SET007 Axioms: SET007+766.ax
%------------------------------------------------------------------------------
% File : SET007+766 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : General Fashoda Meet Theorem for Unit Circle and Square
% 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 : jgraph_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 140 ( 5 unt; 0 def)
% Number of atoms : 1367 ( 242 equ)
% Maximal formula atoms : 34 ( 9 avg)
% Number of connectives : 1380 ( 153 ~; 30 |; 637 &)
% ( 41 <=>; 519 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 13 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-5 aty)
% Number of functors : 104 ( 104 usr; 23 con; 0-4 aty)
% Number of variables : 560 ( 528 !; 32 ?)
% 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_jgraph_6,axiom,
! [A,B,C] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C) )
=> v6_compts_1(k5_jgraph_6(A,B,C),k15_euclid(np__2)) ) ).
fof(fc2_jgraph_6,axiom,
! [A,B,C] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& ~ v3_xreal_0(C) )
=> ( ~ v1_xboole_0(k5_jgraph_6(A,B,C))
& v6_compts_1(k5_jgraph_6(A,B,C),k15_euclid(np__2)) ) ) ).
fof(t1_jgraph_6,axiom,
$true ).
fof(t2_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(np__0,C)
& r1_xreal_0(C,np__1)
& r1_xreal_0(A,B) )
=> ( r1_xreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,C),A),k3_xcmplx_0(C,B)))
& r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,C),A),k3_xcmplx_0(C,B)),B) ) ) ) ) ) ).
fof(t3_jgraph_6,axiom,
$true ).
fof(t4_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& r1_xreal_0(k1_real_1(np__1),B)
& r1_xreal_0(B,np__1) )
=> r1_xreal_0(k3_xcmplx_0(k5_square_1(A),k5_square_1(B)),np__1) ) ) ) ).
fof(t5_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__0,B) )
=> k3_xcmplx_0(A,k8_square_1(B)) = k8_square_1(k3_xcmplx_0(k5_square_1(A),B)) ) ) ) ).
fof(t6_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& r1_xreal_0(k1_real_1(np__1),B)
& r1_xreal_0(B,np__1) )
=> ( r1_xreal_0(k3_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B))))
& r1_xreal_0(k4_xcmplx_0(k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B)))),k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A))))) ) ) ) ) ).
fof(t7_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& r1_xreal_0(k1_real_1(np__1),B)
& r1_xreal_0(B,np__1) )
=> r1_xreal_0(k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B)))) ) ) ) ).
fof(t8_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(B,A)
=> r1_xreal_0(k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),k3_xcmplx_0(A,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B))))) ) ) ) ).
fof(t9_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(B,C)
& r2_hidden(D,k3_topreal1(np__2,k23_euclid(A,B),k23_euclid(A,C))) )
=> ( k21_euclid(D) = A
& r1_xreal_0(B,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),C) ) ) ) ) ) ) ).
fof(t10_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( k21_euclid(D) = A
& r1_xreal_0(B,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),C) )
=> ( r1_xreal_0(C,B)
| r2_hidden(D,k3_topreal1(np__2,k23_euclid(A,B),k23_euclid(A,C))) ) ) ) ) ) ) ).
fof(t11_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(A,B)
& r2_hidden(D,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C))) )
=> ( k22_euclid(D) = C
& r1_xreal_0(A,k21_euclid(D))
& r1_xreal_0(k21_euclid(D),B) ) ) ) ) ) ) ).
fof(t12_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ( C = k1_rcomp_1(A,B)
=> v4_pre_topc(C,k5_topmetr) ) ) ) ) ).
fof(t13_jgraph_6,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( k1_relat_1(D) = k1_relat_1(E)
& k1_relat_1(D) = u1_struct_0(A)
& k1_relat_1(D) = k2_pre_topc(A) ) ) ) ) ) ) ).
fof(t14_jgraph_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(A,B)),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(A,B)),u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k3_pre_topc(A,B)))
=> k8_funct_2(u1_struct_0(k3_pre_topc(A,B)),u1_struct_0(A),C,D) = D )
& v5_pre_topc(C,k3_pre_topc(A,B),A) ) ) ) ).
fof(t15_jgraph_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k6_xcmplx_0(F,C) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t16_jgraph_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k6_xcmplx_0(C,F) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t17_jgraph_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(B)))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(D,A,k3_topmetr)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
=> ~ ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),E,F) = k18_euclid(k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,F),B,C) )
& v5_pre_topc(E,A,k15_euclid(B)) ) ) ) ) ) ) ) ).
