SET007 Axioms: SET007+872.ax
%------------------------------------------------------------------------------
% File : SET007+872 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Some Points of a Simple Closed Curve. Part II
% 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 : jordan22 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 17 ( 0 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 55 ( 2 ~; 1 |; 31 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 11 usr; 0 prp; 1-3 aty)
% Number of functors : 21 ( 21 usr; 4 con; 0-3 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% 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_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k8_jordan6(A))
& v4_pre_topc(k8_jordan6(A),k15_euclid(np__2))
& v2_connsp_1(k8_jordan6(A),k15_euclid(np__2))
& v1_jordan2c(k8_jordan6(A),np__2)
& v6_compts_1(k8_jordan6(A),k15_euclid(np__2))
& v1_jordan21(k8_jordan6(A)) ) ) ).
fof(fc2_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k9_jordan6(A))
& v4_pre_topc(k9_jordan6(A),k15_euclid(np__2))
& v2_connsp_1(k9_jordan6(A),k15_euclid(np__2))
& v1_jordan2c(k9_jordan6(A),np__2)
& v6_compts_1(k9_jordan6(A),k15_euclid(np__2))
& v1_jordan21(k9_jordan6(A)) ) ) ).
fof(fc3_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v6_compts_1(k3_jordan19(A),k15_euclid(np__2)) ) ).
fof(fc4_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v6_compts_1(k4_jordan19(A),k15_euclid(np__2)) ) ).
fof(t1_jordan22,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)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),k1_jordan19(A),B),k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_jordan9(A,np__0)))) ) ) ).
fof(t2_jordan22,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)
=> r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),k2_jordan19(A),B),k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_jordan9(A,np__0)))) ) ) ).
fof(t3_jordan22,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)
=> ( v6_compts_1(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),k1_jordan19(A),B),k15_euclid(np__2))
& v2_connsp_1(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),k1_jordan19(A),B),k15_euclid(np__2)) ) ) ) ).
fof(t4_jordan22,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)
=> ( v6_compts_1(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),k2_jordan19(A),B),k15_euclid(np__2))
& v2_connsp_1(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),k2_jordan19(A),B),k15_euclid(np__2)) ) ) ) ).
fof(t5_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k30_pscomp_1(A),k3_jordan19(A)) ) ).
fof(t6_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k34_pscomp_1(A),k3_jordan19(A)) ) ).
fof(t7_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k30_pscomp_1(A),k4_jordan19(A)) ) ).
fof(t8_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k34_pscomp_1(A),k4_jordan19(A)) ) ).
fof(t9_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k1_jordan21(A),k3_jordan19(A)) ) ).
fof(t10_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k2_jordan21(A),k4_jordan19(A)) ) ).
fof(t11_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k3_jordan19(A),A) ) ).
fof(t12_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k4_jordan19(A),A) ) ).
fof(t13_jordan22,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r2_hidden(k2_jordan21(A),k9_jordan6(A))
& r2_hidden(k1_jordan21(A),k8_jordan6(A)) )
| ( r2_hidden(k1_jordan21(A),k9_jordan6(A))
& r2_hidden(k2_jordan21(A),k8_jordan6(A)) ) ) ) ).
%------------------------------------------------------------------------------