SET007 Axioms: SET007+734.ax
%------------------------------------------------------------------------------
% File : SET007+734 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Ordering of Points on a Curve. Part IV
% 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 : jordan18 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 51 ( 0 unt; 0 def)
% Number of atoms : 287 ( 32 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 282 ( 46 ~; 2 |; 88 &)
% ( 1 <=>; 145 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 26 ( 25 usr; 0 prp; 1-6 aty)
% Number of functors : 32 ( 32 usr; 5 con; 0-4 aty)
% Number of variables : 138 ( 138 !; 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_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_xboole_0(k9_relat_1(k17_pscomp_1,k2_jordan1a(A))) ) ).
fof(fc2_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_xboole_0(k9_relat_1(k17_pscomp_1,k4_jordan1a(A))) ) ).
fof(fc3_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_xboole_0(k9_relat_1(k16_pscomp_1,k5_jordan1a(A))) ) ).
fof(fc4_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_xboole_0(k9_relat_1(k16_pscomp_1,k3_jordan1a(A))) ) ).
fof(fc5_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k2_jordan1a(A))
& v4_pre_topc(k2_jordan1a(A),k15_euclid(np__2))
& v2_connsp_1(k2_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k2_jordan1a(A),np__2) ) ) ).
fof(fc6_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k4_jordan1a(A))
& v4_pre_topc(k4_jordan1a(A),k15_euclid(np__2))
& v2_connsp_1(k4_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k4_jordan1a(A),np__2) ) ) ).
fof(fc7_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k3_jordan1a(A))
& v4_pre_topc(k3_jordan1a(A),k15_euclid(np__2))
& v2_connsp_1(k3_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k3_jordan1a(A),np__2) ) ) ).
fof(fc8_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k5_jordan1a(A))
& v4_pre_topc(k5_jordan1a(A),k15_euclid(np__2))
& v2_connsp_1(k5_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k5_jordan1a(A),np__2) ) ) ).
fof(t1_jordan18,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k5_square_1(k6_xcmplx_0(A,B)) = k5_square_1(k6_xcmplx_0(B,A)) ) ) ).
fof(t2_jordan18,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_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_tops_2(C,A,B)
& v2_connsp_1(D,B) )
=> v2_connsp_1(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ).
fof(t3_jordan18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_tops_2(C,A,B)
& v6_compts_1(D,B) )
=> v6_compts_1(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ).
fof(t4_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1a(A))) ) ).
fof(t5_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k4_jordan1a(A))) ) ).
fof(t6_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k5_jordan1a(A))) ) ).
fof(t7_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k3_jordan1a(A))) ) ).
fof(t8_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1a(A))) = k22_euclid(A) ) ).
fof(t9_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k4_jordan1a(A))) = k22_euclid(A) ) ).
fof(t10_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k5_jordan1a(A))) = k21_euclid(A) ) ).
fof(t11_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k3_jordan1a(A))) = k21_euclid(A) ) ).
fof(t12_jordan18,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)))
=> ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
& r1_tarski(k2_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t13_jordan18,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)))
=> ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
& r1_tarski(k4_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t14_jordan18,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)))
=> ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
& r1_tarski(k3_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t15_jordan18,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)))
=> ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
& r1_tarski(k5_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t16_jordan18,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)
& D != C
& r2_hidden(C,k3_jordan6(A,B,C,D)) ) ) ) ) ) ).
fof(t17_jordan18,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)
& D != B
& r2_hidden(B,k4_jordan6(A,B,C,D)) ) ) ) ) ) ).
fof(t18_jordan18,axiom,
! [A] :
( ( v1_topreal2(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,B)
& r1_tarski(B,A)
& ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_topreal1(k15_euclid(np__2),C,D,E)
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,E) = A
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,E) = k2_struct_0(k15_euclid(np__2),C,D) ) ) ) ) ) ) ) ).
fof(t19_jordan18,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)
& D != B
& D != C
& E != B
& E != C
& D != E
& ! [F] :
( ( ~ v1_xboole_0(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_topreal1(k15_euclid(np__2),D,E,F)
& r1_tarski(F,A)
& r1_xboole_0(F,k2_struct_0(k15_euclid(np__2),B,C)) ) ) ) ) ) ) ) ) ).
fof(d1_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k1_jordan18(A,B) = k23_euclid(k21_euclid(A),k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k2_jordan1a(A))))) ) ) ).
fof(d2_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k2_jordan18(A,B) = k23_euclid(k21_euclid(A),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k4_jordan1a(A))))) ) ) ).
