SET007 Axioms: SET007+886.ax
%------------------------------------------------------------------------------
% File : SET007+886 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Fashoda Meet Theorem for Rectangles
% 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_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 137 ( 0 unt; 0 def)
% Number of atoms : 3528 ( 607 equ)
% Maximal formula atoms : 39 ( 25 avg)
% Number of connectives : 3775 ( 384 ~; 225 |;1916 &)
% ( 0 <=>;1250 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 32 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 17 ( 16 usr; 0 prp; 1-5 aty)
% Number of functors : 26 ( 26 usr; 6 con; 0-5 aty)
% Number of variables : 1184 (1184 !; 0 ?)
% 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_jgraph_7,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)))
=> ( ( k22_euclid(D) = C
& r1_xreal_0(A,k21_euclid(D))
& r1_xreal_0(k21_euclid(D),B) )
=> ( r1_xreal_0(B,A)
| r2_hidden(D,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C))) ) ) ) ) ) ) ).
fof(t2_jgraph_7,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)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(E,k5_topmetr,k15_euclid(A))
& v2_funct_1(E)
& k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),E) = B
& k1_funct_1(E,np__0) = C
& k1_funct_1(E,np__1) = D ) ) ) ) ) ) ) ).
fof(t3_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ( ( k21_euclid(A) = k21_euclid(B)
& r1_xreal_0(D,k22_euclid(A))
& r1_xreal_0(k22_euclid(B),E) )
=> ( r1_xreal_0(C,k21_euclid(A))
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_jordan6(k1_sppol_2(k21_euclid(A),C,D,E),A,B) ) ) ) ) ) ) ) ).
fof(t4_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(D,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k22_euclid(B))
& r1_xreal_0(k21_euclid(A),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),C) )
=> ( r1_xreal_0(C,k21_euclid(A))
| r1_xreal_0(k22_euclid(B),D)
| r1_jordan6(k1_sppol_2(k21_euclid(A),C,D,k22_euclid(B)),A,B) ) ) ) ) ) ) ).
fof(t5_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(C,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),D)
& r1_xreal_0(C,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),D) )
=> ( r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_xreal_0(D,C)
| r1_jordan6(k1_sppol_2(k21_euclid(A),k21_euclid(B),C,D),A,B) ) ) ) ) ) ) ).
fof(t6_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),D)
& r1_xreal_0(k21_euclid(B),C) )
=> ( r1_xreal_0(D,k22_euclid(B))
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_jordan6(k1_sppol_2(k21_euclid(A),C,k22_euclid(B),D),A,B) ) ) ) ) ) ) ).
fof(t7_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k22_euclid(A) = F
& k22_euclid(B) = F
& r1_xreal_0(C,k21_euclid(A))
& r1_xreal_0(k21_euclid(B),D) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) ).
fof(t8_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k22_euclid(A) = F
& k21_euclid(B) = D
& r1_xreal_0(C,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),D)
& r1_xreal_0(E,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),F) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) ).
fof(t9_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k22_euclid(A) = F
& k22_euclid(B) = E
& r1_xreal_0(C,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),D)
& r1_xreal_0(k21_euclid(B),D) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_xreal_0(k21_euclid(B),C)
| r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) ).
fof(t10_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k21_euclid(A) = D
& k21_euclid(B) = D
& r1_xreal_0(E,k22_euclid(B))
& r1_xreal_0(k22_euclid(A),F) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_xreal_0(k22_euclid(A),k22_euclid(B))
| r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) ).
fof(t11_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k21_euclid(A) = D
& k22_euclid(B) = E
& r1_xreal_0(E,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),F)
& r1_xreal_0(k21_euclid(B),D) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_xreal_0(k21_euclid(B),C)
| r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) ).
fof(t12_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k22_euclid(A) = E
& k22_euclid(B) = E
& r1_xreal_0(k21_euclid(A),D) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_xreal_0(k21_euclid(B),C)
| r1_xreal_0(k21_euclid(A),k21_euclid(B))
| r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) ).
fof(t13_jgraph_7,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_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ( ( k22_euclid(A) = F
& k21_euclid(B) = D
& r1_xreal_0(C,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),D)
& r1_xreal_0(E,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),F) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(F,E)
| r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) ).
fof(t14_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k21_euclid(D) = E
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(D),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k22_euclid(C),k22_euclid(B))
| r1_xreal_0(k22_euclid(D),k22_euclid(C))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(E,k21_euclid(D))
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k22_euclid(C),k22_euclid(B))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k22_euclid(C),k22_euclid(B))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k22_euclid(C),k22_euclid(B))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k21_euclid(D),k21_euclid(C))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k22_euclid(C),k22_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(k21_euclid(C),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(A))
| r1_xreal_0(k21_euclid(D),E)
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(C),k21_euclid(B))
| r1_xreal_0(k21_euclid(D),k21_euclid(C))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(C),k21_euclid(B))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(C),k21_euclid(B))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k22_euclid(B) = H
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(C),k22_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_jgraph_7,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)))
=> ( ( r1_xreal_0(k22_euclid(D),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k22_euclid(B))
& r1_xreal_0(k21_euclid(A),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),k21_euclid(C))
& r1_xreal_0(k22_euclid(D),k22_euclid(C))
& r1_xreal_0(k22_euclid(C),k22_euclid(B))
& r1_xreal_0(k21_euclid(D),k21_euclid(C)) )
=> ( k21_euclid(A) = k21_euclid(C)
| k22_euclid(D) = k22_euclid(B)
| r1_xreal_0(k21_euclid(D),k21_euclid(A))
| r1_jordan17(k1_sppol_2(k21_euclid(A),k21_euclid(C),k22_euclid(D),k22_euclid(B)),A,B,C,D) ) ) ) ) ) ) ).
