SET007 Axioms: SET007+535.ax
%------------------------------------------------------------------------------
% File : SET007+535 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Decomposition of Simple Closed Curves and the Order of Their Points
% 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 : jordan6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 104 ( 14 unt; 0 def)
% Number of atoms : 620 ( 101 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 562 ( 46 ~; 0 |; 185 &)
% ( 21 <=>; 310 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-5 aty)
% Number of functors : 55 ( 55 usr; 8 con; 0-5 aty)
% Number of variables : 310 ( 298 !; 12 ?)
% 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_jordan6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_topmetr))
=> ( v1_xreal_0(A)
& v1_xcmplx_0(A) ) ) ).
fof(t1_jordan6,axiom,
$true ).
fof(t2_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(A,k7_xcmplx_0(k2_xcmplx_0(A,B),np__2))
& r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(A,B),np__2),B) ) ) ) ) ).
fof(t3_jordan6,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(k3_pre_topc(A,B))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(D,A)
& C = k5_subset_1(u1_struct_0(A),D,B) )
=> v4_pre_topc(C,k3_pre_topc(A,B)) ) ) ) ) ) ).
fof(t4_jordan6,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] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,C)))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,C))) )
=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( E = D
& v5_pre_topc(D,A,k3_pre_topc(B,C)) )
=> v5_pre_topc(E,A,B) ) ) ) ) ) ) ) ).
fof(t11_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ( r1_topreal1(k15_euclid(A),C,D,B)
=> v2_connsp_1(B,k15_euclid(A)) ) ) ) ) ) ).
fof(t12_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> v4_pre_topc(A,k15_euclid(np__2)) ) ) ) ) ).
fof(t13_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(D,A)
& k21_euclid(D) = k6_real_1(k3_real_1(k21_euclid(B),k21_euclid(C)),np__2) ) ) ) ) ) ) ).
fof(t16_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> ( r2_hidden(k1_jordan6(A,B,C),A)
& r2_hidden(k2_jordan6(A,B,C),A) ) ) ) ) ) ).
fof(t17_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> ( B = k1_jordan6(A,B,C)
<=> k21_euclid(B) = k21_euclid(C) ) ) ) ) ) ).
fof(t18_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> ( B = k2_jordan6(A,B,C)
<=> k22_euclid(B) = k22_euclid(C) ) ) ) ) ) ).
fof(t19_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r1_jordan5c(A,B,C,D,E) )
=> r1_jordan5c(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t20_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> r1_tarski(k3_jordan6(A,B,C,D),A) ) ) ) ) ).
fof(t21_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> r1_tarski(k4_jordan6(A,B,C,D),A) ) ) ) ) ).
fof(t22_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> k3_jordan6(A,B,C,B) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) ).
fof(t23_jordan6,axiom,
$true ).
fof(t24_jordan6,axiom,
$true ).
fof(t25_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> k3_jordan6(A,B,C,C) = A ) ) ) ) ).
fof(t26_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> k4_jordan6(A,B,C,C) = k1_struct_0(k15_euclid(np__2),C) ) ) ) ) ).
fof(t27_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> k4_jordan6(A,B,C,B) = A ) ) ) ) ).
fof(t28_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r2_hidden(D,A) )
=> k4_jordan6(A,B,C,D) = k3_jordan6(A,C,B,D) ) ) ) ) ) ).
fof(d5_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> k5_jordan6(A,B,C,D,E) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan6(A,B,C,D),k3_jordan6(A,B,C,E)) ) ) ) ) ) ).
fof(t30_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> ( r1_jordan5c(A,B,C,D,E)
<=> r1_jordan5c(A,C,B,E,D) ) ) ) ) ) ) ) ).
fof(t31_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r2_hidden(D,A) )
=> k3_jordan6(A,B,C,D) = k4_jordan6(A,C,B,D) ) ) ) ) ) ).
fof(t32_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r2_hidden(D,A)
& r2_hidden(E,A) )
=> k5_jordan6(A,B,C,D,E) = k5_jordan6(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t33_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( v4_pre_topc(k6_jordan6(A),k15_euclid(np__2))
& v4_pre_topc(k7_jordan6(A),k15_euclid(np__2)) ) ) ).
fof(t34_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k6_jordan6(A))
<=> k21_euclid(B) = A ) ) ) ).
