SET007 Axioms: SET007+728.ax
%------------------------------------------------------------------------------
% File : SET007+728 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Properties of the Upper and Lower Sequence on the Cage
% 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 : jordan15 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 53 ( 0 unt; 0 def)
% Number of atoms : 797 ( 36 equ)
% Maximal formula atoms : 23 ( 15 avg)
% Number of connectives : 899 ( 155 ~; 0 |; 467 &)
% ( 0 <=>; 277 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 19 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 25 ( 24 usr; 0 prp; 1-3 aty)
% Number of functors : 30 ( 30 usr; 6 con; 0-4 aty)
% Number of variables : 268 ( 268 !; 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(t1_jordan15,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))))
=> ~ ( ~ r1_xboole_0(A,B)
& r1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A),k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B)) ) ) ) ).
fof(t2_jordan15,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] :
( v1_xreal_0(C)
=> ( ( r1_xboole_0(A,B)
& r1_tarski(A,k7_jordan6(C))
& r1_tarski(B,k7_jordan6(C)) )
=> r1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A),k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B)) ) ) ) ) ).
fof(t3_jordan15,axiom,
! [A] :
( ( v4_pre_topc(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( v1_jordan2c(A,np__2)
=> v2_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) ) ) ).
fof(t4_jordan15,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v1_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) ) ).
fof(t5_jordan15,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] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( v2_sppol_1(k3_topreal1(np__2,A,B))
& v2_sppol_1(k3_topreal1(np__2,C,D))
& k21_euclid(A) = k21_euclid(C)
& r1_xreal_0(k22_euclid(A),k22_euclid(C))
& r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(k22_euclid(D),k22_euclid(B)) )
=> r1_tarski(k3_topreal1(np__2,C,D),k3_topreal1(np__2,A,B)) ) ) ) ) ) ).
fof(t6_jordan15,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] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_sppol_1(k3_topreal1(np__2,A,B))
& v1_sppol_1(k3_topreal1(np__2,C,D))
& k22_euclid(A) = k22_euclid(C)
& r1_xreal_0(k21_euclid(A),k21_euclid(C))
& r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(D),k21_euclid(B)) )
=> r1_tarski(k3_topreal1(np__2,C,D),k3_topreal1(np__2,A,B)) ) ) ) ) ) ).
fof(t7_jordan15,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_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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,D)
& r1_xreal_0(D,k1_matrix_1(A)) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,F)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D))) ) ) ) ) ) ) ) ).
fof(t8_jordan15,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_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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,E)
& r1_xreal_0(E,F)
& r1_xreal_0(F,D)
& r1_xreal_0(D,k3_finseq_1(A)) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,E,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,F,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,B))) ) ) ) ) ) ) ) ).
fof(t9_jordan15,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_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_xreal_0(np__1,B)
& r1_xreal_0(B,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,C)
& r1_xreal_0(C,k1_matrix_1(A)) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),E)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan1a(A),C))) ) ) ) ) ) ) ).
fof(t10_jordan15,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)))) )
=> ( k3_finseq_1(A) = k1_matrix_1(A)
=> ! [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_xreal_0(np__1,B)
& r1_xreal_0(B,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,C)
& r1_xreal_0(C,k3_finseq_1(A)) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,k1_jordan1a(A)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,E,k1_jordan1a(A))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_jordan1a(A)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,k1_jordan1a(A)))) ) ) ) ) ) ) ) ).
fof(t11_jordan15,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)
=> ! [E] :
( m2_subset_1(E,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,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,D),k5_topreal1(np__2,k2_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),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,F)) ) ) ) ) ) ) ) ) ).
fof(t12_jordan15,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)
=> ! [E] :
( m2_subset_1(E,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,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,k1_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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,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,F)) ) ) ) ) ) ) ) ) ).
fof(t13_jordan15,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)
=> ! [E] :
( m2_subset_1(E,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,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,D),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,E),k5_topreal1(np__2,k1_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,G)
& r1_xreal_0(G,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,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),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,F))
& 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,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),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,G)) ) ) ) ) ) ) ) ) ) ).
fof(t14_jordan15,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),F,C)) ) ) ) ) ) ) ) ) ).
