SET007 Axioms: SET007+725.ax
%------------------------------------------------------------------------------
% File : SET007+725 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : General Fashoda Meet Theorem for Unit Circle
% 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_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 83 ( 1 unt; 0 def)
% Number of atoms : 1316 ( 255 equ)
% Maximal formula atoms : 44 ( 15 avg)
% Number of connectives : 1462 ( 229 ~; 61 |; 758 &)
% ( 9 <=>; 405 =>; 0 <=; 0 <~>)
% Maximal formula depth : 51 ( 18 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 16 con; 0-5 aty)
% Number of variables : 377 ( 362 !; 15 ?)
% 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_5,axiom,
$true ).
fof(t2_jgraph_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(A,np__0)
& ~ r1_xreal_0(A,B)
& r1_xreal_0(k5_square_1(B),k5_square_1(A)) ) ) ) ).
fof(t3_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k5_toprns_1(np__2,A),np__1)
=> ( r1_xreal_0(k1_real_1(np__1),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),np__1) ) ) ) ).
fof(t4_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k5_toprns_1(np__2,A),np__1)
=> ( k21_euclid(A) = np__0
| k22_euclid(A) = np__0
| ( ~ r1_xreal_0(k21_euclid(A),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k21_euclid(A))
& ~ r1_xreal_0(k22_euclid(A),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k22_euclid(A)) ) ) ) ) ).
fof(t5_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_metric_1(F) )
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_metric_1(G) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(F))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(G))
=> ( ( r1_xreal_0(C,A)
& r1_xreal_0(A,B)
& r1_xreal_0(B,D)
& F = k2_topmetr(A,B)
& G = k2_topmetr(C,D)
& H = I
& r2_hidden(H,u1_struct_0(F))
& r2_hidden(I,u1_struct_0(G)) )
=> r1_tarski(k9_metric_1(F,H,E),k9_metric_1(G,I,E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_jgraph_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D))))
=> ( ( r1_xreal_0(C,A)
& r1_xreal_0(A,B)
& r1_xreal_0(B,D)
& E = k1_rcomp_1(A,B) )
=> k4_topmetr(A,B) = k3_pre_topc(k4_topmetr(C,D),E) ) ) ) ) ) ) ).
fof(t7_jgraph_5,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,B)
& r1_xreal_0(B,np__1)
& C = k1_rcomp_1(A,B) )
=> k4_topmetr(A,B) = k3_pre_topc(k5_topmetr,C) ) ) ) ) ).
fof(t8_jgraph_5,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v3_tops_2(E,B,C)
& v5_pre_topc(D,A,B) )
=> v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t9_jgraph_5,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( l1_pre_topc(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v3_tops_2(E,B,C)
& v2_funct_1(D) )
=> v2_funct_1(k5_relat_1(D,E)) ) ) ) ) ) ) ).
fof(t10_jgraph_5,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D)))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(G,u1_struct_0(A),u1_struct_0(C)) )
=> ( ( G = k5_relat_1(E,F)
& v5_pre_topc(E,A,k3_pre_topc(B,D))
& v5_pre_topc(F,B,C) )
=> v5_pre_topc(G,A,C) ) ) ) ) ) ) ) ) ).
fof(t11_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ( ( v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D))
& k1_funct_1(I,E) = G
& k1_funct_1(I,F) = H
& k1_funct_1(I,A) = C
& k1_funct_1(I,B) = D
& r1_xreal_0(C,D)
& r1_xreal_0(G,H)
& r2_hidden(E,k1_rcomp_1(A,B))
& r2_hidden(F,k1_rcomp_1(A,B)) )
=> r1_xreal_0(E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
& m2_relset_1(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
=> ( ( v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D))
& k1_funct_1(I,E) = G
& k1_funct_1(I,F) = H
& k1_funct_1(I,A) = D
& k1_funct_1(I,B) = C
& r1_xreal_0(C,D)
& r1_xreal_0(H,G)
& r2_hidden(E,k1_rcomp_1(A,B))
& r2_hidden(F,k1_rcomp_1(A,B)) )
=> r1_xreal_0(E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_jgraph_5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k19_euclid(A,k16_euclid(A)) = k16_euclid(A) ) ).
