SET007 Axioms: SET007+790.ax
%------------------------------------------------------------------------------
% File : SET007+790 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Kuratowski Limit Operators
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 116 ( 3 unt; 0 def)
% Number of atoms : 964 ( 77 equ)
% Maximal formula atoms : 25 ( 8 avg)
% Number of connectives : 925 ( 77 ~; 4 |; 452 &)
% ( 24 <=>; 368 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 1 prp; 0-3 aty)
% Number of functors : 59 ( 59 usr; 8 con; 0-6 aty)
% Number of variables : 403 ( 384 !; 19 ?)
% 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_kurato_2,axiom,
! [A,B] :
( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( ~ v1_xboole_0(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v1_partfun1(B,k5_numbers,k1_zfmisc_1(A)) ) ) ) ).
fof(rc1_kurato_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v1_partfun1(B,k5_numbers,k1_zfmisc_1(A)) ) ) ).
fof(cc2_kurato_2,axiom,
! [A,B] :
( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v5_seqm_3(B) )
=> ( ~ v1_xboole_0(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v1_partfun1(B,k5_numbers,k1_zfmisc_1(A))
& v1_kurato_2(B,A)
& v2_kurato_2(B,A)
& v3_kurato_2(B,A) ) ) ) ).
fof(rc2_kurato_2,axiom,
! [A] :
? [B] :
( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v1_partfun1(B,k5_numbers,k1_zfmisc_1(A))
& v5_seqm_3(B)
& v1_kurato_2(B,A)
& v2_kurato_2(B,A)
& v3_kurato_2(B,A) ) ).
fof(fc1_kurato_2,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v4_pre_topc(k5_topreal1(np__2,A),k15_euclid(np__2))
& v1_jordan2c(k5_topreal1(np__2,A),np__2)
& v2_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2))
& v3_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2))
& v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ) ).
fof(fc2_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ( ~ v3_struct_0(k5_pcomps_1(A))
& v1_pre_topc(k5_pcomps_1(A))
& v2_pre_topc(k5_pcomps_1(A))
& v1_frechet(k5_pcomps_1(A))
& v3_compts_1(k5_pcomps_1(A)) ) ) ).
fof(fc3_kurato_2,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_frechet(k15_euclid(A)) ) ) ).
fof(fc4_kurato_2,axiom,
( v1_relat_1(k6_relat_1(k5_numbers))
& v1_funct_1(k6_relat_1(k5_numbers))
& v1_seq_1(k6_relat_1(k5_numbers))
& v1_relat_2(k6_relat_1(k5_numbers))
& v3_relat_2(k6_relat_1(k5_numbers))
& v4_relat_2(k6_relat_1(k5_numbers))
& v8_relat_2(k6_relat_1(k5_numbers)) ) ).
fof(cc3_kurato_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& v5_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_kurato_2(C,A,B)
=> ( v1_relat_1(C)
& v5_seqm_3(C) ) ) ) ).
fof(t1_kurato_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( r2_hidden(B,A)
=> ( r2_hidden(B,C)
| r2_hidden(B,k3_subset_1(A,C)) ) ) ) ).
fof(t2_kurato_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> r1_tarski(k4_funct_6(A),k1_funct_1(A,B)) ) ) ).
fof(t3_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( B = C
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_prob_1(A,B,D) = k1_prob_1(A,C,D) ) ) ) ) ).
fof(t4_kurato_2,axiom,
! [A,B,C,D] :
~ ( ~ r1_xboole_0(A,B)
& ~ r1_xboole_0(C,D)
& r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ).
fof(d1_kurato_2,axiom,
$true ).
fof(d2_kurato_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,A)
& m2_relset_1(B,k5_numbers,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,A)
& m2_relset_1(D,k5_numbers,A) )
=> ( D = k3_kurato_2(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,A,D,E) = k8_funct_2(k5_numbers,A,B,k1_nat_1(E,C)) ) ) ) ) ) ) ).
fof(d3_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( C = k4_kurato_2(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A))
& C = k1_kurato_2(A,D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,D,E) = k2_kurato_2(A,k3_kurato_2(k1_zfmisc_1(A),B,E)) ) ) ) ) ) ).
