SET007 Axioms: SET007+672.ax
%------------------------------------------------------------------------------
% File : SET007+672 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of Cells and Arcs
% 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 : jordan1b [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 46 ( 0 unt; 0 def)
% Number of atoms : 380 ( 19 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 416 ( 82 ~; 5 |; 203 &)
% ( 1 <=>; 125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 33 ( 32 usr; 0 prp; 1-3 aty)
% Number of functors : 47 ( 47 usr; 6 con; 0-4 aty)
% Number of variables : 114 ( 111 !; 3 ?)
% 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(cc1_jordan1b,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> ( ~ v1_xboole_0(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)
& v1_topreal2(A) ) ) ) ).
fof(rc1_jordan1b,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_connsp_3(B,A)
& ~ v1_xboole_0(B) ) ) ).
fof(t1_jordan1b,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_connsp_3(B,A) )
=> ( v2_connsp_1(B,A)
=> r3_connsp_1(A,B) ) ) ) ).
fof(t2_jordan1b,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_xboole_0(A)
<=> v1_xboole_0(k3_finseq_5(A)) ) ) ).
fof(t3_jordan1b,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [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(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B))
& v1_xboole_0(k1_jordan3(A,B,C,D)) ) ) ) ) ) ).
fof(t4_jordan1b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,k3_finseq_1(A))
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> k1_funct_1(k4_jordan3(A,B),np__1) = k1_funct_1(A,np__1) ) ) ) ).
fof(t5_jordan1b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> k1_funct_1(k3_jordan3(A,B),k3_finseq_1(k3_jordan3(A,B))) = k1_funct_1(A,k3_finseq_1(A)) ) ) ) ).
fof(t6_jordan1b,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k31_pscomp_1(A) != k34_pscomp_1(A) ) ).
fof(t7_jordan1b,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,B)
=> ( r1_xreal_0(np__1,A)
=> ( r1_xreal_0(k3_finseq_1(C),A)
| k8_finseq_1(B,k1_jordan3(B,C,A,k5_binarith(k3_finseq_1(C),np__1)),k13_binarith(B,k4_finseq_4(k5_numbers,B,C,k3_finseq_1(C)))) = k1_jordan3(B,C,A,k3_finseq_1(C)) ) ) ) ) ) ).
fof(t8_jordan1b,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)))
=> ( v2_sppol_1(k3_topreal1(np__2,A,B))
=> ( A = B
| v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t9_jordan1b,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)))
=> ( v1_sppol_1(k3_topreal1(np__2,A,B))
=> ( A = B
| v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t10_jordan1b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(B,A)
=> r1_sprect_2(B,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ).
fof(t11_jordan1b,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> r1_sprect_2(A,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(t12_jordan1b,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> r1_xreal_0(np__1,k1_jordan1a(A)) ) ).
fof(t13_jordan1b,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( r1_xreal_0(np__1,k3_finseq_1(A))
=> r1_xreal_0(k1_jordan1a(A),k3_finseq_1(A)) ) ) ).
fof(t14_jordan1b,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)))) )
=> r1_xreal_0(k1_jordan1a(A),k3_finseq_1(A)) ) ).
fof(t15_jordan1b,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ~ ( r1_xreal_0(np__2,k3_finseq_1(A))
& r1_xreal_0(k1_jordan1a(A),np__1) ) ) ).
fof(t16_jordan1b,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ~ ( r1_xreal_0(np__3,k3_finseq_1(A))
& r1_xreal_0(k3_finseq_1(A),k1_jordan1a(A)) ) ) ).
fof(t17_jordan1b,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)
=> k1_jordan1a(k1_jordan8(A,B)) = k1_nat_1(k1_card_4(np__2,k5_binarith(B,np__1)),np__2) ) ) ).
fof(t18_jordan1b,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)))) )
=> r1_tarski(A,k3_goboard5(k1_jordan8(A,np__0),np__2,np__2)) ) ).
fof(t19_jordan1b,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)))) )
=> ~ r1_tarski(k3_goboard5(k1_jordan8(A,np__0),np__2,np__2),k1_jordan2c(np__2,A)) ) ).
fof(t20_jordan1b,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)))) )
=> k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,np__1),k1_jordan1a(k1_jordan8(A,np__1)),np__1) = k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,np__1)))) ) ).
fof(t21_jordan1b,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)))) )
=> k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,np__1),k1_jordan1a(k1_jordan8(A,np__1)),k3_finseq_1(k1_jordan8(A,np__1))) = k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,np__1)))) ) ).
