SET007 Axioms: SET007+708.ax
%------------------------------------------------------------------------------
% File : SET007+708 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : More on External Approximation of a~Continuum
% 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 : jordan1h [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 89 ( 10 unt; 0 def)
% Number of atoms : 794 ( 63 equ)
% Maximal formula atoms : 23 ( 8 avg)
% Number of connectives : 850 ( 145 ~; 33 |; 411 &)
% ( 2 <=>; 259 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 52 ( 50 usr; 1 prp; 0-3 aty)
% Number of functors : 73 ( 73 usr; 8 con; 0-6 aty)
% Number of variables : 212 ( 206 !; 6 ?)
% 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_jordan1h,axiom,
? [A] :
( ~ v1_xboole_0(A)
& ~ v2_setfam_1(A) ) ).
fof(rc2_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_setfam_1(A) )
=> ? [B] :
( m1_finseq_1(B,k3_finseq_2(A))
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v1_funcop_1(B)
& v1_matrlin(B)
& v1_polynom1(B) ) ) ).
fof(rc3_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A) )
=> ? [B] :
( m1_finseq_1(B,k3_finseq_2(A))
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v1_funcop_1(B)
& v1_matrlin(B)
& v1_polynom1(B) ) ) ).
fof(fc1_jordan1h,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ( v1_relat_1(k3_funct_6(A))
& v2_relat_1(k3_funct_6(A))
& v1_funct_1(k3_funct_6(A)) ) ) ).
fof(fc2_jordan1h,axiom,
( v1_relat_1(k1_jordan1h)
& v1_relat_2(k1_jordan1h)
& v4_relat_2(k1_jordan1h)
& v8_relat_2(k1_jordan1h)
& v1_partfun1(k1_jordan1h,k1_numbers,k1_numbers)
& v3_orders_1(k1_jordan1h) ) ).
fof(fc3_jordan1h,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( v1_relat_1(k2_triang_1(k1_numbers,A,k1_jordan1h))
& v1_funct_1(k2_triang_1(k1_numbers,A,k1_jordan1h))
& v2_funct_1(k2_triang_1(k1_numbers,A,k1_jordan1h))
& v1_finset_1(k2_triang_1(k1_numbers,A,k1_jordan1h))
& v1_finseq_1(k2_triang_1(k1_numbers,A,k1_jordan1h))
& v1_goboard1(k2_triang_1(k1_numbers,A,k1_jordan1h))
& v1_polynom1(k2_triang_1(k1_numbers,A,k1_jordan1h)) ) ) ).
fof(fc4_jordan1h,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A)
& ~ v1_xboole_0(B)
& v2_relat_1(B)
& m1_finseq_1(B,k3_finseq_2(A)) )
=> ( ~ v1_xboole_0(k2_gobrd13(B))
& v1_finset_1(k2_gobrd13(B)) ) ) ).
fof(cc1_jordan1h,axiom,
! [A] :
( m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
=> ( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A) )
=> ( ~ v1_xboole_0(A)
& v2_relat_1(A)
& ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& v1_matrlin(A) ) ) ) ).
fof(fc5_jordan1h,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k2_gobrd13(A))
& v1_finset_1(k2_gobrd13(A)) ) ) ).
fof(t1_jordan1h,axiom,
$true ).
fof(t2_jordan1h,axiom,
$true ).
fof(t3_jordan1h,axiom,
$true ).
fof(t4_jordan1h,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_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k2_struct_0(k15_euclid(np__2),A,B)),np__2) ) ) ).
fof(t5_jordan1h,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_connsp_1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k2_struct_0(k15_euclid(np__2),A,B)),k15_euclid(np__2)) ) ) ).
fof(t6_jordan1h,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)))
=> ( A != B
=> r2_hidden(A,k6_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k2_struct_0(k15_euclid(np__2),A,B)))) ) ) ) ).
fof(t7_jordan1h,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)))
=> ( A != B
=> k6_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k2_struct_0(k15_euclid(np__2),A,B))) = k3_topreal1(np__2,A,B) ) ) ) ).
fof(t8_jordan1h,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,C),k2_struct_0(k15_euclid(np__2),B,C)),A)
=> ( B = C
| r1_tarski(k3_topreal1(np__2,B,C),k6_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) ).
fof(t9_jordan1h,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(k4_tarski(A,B),k1_jordan1h)
=> r1_xreal_0(A,B) ) ) ) ).
fof(t10_jordan1h,axiom,
k3_relat_1(k1_jordan1h) = k1_numbers ).
fof(t11_jordan1h,axiom,
r3_orders_1(k1_jordan1h,k1_numbers) ).