fof(t18_jgraph_6,axiom,
k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,k23_euclid(k1_real_1(np__1),np__0)) = k23_euclid(k1_real_1(np__1),np__0) ).
fof(t20_jgraph_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
=> ~ ( v5_pre_topc(C,A,k15_euclid(B))
& v5_pre_topc(D,A,k15_euclid(B))
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
=> ~ ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),E,F) = k17_euclid(B,k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),C,F),k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),D,F)) )
& v5_pre_topc(E,A,k15_euclid(B)) ) ) ) ) ) ) ) ).
fof(t21_jgraph_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(E,A,k3_topmetr)
& v5_pre_topc(F,A,k3_topmetr)
& ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
& m2_relset_1(G,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
=> ~ ( ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),G,H) = k17_euclid(B,k18_euclid(k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),E,H),B,C),k18_euclid(k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),F,H),B,D)) )
& v5_pre_topc(G,A,k15_euclid(B)) ) ) ) ) ) ) ) ) ) ).
fof(t22_jgraph_6,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v2_funct_1(A)
& r1_tarski(B,k1_relat_1(A)) )
=> k9_relat_1(k2_funct_1(A),k9_relat_1(A,B)) = B ) ) ).
fof(t28_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D)
& r2_hidden(E,k1_sppol_2(A,B,C,D)) )
=> ( r1_xreal_0(A,k21_euclid(E))
& r1_xreal_0(k21_euclid(E),B)
& r1_xreal_0(C,k22_euclid(E))
& r1_xreal_0(k22_euclid(E),D) ) ) ) ) ) ) ) ).
fof(t30_jgraph_6,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))))
=> ( v1_topreal2(A)
=> ( ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ~ v3_tops_2(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) )
| v1_topreal2(B) ) ) ) ) ).
fof(t31_jgraph_6,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> v6_compts_1(A,k15_euclid(np__2)) ) ) ).
fof(t38_jgraph_6,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,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [I] :
( ( ~ v1_xboole_0(I)
& v6_compts_1(I,k15_euclid(np__2))
& m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( I = k5_jgraph_6(np__0,np__0,np__1)
& A = k6_jgraph_6(np__0,np__0,np__1)
& B = k8_jgraph_6(np__0,np__0,np__1)
& C = k7_jgraph_6(np__0,np__0,np__1)
& D = k9_jgraph_6(np__0,np__0,np__1)
& E = k1_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
& F = k3_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
& G = k2_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
& H = k4_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
& J = k1_jgraph_3 )
=> ( k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)) = I
& k9_relat_1(k2_funct_1(J),I) = k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
& k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,E) = A
& k9_relat_1(k2_funct_1(J),A) = E
& k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,F) = B
& k9_relat_1(k2_funct_1(J),B) = F
& k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,G) = C
& k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,H) = D
& k9_relat_1(k2_funct_1(J),C) = G
& k9_relat_1(k2_funct_1(J),D) = H ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_jgraph_6,axiom,
$true ).
fof(t41_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C))) = k1_struct_0(k15_euclid(np__2),k23_euclid(A,C)) ) ) ) ) ) ).
fof(t42_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) = k1_struct_0(k15_euclid(np__2),k23_euclid(B,C)) ) ) ) ) ) ).
fof(t43_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) = k1_struct_0(k15_euclid(np__2),k23_euclid(B,D)) ) ) ) ) ) ).
fof(t44_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))) = k1_struct_0(k15_euclid(np__2),k23_euclid(A,D)) ) ) ) ) ) ).
fof(t46_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k18_pscomp_1(k1_sppol_2(A,B,C,D)) = A ) ) ) ) ) ).
fof(t47_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k19_pscomp_1(k1_sppol_2(A,B,C,D)) = D ) ) ) ) ) ).
fof(t48_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k20_pscomp_1(k1_sppol_2(A,B,C,D)) = B ) ) ) ) ) ).
fof(t49_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k21_pscomp_1(k1_sppol_2(A,B,C,D)) = C ) ) ) ) ) ).
fof(t50_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k23_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(A,D) ) ) ) ) ) ).
fof(t51_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k24_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(B,D) ) ) ) ) ) ).
fof(t52_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k22_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(A,C) ) ) ) ) ) ).