fof(d4_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( C = k5_kurato_2(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A))
& C = k2_kurato_2(A,D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,D,E) = k1_kurato_2(A,k3_kurato_2(k1_zfmisc_1(A),B,E)) ) ) ) ) ) ).
fof(t5_kurato_2,axiom,
$true ).
fof(t6_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( r2_hidden(C,k2_kurato_2(A,B))
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r2_hidden(C,k1_prob_1(A,B,D)) ) ) ) ).
fof(t7_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( r2_hidden(C,k4_kurato_2(A,B))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(C,k1_prob_1(A,B,k1_nat_1(D,E))) ) ) ) ) ).
fof(t8_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( r2_hidden(C,k5_kurato_2(A,B))
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r2_hidden(C,k1_prob_1(A,B,k1_nat_1(D,E))) ) ) ) ) ).
fof(t9_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> r1_tarski(k4_kurato_2(A,B),k5_kurato_2(A,B)) ) ).
fof(t10_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> r1_tarski(k2_kurato_2(A,B),k4_kurato_2(A,B)) ) ).
fof(t11_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> r1_tarski(k5_kurato_2(A,B),k1_kurato_2(A,B)) ) ).
fof(t12_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k4_kurato_2(A,B) = k3_subset_1(A,k5_kurato_2(A,k3_prob_1(A,B))) ) ).
fof(t13_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,D,E) = k5_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
=> k4_kurato_2(A,D) = k5_subset_1(A,k4_kurato_2(A,B),k4_kurato_2(A,C)) ) ) ) ) ).
fof(t14_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,D,E) = k4_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
=> k5_kurato_2(A,D) = k4_subset_1(A,k5_kurato_2(A,B),k5_kurato_2(A,C)) ) ) ) ) ).
fof(t15_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,D,E) = k4_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
=> r1_tarski(k4_subset_1(A,k4_kurato_2(A,B),k4_kurato_2(A,C)),k4_kurato_2(A,D)) ) ) ) ) ).
fof(t16_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,D,E) = k5_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
=> r1_tarski(k5_kurato_2(A,D),k5_subset_1(A,k5_kurato_2(A,B),k5_kurato_2(A,C))) ) ) ) ) ).
fof(t17_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_prob_1(A,B,D) = C )
=> k5_kurato_2(A,B) = C ) ) ) ).
fof(t18_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_prob_1(A,B,D) = C )
=> k4_kurato_2(A,B) = C ) ) ) ).
fof(t19_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,C,E) = k7_subset_1(A,D,k1_prob_1(A,B,E)) )
=> r1_tarski(k7_subset_1(A,D,k4_kurato_2(A,B)),k5_kurato_2(A,C)) ) ) ) ) ).
fof(t20_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_prob_1(A,C,E) = k7_subset_1(A,D,k1_prob_1(A,B,E)) )
=> r1_tarski(k7_subset_1(A,D,k5_kurato_2(A,B)),k5_kurato_2(A,C)) ) ) ) ) ).
fof(d5_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_kurato_2(B,A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_tarski(k1_prob_1(A,B,k1_nat_1(C,np__1)),k1_prob_1(A,B,C)) ) ) ) ).
fof(d6_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_kurato_2(B,A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_tarski(k1_prob_1(A,B,C),k1_prob_1(A,B,k1_nat_1(C,np__1))) ) ) ) ).
fof(t21_kurato_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_tarski(k1_funct_1(A,k1_nat_1(B,np__1)),k1_funct_1(A,B)) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> r1_tarski(k1_funct_1(A,C),k1_funct_1(A,B)) ) ) ) ) ) ).
fof(t22_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_kurato_2(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,C)
=> r1_tarski(k1_prob_1(A,B,C),k1_prob_1(A,B,D)) ) ) ) ) ) ).
fof(t23_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_kurato_2(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,C)
=> r1_tarski(k1_prob_1(A,B,D),k1_prob_1(A,B,C)) ) ) ) ) ) ).
fof(t24_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( v1_kurato_2(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& ~ r1_xreal_0(E,D)
& ~ r2_hidden(C,k1_prob_1(A,B,E)) ) )
| r2_hidden(C,k2_kurato_2(A,B)) ) ) ) ).