fof(t14_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k5_topmetr))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ~ ( G = np__0
& H = np__1
& v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B)
& C != D
& E != F
& k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)) = C
& r1_xreal_0(E,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)),F)
& k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H)) = D
& r1_xreal_0(E,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H)),F)
& k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)) = E
& r1_xreal_0(C,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)),D)
& k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H)) = F
& r1_xreal_0(C,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H)),D)
& ! [I] :
( m1_subset_1(I,u1_struct_0(k5_topmetr))
=> ( ~ ( ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)),C)
& ~ r1_xreal_0(D,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)))
& ~ r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)),E)
& ~ r1_xreal_0(F,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I))) )
& ~ ( ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)),C)
& ~ r1_xreal_0(D,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)))
& ~ r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)),E)
& ~ r1_xreal_0(F,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I))) ) ) )
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ).
fof(t15_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k1_funct_1(B,np__0) = k1_funct_1(A,np__1)
& k1_funct_1(B,np__1) = k1_funct_1(A,np__0)
& k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B) = k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B) ) ) ) ) ).
fof(t21_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k22_euclid(B),np__0)
& ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
& r1_xreal_0(k22_euclid(C),np__0) ) ) ) ) ).
fof(t22_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(np__0,k22_euclid(B))
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
=> r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ) ).
fof(t23_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(np__0,k22_euclid(B))
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
| k5_toprns_1(np__2,B) = np__0
| ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
=> ( r1_xreal_0(np__0,k22_euclid(C))
& ~ r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ) ) ) ) ).
fof(t24_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__0,k22_euclid(B))
& r1_xreal_0(np__0,k22_euclid(C)) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| k5_toprns_1(np__2,B) = np__0
| k5_toprns_1(np__2,C) = np__0
| r1_xreal_0(k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)),k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
| ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
& E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),C)
& r1_xreal_0(k6_real_1(k21_euclid(E),k5_toprns_1(np__2,E)),k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D))) ) ) ) ) ) ) ) ) ).
fof(t25_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k21_euclid(B),np__0)
& ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
& r1_xreal_0(k21_euclid(C),np__0) ) ) ) ) ).
fof(t26_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(np__0,k21_euclid(B))
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
| k5_toprns_1(np__2,B) = np__0
| ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
=> ( r1_xreal_0(np__0,k21_euclid(C))
& ~ r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ) ) ).
fof(t27_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__0,k21_euclid(B))
& r1_xreal_0(np__0,k21_euclid(C)) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| k5_toprns_1(np__2,B) = np__0
| k5_toprns_1(np__2,C) = np__0
| r1_xreal_0(k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)),k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
| ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
& E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),C)
& r1_xreal_0(k6_real_1(k22_euclid(E),k5_toprns_1(np__2,E)),k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D))) ) ) ) ) ) ) ) ) ).
fof(t28_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(np__0,k22_euclid(B))
& ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ).
fof(t29_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(np__0,k22_euclid(B))
& ~ r1_xreal_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A)
& ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& ~ ( ~ r1_xreal_0(np__0,k22_euclid(C))
& ~ r1_xreal_0(k21_euclid(C),np__0) ) ) ) ) ) ).
fof(t30_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(k22_euclid(B),np__0)
& r1_xreal_0(k22_euclid(C),np__0) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| k5_toprns_1(np__2,B) = np__0
| k5_toprns_1(np__2,C) = np__0
| r1_xreal_0(k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)),k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
| ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),C)
& r1_xreal_0(k6_real_1(k21_euclid(E),k5_toprns_1(np__2,E)),k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D))) ) ) ) ) ) ) ) ) ).
fof(t34_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr))
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr)) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr),A,B) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B) )
=> v5_pre_topc(A,k15_euclid(np__2),k3_topmetr) ) ) ).