fof(t53_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k25_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(B,C) ) ) ) ) ) ).
fof(t54_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k26_pscomp_1(k1_sppol_2(A,B,C,D)) = k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)) ) ) ) ) ) ).
fof(t55_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k28_pscomp_1(k1_sppol_2(A,B,C,D)) = k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)) ) ) ) ) ) ).
fof(t56_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ( k30_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(A,C)
& k34_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(B,D) ) ) ) ) ) ) ).
fof(t57_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& ~ ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(k1_sppol_2(A,B,C,D)),k34_pscomp_1(k1_sppol_2(A,B,C,D)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))))
& r1_topreal1(k15_euclid(np__2),k34_pscomp_1(k1_sppol_2(A,B,C,D)),k30_pscomp_1(k1_sppol_2(A,B,C,D)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)))) ) ) ) ) ) ) ).
fof(t58_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(k15_euclid(np__2)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ( ( G = k23_euclid(A,C)
& H = k23_euclid(B,D)
& I = k23_euclid(A,D)
& J = k23_euclid(B,C)
& E = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),G,I,H)
& F = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),G,J,H) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( v4_topreal1(E)
& k5_topreal1(np__2,E) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,G,I),k3_topreal1(np__2,I,H))
& v4_topreal1(F)
& k5_topreal1(np__2,F) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,G,J),k3_topreal1(np__2,J,H))
& k1_sppol_2(A,B,C,D) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,E),k5_topreal1(np__2,F))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,E),k5_topreal1(np__2,F)) = k2_struct_0(k15_euclid(np__2),G,H)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,np__1) = G
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E)) = H
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,np__1) = G
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,k3_finseq_1(F)) = H ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t59_jgraph_6,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] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( m2_finseq_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m2_finseq_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ( ( I = k23_euclid(C,E)
& J = k23_euclid(D,F)
& G = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),k23_euclid(C,E),k23_euclid(C,F),k23_euclid(D,F))
& H = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),k23_euclid(C,E),k23_euclid(D,E),k23_euclid(D,F))
& A = k5_topreal1(np__2,G)
& B = k5_topreal1(np__2,H) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| ( r1_topreal1(k15_euclid(np__2),I,J,A)
& r1_topreal1(k15_euclid(np__2),I,J,B)
& ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& k1_sppol_2(C,D,E,F) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B) = k2_struct_0(k15_euclid(np__2),I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t60_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& ~ v1_topreal2(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ).
fof(t61_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& k8_jordan6(k1_sppol_2(A,B,C,D)) != k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))) ) ) ) ) ) ).
fof(t62_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& k9_jordan6(k1_sppol_2(A,B,C,D)) != k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) ) ) ) ) ) ).
fof(t63_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D)))))
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D))))) )
=> ~ ( v3_tops_2(E,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D))))
& k1_funct_1(E,np__0) = k30_pscomp_1(k1_sppol_2(A,B,C,D))
& k1_funct_1(E,np__1) = k34_pscomp_1(k1_sppol_2(A,B,C,D))
& k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D)))),E) = k8_jordan6(k1_sppol_2(A,B,C,D))
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)))
=> k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k4_real_1(np__2,F)),np__2,k23_euclid(A,C)),k18_euclid(k4_real_1(np__2,F),np__2,k23_euclid(A,D))) ) )
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,k1_rcomp_1(k6_real_1(np__1,np__2),np__1))
=> k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k5_real_1(k4_real_1(np__2,F),np__1)),np__2,k23_euclid(A,D)),k18_euclid(k5_real_1(k4_real_1(np__2,F),np__1),np__2,k23_euclid(B,D))) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
=> ( r1_xreal_0(np__0,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),C),k6_xcmplx_0(D,C)),np__2))
& r1_xreal_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),C),k6_xcmplx_0(D,C)),np__2),np__1)
& k1_funct_1(E,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),C),k6_xcmplx_0(D,C)),np__2)) = F ) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
=> ( r1_xreal_0(np__0,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),A),k6_xcmplx_0(B,A)),np__2),k6_real_1(np__1,np__2)))
& r1_xreal_0(k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),A),k6_xcmplx_0(B,A)),np__2),k6_real_1(np__1,np__2)),np__1)
& k1_funct_1(E,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),A),k6_xcmplx_0(B,A)),np__2),k6_real_1(np__1,np__2))) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t64_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D)))))
