SET007 Axioms: SET007+707.ax
%------------------------------------------------------------------------------
% File : SET007+707 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Upper and Lower Sequence on the Cage. Part II
% 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 : jordan1g [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 69 ( 8 unt; 0 def)
% Number of atoms : 542 ( 62 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 650 ( 177 ~; 12 |; 309 &)
% ( 0 <=>; 152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 5 con; 0-4 aty)
% Number of variables : 139 ( 138 !; 1 ?)
% 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(rc1_jordan1g,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_realset1(A)
& v5_seqm_3(A) ) ).
fof(fc1_jordan1g,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& ~ v1_realset1(A) )
=> ( ~ v1_xboole_0(k3_finseq_5(A))
& v1_relat_1(k3_finseq_5(A))
& v1_funct_1(k3_finseq_5(A))
& v1_finset_1(k3_finseq_5(A))
& v1_finseq_1(k3_finseq_5(A))
& ~ v1_realset1(k3_finseq_5(A)) ) ) ).
fof(fc2_jordan1g,axiom,
! [A,B] :
( ( 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))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k1_jordan1e(A,B))
& v1_relat_1(k1_jordan1e(A,B))
& v1_funct_1(k1_jordan1e(A,B))
& v2_funct_1(k1_jordan1e(A,B))
& v1_finset_1(k1_jordan1e(A,B))
& v1_finseq_1(k1_jordan1e(A,B))
& ~ v1_realset1(k1_jordan1e(A,B))
& v1_topreal1(k1_jordan1e(A,B))
& v2_topreal1(k1_jordan1e(A,B))
& v3_topreal1(k1_jordan1e(A,B))
& v4_topreal1(k1_jordan1e(A,B))
& v2_goboard5(k1_jordan1e(A,B)) ) ) ).
fof(fc3_jordan1g,axiom,
! [A,B] :
( ( 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))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k2_jordan1e(A,B))
& v1_relat_1(k2_jordan1e(A,B))
& v1_funct_1(k2_jordan1e(A,B))
& v2_funct_1(k2_jordan1e(A,B))
& v1_finset_1(k2_jordan1e(A,B))
& v1_finseq_1(k2_jordan1e(A,B))
& ~ v1_realset1(k2_jordan1e(A,B))
& v1_topreal1(k2_jordan1e(A,B))
& v2_topreal1(k2_jordan1e(A,B))
& v3_topreal1(k2_jordan1e(A,B))
& v4_topreal1(k2_jordan1e(A,B))
& v2_goboard5(k2_jordan1e(A,B)) ) ) ).
fof(t1_jordan1g,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_realset1(A) )
=> ~ ( ~ v1_xboole_0(A)
& ! [B] : A != k9_finseq_1(B) ) ) ).
fof(t2_jordan1g,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(A)) )
=> ! [D] :
( r1_goboard1(A,B,C)
=> r1_goboard1(A,k1_finseq_5(A,B,D),C) ) ) ) ) ).
fof(t3_jordan1g,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(A)) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( ( r2_hidden(D,k2_relat_1(B))
& r1_goboard1(A,B,C) )
=> r1_goboard1(A,k2_finseq_5(A,B,D),C) ) ) ) ) ) ).
fof(t4_jordan1g,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_goboard1(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(B,A),k1_jordan8(B,A)) ) ) ).
fof(t5_jordan1g,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_goboard1(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(B,A),k1_jordan8(B,A)) ) ) ).
fof(t6_jordan1g,axiom,
! [A] :
( ( v1_matrix_1(A)
& v4_goboard1(A)
& v5_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)
=> ( ( r2_hidden(k4_tarski(B,D),k2_matrix_1(A))
& r2_hidden(k4_tarski(C,E),k2_matrix_1(A))
& k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D)) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)) )
=> D = E ) ) ) ) ) ) ).
fof(t7_jordan1g,axiom,
! [A] :
( ( v1_matrix_1(A)
& v3_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)
=> ( ( r2_hidden(k4_tarski(B,D),k2_matrix_1(A))
& r2_hidden(k4_tarski(C,E),k2_matrix_1(A))
& k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)) )
=> B = C ) ) ) ) ) ) ).