fof(t35_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr))
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr)) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr),A,B) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,B) )
=> v5_pre_topc(A,k15_euclid(np__2),k3_topmetr) ) ) ).
fof(t39_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r1_xreal_0(A,B)
& ~ r1_xreal_0(D,np__0)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,A),C),k3_real_1(k4_real_1(D,B),C))))
& m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,A),C),k3_real_1(k4_real_1(D,B),C)))) )
=> ~ ( v3_tops_2(E,k4_topmetr(A,B),k4_topmetr(k3_real_1(k4_real_1(D,A),C),k3_real_1(k4_real_1(D,B),C)))
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,k1_rcomp_1(A,B))
=> k1_funct_1(E,F) = k3_real_1(k4_real_1(D,F),C) ) ) ) ) ) ) ) ) ) ).
fof(t40_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r1_xreal_0(A,B)
& ~ r1_xreal_0(np__0,D)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,B),C),k3_real_1(k4_real_1(D,A),C))))
& m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,B),C),k3_real_1(k4_real_1(D,A),C)))) )
=> ~ ( v3_tops_2(E,k4_topmetr(A,B),k4_topmetr(k3_real_1(k4_real_1(D,B),C),k3_real_1(k4_real_1(D,A),C)))
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,k1_rcomp_1(A,B))
=> k1_funct_1(E,F) = k3_real_1(k4_real_1(D,F),C) ) ) ) ) ) ) ) ) ) ).
fof(t41_jgraph_5,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
& v3_tops_2(A,k5_topmetr,k4_topmetr(k1_real_1(np__1),np__1))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(B,k1_rcomp_1(np__0,np__1))
=> k1_funct_1(A,B) = k3_real_1(k4_real_1(k1_real_1(np__2),B),np__1) ) )
& k1_funct_1(A,np__0) = np__1
& k1_funct_1(A,np__1) = k1_real_1(np__1) ) ).
fof(t42_jgraph_5,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
& v3_tops_2(A,k5_topmetr,k4_topmetr(k1_real_1(np__1),np__1))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(B,k1_rcomp_1(np__0,np__1))
=> k1_funct_1(A,B) = k5_real_1(k4_real_1(np__2,B),np__1) ) )
& k1_funct_1(A,np__0) = k1_real_1(np__1)
& k1_funct_1(A,np__1) = np__1 ) ).
fof(t60_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k22_euclid(B),np__0)
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
=> r1_xreal_0(k22_euclid(C),np__0) ) ) ) ) ) ) ).
fof(t16_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k5_topmetr))
=> ~ ( H = np__0
& I = np__1
& v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B)
& C = a_0_0_jgraph_5
& D = a_0_1_jgraph_5
& E = a_0_2_jgraph_5
& F = a_0_3_jgraph_5
& G = a_0_4_jgraph_5
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),E)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),D)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H),F)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I),G)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k5_topmetr))
=> ~ ( H = np__0
& I = np__1
& v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B)
& C = a_0_5_jgraph_5
& D = a_0_1_jgraph_5
& E = a_0_2_jgraph_5
& F = a_0_3_jgraph_5
& G = a_0_4_jgraph_5
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),E)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),D)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H),G)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k5_topmetr))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k5_topmetr))
=> ~ ( H = np__0
& I = np__1
& v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B)
& C = a_0_5_jgraph_5
& D = a_0_1_jgraph_5
& E = a_0_2_jgraph_5
& F = a_0_3_jgraph_5
& G = a_0_4_jgraph_5
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),E)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),D)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H),F)
& r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I),G)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_jgraph_5,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( C = a_0_5_jgraph_5
& v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(A)
& v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(B)
& k1_funct_1(A,np__0) = k23_euclid(k1_real_1(np__1),np__0)
& k1_funct_1(A,np__1) = k23_euclid(np__1,np__0)
& k1_funct_1(B,np__1) = k23_euclid(np__0,np__1)
& k1_funct_1(B,np__0) = k23_euclid(np__0,k1_real_1(np__1))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ).
