SET007 Axioms: SET007+704.ax
%------------------------------------------------------------------------------
% File : SET007+704 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Simple Closed Curve Property of the Circle
% Version : [Urb08] axioms.
% English : Simple Closed Curve Property of the Circle and the Fashoda Meet
% Theorem for It
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 73 ( 5 unt; 0 def)
% Number of atoms : 691 ( 154 equ)
% Maximal formula atoms : 32 ( 9 avg)
% Number of connectives : 730 ( 112 ~; 6 |; 370 &)
% ( 15 <=>; 227 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 10 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-3 aty)
% Number of functors : 58 ( 58 usr; 21 con; 0-4 aty)
% Number of variables : 207 ( 191 !; 16 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_jgraph_3,axiom,
( v1_relat_1(k1_jgraph_3)
& v1_funct_1(k1_jgraph_3)
& v2_funct_1(k1_jgraph_3)
& v1_funct_2(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ).
fof(t1_jgraph_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( k5_square_1(A) = k5_square_1(B)
& A != B
& A != k4_xcmplx_0(B) ) ) ) ).
fof(t2_jgraph_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ~ ( k5_square_1(A) = np__1
& A != np__1
& A != k1_real_1(np__1) ) ) ).
fof(t3_jgraph_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,np__1) )
=> r1_xreal_0(k5_square_1(A),A) ) ) ).
fof(t4_jgraph_3,axiom,
$true ).
fof(t5_jgraph_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(k6_xcmplx_0(k5_square_1(A),np__1),np__0)
=> ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) ) ) ) ).
fof(t6_jgraph_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,A) )
<=> ~ r1_xreal_0(k1_square_1(B,C),A) ) ) ) ) ).
fof(t7_jgraph_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(A,np__0)
=> ( ~ r1_xreal_0(A,k7_xcmplx_0(A,np__3))
& ~ r1_xreal_0(A,k7_xcmplx_0(A,np__4)) ) ) ) ).
fof(t8_jgraph_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(np__1,A)
=> r1_xreal_0(np__1,k8_square_1(A)) )
& ~ ( ~ r1_xreal_0(A,np__1)
& r1_xreal_0(k8_square_1(A),np__1) ) ) ) ).
fof(t9_jgraph_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k2_rcomp_1(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) ).
fof(t10_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( k5_toprns_1(np__2,A) = k9_square_1(k3_real_1(k7_square_1(k21_euclid(A)),k7_square_1(k22_euclid(A))))
& k7_square_1(k5_toprns_1(np__2,A)) = k3_real_1(k7_square_1(k21_euclid(A)),k7_square_1(k22_euclid(A))) ) ) ).
fof(t11_jgraph_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] : k9_relat_1(k7_relat_1(A,B),C) = k9_relat_1(A,k3_xboole_0(C,B)) ) ).
fof(t12_jgraph_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,D))
& v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B))
& m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B)) ) ) ) ) ) ).
fof(t13_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( k3_subset_1(u1_struct_0(A),D) = k1_struct_0(A,C)
& k3_subset_1(u1_struct_0(B),E) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C))
& v3_compts_1(A)
& v3_compts_1(B)
& ! [G] :
( m1_subset_1(G,u1_struct_0(k3_pre_topc(A,D)))
=> k1_funct_1(F,G) != k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C) )
& v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D))
& v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(k3_pre_topc(B,E)))
& v5_pre_topc(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D),k3_pre_topc(A,D),k3_pre_topc(B,E))
& m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(k3_pre_topc(B,E)))
& ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B)))
=> ~ ( r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C),G)
& v3_pre_topc(G,B)
& ! [H] :
( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(C,H)
& v3_pre_topc(H,A)
& r1_tarski(k4_pre_topc(A,B,F,H),G) ) ) ) ) )
=> v5_pre_topc(F,A,B) ) ) ) ) ) ) ) ).
