SET007 Axioms: SET007+726.ax
%------------------------------------------------------------------------------
% File : SET007+726 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Properties of the Internal Approximation of Jordan's Curve
% 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 : jordan14 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 41 ( 0 unt; 0 def)
% Number of atoms : 321 ( 11 equ)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 311 ( 31 ~; 2 |; 144 &)
% ( 1 <=>; 133 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 35 ( 34 usr; 0 prp; 1-3 aty)
% Number of functors : 42 ( 42 usr; 4 con; 0-4 aty)
% Number of variables : 108 ( 108 !; 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_jordan14,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( v3_pre_topc(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2))
& v2_connsp_1(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2))
& v2_topreal4(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2)) ) ) ).
fof(fc2_jordan14,axiom,
! [A,B] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( v4_pre_topc(k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_jordan13(A,B))),k15_euclid(np__2))
& v6_compts_1(k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_jordan13(A,B))),k15_euclid(np__2)) ) ) ).
fof(t1_jordan14,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k1_jordan2c(np__2,k5_topreal1(np__2,A)) = k3_goboard9(A)
| k1_jordan2c(np__2,k5_topreal1(np__2,A)) = k2_goboard9(A) ) ) ).
fof(t2_jordan14,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k2_jordan2c(np__2,k5_topreal1(np__2,A)) = k3_goboard9(A)
| k2_jordan2c(np__2,k5_topreal1(np__2,A)) = k2_goboard9(A) ) ) ).
fof(t3_jordan14,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
=> v4_pre_topc(k4_gobrd13(B,A,C),k15_euclid(np__2)) ) ) ) ) ).
fof(t4_jordan14,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k1_matrix_1(A)) )
=> ( r2_hidden(B,k1_tops_1(k15_euclid(np__2),k3_goboard5(A,C,D)))
<=> ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)))
& ~ r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1),D)),k21_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)))
& ~ r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,k1_nat_1(D,np__1))),k22_euclid(B)) ) ) ) ) ) ) ) ).
fof(t5_jordan14,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> v2_connsp_1(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2)) ) ).
fof(d1_jordan14,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)
=> k1_jordan14(A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k3_jordan1h(A,B),k3_jordan11(A,B)) ) ) ).
fof(t6_jordan14,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_jordan1h(A,B)
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,B),np__1) = k1_jordan14(A,B) ) ) ) ).
fof(t7_jordan14,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_jordan1h(A,B)
=> r2_hidden(k1_jordan14(A,B),k1_jordan2c(np__2,A)) ) ) ) ).
fof(t8_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_jordan1h(A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan13(A,B))) )
=> ( r1_xboole_0(k3_gobrd13(k1_jordan13(A,B),k1_jordan8(A,B),C),A)
& ~ r1_xboole_0(k4_gobrd13(k1_jordan13(A,B),k1_jordan8(A,B),C),A) ) ) ) ) ) ).
fof(t9_jordan14,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_jordan1h(A,B)
=> r1_subset_1(A,k5_topreal1(np__2,k1_jordan13(A,B))) ) ) ) ).
fof(t10_jordan14,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_jordan1h(A,B)
& r2_subset_1(A,k2_goboard9(k1_jordan13(A,B))) ) ) ) ).
fof(t11_jordan14,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_jordan1h(A,B)
=> r1_subset_1(A,k3_goboard9(k1_jordan13(A,B))) ) ) ) ).
fof(t12_jordan14,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_jordan1h(A,B)
=> r1_tarski(A,k2_goboard9(k1_jordan13(A,B))) ) ) ) ).
fof(t13_jordan14,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_jordan1h(A,B)
=> r1_tarski(A,k2_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) ).
fof(t14_jordan14,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_jordan1h(A,B)
=> r1_tarski(k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B))),k1_jordan2c(np__2,A)) ) ) ) ).
fof(t15_jordan14,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_jordan1h(A,B)
=> r1_tarski(k2_jordan2c(np__2,A),k2_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) ).
fof(t16_jordan14,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_jordan1h(A,B)
=> r1_tarski(k3_goboard9(k1_jordan13(A,B)),k1_jordan2c(np__2,A)) ) ) ) ).
fof(t17_jordan14,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_jordan1h(A,B)
=> r1_tarski(k2_jordan2c(np__2,A),k2_goboard9(k1_jordan13(A,B))) ) ) ) ).
fof(t18_jordan14,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_jordan1h(A,B)
=> r1_xboole_0(k2_jordan2c(np__2,A),k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) ).
fof(t19_jordan14,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_jordan1h(A,B)
=> r1_xboole_0(k2_jordan2c(np__2,A),k3_goboard9(k1_jordan13(A,B))) ) ) ) ).