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D))))) )
=> ~ ( v3_tops_2(E,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D))))
& k1_funct_1(E,np__0) = k34_pscomp_1(k1_sppol_2(A,B,C,D))
& k1_funct_1(E,np__1) = k30_pscomp_1(k1_sppol_2(A,B,C,D))
& k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D)))),E) = k9_jordan6(k1_sppol_2(A,B,C,D))
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)))
=> k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k4_real_1(np__2,F)),np__2,k23_euclid(B,D)),k18_euclid(k4_real_1(np__2,F),np__2,k23_euclid(B,C))) ) )
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,k1_rcomp_1(k6_real_1(np__1,np__2),np__1))
=> k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k5_real_1(k4_real_1(np__2,F),np__1)),np__2,k23_euclid(B,C)),k18_euclid(k5_real_1(k4_real_1(np__2,F),np__1),np__2,k23_euclid(A,C))) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
=> ( r1_xreal_0(np__0,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),D),k6_xcmplx_0(C,D)),np__2))
& r1_xreal_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),D),k6_xcmplx_0(C,D)),np__2),np__1)
& k1_funct_1(E,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),D),k6_xcmplx_0(C,D)),np__2)) = F ) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
=> ( r1_xreal_0(np__0,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),B),k6_xcmplx_0(A,B)),np__2),k6_real_1(np__1,np__2)))
& r1_xreal_0(k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),B),k6_xcmplx_0(A,B)),np__2),k6_real_1(np__1,np__2)),np__1)
& k1_funct_1(E,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),B),k6_xcmplx_0(A,B)),np__2),k6_real_1(np__1,np__2))) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t65_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
& r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D))) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
<=> r1_xreal_0(k22_euclid(E),k22_euclid(F)) ) ) ) ) ) ) ) ) ) ).
fof(t66_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
& r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
<=> r1_xreal_0(k21_euclid(E),k21_euclid(F)) ) ) ) ) ) ) ) ) ) ).
fof(t67_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)))
& r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
<=> r1_xreal_0(k22_euclid(F),k22_euclid(E)) ) ) ) ) ) ) ) ) ) ).
fof(t68_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)))
& r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C))) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
=> ( E = k30_pscomp_1(k1_sppol_2(A,B,C,D))
| ( r1_xreal_0(k21_euclid(F),k21_euclid(E))
& F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) )
& ( r1_xreal_0(k21_euclid(F),k21_euclid(E))
=> ( F = k30_pscomp_1(k1_sppol_2(A,B,C,D))
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
& E != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t69_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
<=> ~ ( ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
& r1_xreal_0(k22_euclid(E),k22_euclid(F)) )
& ~ r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
& ~ r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
& ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
& F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t70_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
<=> ~ ( ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
& r1_xreal_0(k21_euclid(E),k21_euclid(F)) )
& ~ r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
& ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
& F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t71_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
<=> ( ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
& r1_xreal_0(k22_euclid(F),k22_euclid(E)) )
| ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
& F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t72_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| E = k30_pscomp_1(k1_sppol_2(A,B,C,D))
| ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
<=> ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
& r1_xreal_0(k21_euclid(F),k21_euclid(E))
& F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t73_jgraph_6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ~ ( r2_hidden(A,k1_sppol_2(B,C,D,E))
& ~ r1_xreal_0(C,B)
& ~ r1_xreal_0(E,D)
& ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,E)))
& ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(B,E),k23_euclid(C,E)))
& ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(C,E),k23_euclid(C,D)))
& ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(C,D),k23_euclid(B,D))) ) ) ) ) ) ).
fof(t74_jgraph_6,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)))
=> ~ ( r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B)
& r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
& ~ ( r2_hidden(B,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
& r1_xreal_0(k22_euclid(A),k22_euclid(B)) )
& ~ r2_hidden(B,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),np__1),k23_euclid(np__1,np__1)))
& ~ r2_hidden(B,k3_topreal1(np__2,k23_euclid(np__1,np__1),k23_euclid(np__1,k1_real_1(np__1))))
& ~ ( r2_hidden(B,k3_topreal1(np__2,k23_euclid(np__1,k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),k1_real_1(np__1))))
& B != k23_euclid(k1_real_1(np__1),k1_real_1(np__1)) ) ) ) ) ).