fof(d1_jgraph_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( A = k1_jgraph_3
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( B = k16_euclid(np__2)
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A,B) = B )
& ~ ( ( ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) )
| ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) )
& B != k16_euclid(np__2)
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A,B) != k23_euclid(k6_real_1(k21_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(B),k21_euclid(B)))))),k6_real_1(k22_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(B),k21_euclid(B))))))) )
& ~ ( ~ ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) )
& ~ ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) )
& B != k16_euclid(np__2)
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A,B) != k23_euclid(k6_real_1(k21_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(B),k22_euclid(B)))))),k6_real_1(k22_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(B),k22_euclid(B))))))) ) ) ) ) ) ).
fof(t14_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( A != k16_euclid(np__2)
=> ( ( ( ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
& r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
| ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) ) )
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A) = k23_euclid(k6_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A)))))),k6_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A))))))) )
& ~ ( ~ ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
& r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
& ~ ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) )
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A) != k23_euclid(k6_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A)))))),k6_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A))))))) ) ) ) ) ).
fof(t15_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( v1_xreal_0(D)
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C) = D
& r1_xreal_0(np__0,D) ) )
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( v1_xreal_0(E)
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,D) = E
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) = k8_square_1(E) ) ) )
& v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) ).
fof(t16_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k5_square_1(k7_xcmplx_0(F,G)) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t17_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t18_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G)))) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t19_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k7_xcmplx_0(F,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t20_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k7_xcmplx_0(G,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t21_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k6_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k21_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t22_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k6_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k21_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t23_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k6_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k22_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t24_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k6_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k22_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t29_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ~ ( B = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A)
& v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ).
fof(t30_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
=> k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)) ) ) ).
fof(t31_jgraph_3,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& A = k1_jgraph_3
& v5_pre_topc(A,k15_euclid(np__2),k15_euclid(np__2)) ) ).
fof(t32_jgraph_3,axiom,
v2_funct_1(k1_jgraph_3) ).
fof(t38_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ( A = k16_euclid(np__2)
=> k1_funct_1(k2_funct_1(k1_jgraph_3),A) = k16_euclid(np__2) )
& ~ ( ( ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
& r1_xreal_0(k1_real_1(k21_euclid(A)),k22_euclid(A)) )
| ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k1_real_1(k21_euclid(A))) ) )
& A != k16_euclid(np__2)
& k1_funct_1(k2_funct_1(k1_jgraph_3),A) != k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A))))))) )
& ~ ( ~ ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
& r1_xreal_0(k1_real_1(k21_euclid(A)),k22_euclid(A)) )
& ~ ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k1_real_1(k21_euclid(A))) )
& A != k16_euclid(np__2)
& k1_funct_1(k2_funct_1(k1_jgraph_3),A) != k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A))))))) ) ) ) ).
fof(t39_jgraph_3,axiom,
( v1_funct_1(k2_funct_1(k1_jgraph_3))
& v1_funct_2(k2_funct_1(k1_jgraph_3),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k2_funct_1(k1_jgraph_3),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ).
fof(t40_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( A != k16_euclid(np__2)
=> ( ( ( ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
& r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
| ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) ) )
=> k1_funct_1(k2_funct_1(k1_jgraph_3),A) = k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A))))))) )
& ~ ( ~ ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
& r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
& ~ ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) )
& k1_funct_1(k2_funct_1(k1_jgraph_3),A) != k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A))))))) ) ) ) ) ).
fof(t41_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k3_xcmplx_0(F,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t42_jgraph_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k3_xcmplx_0(G,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t43_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k4_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k21_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t44_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k4_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k21_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t45_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k4_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k22_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t46_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k4_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& k22_euclid(C) = np__0 ) ) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t51_jgraph_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ~ ( B = k7_relat_1(k2_funct_1(k1_jgraph_3),A)
& v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ).
fof(t52_jgraph_3,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& A = k2_funct_1(k1_jgraph_3)
& v5_pre_topc(A,k15_euclid(np__2),k15_euclid(np__2)) ) ).
