SET007 Axioms: SET007+720.ax
%------------------------------------------------------------------------------
% File : SET007+720 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Upper and Lower Sequence on the Cage, Upper and Lower 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 : jordan1j [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 66 ( 0 unt; 0 def)
% Number of atoms : 651 ( 63 equ)
% Maximal formula atoms : 19 ( 9 avg)
% Number of connectives : 711 ( 126 ~; 5 |; 363 &)
% ( 0 <=>; 217 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 37 ( 36 usr; 0 prp; 1-3 aty)
% Number of functors : 63 ( 63 usr; 6 con; 0-4 aty)
% Number of variables : 179 ( 177 !; 2 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_jordan1j,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ~ v1_xboole_0(k3_graph_2(A,B))
& v1_relat_1(k3_graph_2(A,B))
& v1_funct_1(k3_graph_2(A,B))
& v1_finset_1(k3_graph_2(A,B))
& v1_finseq_1(k3_graph_2(A,B)) ) ) ).
fof(rc1_jordan1j,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& ~ v1_realset1(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& v4_topreal1(A)
& v1_goboard5(A)
& v2_goboard5(A) ) ).
fof(t1_jordan1j,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,D)
& r1_xreal_0(D,k1_matrix_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(A))
& r1_xreal_0(np__1,B)
& ~ r1_xreal_0(C,B)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D))) ) ) ) ) ) ) ).
fof(t2_jordan1j,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,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& ~ r1_xreal_0(E,D)
& r1_xreal_0(E,k1_matrix_1(A))
& r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,E)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,D))) ) ) ) ) ) ) ).
fof(t3_jordan1j,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),k34_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),k34_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))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(t4_jordan1j,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)))) )
=> k1_jordan1e(B,A) = k2_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(t5_jordan1j,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_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
& r2_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ).
fof(t6_jordan1j,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_hidden(k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
& r2_hidden(k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ).
fof(t7_jordan1j,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_hidden(k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
& r2_hidden(k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ).
fof(t8_jordan1j,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_hidden(k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
& r2_hidden(k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ).
fof(t9_jordan1j,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_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A)))
& r2_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k1_jordan1e(B,A))) ) ) ) ).
fof(t10_jordan1j,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_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
& r2_hidden(k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ).
fof(t11_jordan1j,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_hidden(k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
& r2_hidden(k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ).
fof(t12_jordan1j,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_hidden(k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
& r2_hidden(k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ).
fof(t13_jordan1j,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_hidden(k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
& r2_hidden(k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ).
fof(t14_jordan1j,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_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k2_relat_1(k2_jordan1e(B,A)))
& r2_hidden(k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))),k5_topreal1(np__2,k2_jordan1e(B,A))) ) ) ) ).
fof(t15_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k32_pscomp_1(B),A) )
=> k32_pscomp_1(A) = k32_pscomp_1(B) ) ) ) ).
fof(t16_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k33_pscomp_1(B),A) )
=> k33_pscomp_1(A) = k33_pscomp_1(B) ) ) ) ).
fof(t17_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k35_pscomp_1(B),A) )
=> k35_pscomp_1(A) = k35_pscomp_1(B) ) ) ) ).
fof(t18_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k34_pscomp_1(B),A) )
=> k34_pscomp_1(A) = k34_pscomp_1(B) ) ) ) ).
fof(t19_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k37_pscomp_1(B),A) )
=> k37_pscomp_1(A) = k37_pscomp_1(B) ) ) ) ).
fof(t20_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k36_pscomp_1(B),A) )
=> k36_pscomp_1(A) = k36_pscomp_1(B) ) ) ) ).
fof(t21_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k30_pscomp_1(B),A) )
=> k30_pscomp_1(A) = k30_pscomp_1(B) ) ) ) ).
fof(t22_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_tarski(A,B)
& r2_hidden(k31_pscomp_1(B),A) )
=> k31_pscomp_1(A) = k31_pscomp_1(B) ) ) ) ).
fof(t23_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k19_pscomp_1(A),k19_pscomp_1(B))
=> k19_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k19_pscomp_1(B) ) ) ) ).
fof(t24_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k20_pscomp_1(A),k20_pscomp_1(B))
=> k20_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k20_pscomp_1(B) ) ) ) ).
fof(t25_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k21_pscomp_1(A),k21_pscomp_1(B))
=> k21_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k21_pscomp_1(A) ) ) ) ).
fof(t26_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k18_pscomp_1(A),k18_pscomp_1(B))
=> k18_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k18_pscomp_1(A) ) ) ) ).
fof(t27_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k19_pscomp_1(B),k19_pscomp_1(A))
=> k32_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k32_pscomp_1(B) ) ) ) ).
fof(t28_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k19_pscomp_1(B),k19_pscomp_1(A))
=> k33_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k33_pscomp_1(B) ) ) ) ).
fof(t29_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k20_pscomp_1(B),k20_pscomp_1(A))
=> k35_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k35_pscomp_1(B) ) ) ) ).
fof(t30_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k20_pscomp_1(B),k20_pscomp_1(A))
=> k34_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k34_pscomp_1(B) ) ) ) ).
fof(t31_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(A))
=> k37_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k37_pscomp_1(A) ) ) ) ).
fof(t32_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(A))
=> k36_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k36_pscomp_1(A) ) ) ) ).
fof(t33_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A))
=> k30_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k30_pscomp_1(A) ) ) ) ).
fof(t34_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A))
=> k31_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)) = k31_pscomp_1(A) ) ) ) ).
fof(t35_jordan1j,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)) )
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k3_jordan3(A,B),k3_finseq_1(k3_jordan3(A,B))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) ) ) ) ).