fof(t20_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_5_jgraph_5
& k5_toprns_1(np__2,A) = np__1
& k5_toprns_1(np__2,B) = np__1
& k5_toprns_1(np__2,C) = np__1
& k5_toprns_1(np__2,D) = np__1 )
=> ( ! [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))) )
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& r1_tarski(k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),F,E),E)
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A) = k23_euclid(k1_real_1(np__1),np__0)
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B) = k23_euclid(np__0,np__1)
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C) = k23_euclid(np__1,np__0)
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D) = k23_euclid(np__0,k1_real_1(np__1)) ) )
| ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(F)
& v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& k1_funct_1(F,np__0) = A
& k1_funct_1(F,np__1) = C
& k1_funct_1(G,np__0) = D
& k1_funct_1(G,np__1) = B
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),E)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),E)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = a_0_6_jgraph_5
=> ( k18_pscomp_1(A) = k1_real_1(np__1)
& k20_pscomp_1(A) = np__1
& k21_pscomp_1(A) = k1_real_1(np__1)
& k19_pscomp_1(A) = np__1 ) ) ) ).
fof(t32_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = a_0_6_jgraph_5
=> k30_pscomp_1(A) = k23_euclid(k1_real_1(np__1),np__0) ) ) ).
fof(t33_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = a_0_6_jgraph_5
=> k34_pscomp_1(A) = k23_euclid(np__1,np__0) ) ) ).
fof(t36_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = a_0_6_jgraph_5
=> ( r1_tarski(k8_jordan6(A),A)
& r1_tarski(k9_jordan6(A),A) ) ) ) ).
fof(t37_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = a_0_6_jgraph_5
=> k8_jordan6(A) = a_1_0_jgraph_5(A) ) ) ).
fof(t38_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = a_0_6_jgraph_5
=> k9_jordan6(A) = a_1_1_jgraph_5(A) ) ) ).
fof(t43_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( A = a_0_6_jgraph_5
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A))))
& m2_relset_1(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))) )
=> ~ ( v3_tops_2(B,k4_topmetr(k1_real_1(np__1),np__1),k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k9_jordan6(A))
=> k1_funct_1(B,k21_euclid(C)) = C ) )
& k1_funct_1(B,k1_real_1(np__1)) = k30_pscomp_1(A)
& k1_funct_1(B,np__1) = k34_pscomp_1(A) ) ) ) ) ).
fof(t44_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( A = a_0_6_jgraph_5
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A))))
& m2_relset_1(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))) )
=> ~ ( v3_tops_2(B,k4_topmetr(k1_real_1(np__1),np__1),k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k8_jordan6(A))
=> k1_funct_1(B,k21_euclid(C)) = C ) )
& k1_funct_1(B,k1_real_1(np__1)) = k30_pscomp_1(A)
& k1_funct_1(B,np__1) = k34_pscomp_1(A) ) ) ) ) ).
fof(t45_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( A = a_0_6_jgraph_5
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A))))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))) )
=> ~ ( v3_tops_2(B,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( ( k1_funct_1(B,E) = C
& k1_funct_1(B,F) = D
& r2_hidden(E,k1_rcomp_1(np__0,np__1))
& r2_hidden(F,k1_rcomp_1(np__0,np__1)) )
=> ( ~ ( ~ r1_xreal_0(F,E)
& r1_xreal_0(k21_euclid(C),k21_euclid(D)) )
& ~ ( ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
& r1_xreal_0(F,E) ) ) ) ) ) ) )
& k1_funct_1(B,np__0) = k34_pscomp_1(A)
& k1_funct_1(B,np__1) = k30_pscomp_1(A) ) ) ) ) ).
fof(t46_jgraph_5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( A = a_0_6_jgraph_5
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A))))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))) )
=> ~ ( v3_tops_2(B,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( ( k1_funct_1(B,E) = C
& k1_funct_1(B,F) = D
& r2_hidden(E,k1_rcomp_1(np__0,np__1))
& r2_hidden(F,k1_rcomp_1(np__0,np__1)) )
=> ( ~ ( ~ r1_xreal_0(F,E)
& r1_xreal_0(k21_euclid(D),k21_euclid(C)) )
& ~ ( ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
& r1_xreal_0(F,E) ) ) ) ) ) ) )
& k1_funct_1(B,np__0) = k30_pscomp_1(A)
& k1_funct_1(B,np__1) = k34_pscomp_1(A) ) ) ) ) ).
