,k3_topmetr)
& ~ v4_pre_topc(k6_kurato_1,k3_topmetr) ) ).
fof(fc16_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v1_xboole_0(k2_kurato_1(A,B))
& v1_finset_1(k2_kurato_1(A,B)) ) ) ).
fof(fc17_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k2_kurato_1(A,B))
& v1_kurato_1(k2_kurato_1(A,B),A) ) ) ).
fof(fc18_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k2_kurato_1(A,B))
& v1_prob_1(k2_kurato_1(A,B),u1_struct_0(A)) ) ) ).
fof(fc19_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v1_xboole_0(k5_kurato_1(A,B))
& v1_finset_1(k5_kurato_1(A,B)) ) ) ).
fof(fc20_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k5_kurato_1(A,B))
& v2_kurato_1(k5_kurato_1(A,B),A) ) ) ).
fof(fc21_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_finset_1(k5_kurato_1(A,B))
& v1_kurato_1(k5_kurato_1(A,B),A) ) ) ).
fof(rc2_kurato_1,axiom,
! [A] :
( ( ~ v3_struct_0(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_kurato_1(B,A)
& v2_kurato_1(B,A) ) ) ).
fof(rc3_kurato_1,axiom,
! [A] :
( ( ~ v3_struct_0(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_prob_1(B,u1_struct_0(A))
& v1_kurato_1(B,A) ) ) ).
fof(t1_kurato_1,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)))
=> k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))))) = k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))) ) ) ).
fof(d1_kurato_1,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)))
=> k1_kurato_1(A,B) = k5_enumset1(B,k6_pre_topc(A,B),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))))) ) ) ).
fof(d2_kurato_1,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)))
=> k2_kurato_1(A,B) = k2_xboole_0(k5_enumset1(B,k6_pre_topc(A,B),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))))),k5_enumset1(k3_subset_1(u1_struct_0(A),B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))))) ) ) ).
fof(t2_kurato_1,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)))
=> k2_kurato_1(A,B) = k2_xboole_0(k1_kurato_1(A,B),k1_kurato_1(A,k3_subset_1(u1_struct_0(A),B))) ) ) ).
fof(t3_kurato_1,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)))
=> ( r2_hidden(B,k2_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,B),k2_kurato_1(A,B))
& r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k2_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k2_kurato_1(A,B))
& r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k2_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k2_kurato_1(A,B))
& r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))))),k2_kurato_1(A,B)) ) ) ) ).
fof(t4_kurato_1,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)))
=> ( r2_hidden(k3_subset_1(u1_struct_0(A),B),k2_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),k2_kurato_1(A,B))
& r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))),k2_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))),k2_kurato_1(A,B))
& r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))),k2_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))))),k2_kurato_1(A,B))
& r2_hidden(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))),k2_kurato_1(A,B)) ) ) ) ).
fof(d3_kurato_1,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)))
=> k3_kurato_1(A,B) = k4_enumset1(k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B))))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) ) ) ).
fof(d4_kurato_1,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)))
=> k4_kurato_1(A,B) = k4_enumset1(k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))),k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))))))) ) ) ).
fof(t5_kurato_1,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)))
=> k2_kurato_1(A,B) = k2_xboole_0(k2_xboole_0(k2_tarski(B,k3_subset_1(u1_struct_0(A),B)),k3_kurato_1(A,B)),k4_kurato_1(A,B)) ) ) ).
fof(t6_kurato_1,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)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,k2_kurato_1(A,B))
=> ( r2_hidden(k3_subset_1(u1_struct_0(A),C),k2_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,C),k2_kurato_1(A,B)) ) ) ) ) ) ).
fof(t7_kurato_1,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)))
=> r1_xreal_0(k4_card_1(k2_kurato_1(A,B)),np__14) ) ) ).
fof(d5_kurato_1,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)))
=> k5_kurato_1(A,B) = k5_enumset1(B,k1_tops_1(A,B),k6_pre_topc(A,B),k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) ).