fof(t15_jordan15,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)),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),F,C)) ) ) ) ) ) ) ) ) ).
fof(t16_jordan15,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,G)
& r1_xreal_0(G,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),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),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),F,C))
& 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),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),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),G,C)) ) ) ) ) ) ) ) ) ) ).
fof(t17_jordan15,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)
=> ! [E] :
( m2_subset_1(E,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,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,D),k5_topreal1(np__2,k1_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),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,F)) ) ) ) ) ) ) ) ) ).
fof(t18_jordan15,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)
=> ! [E] :
( m2_subset_1(E,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,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)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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,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),C,F)) ) ) ) ) ) ) ) ) ).
fof(t19_jordan15,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)
=> ! [E] :
( m2_subset_1(E,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,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,D),k5_topreal1(np__2,k1_jordan1e(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)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,G)
& r1_xreal_0(G,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,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),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,F))
& 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,F),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,G)),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,G)) ) ) ) ) ) ) ) ) ) ).
fof(t20_jordan15,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),F,C)) ) ) ) ) ) ) ) ) ).
fof(t21_jordan15,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),F,C)),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),F,C)) ) ) ) ) ) ) ) ) ).
fof(t22_jordan15,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan8(B,A)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(D,F)
& r1_xreal_0(F,G)
& r1_xreal_0(G,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),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),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),F,C))
& 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),F,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),G,C)),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),G,C)) ) ) ) ) ) ) ) ) ) ).
fof(t23_jordan15,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,k1_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,k2_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(t24_jordan15,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,k1_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,k2_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(t25_jordan15,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),k8_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),k9_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(t26_jordan15,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),k8_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),k9_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(t27_jordan15,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)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,D)
& r1_xreal_0(D,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)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k8_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)),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)))))
& r2_subset_1(k3_topreal1(np__2,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),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))),D)),k9_jordan6(B)) ) ) ) ) ) ).
fof(t28_jordan15,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)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,D)
& r1_xreal_0(D,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)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k8_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)),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)))))
& r2_subset_1(k3_topreal1(np__2,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),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))),D)),k8_jordan6(B)) ) ) ) ) ) ).
fof(t29_jordan15,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(D,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& D = E ) ) ) ) ) ) ).
fof(t30_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),E,C))
& 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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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,C))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t31_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),E,C))
& 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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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,C))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t32_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t33_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t34_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),E,C),k8_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),D,C),k9_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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t35_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),E,C),k8_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),D,C),k9_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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t36_jordan15,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_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)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(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,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k9_jordan6(B)) ) ) ) ) ) ).
fof(t37_jordan15,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_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)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(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,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k8_jordan6(B)) ) ) ) ) ) ).
fof(t38_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),D,C))
& 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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),E,C))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t39_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),D,C))
& 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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),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),E,C))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t40_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t41_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k5_topreal1(np__2,k1_jordan1e(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C),k5_topreal1(np__2,k2_jordan1e(B,A)))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t42_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),D,C),k8_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),E,C),k9_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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t43_jordan15,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(D,np__1)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),E)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,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),D,C),k8_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),E,C),k9_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),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t44_jordan15,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_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,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(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,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k9_jordan6(B)) ) ) ) ) ) ).
fof(t45_jordan15,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,np__1))),D)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k8_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,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(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,k1_nat_1(A,np__1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1)))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))))),k8_jordan6(B)) ) ) ) ) ) ).
fof(t46_jordan15,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),D,F))
& 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),C,E))
& 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(t47_jordan15,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),D,F))
& 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),C,E))
& 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(t48_jordan15,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),D,F))
& 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),C,E))
& 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(t49_jordan15,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),D,F))
& 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),C,E))
& 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(t50_jordan15,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),k8_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),k9_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(t51_jordan15,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),k8_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),k9_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(t52_jordan15,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,k1_nat_1(A,np__1))),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,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,E),k8_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)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k9_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)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),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))),E)),k3_topreal1(np__2,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))),E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,E))),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t53_jordan15,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,k1_nat_1(A,np__1))),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,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,E),k8_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)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),k9_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)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),D),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))),E)),k3_topreal1(np__2,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))),E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),C,E))),k9_jordan6(B)) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------