fof(t20_jordan18,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)))
=> ( k21_euclid(k1_jordan18(B,A)) = k21_euclid(B)
& k21_euclid(k2_jordan18(B,A)) = k21_euclid(B) ) ) ) ).
fof(t21_jordan18,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)))
=> ( k22_euclid(k1_jordan18(B,A)) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k2_jordan1a(B))))
& k22_euclid(k2_jordan18(B,A)) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k4_jordan1a(B)))) ) ) ) ).
fof(t22_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k1_jordan2c(np__2,B))
=> ( r2_hidden(k1_jordan18(A,B),B)
& r2_hidden(k1_jordan18(A,B),k2_jordan1a(A))
& r2_hidden(k2_jordan18(A,B),B)
& r2_hidden(k2_jordan18(A,B),k4_jordan1a(A)) ) ) ) ) ).
fof(t23_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k1_jordan2c(np__2,B))
=> ( ~ r1_xreal_0(k22_euclid(A),k22_euclid(k2_jordan18(A,B)))
& ~ r1_xreal_0(k22_euclid(k1_jordan18(A,B)),k22_euclid(A)) ) ) ) ) ).
fof(t24_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r2_hidden(A,k1_jordan2c(np__2,B))
& r1_xreal_0(k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k2_jordan1a(A)))),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k4_jordan1a(A))))) ) ) ) ).
fof(t25_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r2_hidden(A,k1_jordan2c(np__2,B))
& k2_jordan18(A,B) = k1_jordan18(A,B) ) ) ) ).
fof(t26_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> v2_sppol_1(k3_topreal1(np__2,k1_jordan18(A,B),k2_jordan18(A,B))) ) ) ).
fof(t27_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k1_jordan2c(np__2,B))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k1_jordan18(A,B),k2_jordan18(A,B)),B) = k2_struct_0(k15_euclid(np__2),k1_jordan18(A,B),k2_jordan18(A,B)) ) ) ) ).
fof(t28_jordan18,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r2_hidden(A,k1_jordan2c(np__2,C))
& r2_hidden(B,k1_jordan2c(np__2,C)) )
=> ( k21_euclid(A) = k21_euclid(B)
| r2_incproj(k1_jordan18(A,C),k2_jordan18(B,C),k1_jordan18(B,C),k2_jordan18(A,C)) ) ) ) ) ) ).
fof(d3_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ( r1_jordan18(A,B,C,D,E,F)
<=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( r1_topreal1(k15_euclid(A),C,D,G)
& r1_tarski(G,B)
& r1_xboole_0(G,k2_struct_0(k15_euclid(A),E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t29_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> r1_jordan18(A,B,C,C,D,E) ) ) ) ) ) ).
fof(t30_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ( r1_jordan18(A,B,C,D,E,F)
=> r1_jordan18(A,B,D,C,E,F) ) ) ) ) ) ) ) ).
fof(t31_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ( r1_jordan18(A,B,C,D,E,F)
=> r1_jordan18(A,B,C,D,F,E) ) ) ) ) ) ) ) ).
fof(t32_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> r1_jordan18(A,B,C,D,C,E) ) ) ) ) ) ).
fof(t33_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> r1_jordan18(A,B,C,D,E,D) ) ) ) ) ) ).
fof(t34_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> r1_jordan18(A,B,C,D,D,E) ) ) ) ) ) ).
fof(t35_jordan18,axiom,
! [A] :
( m1_subset_1(A,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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> r1_jordan18(A,B,C,D,E,C) ) ) ) ) ) ).
fof(t36_jordan18,axiom,
! [A] :
( ( v1_topreal2(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)))
=> ~ ( r2_hidden(D,A)
& r2_hidden(B,A)
& r2_hidden(C,A)
& B != C
& B != D
& C != D
& r1_jordan18(np__2,A,B,C,D,D) ) ) ) ) ) ).
fof(t37_jordan18,axiom,
! [A] :
( ( v1_topreal2(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)))
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A)
& r1_jordan18(np__2,A,B,C,D,E) )
=> ( B = C
| r1_jordan18(np__2,A,D,E,B,C) ) ) ) ) ) ) ) ).
fof(t38_jordan18,axiom,
! [A] :
( ( v1_topreal2(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)))
=> ~ ( r2_hidden(B,A)
& r2_hidden(C,A)
& r2_hidden(D,A)
& B != C
& D != B
& D != C
& E != B
& E != C
& r1_jordan18(np__2,A,B,C,D,E)
& r1_jordan18(np__2,A,B,D,C,E) ) ) ) ) ) ) ).
fof(dt_k1_jordan18,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> m1_subset_1(k1_jordan18(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k2_jordan18,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> m1_subset_1(k2_jordan18(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
%------------------------------------------------------------------------------