fof(t75_jgraph_6,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] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& 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(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(D,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( C = k5_jgraph_6(np__0,np__0,np__1)
& D = k1_jgraph_3
& r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
& r1_xreal_0(np__0,k22_euclid(A))
& r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B) )
=> r1_jordan6(C,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),D,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),D,B)) ) ) ) ) ) ).
fof(t76_jgraph_6,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] :
( ( ~ v1_xboole_0(D)
& v6_compts_1(D,k15_euclid(np__2))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( D = k5_jgraph_6(np__0,np__0,np__1)
& E = k1_jgraph_3
& r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
& r1_xreal_0(np__0,k22_euclid(A))
& r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B)
& r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),B,C) )
=> r1_jordan6(D,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,C)) ) ) ) ) ) ) ).
fof(t77_jgraph_6,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( B = k1_jgraph_3
& k21_euclid(A) = k1_real_1(np__1) )
=> ( r1_xreal_0(np__0,k22_euclid(A))
| ( ~ r1_xreal_0(np__0,k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,A)))
& ~ r1_xreal_0(np__0,k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,A))) ) ) ) ) ) ).
fof(t78_jgraph_6,axiom,
! [A] :
( m1_subset_1(A,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)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( B = k5_jgraph_6(np__0,np__0,np__1)
& C = k1_jgraph_3 )
=> ( r1_xreal_0(np__0,k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A)))
<=> r1_xreal_0(np__0,k21_euclid(A)) ) ) ) ) ) ).
fof(t79_jgraph_6,axiom,
! [A] :
( m1_subset_1(A,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)))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( B = k5_jgraph_6(np__0,np__0,np__1)
& C = k1_jgraph_3 )
=> ( r1_xreal_0(np__0,k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A)))
<=> r1_xreal_0(np__0,k22_euclid(A)) ) ) ) ) ) ).
fof(t80_jgraph_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( C = k1_jgraph_3
& r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
& r2_hidden(B,k3_topreal1(np__2,k23_euclid(np__1,k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),k1_real_1(np__1)))) )
=> r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A)),k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,B))) ) ) ) ) ).
fof(t81_jgraph_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( C = k1_jgraph_3
& r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
& r2_hidden(B,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
& r1_xreal_0(k22_euclid(B),k22_euclid(A)) )
=> ( r1_xreal_0(np__0,k22_euclid(A))
| r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,B)),k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A))) ) ) ) ) ) ).
fof(t82_jgraph_6,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] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( E = k5_jgraph_6(np__0,np__0,np__1)
& F = k1_jgraph_3
& r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B)
& r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),B,C)
& r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),C,D) )
=> r1_jordan17(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)) ) ) ) ) ) ) ) ).
fof(t83_jgraph_6,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] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v1_topreal2(C)
& r2_hidden(A,C)
& r2_hidden(B,C) )
=> ( r1_jordan6(C,A,B)
| r1_jordan6(C,B,A) ) ) ) ) ) ).
fof(t84_jgraph_6,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] :
( ( ~ v1_xboole_0(D)
& v6_compts_1(D,k15_euclid(np__2))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( v1_topreal2(D)
& r2_hidden(A,D)
& r2_hidden(B,D)
& r2_hidden(C,D)
& ~ ( r1_jordan6(D,A,B)
& r1_jordan6(D,B,C) )
& ~ ( r1_jordan6(D,A,C)
& r1_jordan6(D,C,B) )
& ~ ( r1_jordan6(D,B,A)
& r1_jordan6(D,A,C) )
& ~ ( r1_jordan6(D,B,C)
& r1_jordan6(D,C,A) )
& ~ ( r1_jordan6(D,C,A)
& r1_jordan6(D,A,B) )
& ~ ( r1_jordan6(D,C,B)
& r1_jordan6(D,B,A) ) ) ) ) ) ) ).
fof(t85_jgraph_6,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] :
( ( ~ v1_xboole_0(D)
& v6_compts_1(D,k15_euclid(np__2))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( v1_topreal2(D)
& r2_hidden(A,D)
& r2_hidden(B,D)
& r2_hidden(C,D)
& r1_jordan6(D,B,C)
& ~ r1_jordan6(D,A,B)
& ~ ( r1_jordan6(D,B,A)
& r1_jordan6(D,A,C) )
& ~ r1_jordan6(D,C,A) ) ) ) ) ) ).