fof(t25_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_kurato_2(B,A)
=> k4_kurato_2(A,B) = k2_kurato_2(A,B) ) ) ).
fof(t26_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_kurato_2(B,A)
=> k5_kurato_2(A,B) = k1_kurato_2(A,B) ) ) ).
fof(d7_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v3_kurato_2(B,A)
<=> k5_kurato_2(A,B) = k4_kurato_2(A,B) ) ) ).
fof(t27_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v5_seqm_3(B)
=> m1_subset_1(k1_yellow_6(B),k1_zfmisc_1(A)) ) ) ).
fof(d8_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v5_seqm_3(B)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_prob_1(A,B,D) = C ) ) ) ) ).
fof(d9_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v3_kurato_2(B,A)
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( C = k6_kurato_2(A,B)
<=> ( C = k5_kurato_2(A,B)
& C = k4_kurato_2(A,B) ) ) ) ) ).
fof(t28_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v3_kurato_2(B,A)
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( r2_hidden(C,k6_kurato_2(A,B))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(C,k1_prob_1(A,B,k1_nat_1(D,E))) ) ) ) ) ).
fof(t29_kurato_2,axiom,
$true ).
fof(t30_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
=> ! [C] :
( v1_xreal_0(C)
=> ( v3_pre_topc(k9_metric_1(k14_euclid(A),B,C),k15_euclid(A))
& m1_subset_1(k9_metric_1(k14_euclid(A),B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ) ) ) ).
fof(t31_kurato_2,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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
=> ( ( B = D
& C = E )
=> k4_metric_1(k14_euclid(A),D,E) = k5_toprns_1(A,k20_euclid(A,B,C)) ) ) ) ) ) ) ).
fof(t32_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_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] :
( v1_xreal_0(E)
=> ~ ( B = D
& r2_hidden(C,k9_metric_1(k14_euclid(A),B,E))
& r1_xreal_0(E,k5_toprns_1(A,k20_euclid(A,C,D))) ) ) ) ) ) ) ).
fof(t33_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_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] :
( v1_xreal_0(E)
=> ( B = D
=> ( r1_xreal_0(E,k5_toprns_1(A,k20_euclid(A,C,D)))
| r2_hidden(C,k9_metric_1(k14_euclid(A),B,E)) ) ) ) ) ) ) ) ).
fof(t34_kurato_2,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( r2_hidden(B,k6_pre_topc(k15_euclid(A),C))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(k15_euclid(A)))
& m2_relset_1(D,k5_numbers,u1_struct_0(k15_euclid(A))) )
=> ~ ( r1_tarski(k1_frechet(k15_euclid(A),D),C)
& v3_toprns_1(D,A)
& k7_toprns_1(A,D) = B ) ) ) ) ) ) ).
fof(t35_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( v1_xreal_0(D)
=> ( B = C
=> ( r1_xreal_0(D,np__0)
| m1_connsp_2(k9_metric_1(k14_euclid(A),B,D),k15_euclid(A),C) ) ) ) ) ) ) ).
fof(t36_kurato_2,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(k14_euclid(A)))
=> ( C = D
=> ( r2_hidden(C,k6_pre_topc(k15_euclid(A),B))
<=> ! [E] :
( v1_xreal_0(E)
=> ~ ( ~ r1_xreal_0(E,np__0)
& r1_xboole_0(k9_metric_1(k14_euclid(A),D,E),B) ) ) ) ) ) ) ) ) ).
fof(t37_kurato_2,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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
=> ~ ( D = B
& B != C
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> r2_hidden(C,k9_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ).
fof(t38_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ~ v1_jordan2c(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,B)
& ~ r1_xreal_0(k4_metric_1(k14_euclid(A),D,E),C) ) ) ) ) ) ) ) ) ).
fof(t39_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
=> ~ ( ~ r1_xboole_0(k9_metric_1(k14_euclid(A),D,B),k9_metric_1(k14_euclid(A),E,C))
& r1_xreal_0(k2_xcmplx_0(B,C),k4_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ).