fof(t47_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r2_hidden(B,k8_jordan6(C))
& r1_jordan6(C,A,B) )
=> r2_hidden(A,k8_jordan6(C)) ) ) ) ) ).
fof(t48_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r1_jordan6(C,A,B) )
=> ( A = B
| r1_xreal_0(np__0,k21_euclid(A))
| r1_xreal_0(np__0,k21_euclid(B))
| r1_xreal_0(np__0,k22_euclid(A))
| r1_xreal_0(np__0,k22_euclid(B))
| ( ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) ) ) ) ) ) ) ).
fof(t49_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r1_jordan6(C,A,B)
& r1_xreal_0(np__0,k22_euclid(A))
& r1_xreal_0(np__0,k22_euclid(B)) )
=> ( A = B
| r1_xreal_0(np__0,k21_euclid(A))
| r1_xreal_0(np__0,k21_euclid(B))
| ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) ) ) ) ) ) ) ).
fof(t50_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( C = a_0_6_jgraph_5
& r1_jordan6(C,A,B)
& A != B
& r1_xreal_0(np__0,k22_euclid(A))
& r1_xreal_0(np__0,k22_euclid(B))
& r1_xreal_0(k21_euclid(B),k21_euclid(A)) ) ) ) ) ).
fof(t51_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( C = a_0_6_jgraph_5
& r1_jordan6(C,A,B)
& A != B
& r1_xreal_0(k22_euclid(A),np__0)
& r1_xreal_0(k22_euclid(B),np__0)
& A != k30_pscomp_1(C)
& r1_xreal_0(k21_euclid(A),k21_euclid(B)) ) ) ) ) ).
fof(t52_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( C = a_0_6_jgraph_5
& ( r1_xreal_0(np__0,k22_euclid(B))
| r1_xreal_0(np__0,k21_euclid(B)) )
& r1_jordan6(C,A,B)
& ~ r1_xreal_0(np__0,k22_euclid(A))
& ~ r1_xreal_0(np__0,k21_euclid(A)) ) ) ) ) ).
fof(t53_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( C = a_0_6_jgraph_5
& r1_jordan6(C,A,B)
& A != B
& r1_xreal_0(np__0,k21_euclid(A))
& r1_xreal_0(np__0,k21_euclid(B))
& r1_xreal_0(k22_euclid(A),k22_euclid(B)) ) ) ) ) ).
fof(t54_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r2_hidden(A,C)
& r2_hidden(B,C) )
=> ( r1_xreal_0(np__0,k21_euclid(A))
| r1_xreal_0(np__0,k21_euclid(B))
| r1_xreal_0(np__0,k22_euclid(A))
| r1_xreal_0(np__0,k22_euclid(B))
| ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B)) )
| r1_jordan6(C,A,B) ) ) ) ) ) ).
fof(t55_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r2_hidden(A,C)
& r2_hidden(B,C) )
=> ( r1_xreal_0(k21_euclid(A),np__0)
| r1_xreal_0(k21_euclid(B),np__0)
| r1_xreal_0(np__0,k22_euclid(A))
| r1_xreal_0(np__0,k22_euclid(B))
| ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
& ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) )
| r1_jordan6(C,A,B) ) ) ) ) ) ).
fof(t56_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r2_hidden(A,C)
& r2_hidden(B,C)
& r1_xreal_0(np__0,k22_euclid(A))
& r1_xreal_0(np__0,k22_euclid(B)) )
=> ( r1_xreal_0(np__0,k21_euclid(A))
| r1_xreal_0(np__0,k21_euclid(B))
| ( ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
& ~ r1_xreal_0(k22_euclid(A),k22_euclid(B)) )
| r1_jordan6(C,A,B) ) ) ) ) ) ).