fof(t86_jgraph_6,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] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( v1_topreal2(E)
& r2_hidden(A,E)
& r2_hidden(B,E)
& r2_hidden(C,E)
& r2_hidden(D,E)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& ~ r1_jordan6(E,A,B)
& ~ ( r1_jordan6(E,B,A)
& r1_jordan6(E,A,C) )
& ~ ( r1_jordan6(E,C,A)
& r1_jordan6(E,A,D) )
& ~ r1_jordan6(E,D,A) ) ) ) ) ) ) ).
fof(t87_jgraph_6,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] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( E = k5_jgraph_6(np__0,np__0,np__1)
& F = k1_jgraph_3
& r1_jordan6(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B))
& r1_jordan6(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C))
& r1_jordan6(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)) )
=> r1_jordan17(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B,C,D) ) ) ) ) ) ) ) ).
fof(t88_jgraph_6,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] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ( E = k5_jgraph_6(np__0,np__0,np__1)
& F = k1_jgraph_3 )
=> ( r1_jordan17(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B,C,D)
<=> r1_jordan17(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)) ) ) ) ) ) ) ) ) ).
fof(t89_jgraph_6,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,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan17(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B,C,D)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(F)
& v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& E = k2_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
& k1_funct_1(F,np__0) = A
& k1_funct_1(F,np__1) = C
& k1_funct_1(G,np__0) = B
& k1_funct_1(G,np__1) = D
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),E)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),E)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G)) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> m1_subset_1(k1_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k2_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> m1_subset_1(k2_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k3_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> m1_subset_1(k3_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k4_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> m1_subset_1(k4_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k5_jgraph_6,axiom,
! [A,B,C] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C) )
=> m1_subset_1(k5_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k6_jgraph_6,axiom,
! [A,B,C] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C) )
=> m1_subset_1(k6_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k7_jgraph_6,axiom,
! [A,B,C] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C) )
=> m1_subset_1(k7_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k8_jgraph_6,axiom,
! [A,B,C] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C) )
=> m1_subset_1(k8_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k9_jgraph_6,axiom,
! [A,B,C] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C) )
=> m1_subset_1(k9_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t19_jgraph_6,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)))) )
=> ( A = a_0_0_jgraph_6
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,k23_euclid(k1_real_1(np__1),np__0)) = k30_pscomp_1(A) ) ) ).
fof(t23_jgraph_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k5_topmetr))
=> ~ ( H = np__0
& I = np__1
& v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B)
& C = a_0_1_jgraph_6
& D = a_0_2_jgraph_6
& E = a_0_3_jgraph_6
& F = a_0_4_jgraph_6
& G = a_0_5_jgraph_6
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),D)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),E)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H),F)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I),G)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_jgraph_6,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k5_topmetr))
=> ~ ( H = np__0
& I = np__1
& v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B)
& C = a_0_1_jgraph_6
& D = a_0_2_jgraph_6
& E = a_0_3_jgraph_6
& F = a_0_4_jgraph_6
& G = a_0_5_jgraph_6
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),D)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),E)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H),G)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_jgraph_6,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] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_0_jgraph_6
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(H)
& F = a_0_1_jgraph_6
& k1_funct_1(G,np__0) = C
& k1_funct_1(G,np__1) = A
& k1_funct_1(H,np__0) = B
& k1_funct_1(H,np__1) = D
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_jgraph_6,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] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_0_jgraph_6
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(H)
& F = a_0_1_jgraph_6
& k1_funct_1(G,np__0) = C
& k1_funct_1(G,np__1) = A
& k1_funct_1(H,np__0) = D
& k1_funct_1(H,np__1) = B
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_jgraph_6,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] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_0_jgraph_6
& r1_jordan17(E,A,B,C,D) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(H)
& F = a_0_1_jgraph_6
& k1_funct_1(G,np__0) = A
& k1_funct_1(G,np__1) = C
& k1_funct_1(H,np__0) = B
& k1_funct_1(H,np__1) = D
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k1_jgraph_6(A,B,C,D) = a_4_0_jgraph_6(A,B,C,D) ) ) ) ) ).
fof(d2_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k2_jgraph_6(A,B,C,D) = a_4_1_jgraph_6(A,B,C,D) ) ) ) ) ).
fof(d3_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k3_jgraph_6(A,B,C,D) = a_4_2_jgraph_6(A,B,C,D) ) ) ) ) ).
fof(d4_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k4_jgraph_6(A,B,C,D) = a_4_3_jgraph_6(A,B,C,D) ) ) ) ) ).