fof(t40_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k14_euclid(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k14_euclid(A)))
=> ~ ( ~ r1_xboole_0(k9_metric_1(k14_euclid(A),E,B),k9_metric_1(k14_euclid(A),G,D))
& ~ r1_xboole_0(k9_metric_1(k14_euclid(A),G,D),k9_metric_1(k14_euclid(A),F,C))
& r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(B,C),k3_xcmplx_0(np__2,D)),k4_metric_1(k14_euclid(A),E,F)) ) ) ) ) ) ) ) ) ).
fof(t41_kurato_2,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(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
=> ( m2_connsp_2(E,k6_borsuk_1(A,B),k7_borsuk_1(A,B,k1_struct_0(A,C),k1_struct_0(B,D)))
<=> m1_connsp_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)) ) ) ) ) ) ) ).
fof(t42_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C,B))
& v1_funct_2(k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C,B),k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C,B),k5_numbers,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t43_kurato_2,axiom,
( v1_funct_1(k6_partfun1(k5_numbers))
& v1_funct_2(k6_partfun1(k5_numbers),k5_numbers,k1_numbers)
& v1_seqm_3(k6_partfun1(k5_numbers))
& v7_seqm_3(k6_partfun1(k5_numbers))
& m2_relset_1(k6_partfun1(k5_numbers),k5_numbers,k1_numbers) ) ).
fof(d10_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ( m1_kurato_2(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& v1_seqm_3(D)
& v7_seqm_3(D)
& m2_relset_1(D,k5_numbers,k1_numbers)
& C = k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),D,B) ) ) ) ) ) ).
fof(t44_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_kurato_2(B,A,B) ) ) ).
fof(t45_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_kurato_2(C,A,B)
=> r1_tarski(k1_pscomp_1(k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C),k1_pscomp_1(k5_numbers,k1_zfmisc_1(u1_struct_0(A)),B)) ) ) ) ).
fof(t46_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_kurato_2(C,A,B)
=> ! [D] :
( m1_kurato_2(D,A,C)
=> m1_kurato_2(D,A,B) ) ) ) ) ).
fof(t47_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( m1_kurato_2(C,A,B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(A),B,E) = D ) )
=> C = B ) ) ) ) ) ).
fof(t48_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& v5_seqm_3(B)
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_kurato_2(C,A,B)
=> B = C ) ) ) ).
fof(t49_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_kurato_2(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& k7_kurato_2(u1_struct_0(A),C,D) = k7_kurato_2(u1_struct_0(A),B,E) ) ) ) ) ) ).
fof(d11_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k8_kurato_2(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
<=> ! [E] :
( m1_connsp_2(E,A,D)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(G,F)
& r1_xboole_0(k7_kurato_2(u1_struct_0(A),B,G),E) ) ) ) ) ) ) ) ) ) ) ).
fof(t50_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& m2_relset_1(B,k5_numbers,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(k14_euclid(A)))
=> ( C = D
=> ( r2_hidden(C,k8_kurato_2(k15_euclid(A),B))
<=> ! [E] :
( v1_xreal_0(E)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ? [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& ~ r1_xreal_0(G,F)
& r1_xboole_0(k7_kurato_2(u1_struct_0(k15_euclid(A)),B,G),k9_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t51_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> k6_pre_topc(A,k8_kurato_2(A,B)) = k8_kurato_2(A,B) ) ) ).
fof(t52_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> v4_pre_topc(k8_kurato_2(A,B),A) ) ) ).
fof(t53_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ( m1_kurato_2(B,A,C)
=> r1_tarski(k8_kurato_2(A,C),k8_kurato_2(A,B)) ) ) ) ) ).
fof(t54_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(A),B,D),k7_kurato_2(u1_struct_0(A),C,D)) )
=> r1_tarski(k8_kurato_2(A,B),k8_kurato_2(A,C)) ) ) ) ) ).
fof(t55_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(A),D,E) = k4_subset_1(u1_struct_0(A),k7_kurato_2(u1_struct_0(A),B,E),k7_kurato_2(u1_struct_0(A),C,E)) )
=> r1_tarski(k4_subset_1(u1_struct_0(A),k8_kurato_2(A,B),k8_kurato_2(A,C)),k8_kurato_2(A,D)) ) ) ) ) ) ).