fof(t57_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r2_hidden(A,C)
& r2_hidden(B,C)
& r1_xreal_0(np__0,k22_euclid(A))
& r1_xreal_0(np__0,k22_euclid(B))
& r1_xreal_0(k21_euclid(A),k21_euclid(B)) )
=> r1_jordan6(C,A,B) ) ) ) ) ).
fof(t58_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r2_hidden(A,C)
& r2_hidden(B,C)
& r1_xreal_0(np__0,k21_euclid(A))
& r1_xreal_0(np__0,k21_euclid(B))
& r1_xreal_0(k22_euclid(B),k22_euclid(A)) )
=> r1_jordan6(C,A,B) ) ) ) ) ).
fof(t59_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = a_0_6_jgraph_5
& r2_hidden(A,C)
& r2_hidden(B,C)
& r1_xreal_0(k22_euclid(A),np__0)
& r1_xreal_0(k22_euclid(B),np__0)
& r1_xreal_0(k21_euclid(B),k21_euclid(A)) )
=> ( B = k30_pscomp_1(C)
| r1_jordan6(C,A,B) ) ) ) ) ) ).
fof(t61_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( ( ~ v1_xboole_0(F)
& v6_compts_1(F,k15_euclid(np__2))
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( F = a_0_6_jgraph_5
& r1_jordan6(F,B,C)
& D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),C) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_jordan6(F,D,E) ) ) ) ) ) ) ) ) ).
fof(t62_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& ~ r1_xreal_0(np__0,k21_euclid(A))
& r1_xreal_0(np__0,k22_euclid(A))
& ~ r1_xreal_0(np__0,k21_euclid(B))
& r1_xreal_0(np__0,k22_euclid(B))
& ~ r1_xreal_0(np__0,k21_euclid(C))
& r1_xreal_0(np__0,k22_euclid(C))
& ~ r1_xreal_0(np__0,k21_euclid(D))
& r1_xreal_0(np__0,k22_euclid(D))
& ! [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))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
& G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
& ~ r1_xreal_0(np__0,k21_euclid(G))
& ~ r1_xreal_0(np__0,k22_euclid(G))
& ~ r1_xreal_0(np__0,k21_euclid(H))
& ~ r1_xreal_0(np__0,k22_euclid(H))
& ~ r1_xreal_0(np__0,k21_euclid(I))
& ~ r1_xreal_0(np__0,k22_euclid(I))
& ~ r1_xreal_0(np__0,k21_euclid(J))
& ~ r1_xreal_0(np__0,k22_euclid(J))
& r1_jordan6(E,G,H)
& r1_jordan6(E,H,I)
& r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t63_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& r1_xreal_0(np__0,k22_euclid(A))
& r1_xreal_0(np__0,k22_euclid(B))
& r1_xreal_0(np__0,k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(D),np__0)
& ! [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))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
& G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
& ~ r1_xreal_0(np__0,k21_euclid(G))
& r1_xreal_0(np__0,k22_euclid(G))
& ~ r1_xreal_0(np__0,k21_euclid(H))
& r1_xreal_0(np__0,k22_euclid(H))
& ~ r1_xreal_0(np__0,k21_euclid(I))
& r1_xreal_0(np__0,k22_euclid(I))
& ~ r1_xreal_0(np__0,k21_euclid(J))
& r1_xreal_0(np__0,k22_euclid(J))
& r1_jordan6(E,G,H)
& r1_jordan6(E,H,I)
& r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t64_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& r1_xreal_0(np__0,k22_euclid(A))
& r1_xreal_0(np__0,k22_euclid(B))
& r1_xreal_0(np__0,k22_euclid(C))
& ~ r1_xreal_0(k22_euclid(D),np__0)
& ! [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))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
& G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
& ~ r1_xreal_0(np__0,k21_euclid(G))
& ~ r1_xreal_0(np__0,k22_euclid(G))
& ~ r1_xreal_0(np__0,k21_euclid(H))
& ~ r1_xreal_0(np__0,k22_euclid(H))
& ~ r1_xreal_0(np__0,k21_euclid(I))
& ~ r1_xreal_0(np__0,k22_euclid(I))
& ~ r1_xreal_0(np__0,k21_euclid(J))
& ~ r1_xreal_0(np__0,k22_euclid(J))
& r1_jordan6(E,G,H)
& r1_jordan6(E,H,I)
& r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t65_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& ( r1_xreal_0(np__0,k22_euclid(A))
| r1_xreal_0(np__0,k21_euclid(A)) )
& ( r1_xreal_0(np__0,k22_euclid(B))
