SET007 Axioms: SET007+794.ax
%------------------------------------------------------------------------------
% File : SET007+794 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Upper and Lower Approximations of the 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 : jordan19 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 36 ( 0 unt; 0 def)
% Number of atoms : 385 ( 27 equ)
% Maximal formula atoms : 17 ( 10 avg)
% Number of connectives : 437 ( 88 ~; 1 |; 208 &)
% ( 3 <=>; 137 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 14 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 22 ( 21 usr; 0 prp; 1-3 aty)
% Number of functors : 46 ( 46 usr; 5 con; 0-4 aty)
% Number of variables : 132 ( 132 !; 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(d1_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,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)))) )
=> ( B = k1_jordan19(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C) = k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,C))) ) ) ) ) ).
fof(d2_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,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)))) )
=> ( B = k2_jordan19(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C) = k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,C))) ) ) ) ) ).
fof(d3_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k3_jordan19(A) = k8_kurato_2(k15_euclid(np__2),k1_jordan19(A)) ) ).
fof(d4_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k4_jordan19(A) = k8_kurato_2(k15_euclid(np__2),k2_jordan19(A)) ) ).
fof(t1_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> ( A = np__0
| r1_xreal_0(k6_real_1(k1_nat_1(B,np__1),B),k6_real_1(k1_nat_1(A,np__1),A)) ) ) ) ) ).
fof(t2_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(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(C,A)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A))) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k1_matrix_1(k1_jordan8(B,A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),D)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,C),k1_jordan1a(k1_jordan8(B,C)),k1_matrix_1(k1_jordan8(B,C))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),D))) ) ) ) ) ) ).
fof(t3_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(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(C,k3_finseq_1(k1_jordan8(B,A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k1_jordan9(B,A)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ) ) ).
fof(t4_jordan19,axiom,
! [A] :
( ( v2_connsp_1(A,k15_euclid(np__2))
& 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)
=> ( ~ r1_xreal_0(B,np__0)
=> ! [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(C,k3_finseq_1(k1_jordan8(A,B)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,B)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,D),k5_topreal1(np__2,k1_jordan9(A,B)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,k1_matrix_1(k1_jordan8(A,B))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,D)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) ) ) ) ).
fof(t5_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,np__1),k1_jordan1a(k1_jordan8(B,np__1)),k1_matrix_1(k1_jordan8(B,np__1))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) ) ) ) ) ).
fof(t6_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(B,A))
& k1_gobrd14(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))) != k6_real_1(k5_real_1(k19_pscomp_1(B),k21_pscomp_1(B)),k1_card_4(np__2,A))
& k1_gobrd14(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1))) != k6_real_1(k5_real_1(k20_pscomp_1(B),k18_pscomp_1(B)),k1_card_4(np__2,A)) ) ) ) ) ) ).
fof(t7_jordan19,axiom,
! [A] :
( ( v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(C,k9_metric_1(A,E,B))
& r2_hidden(D,k9_metric_1(A,E,B))
& r1_xreal_0(k3_xcmplx_0(np__2,B),k4_metric_1(A,C,D)) ) ) ) ) ) ) ).
fof(t8_jordan19,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
=> ! [E] :
( v1_xreal_0(E)
=> ( ~ r1_xreal_0(E,np__0)
=> ( r2_hidden(C,k6_pre_topc(k15_euclid(A),B))
<=> ! [F] :
( v1_xreal_0(F)
=> ~ ( ~ r1_xreal_0(F,np__0)
& ~ r1_xreal_0(E,F)
& r1_xboole_0(k9_metric_1(k14_euclid(A),D,F),B) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k19_pscomp_1(B)) ) ) ).
fof(t10_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k20_pscomp_1(B)) ) ) ).
fof(t11_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ).
fof(t12_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ).
fof(t13_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,D)
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t14_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,D)
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t15_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& ~ r1_xreal_0(A,np__0)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t16_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& ~ r1_xreal_0(A,np__0)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t17_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k2_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t18_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k5_topreal1(np__2,k2_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t19_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& ~ r1_xreal_0(A,np__0)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t20_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& ~ r1_xreal_0(A,np__0)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A))))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t21_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),D)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
& r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k8_jordan6(B)) ) ) ) ) ) ) ) ).
fof(t22_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),D)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
& r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k9_jordan6(B)) ) ) ) ) ) ) ) ).
fof(t23_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(D,np__1)
& r1_xreal_0(D,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
& r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k8_jordan6(B)) ) ) ) ) ) ) ) ).
fof(t24_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(D,np__1)
& r1_xreal_0(D,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k5_topreal1(np__2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))
& r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,F))),k9_jordan6(B)) ) ) ) ) ) ) ) ).
fof(t25_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),C)
& ~ r1_xreal_0(D,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
& r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F))),k9_jordan6(B)) ) ) ) ) ) ) ) ).
fof(t26_jordan19,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),C)
& ~ r1_xreal_0(D,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
& r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,F))),k8_jordan6(B)) ) ) ) ) ) ) ) ).
fof(t27_jordan19,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)))
=> ~ ( ~ r1_xreal_0(k21_euclid(B),k18_pscomp_1(A))
& ~ r1_xreal_0(k20_pscomp_1(A),k21_euclid(B))
& r2_hidden(B,k3_jordan19(A))
& r2_hidden(B,k4_jordan19(A)) ) ) ) ).
fof(t28_jordan19,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)))
=> ~ ( k21_euclid(B) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)
& r2_hidden(B,k3_jordan19(A))
& r2_hidden(B,k4_jordan19(A)) ) ) ) ).
fof(dt_k1_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( v1_funct_1(k1_jordan19(A))
& v1_funct_2(k1_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(k1_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ).
fof(dt_k2_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( v1_funct_1(k2_jordan19(A))
& v1_funct_2(k2_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_relset_1(k2_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ).
fof(dt_k3_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> m1_subset_1(k3_jordan19(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k4_jordan19,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> m1_subset_1(k4_jordan19(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
%------------------------------------------------------------------------------