fof(t53_jgraph_3,axiom,
$true ).
fof(t54_jgraph_3,axiom,
( v1_funct_1(k1_jgraph_3)
& v1_funct_2(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& k1_pscomp_1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3) = u1_struct_0(k15_euclid(np__2))
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( A = k1_jgraph_3
=> v3_tops_2(A,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ).
fof(dt_k1_jgraph_3,axiom,
( v1_funct_1(k1_jgraph_3)
& v1_funct_2(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ).
fof(t25_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& A = a_0_0_jgraph_3 )
=> v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ).
fof(t26_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& A = a_0_1_jgraph_3 )
=> v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ).
fof(t27_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,B)
& A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_0_jgraph_3 )
=> ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
& v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) ).
fof(t28_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,B)
& A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_1_jgraph_3 )
=> ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
& v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) ).
fof(t33_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( A = a_0_2_jgraph_3
& B = a_0_3_jgraph_3 )
=> k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) ).
fof(t34_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ( ( B = a_0_2_jgraph_3
& v3_tops_2(C,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),A)) )
=> v1_topreal2(A) ) ) ) ) ).
fof(t35_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( A = a_0_2_jgraph_3
=> ( v1_topreal2(A)
& v6_compts_1(A,k15_euclid(np__2)) ) ) ) ).
fof(t36_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( A = a_0_3_jgraph_3
=> v1_topreal2(A) ) ) ).
fof(t37_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( A = a_0_4_jgraph_3
& B = a_0_5_jgraph_3 )
=> r1_tarski(k5_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,B),A) ) ) ) ).
fof(t47_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),A)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& A = a_0_0_jgraph_3 )
=> v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ).
fof(t48_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),A)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& A = a_0_1_jgraph_3 )
=> v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ).
fof(t49_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),B)
& A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_0_jgraph_3 )
=> ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
& v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) ).
fof(t50_jgraph_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),B)
& A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_1_jgraph_3 )
=> ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
& v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) ).
fof(t55_jgraph_3,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_3
& D = a_0_6_jgraph_3
& E = a_0_7_jgraph_3
& F = a_0_8_jgraph_3
& G = a_0_9_jgraph_3
& 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(s1_jgraph_3,axiom,
r1_tarski(a_0_10_jgraph_3,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) ).
fof(s2_jgraph_3,axiom,
a_0_11_jgraph_3 = k3_xboole_0(a_0_12_jgraph_3,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) ).
fof(fraenkel_a_0_0_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_0_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ( ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) )
| ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) )
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_0_1_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_1_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ( ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
& r1_xreal_0(k1_real_1(k22_euclid(B)),k21_euclid(B)) )
| ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),k1_real_1(k22_euclid(B))) ) )
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_0_2_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_2_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ ( ~ ( k1_real_1(np__1) = k21_euclid(B)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) )
& ~ ( k21_euclid(B) = np__1
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) )
& ~ ( k1_real_1(np__1) = k22_euclid(B)
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1) )
& ~ ( np__1 = k22_euclid(B)
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1) ) ) ) ) ).
fof(fraenkel_a_0_3_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_3_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& k5_toprns_1(np__2,B) = np__1 ) ) ).
fof(fraenkel_a_0_4_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_4_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),np__1) ) ) ).
fof(fraenkel_a_0_5_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_5_jgraph_3)
<=> ? [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_6_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_6_jgraph_3)
<=> ? [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_7_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_7_jgraph_3)
<=> ? [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_8_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_8_jgraph_3)
<=> ? [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_9_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_9_jgraph_3)
<=> ? [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_10_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_10_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& p1_s1_jgraph_3(B)
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_0_11_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_11_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& p1_s2_jgraph_3(B)
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_0_12_jgraph_3,axiom,
! [A] :
( r2_hidden(A,a_0_12_jgraph_3)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& p1_s2_jgraph_3(B) ) ) ).
%------------------------------------------------------------------------------