fof(t8_kurato_1,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)))
=> ( r2_hidden(B,k5_kurato_1(A,B))
& r2_hidden(k1_tops_1(A,B),k5_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,B),k5_kurato_1(A,B))
& r2_hidden(k1_tops_1(A,k6_pre_topc(A,B)),k5_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,k1_tops_1(A,B)),k5_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))),k5_kurato_1(A,B))
& r2_hidden(k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))),k5_kurato_1(A,B)) ) ) ) ).
fof(t9_kurato_1,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)))
=> k5_kurato_1(A,B) = k2_xboole_0(k2_xboole_0(k1_tarski(B),k1_enumset1(k1_tops_1(A,B),k1_tops_1(A,k6_pre_topc(A,B)),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))))),k1_enumset1(k6_pre_topc(A,B),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))))) ) ) ).
fof(t10_kurato_1,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)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,k5_kurato_1(A,B))
=> ( r2_hidden(k1_tops_1(A,C),k5_kurato_1(A,B))
& r2_hidden(k6_pre_topc(A,C),k5_kurato_1(A,B)) ) ) ) ) ) ).
fof(t11_kurato_1,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)))
=> r1_xreal_0(k4_card_1(k5_kurato_1(A,B)),np__7) ) ) ).
fof(d6_kurato_1,axiom,
k6_kurato_1 = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k1_seq_4(np__1),k2_borsuk_5(np__2,np__4)),k2_rcomp_1(np__4,np__5)),k4_limfunc1(np__5)) ).
fof(t12_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k6_kurato_1) = k4_subset_1(k1_numbers,k1_seq_4(np__1),k3_limfunc1(np__2)) ).
fof(t13_kurato_1,axiom,
k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1)) = k4_subset_1(k1_numbers,k12_prob_1(np__1),k2_rcomp_1(np__1,np__2)) ).
fof(t14_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1))) = k2_limfunc1(np__2) ).
fof(t15_kurato_1,axiom,
k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1)))) = k4_limfunc1(np__2) ).
fof(t16_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1))))) = k3_limfunc1(np__2) ).
fof(t17_kurato_1,axiom,
k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k6_kurato_1)))))) = k12_prob_1(np__2) ).
fof(t18_kurato_1,axiom,
k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1) = 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(t19_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)) = k4_subset_1(k1_numbers,k2_limfunc1(np__4),k1_seq_4(np__5)) ).
fof(t20_kurato_1,axiom,
k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1))) = k4_subset_1(k1_numbers,k2_rcomp_1(np__4,np__5),k4_limfunc1(np__5)) ).
fof(t21_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)))) = k3_limfunc1(np__4) ).
fof(t22_kurato_1,axiom,
k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1))))) = k12_prob_1(np__4) ).
fof(t23_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)))))) = k2_limfunc1(np__4) ).
fof(t24_kurato_1,axiom,
k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_pre_topc(k3_topmetr,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1))))))) = k4_limfunc1(np__4) ).
fof(t25_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_kurato_1) = k4_subset_1(k1_numbers,k2_rcomp_1(np__4,np__5),k4_limfunc1(np__5)) ).
fof(t26_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) = k3_limfunc1(np__4) ).
fof(t27_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) = k4_limfunc1(np__4) ).
fof(t28_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) = k4_limfunc1(np__2) ).
fof(t29_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) = k3_limfunc1(np__2) ).
fof(t30_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) ).
fof(t31_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k6_pre_topc(k3_topmetr,k6_kurato_1) ).
fof(t32_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) ).
fof(t33_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) ).
fof(t34_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_kurato_1) ).
fof(t35_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k6_pre_topc(k3_topmetr,k6_kurato_1) ).
fof(t36_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) ).
fof(t37_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) ).
fof(t38_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_kurato_1) ).
fof(t39_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) != k6_pre_topc(k3_topmetr,k6_kurato_1) ).
fof(t40_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k6_pre_topc(k3_topmetr,k6_kurato_1) ).
fof(t41_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_kurato_1) != k6_pre_topc(k3_topmetr,k6_kurato_1) ).
fof(t42_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k6_kurato_1) != k6_kurato_1 ).
