SET007 Axioms: SET007+523.ax
%------------------------------------------------------------------------------
% File : SET007+523 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Ordering of Points on a Curve. Part I
% 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 : jordan5b [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 37 ( 3 unt; 0 def)
% Number of atoms : 278 ( 47 equ)
% Maximal formula atoms : 25 ( 7 avg)
% Number of connectives : 265 ( 24 ~; 14 |; 106 &)
% ( 1 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-4 aty)
% Number of functors : 36 ( 36 usr; 7 con; 0-4 aty)
% Number of variables : 94 ( 93 !; 1 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_jordan5b,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_binarith(A,np__1)) ) ) ).
fof(t2_jordan5b,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k1_nat_1(A,np__1),B)
=> r1_xreal_0(np__1,k5_binarith(B,A)) ) ) ) ).
fof(t3_jordan5b,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B) )
=> r1_xreal_0(k1_nat_1(k5_binarith(B,A),np__1),B) ) ) ) ).
fof(t4_jordan5b,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r2_hidden(A,u1_struct_0(k22_borsuk_1))
=> r2_hidden(k6_xcmplx_0(np__1,A),u1_struct_0(k22_borsuk_1)) ) ) ).
fof(t5_jordan5b,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k3_topreal1(np__2,A,B))
& k22_euclid(C) = k22_euclid(A) )
=> ( k22_euclid(A) = k22_euclid(B)
| C = A ) ) ) ) ) ).
fof(t6_jordan5b,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k3_topreal1(np__2,A,B))
& k21_euclid(C) = k21_euclid(A) )
=> ( k21_euclid(A) = k21_euclid(B)
| C = A ) ) ) ) ) ).
fof(t7_jordan5b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(C,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& v4_topreal1(A)
& B = k5_topreal1(np__2,A)
& v3_tops_2(C,k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B))
& k1_funct_1(C,np__0) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)
& k1_funct_1(C,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,E)
& r1_xreal_0(np__0,E)
& r1_xreal_0(E,np__1)
& r1_xreal_0(np__0,F)
& r1_xreal_0(F,np__1)
& k4_topreal1(np__2,A,D) = k4_pre_topc(k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B),C,k1_rcomp_1(E,F))
& k1_funct_1(C,E) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)
& k1_funct_1(C,F) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)) ) ) ) ) ) ) ) ) ).
fof(t8_jordan5b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k22_borsuk_1),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v1_xboole_0(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k22_borsuk_1))) )
=> ~ ( v4_topreal1(A)
& v3_tops_2(D,k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B))
& k1_funct_1(D,np__0) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)
& k1_funct_1(D,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& k4_pre_topc(k22_borsuk_1,k3_pre_topc(k15_euclid(np__2),B),D,F) = k4_topreal1(np__2,A,E)
& B = k5_topreal1(np__2,A)
& C = k4_topreal1(np__2,A,E)
& ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k3_pre_topc(k22_borsuk_1,F)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(G,u1_struct_0(k3_pre_topc(k22_borsuk_1,F)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ~ ( G = k7_relat_1(D,F)
& v3_tops_2(G,k3_pre_topc(k22_borsuk_1,F),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ) ) ) ).
fof(t9_jordan5b,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k3_topreal1(np__2,A,B))
=> ( A = B
| r2_jordan3(A,B,C,C) ) ) ) ) ) ).
fof(t10_jordan5b,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,k3_topreal1(np__2,B,C))
=> ( B = C
| r2_jordan3(B,C,B,A) ) ) ) ) ) ).
fof(t11_jordan5b,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,k3_topreal1(np__2,B,C))
=> ( B = C
| r2_jordan3(B,C,A,C) ) ) ) ) ) ).
fof(t12_jordan5b,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_jordan3(A,B,C,D)
& r2_jordan3(A,B,D,E) )
=> ( A = B
| r2_jordan3(A,B,C,E) ) ) ) ) ) ) ) ).
fof(t14_jordan5b,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ( r1_topreal1(k15_euclid(A),C,D,B)
=> r1_topreal1(k15_euclid(A),D,C,B) ) ) ) ) ) ).
fof(t15_jordan5b,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( v4_topreal1(B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B))
& C = k4_topreal1(np__2,B,A) )
=> r1_topreal1(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(A,np__1)),C) ) ) ) ) ).
fof(t16_jordan5b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& v4_topreal1(A)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,k3_finseq_1(A)))) )
=> B = np__1 ) ) ) ).