fof(t12_jordan1h,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> v1_goboard1(k2_triang_1(k1_numbers,A,k1_jordan1h)) ) ).
fof(t13_jordan1h,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( B = k2_relat_1(A)
=> k2_triang_1(k1_numbers,B,k1_jordan1h) = k2_goboard2(A) ) ) ) ).
fof(t14_jordan1h,axiom,
$true ).
fof(t15_jordan1h,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& v3_orders_1(C)
& m2_relset_1(C,A,A) )
=> k3_finseq_1(k2_triang_1(A,B,C)) = k4_card_1(B) ) ) ) ).
fof(t16_jordan1h,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> k2_goboard1(A) = k1_partfun1(k5_numbers,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_numbers,A,k16_pscomp_1) ) ).
fof(t17_jordan1h,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> k3_goboard1(A) = k1_partfun1(k5_numbers,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_numbers,A,k17_pscomp_1) ) ).
fof(t18_jordan1h,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k2_finseq_1(k1_matrix_1(B)))
=> r1_tarski(k2_relat_1(k8_matrix_1(A,B,C)),k2_jordan1h(A,B)) ) ) ) ) ).
fof(t19_jordan1h,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> r1_tarski(k2_relat_1(k7_matrix_1(A,B,C)),k2_jordan1h(A,B)) ) ) ) ) ).
fof(t20_jordan1h,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k3_finseq_1(A),k4_card_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A)))) ) ).
fof(t21_jordan1h,axiom,
! [A] :
( ( v1_matrix_1(A)
& v3_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k4_card_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A))),k3_finseq_1(A)) ) ).
fof(t22_jordan1h,axiom,
! [A] :
( ( ~ v3_relat_1(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)))) )
=> k3_finseq_1(A) = k4_card_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A))) ) ).
fof(t23_jordan1h,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v5_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k1_matrix_1(A),k4_card_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A)))) ) ).
fof(t24_jordan1h,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v4_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k4_card_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A))),k1_matrix_1(A)) ) ).
fof(t25_jordan1h,axiom,
! [A] :
( ( ~ v3_relat_1(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)))) )
=> k1_matrix_1(A) = k4_card_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A))) ) ).
fof(t26_jordan1h,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)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
=> r1_tarski(k4_topreal1(np__2,B,C),k4_gobrd13(B,A,C)) ) ) ) ) ) ).
fof(t27_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) )
=> k4_gobrd13(B,k3_goboard2(B),A) = k5_goboard5(B,A) ) ) ) ).
fof(t28_jordan1h,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)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
=> r1_tarski(k4_topreal1(np__2,B,C),k3_gobrd13(B,A,C)) ) ) ) ) ) ).
fof(t29_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) )
=> k3_gobrd13(B,k3_goboard2(B),A) = k4_goboard5(B,A) ) ) ) ).
fof(t30_jordan1h,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,B)),A)
& A != k3_goboard9(B)
& A != k2_goboard9(B) ) ) ) ).
fof(t31_jordan1h,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] :
( ( ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(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)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
=> ( r1_tarski(k1_tops_1(k15_euclid(np__2),k3_gobrd13(B,A,C)),k3_goboard9(B))
& r1_tarski(k1_tops_1(k15_euclid(np__2),k4_gobrd13(B,A,C)),k2_goboard9(B)) ) ) ) ) ) ) ).
fof(t32_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(E))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,D) )
=> ( A = C
& B = D ) ) ) ) ) ) ) ).
fof(t33_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,D)
=> r1_goboard1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B),D) ) ) ) ) ) ).
fof(t34_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B)) )
=> k1_goboard1(k2_triang_1(k1_numbers,k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),B)),k1_jordan1h),A) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,A,np__1)) ) ) ) ).
fof(t35_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(B)) )
=> k1_goboard1(k2_triang_1(k1_numbers,k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),B)),k1_jordan1h),A) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,A)) ) ) ) ).
fof(t36_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(np__1,C),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,C),k2_relat_1(A)) ) )
| ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(k3_finseq_1(B),C),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B),C),k2_relat_1(A)) ) )
| k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_relat_1(A)) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ).
fof(t37_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(C,np__1),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,np__1),k2_relat_1(A)) ) )
| ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(C,k1_matrix_1(B)),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_matrix_1(B)),k2_relat_1(A)) ) )
| k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_relat_1(A)) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ).
fof(t38_jordan1h,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)))) )
=> A = k1_goboard2(k2_triang_1(k1_numbers,k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A)),k1_jordan1h),k2_triang_1(k1_numbers,k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),A)),k1_jordan1h)) ) ).