fof(t35_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k7_jordan6(A))
<=> k22_euclid(B) = A ) ) ) ).
fof(t36_jordan6,axiom,
$true ).
fof(t37_jordan6,axiom,
$true ).
fof(t38_jordan6,axiom,
$true ).
fof(t39_jordan6,axiom,
$true ).
fof(t40_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( v1_topreal2(A)
& ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),B)
& r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),C)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = A
& ~ r1_xreal_0(k22_euclid(k1_jordan5c(B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(C,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ) ) ).
fof(t41_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
=> ( A = k4_xboole_0(u1_struct_0(k22_borsuk_1),k2_tarski(np__0,np__1))
=> v3_pre_topc(A,k22_borsuk_1) ) ) ).
fof(t42_jordan6,axiom,
$true ).
fof(t43_jordan6,axiom,
$true ).
fof(t44_jordan6,axiom,
$true ).
fof(t45_jordan6,axiom,
$true ).
fof(t46_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_rcomp_1(B,C)
=> v3_pre_topc(A,k3_topmetr) ) ) ) ) ).
fof(t47_jordan6,axiom,
! [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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C))))
=> ( ( B = D
& r1_tarski(B,C) )
=> k3_pre_topc(A,B) = k3_pre_topc(k3_pre_topc(A,C),D) ) ) ) ) ) ).
fof(t48_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
=> ( A = k4_xboole_0(u1_struct_0(k22_borsuk_1),k2_tarski(np__0,np__1))
=> ( A != k1_xboole_0
& v2_connsp_1(A,k22_borsuk_1) ) ) ) ).
fof(t49_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,B)
& C = D ) ) ) ) ) ).
fof(t50_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),B))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ( ( r1_topreal1(k15_euclid(A),D,E,B)
& C = k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),D,E)) )
=> v3_pre_topc(C,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ) ).
fof(t51_jordan6,axiom,
$true ).
fof(t52_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),B))))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
=> ( ( r2_hidden(F,B)
& r2_hidden(G,B)
& r1_topreal1(k15_euclid(A),F,G,C)
& r1_topreal1(k15_euclid(A),F,G,D)
& k4_subset_1(u1_struct_0(k15_euclid(A)),C,D) = B
& k5_subset_1(u1_struct_0(k15_euclid(A)),C,D) = k2_struct_0(k15_euclid(A),F,G)
& E = k6_subset_1(u1_struct_0(k15_euclid(A)),C,k2_struct_0(k15_euclid(A),F,G)) )
=> v3_pre_topc(E,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ) ) ) ).
fof(t53_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),B))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ( ( r1_topreal1(k15_euclid(A),D,E,B)
& C = k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),D,E)) )
=> v2_connsp_1(C,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ) ).
fof(t54_jordan6,axiom,
! [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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C))))
=> ( ( r1_tarski(B,C)
& E = D
& v2_connsp_1(D,k3_pre_topc(A,B)) )
=> v2_connsp_1(E,k3_pre_topc(A,C)) ) ) ) ) ) ) ).
fof(t55_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(E,B)
& E != C
& E != D ) ) ) ) ) ) ) ).
fof(t56_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,B)
& k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),C,D)) = k1_xboole_0 ) ) ) ) ) ).
fof(t57_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),C))))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ( ( r1_topreal1(k15_euclid(A),E,F,B)
& r1_tarski(B,C)
& D = k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),E,F)) )
=> v2_connsp_1(D,k3_pre_topc(k15_euclid(A),C)) ) ) ) ) ) ) ) ).
fof(t58_jordan6,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] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D)))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k3_pre_topc(B,E)),u1_struct_0(C))
& m2_relset_1(G,u1_struct_0(k3_pre_topc(B,E)),u1_struct_0(C)) )
=> ~ ( r1_tarski(D,E)
& v5_pre_topc(F,A,k3_pre_topc(B,D))
& v5_pre_topc(G,k3_pre_topc(B,E),C)
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(H,u1_struct_0(A),u1_struct_0(C)) )
=> ~ ( H = k5_relat_1(F,G)
& v5_pre_topc(H,A,C) ) ) ) ) ) ) ) ) ) ) ).
fof(t59_jordan6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ( ( r1_topreal1(k15_euclid(A),D,E,B)
& r1_topreal1(k15_euclid(A),D,E,C)
& r1_tarski(B,C) )
=> B = C ) ) ) ) ) ) ).