fof(t29_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r1_xreal_0(np__0,C)
& D = a_0_0_jgraph_6
& E = a_3_0_jgraph_6(A,B,C) )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(C,A,C,B),D) = E ) ) ) ) ) ) ).
fof(t32_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( D = a_3_0_jgraph_6(A,B,C)
=> ( r1_xreal_0(C,np__0)
| v1_topreal2(D) ) ) ) ) ) ) ).
fof(d5_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> k5_jgraph_6(A,B,C) = a_3_0_jgraph_6(A,B,C) ) ) ) ).
fof(d6_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> k6_jgraph_6(A,B,C) = a_3_1_jgraph_6(A,B,C) ) ) ) ).
fof(d7_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> k7_jgraph_6(A,B,C) = a_3_2_jgraph_6(A,B,C) ) ) ) ).
fof(d8_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> k8_jgraph_6(A,B,C) = a_3_3_jgraph_6(A,B,C) ) ) ) ).
fof(d9_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> k9_jgraph_6(A,B,C) = a_3_4_jgraph_6(A,B,C) ) ) ) ).
fof(t33_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( k6_jgraph_6(np__0,np__0,A) = a_1_0_jgraph_6(A)
& ( ~ r1_xreal_0(A,np__0)
=> k5_jgraph_6(np__0,np__0,A) = a_1_1_jgraph_6(A) )
& k8_jgraph_6(np__0,np__0,A) = a_1_2_jgraph_6(A)
& k7_jgraph_6(np__0,np__0,A) = a_1_3_jgraph_6(A)
& k9_jgraph_6(np__0,np__0,A) = a_1_4_jgraph_6(A) ) ) ).
fof(t34_jgraph_6,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))))
=> ( ( A = a_0_6_jgraph_6
& B = a_0_7_jgraph_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) ).
fof(t35_jgraph_6,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))))
=> ( ( A = a_0_8_jgraph_6
& B = a_0_9_jgraph_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) ).
fof(t36_jgraph_6,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))))
=> ( ( A = a_0_10_jgraph_6
& B = a_0_1_jgraph_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) ).
fof(t37_jgraph_6,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))))
=> ( ( A = a_0_11_jgraph_6
& B = a_0_12_jgraph_6 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) ).
fof(t39_jgraph_6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ( k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)) = a_3_5_jgraph_6(A,C,D)
& k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)) = a_3_6_jgraph_6(A,B,D)
& k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)) = a_3_6_jgraph_6(A,B,C)
& k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)) = a_3_5_jgraph_6(B,C,D) ) ) ) ) ) ) ).
fof(t45_jgraph_6,axiom,
a_0_13_jgraph_6 = a_0_14_jgraph_6 ).
fof(fraenkel_a_0_0_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_0_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1 ) ) ).
fof(fraenkel_a_0_1_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_1_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k5_toprns_1(np__2,B),np__1) ) ) ).
fof(fraenkel_a_0_2_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_2_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_3_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_3_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ).
fof(fraenkel_a_0_4_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_4_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_5_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_5_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ).
fof(fraenkel_a_4_0_jgraph_6,axiom,
! [A,B,C,D,E] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D)
& v1_xreal_0(E) )
=> ( r2_hidden(A,a_4_0_jgraph_6(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
& A = F
& ~ r1_xreal_0(k21_euclid(F),B)
& ~ r1_xreal_0(C,k21_euclid(F))
& ~ r1_xreal_0(k22_euclid(F),D)
& ~ r1_xreal_0(E,k22_euclid(F)) ) ) ) ).
fof(fraenkel_a_4_1_jgraph_6,axiom,
! [A,B,C,D,E] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D)
& v1_xreal_0(E) )
=> ( r2_hidden(A,a_4_1_jgraph_6(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
& A = F
& r1_xreal_0(B,k21_euclid(F))
& r1_xreal_0(k21_euclid(F),C)
& r1_xreal_0(D,k22_euclid(F))
& r1_xreal_0(k22_euclid(F),E) ) ) ) ).
fof(fraenkel_a_4_2_jgraph_6,axiom,
! [A,B,C,D,E] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D)
& v1_xreal_0(E) )
=> ( r2_hidden(A,a_4_2_jgraph_6(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
& A = F
& ~ ( r1_xreal_0(B,k21_euclid(F))
& r1_xreal_0(k21_euclid(F),C)
& r1_xreal_0(D,k22_euclid(F))
& r1_xreal_0(k22_euclid(F),E) ) ) ) ) ).
