SET007 Axioms: SET007+522.ax
%------------------------------------------------------------------------------
% File : SET007+522 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of Real Maps
% 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 : jordan5a [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 25 ( 0 unt; 0 def)
% Number of atoms : 340 ( 66 equ)
% Maximal formula atoms : 29 ( 13 avg)
% Number of connectives : 347 ( 32 ~; 18 |; 149 &)
% ( 2 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 17 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 30 ( 29 usr; 0 prp; 1-4 aty)
% Number of functors : 34 ( 34 usr; 8 con; 0-4 aty)
% Number of variables : 134 ( 129 !; 5 ?)
% 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_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v3_struct_0(k15_euclid(A))
& v1_pre_topc(k15_euclid(A))
& v2_pre_topc(k15_euclid(A))
& v3_compts_1(k15_euclid(A))
& v1_borsuk_2(k15_euclid(A)) ) ) ).
fof(rc1_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( m1_pre_topc(B,k15_euclid(A))
& ~ v3_struct_0(B)
& v1_pre_topc(B)
& v2_pre_topc(B)
& v2_compts_1(B)
& v3_compts_1(B) ) ) ).
fof(t1_jordan5a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r1_topreal1(k15_euclid(A),B,C,D)
=> v6_compts_1(D,k15_euclid(A)) ) ) ) ) ) ).
fof(t2_jordan5a,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,np__1) )
<=> r2_hidden(A,u1_struct_0(k5_topmetr)) ) ) ).
fof(t3_jordan5a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ~ ( k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,D),A,B),k18_euclid(D,A,C)) = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,E),A,B),k18_euclid(E,A,C))
& D != E
& B != C ) ) ) ) ) ) ).
fof(t4_jordan5a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ~ ( B != C
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))))
& m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C)))) )
=> ~ ( ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,k1_rcomp_1(np__0,np__1))
=> k1_funct_1(D,E) = k17_euclid(A,k18_euclid(k5_real_1(np__1,E),A,B),k18_euclid(E,A,C)) ) )
& v3_tops_2(D,k5_topmetr,k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C)))
& k1_funct_1(D,np__0) = B
& k1_funct_1(D,np__1) = C ) ) ) ) ) ) ).
fof(t5_jordan5a,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_borsuk_2(C,k15_euclid(np__2),A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_compts_1(D)
& m1_pre_topc(D,k15_euclid(np__2)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(D)) )
=> ( ( v2_funct_1(C)
& E = C
& k2_pre_topc(D) = k2_relat_1(C) )
=> v3_tops_2(E,k5_topmetr,D) ) ) ) ) ) ) ).
fof(t6_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(A,k4_pcomps_1(k8_metric_1))
<=> v3_rcomp_1(A) ) ) ).
fof(t7_jordan5a,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr))
& m2_relset_1(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_topmetr))
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r1_tmap_1(k3_topmetr,k3_topmetr,A,B)
& A = C
& B = D )
=> r1_fcont_1(C,D) ) ) ) ) ) ).
fof(t8_jordan5a,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr))
& v5_pre_topc(A,k3_topmetr,k3_topmetr)
& m2_relset_1(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( A = B
=> r2_fcont_1(B,k1_numbers) ) ) ) ).
fof(t9_jordan5a,axiom,
! [A] :
( ( v1_funct_1(A)
& v2_funct_1(A)
& v1_funct_2(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr))
& v5_pre_topc(A,k3_topmetr,k3_topmetr)
& m2_relset_1(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( B = D
& C = E
& ~ r1_xreal_0(E,D)
& F = k1_funct_1(A,B)
& G = k1_funct_1(A,C)
& r1_xreal_0(G,F) ) ) ) ) ) ) )
| ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( B = D
& C = E
& ~ r1_xreal_0(E,D)
& F = k1_funct_1(A,B)
& G = k1_funct_1(A,C)
& r1_xreal_0(F,G) ) ) ) ) ) ) ) ) ) ).
fof(t10_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_topmetr(C,D)))
=> ( ( r1_xreal_0(C,D)
& E = A
& r1_tarski(k2_rcomp_1(k5_real_1(A,B),k3_real_1(A,B)),k1_rcomp_1(C,D)) )
=> ( r1_xreal_0(B,np__0)
| k2_rcomp_1(k5_real_1(A,B),k3_real_1(A,B)) = k9_metric_1(k2_topmetr(C,D),E,B) ) ) ) ) ) ) ) ).
fof(t11_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(C,k4_pcomps_1(k2_topmetr(A,B)))
=> ( r1_xreal_0(B,A)
| r2_hidden(A,C)
| r2_hidden(B,C)
| v3_rcomp_1(C) ) ) ) ) ) ).