fof(t39_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_relat_1(A)) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),B))
& k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_relat_1(A)) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(np__2)),B)) )
=> B = k3_goboard2(A) ) ) ) ).
fof(t40_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(np__1,C),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,C),k2_relat_1(A)) ) )
| ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(C,np__1),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,np__1),k2_relat_1(A)) ) )
| ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(k3_finseq_1(B),C),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B),C),k2_relat_1(A)) ) )
| ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(C,k1_matrix_1(B)),k2_matrix_1(B))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_matrix_1(B)),k2_relat_1(A)) ) )
| B = k3_goboard2(A) ) ) ) ) ).
fof(t41_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(D,B))) )
=> m2_subset_1(k1_int_1(k3_real_1(k6_real_1(k5_real_1(C,np__2),k1_card_4(np__2,k5_binarith(B,A))),np__2)),k1_numbers,k5_numbers) ) ) ) ) ) ).
fof(t42_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(D,B))) )
=> ( r1_xreal_0(np__1,k1_int_1(k3_real_1(k6_real_1(k5_real_1(C,np__2),k1_card_4(np__2,k5_binarith(B,A))),np__2)))
& r1_xreal_0(k2_xcmplx_0(k1_int_1(k3_real_1(k6_real_1(k5_real_1(C,np__2),k1_card_4(np__2,k5_binarith(B,A))),np__2)),np__1),k3_finseq_1(k1_jordan8(D,A))) ) ) ) ) ) ) ).
fof(t43_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k1_matrix_1(k1_jordan8(E,B)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( F = k1_int_1(k3_real_1(k6_real_1(k5_real_1(C,np__2),k1_card_4(np__2,k5_binarith(B,A))),np__2))
& G = k1_int_1(k3_real_1(k6_real_1(k5_real_1(D,np__2),k1_card_4(np__2,k5_binarith(B,A))),np__2))
& r1_tarski(k3_goboard5(k1_jordan8(E,B),C,D),k3_goboard5(k1_jordan8(E,A),F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t44_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k1_matrix_1(k1_jordan8(E,B)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,F)
& r1_xreal_0(k1_nat_1(F,np__1),k3_finseq_1(k1_jordan8(E,A)))
& r1_xreal_0(np__1,G)
& r1_xreal_0(k1_nat_1(G,np__1),k1_matrix_1(k1_jordan8(E,A)))
& r1_tarski(k3_goboard5(k1_jordan8(E,B),C,D),k3_goboard5(k1_jordan8(E,A),F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t45_jordan1h,axiom,
$true ).
fof(t46_jordan1h,axiom,
$true ).
fof(t47_jordan1h,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( v1_jordan2c(A,np__2)
& v1_jordan2c(k2_jordan2c(np__2,A),np__2) ) ) ).
fof(t48_jordan1h,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_sprect_2(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
=> v1_sprect_2(B) ) ) ) ).
fof(t49_jordan1h,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))) )
=> ( k2_goboard9(A) = k2_jordan2c(np__2,k5_topreal1(np__2,A))
=> v1_sprect_2(A) ) ) ).
fof(t50_jordan1h,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))) )
=> k3_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),k2_goboard9(A))) = k3_goboard9(A) ) ).
fof(t51_jordan1h,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))) )
=> k3_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),k3_goboard9(A))) = k2_goboard9(A) ) ).
fof(t52_jordan1h,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)))) )
=> ( v2_connsp_1(B,k15_euclid(np__2))
=> k3_goboard2(k1_jordan9(B,A)) = k1_jordan8(B,A) ) ) ) ).
fof(t53_jordan1h,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)))) )
=> ( v2_connsp_1(B,k15_euclid(np__2))
=> r2_hidden(k32_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),np__1)) ) ) ) ).
fof(t54_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v2_connsp_1(C,k15_euclid(np__2))
& r1_xreal_0(A,B) )
=> r1_tarski(k5_topreal1(np__2,k1_jordan9(C,B)),k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_jordan9(C,A)))) ) ) ) ) ).
fof(t55_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v2_connsp_1(C,k15_euclid(np__2))
& r1_xreal_0(A,B) )
=> r1_tarski(k2_goboard9(k1_jordan9(C,A)),k2_goboard9(k1_jordan9(C,B))) ) ) ) ) ).
fof(t56_jordan1h,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v2_connsp_1(C,k15_euclid(np__2))
& r1_xreal_0(A,B) )
=> r1_tarski(k3_goboard9(k1_jordan9(C,B)),k3_goboard9(k1_jordan9(C,A))) ) ) ) ) ).