fof(fraenkel_a_4_3_jgraph_6,axiom,
! [A,B,C,D,E] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D)
& v1_xreal_0(E) )
=> ( r2_hidden(A,a_4_3_jgraph_6(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
& A = F
& ~ ( ~ r1_xreal_0(k21_euclid(F),B)
& ~ r1_xreal_0(C,k21_euclid(F))
& ~ r1_xreal_0(k22_euclid(F),D)
& ~ r1_xreal_0(E,k22_euclid(F)) ) ) ) ) ).
fof(fraenkel_a_3_0_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_0_jgraph_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& A = E
& k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C))) = D ) ) ) ).
fof(fraenkel_a_3_1_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_1_jgraph_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& A = E
& ~ r1_xreal_0(D,k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C)))) ) ) ) ).
fof(fraenkel_a_3_2_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_2_jgraph_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& A = E
& r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C))),D) ) ) ) ).
fof(fraenkel_a_3_3_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_3_jgraph_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& A = E
& ~ r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C))),D) ) ) ) ).
fof(fraenkel_a_3_4_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_4_jgraph_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& A = E
& r1_xreal_0(D,k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C)))) ) ) ) ).
fof(fraenkel_a_1_0_jgraph_6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_0_jgraph_6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& ~ r1_xreal_0(B,k5_toprns_1(np__2,C)) ) ) ) ).
fof(fraenkel_a_1_1_jgraph_6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_1_jgraph_6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& k5_toprns_1(np__2,C) = B ) ) ) ).
fof(fraenkel_a_1_2_jgraph_6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_2_jgraph_6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& ~ r1_xreal_0(k5_toprns_1(np__2,C),B) ) ) ) ).
fof(fraenkel_a_1_3_jgraph_6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_3_jgraph_6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k5_toprns_1(np__2,C),B) ) ) ) ).
fof(fraenkel_a_1_4_jgraph_6,axiom,
! [A,B] :
( v1_xreal_0(B)
=> ( r2_hidden(A,a_1_4_jgraph_6(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(B,k5_toprns_1(np__2,C)) ) ) ) ).
fof(fraenkel_a_0_6_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_6_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ r1_xreal_0(k21_euclid(B),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k21_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_7_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_7_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ r1_xreal_0(np__1,k5_toprns_1(np__2,B)) ) ) ).
fof(fraenkel_a_0_8_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_8_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ ( r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) ) ) ) ).
fof(fraenkel_a_0_9_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_9_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ r1_xreal_0(k5_toprns_1(np__2,B),np__1) ) ) ).
fof(fraenkel_a_0_10_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_10_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) ) ) ).
fof(fraenkel_a_0_11_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_11_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ ( ~ r1_xreal_0(k21_euclid(B),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k21_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k22_euclid(B)) ) ) ) ).
fof(fraenkel_a_0_12_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_12_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(np__1,k5_toprns_1(np__2,B)) ) ) ).
fof(fraenkel_a_3_5_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_5_jgraph_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& A = E
& k21_euclid(E) = B
& r1_xreal_0(k22_euclid(E),D)
& r1_xreal_0(C,k22_euclid(E)) ) ) ) ).
fof(fraenkel_a_3_6_jgraph_6,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_6_jgraph_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
& A = E
& r1_xreal_0(k21_euclid(E),C)
& r1_xreal_0(B,k21_euclid(E))
& k22_euclid(E) = D ) ) ) ).
fof(fraenkel_a_0_13_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_13_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ ( ~ ( k1_real_1(np__1) = k21_euclid(B)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) )
& ~ ( k21_euclid(B) = np__1
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) )
& ~ ( k1_real_1(np__1) = k22_euclid(B)
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1) )
& ~ ( np__1 = k22_euclid(B)
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1) ) ) ) ) ).
fof(fraenkel_a_0_14_jgraph_6,axiom,
! [A] :
( r2_hidden(A,a_0_14_jgraph_6)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ ( ~ ( k21_euclid(B) = k1_real_1(np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) )
& ~ ( k22_euclid(B) = np__1
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1) )
& ~ ( k21_euclid(B) = np__1
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) )
& ~ ( k22_euclid(B) = k1_real_1(np__1)
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1) ) ) ) ) ).
%------------------------------------------------------------------------------