fof(t29_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(k21_euclid(C),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(D),E)
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(D)) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(C))
| r1_xreal_0(k22_euclid(C),k22_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(C))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(k21_euclid(C),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(D),E)
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = E
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(k21_euclid(B),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(D),E)
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_xreal_0(k21_euclid(B),k21_euclid(C))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_xreal_0(k21_euclid(C),k21_euclid(B))
| r1_xreal_0(k21_euclid(D),k21_euclid(C))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_xreal_0(k21_euclid(C),k21_euclid(B))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_xreal_0(k21_euclid(C),k21_euclid(B))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k22_euclid(B) = H
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_xreal_0(k22_euclid(C),k22_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k22_euclid(B) = H
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(k21_euclid(C),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(B),k21_euclid(A))
| r1_xreal_0(k21_euclid(D),E)
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(D)) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(C))
| r1_xreal_0(k22_euclid(C),k22_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(B),k22_euclid(C))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(k21_euclid(C),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(D),E)
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = H
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(k21_euclid(B),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(D),E)
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_xreal_0(k21_euclid(B),k21_euclid(C))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = F
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(D)) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(A),k22_euclid(B))
| r1_xreal_0(k22_euclid(B),k22_euclid(C))
| r1_xreal_0(k22_euclid(C),k22_euclid(D))
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = F
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k21_euclid(D),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(A),k22_euclid(B))
| r1_xreal_0(k22_euclid(B),k22_euclid(C))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = F
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k21_euclid(C),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k22_euclid(A),k22_euclid(B))
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t47_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k21_euclid(A) = F
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(k21_euclid(B),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(B),k21_euclid(C))
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t48_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ( ( k22_euclid(A) = G
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(k21_euclid(A),F) )
=> ( r1_xreal_0(F,E)
| r1_xreal_0(H,G)
| r1_xreal_0(k21_euclid(A),k21_euclid(B))
| r1_xreal_0(k21_euclid(B),k21_euclid(C))
| r1_xreal_0(k21_euclid(C),k21_euclid(D))
| r1_xreal_0(k21_euclid(D),E)
| r1_jordan17(k1_sppol_2(E,F,G,H),A,B,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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 = k2_jgraph_2(A,B,C,D)
& F = k2_jgraph_2(k7_xcmplx_0(np__1,A),k4_xcmplx_0(k7_xcmplx_0(B,A)),k7_xcmplx_0(np__1,C),k4_xcmplx_0(k7_xcmplx_0(D,C))) )
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(C,np__0)
| ( F = k2_funct_1(E)
& E = k2_funct_1(F) ) ) ) ) ) ) ) ) ) ).
fof(t50_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ( E = k2_jgraph_2(A,B,C,D)
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(C,np__0)
| ( v3_tops_2(E,k15_euclid(np__2),k15_euclid(np__2))
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(k21_euclid(G),k21_euclid(F))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,G)),k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,F))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t51_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ( E = k2_jgraph_2(A,B,C,D)
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(C,np__0)
| ( v3_tops_2(E,k15_euclid(np__2),k15_euclid(np__2))
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(k22_euclid(G),k22_euclid(F))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,G)),k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,F))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t52_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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))) )
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),k2_jgraph_6(A,B,C,D)) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E)),k2_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)) ) ) ) ) ) ) ) ) ).
fof(t53_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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))) )
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& v5_pre_topc(F,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(F) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( v5_pre_topc(k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),k5_topmetr,k15_euclid(np__2))
& v2_funct_1(k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E)) ) ) ) ) ) ) ) ) ) ).
fof(t54_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)) = A )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)) = k1_real_1(np__1) ) ) ) ) ) ) ) ) ) ).
fof(t55_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)) = D )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)) = np__1 ) ) ) ) ) ) ) ) ) ).
fof(t56_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)) = B )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)) = np__1 ) ) ) ) ) ) ) ) ) ).
fof(t57_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)) = C )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)) = k1_real_1(np__1) ) ) ) ) ) ) ) ) ) ).