fof(t17_jordan5b,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)
& B = k1_funct_1(A,k3_finseq_1(A)) )
=> k3_jordan3(A,B) = k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B) ) ) ) ).
fof(t18_jordan5b,axiom,
$true ).
fof(t19_jordan5b,axiom,
$true ).
fof(t20_jordan5b,axiom,
$true ).
fof(t21_jordan5b,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))
& v4_topreal1(A) )
=> ( B = k1_funct_1(A,k3_finseq_1(A))
| k2_jordan3(k3_jordan3(A,B),B) = np__1 ) ) ) ) ).
fof(t22_jordan5b,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))
& v4_topreal1(A) )
=> ( B = k1_funct_1(A,k3_finseq_1(A))
| r2_hidden(B,k5_topreal1(np__2,k3_jordan3(A,B))) ) ) ) ) ).
fof(t23_jordan5b,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))
& v4_topreal1(A) )
=> ( B = k1_funct_1(A,np__1)
| r2_hidden(B,k5_topreal1(np__2,k4_jordan3(A,B))) ) ) ) ) ).
fof(t24_jordan5b,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))
& v2_funct_1(A) )
=> k5_jordan3(A,B,B) = k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B) ) ) ) ).
fof(t25_jordan5b,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)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A))
& B = k1_funct_1(A,k3_finseq_1(A))
& v4_topreal1(A) )
=> ( C = k1_funct_1(A,k3_finseq_1(A))
| r2_hidden(B,k5_topreal1(np__2,k3_jordan3(A,C))) ) ) ) ) ) ).
fof(t26_jordan5b,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)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ ( B = k1_funct_1(A,k3_finseq_1(A))
& C = k1_funct_1(A,k3_finseq_1(A)) )
& r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A))
& v4_topreal1(A)
& ~ r2_hidden(B,k5_topreal1(np__2,k3_jordan3(A,C)))
& ~ r2_hidden(C,k5_topreal1(np__2,k3_jordan3(A,B))) ) ) ) ) ).
fof(t27_jordan5b,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)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A))
& v4_topreal1(A) )
=> r1_tarski(k5_topreal1(np__2,k5_jordan3(A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t28_jordan5b,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(C,k3_finseq_1(k3_goboard2(A))) )
=> ( r1_xreal_0(C,B)
| k3_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A)))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))))) = k1_xboole_0 ) ) ) ) ) ).
fof(t29_jordan5b,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(C,k1_matrix_1(k3_goboard2(A))) )
=> ( r1_xreal_0(C,B)
| k3_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))))) = k1_xboole_0 ) ) ) ) ) ).
fof(t30_jordan5b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v4_topreal1(A)
=> k3_jordan3(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) = A ) ) ).
fof(t31_jordan5b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v4_topreal1(A)
=> k4_jordan3(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = A ) ) ).
fof(t32_jordan5b,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))
=> r2_hidden(B,k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k2_jordan3(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1)))) ) ) ) ).
fof(t33_jordan5b,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( v2_topreal1(A)
& v3_topreal1(A)
& v2_funct_1(A)
& r1_xreal_0(np__2,k3_finseq_1(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_topreal1(np__2,A,B)) )
=> B = np__1 ) ) ) ).
fof(t34_jordan5b,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(k3_goboard2(A)))
& C = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),B)) )
=> r1_topreal4(C,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),B)) ) ) ) ) ).
fof(t35_jordan5b,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(k3_goboard2(A)))
& C = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A)))) )
=> r1_topreal4(C,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A)))) ) ) ) ) ).
fof(t36_jordan5b,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)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A)) )
=> ( ( r1_xreal_0(k2_jordan3(A,C),k2_jordan3(A,B))
& ~ ( k2_jordan3(A,B) = k2_jordan3(A,C)
& r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k2_jordan3(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1)),B,C) ) )
| B = C
| r1_tarski(k5_topreal1(np__2,k5_jordan3(A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) ) ).
fof(t13_jordan5b,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
=> k3_topreal1(np__2,A,B) = a_2_0_jordan5b(A,B) ) ) ) ).
fof(fraenkel_a_2_0_jordan5b,axiom,
! [A,B,C] :
( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_2_0_jordan5b(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& A = D
& r2_jordan3(B,C,B,D)
& r2_jordan3(B,C,D,C) ) ) ) ).
%------------------------------------------------------------------------------