fof(d2_jordan1h,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)
=> k3_jordan1h(A,B) = k1_nat_1(k1_card_4(np__2,k5_binarith(B,np__1)),np__2) ) ) ).
fof(t57_jordan1h,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)))) )
=> k3_jordan1h(B,A) = k1_jordan1a(k1_jordan8(B,A)) ) ) ).
fof(t58_jordan1h,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(k3_jordan1h(B,A),np__2)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),k3_jordan1h(B,A)) ) ) ) ).
fof(t59_jordan1h,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(np__1,k5_binarith(k3_jordan1h(B,A),np__1))
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),k5_binarith(k3_jordan1h(B,A),np__1)) ) ) ) ).
fof(d3_jordan1h,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_jordan1h(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ~ r1_xreal_0(k1_matrix_1(k1_jordan8(A,B)),C)
& r1_tarski(k3_goboard5(k1_jordan8(A,B),k5_binarith(k3_jordan1h(A,B),np__1),C),k1_jordan2c(np__2,A)) ) ) ) ) ).
fof(t60_jordan1h,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_jordan1h(B,A)
=> r1_xreal_0(np__1,A) ) ) ) ).
fof(t61_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E)
& r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k1_nat_1(E,np__1)) )
=> ( r1_xboole_0(k4_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k5_binarith(D,np__1),k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t62_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E)
& r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_nat_1(D,np__1),E) )
=> ( r1_xboole_0(k4_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k1_nat_1(D,np__1),k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t63_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(k1_nat_1(E,np__1),D),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_nat_1(E,np__1),D)
& r2_hidden(k4_tarski(E,D),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),E,D) )
=> ( r1_xboole_0(k4_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(E,k5_binarith(D,np__1)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t64_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k1_nat_1(E,np__1))
& r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E) )
=> ( r1_xboole_0(k4_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t65_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E)
& r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k1_nat_1(E,np__1)) )
=> ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(D,k1_nat_1(E,np__2)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t66_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E)
& r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_nat_1(D,np__1),E) )
=> ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k1_nat_1(D,np__2),E),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t67_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(k1_nat_1(E,np__1),D),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_nat_1(E,np__1),D)
& r2_hidden(k4_tarski(E,D),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),E,D) )
=> ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k5_binarith(E,np__1),D),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t68_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k1_nat_1(E,np__1))
& r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E) )
=> ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(D,k5_binarith(E,np__1)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t69_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E)
& r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k1_nat_1(E,np__1)) )
=> ( r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k1_nat_1(D,np__1),k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t70_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E)
& r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_nat_1(D,np__1),E) )
=> ( r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k1_nat_1(D,np__1),k5_binarith(E,np__1)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t71_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(k1_nat_1(E,np__1),D),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_nat_1(E,np__1),D)
& r2_hidden(k4_tarski(E,D),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),E,D) )
=> ( r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(E,k1_nat_1(D,np__1)),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(t72_jordan1h,axiom,
! [A] :
( ( ~ v1_xboole_0(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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k1_jordan8(A,B))
=> ( r1_xreal_0(k3_finseq_1(C),np__1)
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,k1_nat_1(E,np__1))
& r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_jordan8(A,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),D,E) )
=> ( r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),k5_binarith(k3_finseq_1(C),np__1)),A)
| r2_hidden(k4_tarski(k5_binarith(D,np__1),E),k2_matrix_1(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_jordan1h,axiom,
m2_relset_1(k1_jordan1h,k1_numbers,k1_numbers) ).
fof(dt_k2_jordan1h,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,k3_finseq_2(A)) )
=> m1_subset_1(k2_jordan1h(A,B),k1_zfmisc_1(A)) ) ).
fof(redefinition_k2_jordan1h,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,k3_finseq_2(A)) )
=> k2_jordan1h(A,B) = k2_gobrd13(B) ) ).
fof(dt_k3_jordan1h,axiom,
! [A,B] :
( ( 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) )
=> m2_subset_1(k3_jordan1h(A,B),k1_numbers,k5_numbers) ) ).
fof(d1_jordan1h,axiom,
k1_jordan1h = a_0_0_jordan1h ).
fof(fraenkel_a_0_0_jordan1h,axiom,
! [A] :
( r2_hidden(A,a_0_0_jordan1h)
<=> ? [B,C] :
( m1_subset_1(B,k1_numbers)
& m1_subset_1(C,k1_numbers)
& A = k4_tarski(B,C)
& r1_xreal_0(B,C) ) ) ).
%------------------------------------------------------------------------------