| r1_xreal_0(np__0,k21_euclid(B)) )
& ( r1_xreal_0(np__0,k22_euclid(C))
| r1_xreal_0(np__0,k21_euclid(C)) )
& ~ ( r1_xreal_0(k22_euclid(D),np__0)
& r1_xreal_0(k21_euclid(D),np__0) )
& ! [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))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
& G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
& r1_xreal_0(np__0,k22_euclid(G))
& r1_xreal_0(np__0,k22_euclid(H))
& r1_xreal_0(np__0,k22_euclid(I))
& ~ r1_xreal_0(k22_euclid(J),np__0)
& r1_jordan6(E,G,H)
& r1_jordan6(E,H,I)
& r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t66_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& ( r1_xreal_0(np__0,k22_euclid(A))
| r1_xreal_0(np__0,k21_euclid(A)) )
& ( r1_xreal_0(np__0,k22_euclid(B))
| r1_xreal_0(np__0,k21_euclid(B)) )
& ( r1_xreal_0(np__0,k22_euclid(C))
| r1_xreal_0(np__0,k21_euclid(C)) )
& ~ ( r1_xreal_0(k22_euclid(D),np__0)
& r1_xreal_0(k21_euclid(D),np__0) )
& ! [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))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
& G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
& ~ r1_xreal_0(np__0,k21_euclid(G))
& ~ r1_xreal_0(np__0,k22_euclid(G))
& ~ r1_xreal_0(np__0,k21_euclid(H))
& ~ r1_xreal_0(np__0,k22_euclid(H))
& ~ r1_xreal_0(np__0,k21_euclid(I))
& ~ r1_xreal_0(np__0,k22_euclid(I))
& ~ r1_xreal_0(np__0,k21_euclid(J))
& ~ r1_xreal_0(np__0,k22_euclid(J))
& r1_jordan6(E,G,H)
& r1_jordan6(E,H,I)
& r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t67_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& D = k30_pscomp_1(E)
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& ! [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))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
& G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
& ~ r1_xreal_0(np__0,k21_euclid(G))
& ~ r1_xreal_0(np__0,k22_euclid(G))
& ~ r1_xreal_0(np__0,k21_euclid(H))
& ~ r1_xreal_0(np__0,k22_euclid(H))
& ~ r1_xreal_0(np__0,k21_euclid(I))
& ~ r1_xreal_0(np__0,k22_euclid(I))
& ~ r1_xreal_0(np__0,k21_euclid(J))
& ~ r1_xreal_0(np__0,k22_euclid(J))
& r1_jordan6(E,G,H)
& r1_jordan6(E,H,I)
& r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t68_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& ! [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))) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
& G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
& ~ r1_xreal_0(np__0,k21_euclid(G))
& ~ r1_xreal_0(np__0,k22_euclid(G))
& ~ r1_xreal_0(np__0,k21_euclid(H))
& ~ r1_xreal_0(np__0,k22_euclid(H))
& ~ r1_xreal_0(np__0,k21_euclid(I))
& ~ r1_xreal_0(np__0,k22_euclid(I))
& ~ r1_xreal_0(np__0,k21_euclid(J))
& ~ r1_xreal_0(np__0,k22_euclid(J))
& r1_jordan6(E,G,H)
& r1_jordan6(E,H,I)
& r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t69_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& A != B
& B != C
& C != D
& ~ r1_xreal_0(np__0,k21_euclid(A))
& ~ r1_xreal_0(np__0,k21_euclid(B))
& ~ r1_xreal_0(np__0,k21_euclid(C))
& ~ r1_xreal_0(np__0,k21_euclid(D))
& ~ r1_xreal_0(np__0,k22_euclid(A))
& ~ r1_xreal_0(np__0,k22_euclid(B))
& ~ r1_xreal_0(np__0,k22_euclid(C))
& ~ r1_xreal_0(np__0,k22_euclid(D))
& ! [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))) )
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,G)) = k5_toprns_1(np__2,G) )
& k23_euclid(k1_real_1(np__1),np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& k23_euclid(np__0,np__1) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& k23_euclid(np__1,np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& k23_euclid(np__0,k1_real_1(np__1)) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D) ) ) ) ) ) ) ) ) ).