fof(t60_jordan6,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(k3_pre_topc(k15_euclid(np__2),A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v1_topreal2(A)
& r2_hidden(C,A)
& r2_hidden(D,A)
& C != D
& B = k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k2_struct_0(k15_euclid(np__2),C,D))
& v2_connsp_1(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) ).
fof(t61_jordan6,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))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v1_topreal2(A)
& r1_topreal1(k15_euclid(np__2),F,G,B)
& r1_topreal1(k15_euclid(np__2),F,G,C)
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = A
& r1_topreal1(k15_euclid(np__2),F,G,D)
& r1_topreal1(k15_euclid(np__2),F,G,E)
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),D,E) = A
& ~ ( B = D
& C = E )
& ~ ( B = E
& C = D ) ) ) ) ) ) ) ) ) ).
fof(t62_jordan6,axiom,
$true ).
fof(t63_jordan6,axiom,
$true ).
fof(t64_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(k21_euclid(C),B)
& r1_xreal_0(B,k21_euclid(D))
& r1_topreal1(k15_euclid(np__2),C,D,A) )
=> ( ~ r1_xboole_0(A,k6_jordan6(B))
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(B)),k15_euclid(np__2)) ) ) ) ) ) ) ).
fof(d8_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( B = k8_jordan6(A)
<=> ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),B)
& ? [C] :
( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),C)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = A
& ~ r1_xreal_0(k22_euclid(k1_jordan5c(B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(C,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ) ) ) ).
fof(d9_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( B = k9_jordan6(A)
<=> ( r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),B) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),B) = A
& ~ r1_xreal_0(k22_euclid(k1_jordan5c(k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ) ) ).
fof(t65_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),k8_jordan6(A))
& r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),k8_jordan6(A))
& r1_topreal1(k15_euclid(np__2),k34_pscomp_1(A),k30_pscomp_1(A),k9_jordan6(A))
& r1_topreal1(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A),k9_jordan6(A))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k9_jordan6(A)) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k9_jordan6(A)) = A
& ~ r1_xreal_0(k22_euclid(k1_jordan5c(k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(k9_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ).
fof(t66_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> ( k9_jordan6(A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k8_jordan6(A)),k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A)))
& k8_jordan6(A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k9_jordan6(A)),k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))) ) ) ) ).
fof(t67_jordan6,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(k3_pre_topc(k15_euclid(np__2),A))))
=> ( ( v1_topreal2(A)
& k3_xboole_0(k8_jordan6(A),B) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
& k2_xboole_0(k8_jordan6(A),B) = A )
=> B = k9_jordan6(A) ) ) ) ).
fof(t68_jordan6,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(k3_pre_topc(k15_euclid(np__2),A))))
=> ( ( v1_topreal2(A)
& k3_xboole_0(B,k9_jordan6(A)) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(A),k34_pscomp_1(A))
& k2_xboole_0(B,k9_jordan6(A)) = A )
=> B = k8_jordan6(A) ) ) ) ).
fof(t69_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r1_jordan5c(A,B,C,D,B) )
=> D = B ) ) ) ) ) ).
fof(t70_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r1_jordan5c(A,B,C,C,D) )
=> D = C ) ) ) ) ) ).
fof(d10_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_jordan6(A,B,C)
<=> ~ ( ~ ( r2_hidden(B,k8_jordan6(A))
& r2_hidden(C,k9_jordan6(A))
& C != k30_pscomp_1(A) )
& ~ ( r2_hidden(B,k8_jordan6(A))
& r2_hidden(C,k8_jordan6(A))
& r1_jordan5c(k8_jordan6(A),k30_pscomp_1(A),k34_pscomp_1(A),B,C) )
& ~ ( r2_hidden(B,k9_jordan6(A))
& r2_hidden(C,k9_jordan6(A))
& C != k30_pscomp_1(A)
& r1_jordan5c(k9_jordan6(A),k34_pscomp_1(A),k30_pscomp_1(A),B,C) ) ) ) ) ) ) ).
fof(t71_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_topreal2(A)
& r2_hidden(B,A) )
=> r1_jordan6(A,B,B) ) ) ) ).
fof(t72_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_topreal2(A)
& r1_jordan6(A,B,C)
& r1_jordan6(A,C,B) )
=> B = C ) ) ) ) ).