fof(t36_jordan1j,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [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] :
( ( v2_connsp_1(D,k15_euclid(np__2))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r2_hidden(B,k3_goboard9(A))
& r2_hidden(C,k2_goboard9(A))
& r2_hidden(B,D)
& r2_hidden(C,D)
& r1_xboole_0(D,k5_topreal1(np__2,A)) ) ) ) ) ) ).
fof(t37_jordan1j,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))
=> k3_jordan3(A,B) = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_finseq_4(A,B),k3_finseq_1(A)) ) ) ) ).
fof(t38_jordan1j,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] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k2_relat_1(B))
=> r1_goboard1(u1_struct_0(k15_euclid(np__2)),k4_jordan3(B,C),A) ) ) ) ) ) ).
fof(t39_jordan1j,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] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k2_relat_1(B))
=> r1_goboard1(u1_struct_0(k15_euclid(np__2)),k3_jordan3(B,C),A) ) ) ) ) ) ).
fof(t40_jordan1j,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
=> ! [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(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(A))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D),k5_topreal1(np__2,B)) )
=> r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D),k2_relat_1(B)) ) ) ) ) ) ) ).
fof(t41_jordan1j,axiom,
! [A] :
( ( v4_topreal1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v2_topreal1(B)
& v3_topreal1(B)
& v2_funct_1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_struct_0(k15_euclid(np__2),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,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(A)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) = k1_xboole_0 ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__2,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,B,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) = k1_xboole_0 ) ) )
=> v1_goboard5(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t42_jordan1j,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(B,A)))
& r2_hidden(k30_pscomp_1(B),k3_goboard5(k1_jordan8(B,A),np__1,C))
& k30_pscomp_1(B) != k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__2,C) ) ) ) ).
fof(t43_jordan1j,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,k5_topreal1(np__2,A))
& r2_hidden(k1_funct_1(A,k3_finseq_1(A)),k5_topreal1(np__2,k4_jordan3(A,B))) )
=> k1_funct_1(A,k3_finseq_1(A)) = B ) ) ) ).
fof(t44_jordan1j,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)))
=> k4_jordan3(A,B) != k1_xboole_0 ) ) ).
fof(t45_jordan1j,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k4_jordan3(A,B),k3_finseq_1(k4_jordan3(A,B))) = B ) ) ) ).
fof(t46_jordan1j,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] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k5_topreal1(np__2,k1_jordan1e(B,A)))
& k21_euclid(C) = k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
=> C = k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t47_jordan1j,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] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k5_topreal1(np__2,k2_jordan1e(B,A)))
& k21_euclid(C) = k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
=> C = k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t48_jordan1j,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C),A) )
=> ( r1_xreal_0(k3_finseq_1(B),D)
| ( k4_gobrd13(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k4_gobrd13(B,A,D)
& k3_gobrd13(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) ).
fof(t49_jordan1j,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k3_finseq_1(B))
=> k16_finseq_1(A,k4_graph_2(A,B,C),D) = k16_finseq_1(A,B,D) ) ) ) ) ).
fof(t50_jordan1j,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> k16_finseq_1(A,k4_graph_2(A,B,C),k3_finseq_1(B)) = B ) ) ).
fof(t51_jordan1j,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A) )
=> ( r1_xreal_0(k3_finseq_1(B),D)
| ( k4_gobrd13(k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k4_gobrd13(B,A,D)
& k3_gobrd13(k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) ).
fof(t52_jordan1j,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] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
& r2_hidden(C,k2_relat_1(B)) )
=> ( r1_xreal_0(k5_finseq_4(B,C),D)
| ( k4_gobrd13(k4_jordan3(B,C),A,D) = k4_gobrd13(B,A,D)
& k3_gobrd13(k4_jordan3(B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) ).
fof(t53_jordan1j,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
=> ( r1_xreal_0(k5_finseq_4(B,C),D)
| ( k4_gobrd13(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k4_gobrd13(B,A,D)
& k3_gobrd13(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) ).
fof(t54_jordan1j,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)))
=> ( ( v2_topreal1(A)
& v3_topreal1(A)
& v2_funct_1(A)
& v2_topreal1(B)
& v3_topreal1(B)
& v2_funct_1(B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
=> v3_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t55_jordan1j,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)))
=> ( ( v2_funct_1(A)
& v2_funct_1(B)
& r1_tarski(k3_xboole_0(k2_relat_1(A),k2_relat_1(B)),k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) )
=> v2_funct_1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t56_jordan1j,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,k2_relat_1(A)) )
=> ( B = k1_funct_1(A,np__1)
| k1_nat_1(k2_jordan3(A,B),np__1) = k5_finseq_4(A,B) ) ) ) ) ).
fof(t57_jordan1j,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(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& 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)))
& D = E ) ) ) ) ) ) ).
fof(t58_jordan1j,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)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),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,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t59_jordan1j,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)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k5_topreal1(np__2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),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,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t60_jordan1j,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& ~ r1_xreal_0(A,np__0)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) ).
fof(t61_jordan1j,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_topreal2(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A)))
& ~ r1_xreal_0(A,np__0)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,A)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) ).
fof(t62_jordan1j,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C),k8_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1)))))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,k1_nat_1(A,np__1))))
& r2_subset_1(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,np__1),k1_jordan1a(k1_jordan8(B,np__1)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,k1_nat_1(A,np__1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,np__1))),C)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) ) ) ) ) ).
fof(t63_jordan1j,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))))
& 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
& 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
& 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(t64_jordan1j,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))))
& 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
& 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,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(k5_topreal1(np__2,k1_jordan9(B,k1_nat_1(A,np__1))))) = k1_struct_0(k15_euclid(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))
& 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)) ) ) ) ) ) ).
%------------------------------------------------------------------------------