fof(t12_jordan5a,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_tarski(A,k1_rcomp_1(B,C))
=> ( ~ r2_hidden(B,A)
& ~ r2_hidden(C,A) ) ) ) ) ) ).
fof(t13_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_topmetr(A,B))))
=> ( ( r1_xreal_0(A,B)
& D = C
& v3_rcomp_1(C) )
=> r2_hidden(D,k4_pcomps_1(k2_topmetr(A,B))) ) ) ) ) ) ).
fof(t14_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(F,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k4_topmetr(A,B)))
=> ! [H] :
( ( v1_funct_1(H)
& m2_relset_1(H,k1_numbers,k1_numbers) )
=> ( ( r1_tmap_1(k4_topmetr(A,B),k4_topmetr(C,D),F,G)
& k1_funct_1(F,A) = C
& k1_funct_1(F,B) = D
& v2_funct_1(F)
& F = H
& G = E )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,H,k1_rcomp_1(A,B)),E) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,k1_numbers,k1_numbers) )
=> ( ( v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
& v2_funct_1(E)
& E = F
& k1_funct_1(E,A) = C
& k1_funct_1(E,B) = D )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r2_fcont_1(F,k1_rcomp_1(A,B)) ) ) ) ) ) ) ) ) ).
fof(t16_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ( ( v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
& v2_funct_1(E)
& k1_funct_1(E,A) = C
& k1_funct_1(E,B) = D )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ! [F] :
( m1_subset_1(F,u1_struct_0(k4_topmetr(A,B)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k4_topmetr(A,B)))
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ! [J] :
( m1_subset_1(J,k1_numbers)
=> ! [K] :
( m1_subset_1(K,k1_numbers)
=> ~ ( F = H
& G = I
& ~ r1_xreal_0(I,H)
& J = k8_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)),E,F)
& K = k8_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)),E,G)
& r1_xreal_0(K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_jordan5a,axiom,
! [A] :
( ( v1_funct_1(A)
& v2_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
& v5_pre_topc(A,k5_topmetr,k5_topmetr)
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
=> ( ( k1_funct_1(A,np__0) = np__0
& k1_funct_1(A,np__1) = np__1 )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_topmetr))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_topmetr))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( B = D
& C = E
& ~ r1_xreal_0(E,D)
& F = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B)
& G = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,C)
& r1_xreal_0(G,F) ) ) ) ) ) ) ) ) ) ).
fof(t18_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ! [F] :
( ( ~ v1_xboole_0(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( ( G = F
& v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
& v2_funct_1(E)
& v6_compts_1(G,k3_topmetr)
& k1_funct_1(E,A) = C
& k1_funct_1(E,B) = D
& k4_pre_topc(k4_topmetr(A,B),k4_topmetr(C,D),E,F) = H )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| k1_funct_1(E,k5_seq_4(k3_weierstr(G))) = k5_seq_4(k3_weierstr(H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ! [F] :
( ( ~ v1_xboole_0(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
=> ! [G] :
( ( ~ v1_xboole_0(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( ( H = F
& I = G
& v5_pre_topc(E,k4_topmetr(A,B),k4_topmetr(C,D))
& v2_funct_1(E)
& v6_compts_1(H,k3_topmetr)
& k1_funct_1(E,A) = C
& k1_funct_1(E,B) = D
& k4_pre_topc(k4_topmetr(A,B),k4_topmetr(C,D),E,F) = G )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| k1_funct_1(E,k4_seq_4(k3_weierstr(H))) = k4_seq_4(k3_weierstr(I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_jordan5a,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> ( k5_seq_4(k1_rcomp_1(A,B)) = A
& k4_seq_4(k1_rcomp_1(A,B)) = B ) ) ) ) ).
fof(t21_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ( ( r1_xreal_0(A,E)
& r1_xreal_0(F,B)
& v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D))
& k1_funct_1(I,A) = C
& k1_funct_1(I,B) = D
& G = k1_funct_1(I,E)
& H = k1_funct_1(I,F) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| k4_pre_topc(k4_topmetr(A,B),k4_topmetr(C,D),I,k1_rcomp_1(E,F)) = k1_rcomp_1(G,H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xboole_0(A,B)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
& r1_topreal1(k15_euclid(np__2),C,D,A)
& ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B))
& ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& ? [G] :
( m1_subset_1(G,k1_numbers)
& v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = D
& k1_funct_1(F,G) = E
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1)
& ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( r1_xreal_0(np__0,H)
& ~ r1_xreal_0(G,H)
& r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_jordan5a,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xboole_0(A,B)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
& r1_topreal1(k15_euclid(np__2),C,D,A)
& ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B))
& ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& ? [G] :
( m1_subset_1(G,k1_numbers)
& v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = D
& k1_funct_1(F,G) = E
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1)
& ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( r1_xreal_0(H,np__1)
& ~ r1_xreal_0(H,G)
& r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------