fof(t20_jordan14,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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_jordan1h(A,C)
& r2_jordan2c(np__2,A,B) )
=> r1_xboole_0(B,k5_topreal1(np__2,k1_jordan13(A,C))) ) ) ) ) ).
fof(t21_jordan14,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_jordan1h(A,B)
=> r1_xboole_0(k2_jordan2c(np__2,A),k5_topreal1(np__2,k1_jordan13(A,B))) ) ) ) ).
fof(t22_jordan14,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_jordan1h(A,B)
=> r1_tarski(k5_topreal1(np__2,k1_jordan13(A,B)),k1_jordan2c(np__2,A)) ) ) ) ).
fof(t23_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_jordan1h(A,E)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
& r1_xreal_0(B,np__1) ) ) ) ) ) ) ).
fof(t24_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_jordan1h(A,E)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
& r1_xreal_0(k3_finseq_1(k1_jordan8(A,E)),B) ) ) ) ) ) ) ).
fof(t25_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_jordan1h(A,E)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
& r1_xreal_0(C,np__1) ) ) ) ) ) ) ).
fof(t26_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_jordan1h(A,E)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
& r1_xreal_0(k1_matrix_1(k1_jordan8(A,E)),C) ) ) ) ) ) ) ).
fof(t27_jordan14,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_jordan1h(A,B)
& r1_xreal_0(k1_matrix_1(k1_jordan8(A,B)),k3_jordan11(A,B)) ) ) ) ).
fof(t28_jordan14,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(B,C)
& r1_xreal_0(np__1,B) )
=> k3_jordan1h(A,C) = k3_real_1(k4_real_1(k1_card_4(np__2,k5_binarith(C,B)),k5_real_1(k3_jordan1h(A,B),np__2)),np__2) ) ) ) ) ).
fof(t29_jordan14,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(B,C)
& r1_jordan1h(A,B) )
=> r1_jordan1h(A,C) ) ) ) ) ).
fof(t30_jordan14,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
& v1_topreal1(B)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(D,k1_matrix_1(A)) )
=> v2_connsp_1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_goboard5(A,C,D),k5_topreal1(np__2,B)),k15_euclid(np__2)) ) ) ) ) ) ).
fof(t31_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_jordan1h(A,B)
& r1_xreal_0(k3_jordan11(A,B),C)
& r1_xreal_0(C,k1_nat_1(k2_nat_1(k1_card_4(np__2,k5_binarith(B,k1_jordan11(A))),k5_binarith(k2_jordan11(A),np__2)),np__2)) )
=> r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_goboard5(k1_jordan8(A,B),k5_binarith(k3_jordan1h(A,B),np__1),C),k5_topreal1(np__2,k1_jordan13(A,B))),k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) ) ).
fof(t32_jordan14,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(C,B)
& ~ r1_xreal_0(D,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(A,C)),k1_nat_1(D,np__1))
& r1_xreal_0(k3_finseq_1(k1_jordan8(A,B)),k3_real_1(k3_real_1(k4_real_1(k1_card_4(np__2,k5_binarith(B,C)),k5_real_1(D,np__2)),np__2),np__1)) ) ) ) ) ) ).
fof(t33_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_jordan1h(A,B)
& r1_xreal_0(B,C)
& r2_subset_1(k3_goboard9(k1_jordan13(A,B)),k3_goboard9(k1_jordan13(A,C))) ) ) ) ) ).
fof(t34_jordan14,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
& v1_topreal1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(D,k1_matrix_1(A)) )
=> r1_tarski(k1_tops_1(k15_euclid(np__2),k3_goboard5(A,C,D)),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,B))) ) ) ) ) ) ) ).
fof(t35_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_jordan1h(A,B)
& r1_xreal_0(B,C) )
=> r1_tarski(k5_topreal1(np__2,k1_jordan13(A,C)),k6_pre_topc(k15_euclid(np__2),k2_goboard9(k1_jordan13(A,B)))) ) ) ) ) ).
fof(t36_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_jordan1h(A,B)
& r1_xreal_0(B,C) )
=> r1_tarski(k3_goboard9(k1_jordan13(A,B)),k3_goboard9(k1_jordan13(A,C))) ) ) ) ) ).
fof(t37_jordan14,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_jordan1h(A,B)
& r1_xreal_0(B,C) )
=> r1_tarski(k2_goboard9(k1_jordan13(A,C)),k2_goboard9(k1_jordan13(A,B))) ) ) ) ) ).
fof(dt_k1_jordan14,axiom,
! [A,B] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k1_jordan14(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
%------------------------------------------------------------------------------