fof(t56_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(A),D,E) = k5_subset_1(u1_struct_0(A),k7_kurato_2(u1_struct_0(A),B,E),k7_kurato_2(u1_struct_0(A),C,E)) )
=> r1_tarski(k8_kurato_2(A,D),k5_subset_1(u1_struct_0(A),k8_kurato_2(A,B),k8_kurato_2(A,C))) ) ) ) ) ) ).
fof(t57_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(A),C,D) = k6_pre_topc(A,k7_kurato_2(u1_struct_0(A),B,D)) )
=> k8_kurato_2(A,C) = k8_kurato_2(A,B) ) ) ) ) ).
fof(t58_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ( ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(k15_euclid(A)))
& m2_relset_1(D,k5_numbers,u1_struct_0(k15_euclid(A)))
& v3_toprns_1(D,A)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(k2_normsp_1(k15_euclid(A),D,E),k7_kurato_2(u1_struct_0(k15_euclid(A)),B,E)) )
& C = k7_toprns_1(A,D) )
=> r2_hidden(C,k8_kurato_2(k15_euclid(A),B)) ) ) ) ) ).
fof(t59_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(A),C,D),B) )
=> r1_tarski(k8_kurato_2(A,C),k6_pre_topc(A,B)) ) ) ) ) ).
fof(t60_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(A),B,D) = C )
=> k8_kurato_2(A,B) = k6_pre_topc(A,C) ) ) ) ) ).
fof(t61_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v4_pre_topc(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(A),B,D) = C )
=> k8_kurato_2(A,B) = C ) ) ) ) ).
fof(t62_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( v1_jordan2c(C,A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(A)),B,D),C) ) )
=> v1_jordan2c(k8_kurato_2(k15_euclid(A),B),A) ) ) ) ) ).
fof(t63_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,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))))
=> ( ( v1_jordan2c(B,np__2)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C),B) ) )
=> v6_compts_1(k8_kurato_2(k15_euclid(np__2),A),k15_euclid(np__2)) ) ) ) ).
fof(t64_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A)))))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))))) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),D,E) = k7_borsuk_1(k15_euclid(A),k15_euclid(A),k7_kurato_2(u1_struct_0(k15_euclid(A)),B,E),k7_kurato_2(u1_struct_0(k15_euclid(A)),C,E)) )
=> k7_borsuk_1(k15_euclid(A),k15_euclid(A),k8_kurato_2(k15_euclid(A),B),k8_kurato_2(k15_euclid(A),C)) = k8_kurato_2(k6_borsuk_1(k15_euclid(A),k15_euclid(A)),D) ) ) ) ) ) ).
fof(t65_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k4_kurato_2(u1_struct_0(k15_euclid(np__2)),A),k8_kurato_2(k15_euclid(np__2),A)) ) ).
fof(t66_kurato_2,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_tops_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan2c(np__2,k5_topreal1(np__2,k1_jordan9(A,B))))) = k5_topreal1(np__2,k1_jordan9(A,B)) ) ) ).
fof(d12_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k9_kurato_2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( m1_kurato_2(E,A,B)
& r2_hidden(D,k8_kurato_2(A,E)) ) ) ) ) ) ) ).
fof(t67_kurato_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(k15_euclid(A)))
& m2_relset_1(B,k5_numbers,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(k14_euclid(A)))
=> ( C = D
=> ( r1_frechet2(k15_euclid(A),B,C)
<=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(F,G)
& r2_hidden(k2_normsp_1(k15_euclid(A),B,G),k9_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t68_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> r1_tarski(k8_kurato_2(A,B),k9_kurato_2(A,B)) ) ) ).
fof(t69_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
& m1_kurato_2(C,k15_euclid(np__2),A)
& ! [D] :
( m1_kurato_2(D,k15_euclid(np__2),B)
=> ~ ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,E),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),D,E)) ) ) ) ) ) ) ).
fof(t70_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
& m1_kurato_2(C,k15_euclid(np__2),B)
& ! [D] :
( m1_kurato_2(D,k15_euclid(np__2),A)
=> ~ ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),D,E),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,E)) ) ) ) ) ) ) ).