fof(t73_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_topreal2(A)
& r1_jordan6(A,B,C)
& r1_jordan6(A,C,D) )
=> r1_jordan6(A,B,D) ) ) ) ) ) ).
fof(dt_k1_jordan6,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k1_jordan6(A,B,C),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k2_jordan6,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k2_jordan6(A,B,C),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k3_jordan6,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k3_jordan6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k4_jordan6,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k4_jordan6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k5_jordan6,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(E,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k5_jordan6(A,B,C,D,E),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k6_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> m1_subset_1(k6_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k7_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> m1_subset_1(k7_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k8_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k8_jordan6(A))
& m1_subset_1(k8_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ).
fof(dt_k9_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k9_jordan6(A))
& m1_subset_1(k9_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ).
fof(t5_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_0_jordan6(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t6_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_1_jordan6(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t7_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_2_jordan6(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t8_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_3_jordan6(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t9_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_4_jordan6(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t10_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_5_jordan6(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t14_jordan6,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))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),C,D,A)
& B = a_2_0_jordan6(C,D) )
=> ( ~ r1_xboole_0(A,B)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2)) ) ) ) ) ) ) ).
fof(t15_jordan6,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))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),C,D,A)
& B = a_2_1_jordan6(C,D) )
=> ( ~ r1_xboole_0(A,B)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2)) ) ) ) ) ) ) ).
fof(d1_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( D = k1_jordan6(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( E = a_2_0_jordan6(B,C)
=> D = k1_jordan5c(A,E,B,C) ) ) ) ) ) ) ) ).
fof(d2_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( D = k2_jordan6(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( E = a_2_1_jordan6(B,C)
=> D = k1_jordan5c(A,E,B,C) ) ) ) ) ) ) ) ).
fof(d3_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> k3_jordan6(A,B,C,D) = a_4_0_jordan6(A,B,C,D) ) ) ) ) ).
fof(d4_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> k4_jordan6(A,B,C,D) = a_4_1_jordan6(A,B,C,D) ) ) ) ) ).
fof(t29_jordan6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> k5_jordan6(A,B,C,D,E) = a_5_0_jordan6(A,B,C,D,E) ) ) ) ) ) ).
fof(d6_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> k6_jordan6(A) = a_1_2_jordan6(A) ) ).
fof(d7_jordan6,axiom,
! [A] :
( v1_xreal_0(A)
=> k7_jordan6(A) = a_1_5_jordan6(A) ) ).
fof(fraenkel_a_1_0_jordan6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_0_jordan6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(B,k21_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_1_jordan6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_1_jordan6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k21_euclid(C),B) ) ) ) ).
fof(fraenkel_a_1_2_jordan6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_2_jordan6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& k21_euclid(C) = B ) ) ) ).
fof(fraenkel_a_1_3_jordan6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_3_jordan6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(B,k22_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_4_jordan6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_4_jordan6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k22_euclid(C),B) ) ) ) ).
fof(fraenkel_a_1_5_jordan6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_5_jordan6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& k22_euclid(C) = B ) ) ) ).
fof(fraenkel_a_2_0_jordan6,axiom,
! [A,B,C] :
( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_2_0_jordan6(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& A = D
& k21_euclid(D) = k6_real_1(k3_real_1(k21_euclid(B),k21_euclid(C)),np__2) ) ) ) ).
fof(fraenkel_a_2_1_jordan6,axiom,
! [A,B,C] :
( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_2_1_jordan6(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& A = D
& k22_euclid(D) = k6_real_1(k3_real_1(k22_euclid(B),k22_euclid(C)),np__2) ) ) ) ).
fof(fraenkel_a_4_0_jordan6,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(E,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_4_0_jordan6(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
& A = F
& r1_jordan5c(B,C,D,F,E) ) ) ) ).
fof(fraenkel_a_4_1_jordan6,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(E,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_4_1_jordan6(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
& A = F
& r1_jordan5c(B,C,D,E,F) ) ) ) ).
fof(fraenkel_a_5_0_jordan6,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(F,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_5_0_jordan6(B,C,D,E,F))
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
& A = G
& r1_jordan5c(B,C,D,E,G)
& r1_jordan5c(B,C,D,G,F) ) ) ) ).
%------------------------------------------------------------------------------