fof(t43_kurato_1,axiom,
k6_kurato_1 != k1_tops_1(k3_topmetr,k6_kurato_1) ).
fof(t44_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) ).
fof(t45_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_kurato_1) ).
fof(t46_kurato_1,axiom,
k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_kurato_1) ).
fof(t47_kurato_1,axiom,
k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))) != k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)) ).
fof(t48_kurato_1,axiom,
r1_incproj(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))) ).
fof(t49_kurato_1,axiom,
r1_incproj(k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))) ).
fof(t50_kurato_1,axiom,
! [A] :
( r2_hidden(A,k1_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))))
=> ( ~ v1_xboole_0(A)
& v3_pre_topc(A,k3_topmetr)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) ) ).
fof(t51_kurato_1,axiom,
$true ).
fof(t52_kurato_1,axiom,
! [A] :
~ ( r2_hidden(A,k1_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))))
& A = k1_numbers ) ).
fof(t53_kurato_1,axiom,
! [A] :
~ ( r2_hidden(A,k1_enumset1(k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))))
& A = k1_numbers ) ).
fof(t54_kurato_1,axiom,
r1_xboole_0(k1_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)))),k1_enumset1(k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1))))) ).
fof(t55_kurato_1,axiom,
r1_borsuk_5(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))),k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))) ).
fof(t56_kurato_1,axiom,
r1_xboole_0(k4_enumset1(k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))),k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))),k1_tarski(k6_kurato_1)) ).
fof(t57_kurato_1,axiom,
r2_borsuk_5(k6_kurato_1,k1_tops_1(k3_topmetr,k6_kurato_1),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)),k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1))),k6_pre_topc(k3_topmetr,k6_kurato_1),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)),k6_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_pre_topc(k3_topmetr,k6_kurato_1)))) ).
fof(t58_kurato_1,axiom,
k4_card_1(k5_kurato_1(k3_topmetr,k6_kurato_1)) = np__7 ).
fof(t59_kurato_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( r1_tarski(B,A)
=> v1_setfam_1(B) ) ) ).
fof(t60_kurato_1,axiom,
! [A] :
( ( v1_borsuk_5(A,k3_topmetr)
& v1_setfam_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr)))) )
=> ! [B] :
( ( v1_borsuk_5(B,k3_topmetr)
& v1_setfam_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr)))) )
=> ( ( v1_tops_2(A,k3_topmetr)
& v2_tops_2(B,k3_topmetr) )
=> r1_xboole_0(A,B) ) ) ) ).
fof(t61_kurato_1,axiom,
r1_xboole_0(k3_kurato_1(k3_topmetr,k6_kurato_1),k4_kurato_1(k3_topmetr,k6_kurato_1)) ).
fof(t62_kurato_1,axiom,
k4_card_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) = np__6 ).
fof(t63_kurato_1,axiom,
k4_card_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) = np__6 ).
fof(t64_kurato_1,axiom,
r1_xboole_0(k2_tarski(k6_kurato_1,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)),k3_kurato_1(k3_topmetr,k6_kurato_1)) ).
fof(t65_kurato_1,axiom,
k6_kurato_1 != k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1) ).
fof(t66_kurato_1,axiom,
r1_xboole_0(k2_tarski(k6_kurato_1,k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1)),k4_kurato_1(k3_topmetr,k6_kurato_1)) ).
fof(t67_kurato_1,axiom,
k4_card_1(k2_kurato_1(k3_topmetr,k6_kurato_1)) = np__14 ).
fof(d7_kurato_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_kurato_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r2_hidden(k6_pre_topc(A,C),B) ) ) ) ) ) ).
fof(d8_kurato_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_kurato_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r2_hidden(k1_tops_1(A,C),B) ) ) ) ) ) ).
fof(dt_k1_kurato_1,axiom,
$true ).
fof(dt_k2_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k2_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k3_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k3_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k4_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k4_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k5_kurato_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k5_kurato_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k6_kurato_1,axiom,
m1_subset_1(k6_kurato_1,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ).
%------------------------------------------------------------------------------