fof(t22_jordan1b,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] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(A))
& r2_hidden(E,k3_goboard5(A,k3_finseq_1(A),B))
& k21_euclid(E) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)) )
=> ( r1_xreal_0(k1_matrix_1(A),B)
| k3_finseq_1(A) = C ) ) ) ) ) ) ) ).
fof(t23_jordan1b,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] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k1_matrix_1(A),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(A))
& r2_hidden(F,k3_goboard5(A,B,C))
& k21_euclid(F) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E))
& B != D
& B != k5_binarith(D,np__1) ) ) ) ) ) ) ) ).
fof(t24_jordan1b,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] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(A))
& r2_hidden(E,k3_goboard5(A,B,k1_matrix_1(A)))
& k22_euclid(E) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)) )
=> ( r1_xreal_0(k3_finseq_1(A),B)
| k1_matrix_1(A) = D ) ) ) ) ) ) ) ).
fof(t25_jordan1b,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] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(A),B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(A))
& r2_hidden(F,k3_goboard5(A,B,C))
& k22_euclid(F) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E))
& C != E
& C != k5_binarith(E,np__1) ) ) ) ) ) ) ) ).
fof(t26_jordan1b,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(k18_pscomp_1(A),B)
& r1_xreal_0(B,k20_pscomp_1(A))
& r2_subset_1(k3_topreal1(np__2,k23_euclid(B,k21_pscomp_1(A)),k23_euclid(B,k19_pscomp_1(A))),k8_jordan6(A)) ) ) ) ).
fof(t27_jordan1b,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(k18_pscomp_1(A),B)
& r1_xreal_0(B,k20_pscomp_1(A))
& r2_subset_1(k3_topreal1(np__2,k23_euclid(B,k21_pscomp_1(A)),k23_euclid(B,k19_pscomp_1(A))),k9_jordan6(A)) ) ) ) ).
fof(t28_jordan1b,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& 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,k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(B)) ) ) ) ) ).
fof(t29_jordan1b,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)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& 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,k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(B)) ) ) ) ) ).
fof(t30_jordan1b,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)))) )
=> ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(B)) ) ) ).
fof(t31_jordan1b,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)))) )
=> ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(B)) ) ) ).
fof(t32_jordan1b,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(C,k3_finseq_1(k1_jordan8(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,k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ) ) ).
fof(t33_jordan1b,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(C,k3_finseq_1(k1_jordan8(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,k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ) ) ).
fof(t34_jordan1b,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)))) )
=> ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ).
fof(t35_jordan1b,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)))) )
=> ~ r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) ) ) ).
fof(t36_jordan1b,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)
=> ~ ( r1_xreal_0(B,k1_matrix_1(A))
& v1_jordan2c(k3_goboard5(A,np__0,B),np__2) ) ) ) ).
fof(t37_jordan1b,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)
=> ~ ( r1_xreal_0(B,k1_matrix_1(A))
& v1_jordan2c(k3_goboard5(A,k3_finseq_1(A),B),np__2) ) ) ) ).
fof(t38_jordan1b,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(B,k1_matrix_1(k1_jordan8(A,C)))
=> r1_tarski(k3_goboard5(k1_jordan8(A,C),np__0,B),k2_jordan2c(np__2,A)) ) ) ) ) ).
fof(t39_jordan1b,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
=> r1_tarski(k3_goboard5(k1_jordan8(A,C),k3_finseq_1(k1_jordan8(A,C)),B),k2_jordan2c(np__2,A)) ) ) ) ) ).
fof(t40_jordan1b,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
& r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
& r1_xreal_0(D,np__1) ) ) ) ) ) ).
fof(t41_jordan1b,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
& r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
& r1_xreal_0(B,np__1) ) ) ) ) ) ).
fof(t42_jordan1b,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
& r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
& r1_xreal_0(k1_matrix_1(k1_jordan8(A,C)),k1_nat_1(D,np__1)) ) ) ) ) ) ).
fof(t43_jordan1b,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(B,k3_finseq_1(k1_jordan8(A,C)))
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,C)))
& r1_tarski(k3_goboard5(k1_jordan8(A,C),B,D),k1_jordan2c(np__2,A))
& r1_xreal_0(k3_finseq_1(k1_jordan8(A,C)),k1_nat_1(B,np__1)) ) ) ) ) ) ).
fof(t44_jordan1b,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)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B)))
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(A,B)))
& r1_tarski(k3_goboard5(k1_jordan8(A,B),C,D),k1_jordan2c(np__2,A)) ) )
=> r1_xreal_0(np__1,B) ) ) ) ).
%------------------------------------------------------------------------------