fof(t71_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C)) )
=> r1_tarski(k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B)) ) ) ) ).
fof(t72_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,D) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
=> r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B)),k9_kurato_2(k15_euclid(np__2),C)) ) ) ) ) ).
fof(t73_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,D) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
=> r1_tarski(k9_kurato_2(k15_euclid(np__2),C),k5_subset_1(u1_struct_0(k15_euclid(np__2)),k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B))) ) ) ) ) ).
fof(t74_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)))))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))) )
=> ~ ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),C,E) = k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,E),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,E)) )
& m1_kurato_2(D,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),C)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(E,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(F,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( m1_kurato_2(E,k15_euclid(np__2),A)
& m1_kurato_2(F,k15_euclid(np__2),B)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),D,G) = k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),E,G),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t75_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)))))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),C,D) = k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
=> r1_tarski(k9_kurato_2(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),C),k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B))) ) ) ) ) ).
fof(t76_kurato_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(A),B,D) = C )
=> k8_kurato_2(A,B) = k9_kurato_2(A,B) ) ) ) ) ).
fof(t77_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,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))))
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C) = B )
=> k9_kurato_2(k15_euclid(np__2),A) = k6_pre_topc(k15_euclid(np__2),B) ) ) ) ).
fof(t78_kurato_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C) = k6_pre_topc(k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C)) )
=> k9_kurato_2(k15_euclid(np__2),B) = k9_kurato_2(k15_euclid(np__2),A) ) ) ) ).
fof(s1_kurato_2,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(f1_s1_kurato_2))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(f1_s1_kurato_2))
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_prob_1(f1_s1_kurato_2,A,B) = f2_s1_kurato_2(B) ) ) ).
fof(s2_kurato_2,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& r1_xreal_0(A,B)
& p1_s2_kurato_2(k7_kurato_2(u1_struct_0(f1_s2_kurato_2),f2_s2_kurato_2,B)) ) )
=> ? [A] :
( m1_kurato_2(A,f1_s2_kurato_2,f2_s2_kurato_2)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> p1_s2_kurato_2(k7_kurato_2(u1_struct_0(f1_s2_kurato_2),A,B)) ) ) ) ).
fof(dt_m1_kurato_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_kurato_2(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(existence_m1_kurato_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] : m1_kurato_2(C,A,B) ) ).
fof(redefinition_v4_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v4_kurato_2(B,A)
<=> v5_seqm_3(B) ) ) ).
fof(dt_k1_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> m1_subset_1(k1_kurato_2(A,B),k1_zfmisc_1(A)) ) ).
fof(redefinition_k1_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k1_kurato_2(A,B) = k3_card_3(B) ) ).
fof(dt_k2_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> m1_subset_1(k2_kurato_2(A,B),k1_zfmisc_1(A)) ) ).
fof(redefinition_k2_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k2_kurato_2(A,B) = k4_funct_6(B) ) ).
fof(dt_k3_kurato_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,A)
& m1_relset_1(B,k5_numbers,A)
& m1_subset_1(C,k5_numbers) )
=> ( v1_funct_1(k3_kurato_2(A,B,C))
& v1_funct_2(k3_kurato_2(A,B,C),k5_numbers,A)
& m2_relset_1(k3_kurato_2(A,B,C),k5_numbers,A) ) ) ).
fof(dt_k4_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> m1_subset_1(k4_kurato_2(A,B),k1_zfmisc_1(A)) ) ).
fof(dt_k5_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> m1_subset_1(k5_kurato_2(A,B),k1_zfmisc_1(A)) ) ).
fof(dt_k6_kurato_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& v3_kurato_2(B,A)
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> m1_subset_1(k6_kurato_2(A,B),k1_zfmisc_1(A)) ) ).
fof(dt_k7_kurato_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k7_kurato_2(A,B,C),k1_zfmisc_1(A)) ) ).
fof(redefinition_k7_kurato_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
& m1_subset_1(C,k5_numbers) )
=> k7_kurato_2(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k8_kurato_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k8_kurato_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k9_kurato_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k9_kurato_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
%------------------------------------------------------------------------------