fof(t8_jordan1g,axiom,
$true ).
fof(t9_jordan1g,axiom,
$true ).
fof(t10_jordan1g,axiom,
$true ).
fof(t11_jordan1g,axiom,
$true ).
fof(t12_jordan1g,axiom,
$true ).
fof(t13_jordan1g,axiom,
$true ).
fof(t14_jordan1g,axiom,
$true ).
fof(t15_jordan1g,axiom,
$true ).
fof(t16_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k32_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k32_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k33_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k33_pscomp_1(k5_topreal1(np__2,A)) ) )
& r1_xreal_0(k21_euclid(k33_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k32_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t17_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k32_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k32_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k33_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k33_pscomp_1(k5_topreal1(np__2,A)) ) )
& k32_pscomp_1(k5_topreal1(np__2,A)) = k33_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t18_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k37_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k37_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k36_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k36_pscomp_1(k5_topreal1(np__2,A)) ) )
& r1_xreal_0(k21_euclid(k36_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k37_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t19_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k37_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k37_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k36_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k36_pscomp_1(k5_topreal1(np__2,A)) ) )
& k37_pscomp_1(k5_topreal1(np__2,A)) = k36_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t20_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k30_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k30_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k31_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k31_pscomp_1(k5_topreal1(np__2,A)) ) )
& r1_xreal_0(k22_euclid(k31_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k30_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t21_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k30_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k30_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k31_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k31_pscomp_1(k5_topreal1(np__2,A)) ) )
& k30_pscomp_1(k5_topreal1(np__2,A)) = k31_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t22_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k35_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k35_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k34_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k34_pscomp_1(k5_topreal1(np__2,A)) ) )
& r1_xreal_0(k22_euclid(k34_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k35_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t23_jordan1g,axiom,
! [A] :
( ( ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k35_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k35_pscomp_1(k5_topreal1(np__2,A)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) != k34_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) != k34_pscomp_1(k5_topreal1(np__2,A)) ) )
& k35_pscomp_1(k5_topreal1(np__2,A)) = k34_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t24_jordan1g,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ( ( r2_hidden(C,k2_relat_1(B))
& r2_hidden(D,k2_relat_1(B))
& r1_xreal_0(k5_finseq_4(B,D),k5_finseq_4(B,C)) )
=> k2_finseq_5(A,k1_finseq_5(A,B,C),D) = k1_finseq_5(A,k2_finseq_5(A,B,D),C) ) ) ) ) ) ).
fof(t25_jordan1g,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)
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),k5_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))))) = k2_struct_0(k15_euclid(np__2),k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(t26_jordan1g,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)))) )
=> k2_jordan1e(B,A) = k1_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ).
fof(t27_jordan1g,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)))) )
=> k5_finseq_4(k1_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = np__1 ) ) ).
fof(t28_jordan1g,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)))) )
=> ~ r1_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t29_jordan1g,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)))) )
=> r1_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t30_jordan1g,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)))) )
=> ~ r1_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t31_jordan1g,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)))) )
=> r1_xreal_0(k5_finseq_4(k1_jordan1e(B,A),k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k1_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t32_jordan1g,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)))) )
=> k5_finseq_4(k1_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_finseq_1(k1_jordan1e(B,A)) ) ) ).
fof(t33_jordan1g,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)))) )
=> k5_finseq_4(k2_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = np__1 ) ) ).
fof(t34_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t35_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t36_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t37_jordan1g,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(k5_finseq_4(k2_jordan1e(B,A),k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),k5_finseq_4(k2_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))))) ) ) ).
fof(t38_jordan1g,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)))) )
=> k5_finseq_4(k2_jordan1e(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_finseq_1(k2_jordan1e(B,A)) ) ) ).
fof(t39_jordan1g,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)))) )
=> k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan1e(B,A),np__2)) = k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ).
fof(t40_jordan1g,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)))) )
=> k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k2_jordan1e(B,A),np__2)) = k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ).
fof(t41_jordan1g,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)))) )
=> k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)) ) ) ).
fof(t42_jordan1g,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)))) )
=> k3_real_1(k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))) = k3_real_1(k21_pscomp_1(B),k19_pscomp_1(B)) ) ) ).