fof(t58_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),D) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
| ( r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& ~ r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t59_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),D)
& r1_xreal_0(A,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),B) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1)
& r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t60_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),D)
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),D) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t61_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),D)
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),B) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),A)
| ( r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1)
& ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),k1_real_1(np__1))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t62_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(A,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),B) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
| ( r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t63_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(A,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),B)
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),D) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| ( r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t64_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(A,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),B)
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),B) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),A)
| ( r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1)
& ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),k1_real_1(np__1))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t65_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),D)
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H))) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)))
| ( r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1)
& ~ r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)))
& r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t66_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(C,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),D)
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),B) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),A)
| ( r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1)
& ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),k1_real_1(np__1))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t67_jgraph_7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [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))) )
=> ! [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] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ( ( E = k2_jgraph_2(k7_xcmplx_0(np__2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(np__2,k6_xcmplx_0(D,C)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(D,C),k6_xcmplx_0(D,C))))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),B) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)),A)
| r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,G)),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F,H)))
| ( ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)),k1_real_1(np__1))
& ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),H)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,E),G)),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t68_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k21_euclid(D) = E
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& ~ r1_xreal_0(k22_euclid(D),k22_euclid(C))
& r1_xreal_0(k22_euclid(D),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t69_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k21_euclid(D) = E
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& ~ r1_xreal_0(k22_euclid(D),k22_euclid(C))
& r1_xreal_0(k22_euclid(D),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t70_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(E,k21_euclid(D))
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t71_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(E,k21_euclid(D))
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t72_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t73_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& r1_xreal_0(k22_euclid(C),H)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t74_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t75_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = E
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(B))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t76_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t77_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t78_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t79_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t80_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t81_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(E,k21_euclid(C))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t82_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t83_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t84_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t85_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t86_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t87_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = E
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t88_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t89_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t90_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t91_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t92_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t93_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t94_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t95_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t96_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t97_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t98_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t99_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = H
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(E,k21_euclid(B))
& r1_xreal_0(k21_euclid(B),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t100_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(k22_euclid(B),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t101_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(k22_euclid(B),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t102_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t103_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t104_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t105_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t106_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& r1_xreal_0(k21_euclid(B),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t107_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = E
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& r1_xreal_0(k21_euclid(B),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t108_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t109_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = H
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t110_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t111_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& r1_xreal_0(G,k22_euclid(D))
& r1_xreal_0(k22_euclid(D),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t112_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t113_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = H
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t114_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t115_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(D))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(k22_euclid(C),H)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t116_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t117_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& r1_xreal_0(G,k22_euclid(C))
& r1_xreal_0(k22_euclid(C),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t118_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t119_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = H
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(B),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t120_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(G,k22_euclid(D))
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t121_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(G,k22_euclid(D))
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t122_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(G,k22_euclid(C))
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t123_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(G,k22_euclid(C))
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t124_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t125_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k22_euclid(B),H)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(k21_euclid(C),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t126_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& r1_xreal_0(k21_euclid(B),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t127_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = H
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(E,k21_euclid(A))
& r1_xreal_0(k21_euclid(A),F)
& ~ r1_xreal_0(k21_euclid(D),E)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& r1_xreal_0(k21_euclid(B),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t128_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(G,k22_euclid(D))
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t129_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k21_euclid(B) = F
& k21_euclid(C) = F
& k21_euclid(D) = F
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(C),k22_euclid(D))
& r1_xreal_0(G,k22_euclid(D))
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t130_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(G,k22_euclid(C))
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t131_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k21_euclid(B) = F
& k21_euclid(C) = F
& k22_euclid(D) = G
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(C))
& r1_xreal_0(G,k22_euclid(C))
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_xreal_0(k21_euclid(D),F)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t132_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B))
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(D),E)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t133_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k21_euclid(B) = F
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(k22_euclid(A),H)
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B))
& r1_xreal_0(G,k22_euclid(B))
& r1_xreal_0(k21_euclid(C),F)
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t134_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(k21_euclid(B),F)
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(D),E)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t135_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k21_euclid(A) = F
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(G,k22_euclid(A))
& r1_xreal_0(k22_euclid(A),H)
& r1_xreal_0(k21_euclid(B),F)
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t136_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = G
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(k21_euclid(A),F)
& ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(D),E)
& k1_funct_1(I,np__0) = A
& k1_funct_1(I,np__1) = C
& k1_funct_1(J,np__0) = B
& k1_funct_1(J,np__1) = D
& v5_pre_topc(I,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(I)
& v5_pre_topc(J,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(J)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k2_jgraph_6(E,F,G,H))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J),k2_jgraph_6(E,F,G,H))
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),I),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t137_jgraph_7,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_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xreal_0(F,E)
& ~ r1_xreal_0(H,G)
& k22_euclid(A) = G
& k22_euclid(B) = G
& k22_euclid(C) = G
& k22_euclid(D) = G
& r1_xreal_0(k21_euclid(A),F)
& ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
& ~ r1_xreal_0(k21_euclid(B),k21_euclid(C))
& ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& ~ r1_xreal_0(k21_euclid(D),E)
& r1_topreal1(k15_euclid(np__2),A,C,I)
& r1_topreal1(k15_euclid(np__2),B,D,J)
& r1_tarski(I,k2_jgraph_6(E,F,G,H))
& r1_tarski(J,k2_jgraph_6(E,F,G,H))
& r1_xboole_0(I,J) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------