fof(t70_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D)
& A != B
& B != C
& C != D
& ! [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))) )
=> ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
& ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
=> k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,G)) = k5_toprns_1(np__2,G) )
& k23_euclid(k1_real_1(np__1),np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
& k23_euclid(np__0,np__1) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
& k23_euclid(np__1,np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
& k23_euclid(np__0,k1_real_1(np__1)) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D) ) ) ) ) ) ) ) ) ).
fof(t71_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(H)
& F = a_0_0_jgraph_5
& k1_funct_1(G,np__0) = A
& k1_funct_1(G,np__1) = C
& k1_funct_1(H,np__0) = B
& k1_funct_1(H,np__1) = D
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t72_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(H)
& F = a_0_0_jgraph_5
& k1_funct_1(G,np__0) = A
& k1_funct_1(G,np__1) = C
& k1_funct_1(H,np__0) = D
& k1_funct_1(H,np__1) = B
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t73_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(H)
& F = a_0_5_jgraph_5
& k1_funct_1(G,np__0) = A
& k1_funct_1(G,np__1) = C
& k1_funct_1(H,np__0) = D
& k1_funct_1(H,np__1) = B
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t74_jgraph_5,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v6_compts_1(E,k15_euclid(np__2))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( E = a_0_6_jgraph_5
& r1_jordan6(E,A,B)
& r1_jordan6(E,B,C)
& r1_jordan6(E,C,D) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(G)
& v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
& v2_funct_1(H)
& F = a_0_5_jgraph_5
& k1_funct_1(G,np__0) = A
& k1_funct_1(G,np__1) = C
& k1_funct_1(H,np__0) = B
& k1_funct_1(H,np__1) = D
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_0_0_jgraph_5,axiom,
! [A] :
( r2_hidden(A,a_0_0_jgraph_5)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k5_toprns_1(np__2,B),np__1) ) ) ).
fof(fraenkel_a_0_1_jgraph_5,axiom,
! [A] :
( r2_hidden(A,a_0_1_jgraph_5)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_2_jgraph_5,axiom,
! [A] :
( r2_hidden(A,a_0_2_jgraph_5)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ).
fof(fraenkel_a_0_3_jgraph_5,axiom,
! [A] :
( r2_hidden(A,a_0_3_jgraph_5)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_4_jgraph_5,axiom,
! [A] :
( r2_hidden(A,a_0_4_jgraph_5)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1
& r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ).
fof(fraenkel_a_0_5_jgraph_5,axiom,
! [A] :
( r2_hidden(A,a_0_5_jgraph_5)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(np__1,k5_toprns_1(np__2,B)) ) ) ).
fof(fraenkel_a_0_6_jgraph_5,axiom,
! [A] :
( r2_hidden(A,a_0_6_jgraph_5)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1 ) ) ).
fof(fraenkel_a_1_0_jgraph_5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_1_0_jgraph_5(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r2_hidden(C,B)
& r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_1_jgraph_5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_1_1_jgraph_5(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r2_hidden(C,B)
& r1_xreal_0(k22_euclid(C),np__0) ) ) ) ).
%------------------------------------------------------------------------------