fof(t43_jordan1g,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(A,B))) )
=> ( r1_xreal_0(B,np__0)
| k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2) ) ) ) ) ) ).
fof(t44_jordan1g,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)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B))) )
=> ( r1_xreal_0(B,np__0)
| k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,k1_jordan1a(k1_jordan8(A,B)))) = k6_real_1(k3_real_1(k21_pscomp_1(A),k19_pscomp_1(A)),np__2) ) ) ) ) ) ).
fof(t45_jordan1g,axiom,
! [A] :
( ( v4_topreal1(A)
& m2_finseq_1(A,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(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
& B != np__1
& C != np__1 ) ) ) ) ).
fof(t46_jordan1g,axiom,
! [A] :
( ( v4_topreal1(A)
& m2_finseq_1(A,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(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
& B != k3_finseq_1(A)
& C != k3_finseq_1(A) ) ) ) ) ).
fof(t47_jordan1g,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)
=> ( r1_tarski(k2_relat_1(k1_jordan1e(A,B)),k2_relat_1(k1_jordan9(A,B)))
& r1_tarski(k2_relat_1(k2_jordan1e(A,B)),k2_relat_1(k1_jordan9(A,B))) ) ) ) ).
fof(t48_jordan1g,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)))) )
=> r2_sprect_2(k1_jordan9(B,A),k1_jordan1e(B,A)) ) ) ).
fof(t49_jordan1g,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)))) )
=> r2_sprect_2(k1_jordan9(B,A),k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(B,A))) ) ) ).
fof(t50_jordan1g,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k2_relat_1(k1_jordan1e(B,A))) ) ) ) ) ).
fof(t51_jordan1g,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)
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))),k2_relat_1(k2_jordan1e(B,A))) ) ) ) ) ).
fof(t52_jordan1g,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ) ).
fof(t53_jordan1g,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)
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ) ).
fof(t54_jordan1g,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,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D)),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ) ) ).
fof(t55_jordan1g,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)
=> r2_hidden(k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k2_relat_1(k1_jordan1e(A,B))) ) ) ) ).
fof(t56_jordan1g,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)
=> r2_hidden(k2_jordan5c(k5_topreal1(np__2,k2_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k2_relat_1(k2_jordan1e(A,B))) ) ) ) ).
fof(t57_jordan1g,axiom,
! [A] :
( ( v4_topreal1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k2_relat_1(A))
=> k4_jordan3(A,B) = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_finseq_4(A,B)) ) ) ) ).
fof(t58_jordan1g,axiom,
! [A] :
( ( v4_topreal1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v4_pre_topc(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k2_relat_1(A))
=> ( r1_xboole_0(k5_topreal1(np__2,A),B)
| r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),B)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_finseq_4(A,k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))))),B) = k1_struct_0(k15_euclid(np__2),k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))) ) ) ) ) ).
fof(t59_jordan1g,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)
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k5_finseq_4(k1_jordan1e(A,B),k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),C)
& r1_xreal_0(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),C))) ) ) ) ) ) ).
fof(t60_jordan1g,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)
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k5_finseq_4(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(A,B)),k1_jordan5c(k5_topreal1(np__2,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(A,B))),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),C)
& r1_xreal_0(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k2_jordan1e(A,B)),C))) ) ) ) ) ) ).
fof(t61_jordan1g,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] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k2_relat_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),np__2,k5_finseq_4(k1_jordan1e(A,B),k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))))))
=> r1_xreal_0(k21_euclid(C),k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)) ) ) ) ) ) ).
fof(t62_jordan1g,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)
& r1_xreal_0(k22_euclid(k1_jordan5c(k5_topreal1(np__2,k1_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),k22_euclid(k2_jordan5c(k5_topreal1(np__2,k2_jordan1e(A,B)),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2)),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))))) ) ) ) ).
fof(t63_jordan1g,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)
=> k5_topreal1(np__2,k1_jordan1e(A,B)) = k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))) ) ) ) ).
fof(t64_jordan1g,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)
=> k5_topreal1(np__2,k2_jordan1e(A,B)) = k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))) ) ) ) ).
fof(t65_jordan1g,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,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),C,D)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------