SET007 Axioms: SET007+692.ax
%------------------------------------------------------------------------------
% File : SET007+692 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Outside Fashoda Meet Theorem
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 82 ( 5 unt; 0 def)
% Number of atoms : 777 ( 140 equ)
% Maximal formula atoms : 43 ( 9 avg)
% Number of connectives : 827 ( 132 ~; 7 |; 416 &)
% ( 19 <=>; 253 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 11 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 26 con; 0-6 aty)
% Number of variables : 252 ( 235 !; 17 ?)
% 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_2,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( v1_relat_1(k2_jgraph_2(A,B,C,D))
& v1_funct_1(k2_jgraph_2(A,B,C,D))
& v1_funct_2(k2_jgraph_2(A,B,C,D),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& v5_pre_topc(k2_jgraph_2(A,B,C,D),k15_euclid(np__2),k15_euclid(np__2)) ) ) ).
fof(t1_jgraph_2,axiom,
$true ).
fof(t2_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,A)
=> r1_xreal_0(A,k5_square_1(A)) ) ) ).
fof(t3_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(A,k1_real_1(np__1))
=> r1_xreal_0(k4_xcmplx_0(A),k5_square_1(A)) ) ) ).
fof(t4_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(k5_square_1(A),k4_xcmplx_0(A)) ) ) ).
fof(t5_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(k5_square_1(B),k5_square_1(A))
& r1_xreal_0(np__0,A) )
=> ( r1_xreal_0(k4_xcmplx_0(A),B)
& r1_xreal_0(B,A) ) ) ) ) ).
fof(t6_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(np__0,A)
=> ( r1_xreal_0(k5_square_1(A),k5_square_1(B))
| ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
& ~ r1_xreal_0(A,B) ) ) ) ) ) ).
fof(t7_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(k4_xcmplx_0(A),B)
& r1_xreal_0(B,A) )
=> r1_xreal_0(k5_square_1(B),k5_square_1(A)) ) ) ) ).
fof(t8_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
& ~ r1_xreal_0(A,B)
& r1_xreal_0(k5_square_1(A),k5_square_1(B)) ) ) ) ).
fof(t9_jgraph_2,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] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(D)))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(D)))
=> ~ ( m1_pre_topc(A,D)
& m1_pre_topc(C,D)
& G = k2_pre_topc(A)
& H = k2_pre_topc(C)
& k2_xboole_0(k2_pre_topc(A),k2_pre_topc(C)) = k2_pre_topc(D)
& v4_pre_topc(G,D)
& v4_pre_topc(H,D)
& v5_pre_topc(E,A,B)
& v5_pre_topc(F,C,B)
& ! [I] :
( r2_hidden(I,k3_xboole_0(k2_pre_topc(A),k2_pre_topc(C)))
=> k1_funct_1(E,I) = k1_funct_1(F,I) )
& ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(I,u1_struct_0(D),u1_struct_0(B)) )
=> ~ ( I = k1_funct_4(E,F)
& v5_pre_topc(I,D,B) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_jgraph_2,axiom,
( k21_euclid(k16_euclid(np__2)) = np__0
& k22_euclid(k16_euclid(np__2)) = np__0 ) ).
fof(t12_jgraph_2,axiom,
k5_jordan2c(np__2) = k10_finseq_1(np__1,np__1) ).
fof(t13_jgraph_2,axiom,
( k21_euclid(k5_jordan2c(np__2)) = np__1
& k22_euclid(k5_jordan2c(np__2)) = np__1 ) ).
fof(t14_jgraph_2,axiom,
( k1_wellfnd1(k15_euclid(np__2),k1_numbers,k16_pscomp_1) = u1_struct_0(k15_euclid(np__2))
& k1_wellfnd1(k15_euclid(np__2),k1_numbers,k16_pscomp_1) = k1_euclid(np__2) ) ).
fof(t15_jgraph_2,axiom,
( k1_wellfnd1(k15_euclid(np__2),k1_numbers,k17_pscomp_1) = u1_struct_0(k15_euclid(np__2))
& k1_wellfnd1(k15_euclid(np__2),k1_numbers,k17_pscomp_1) = k1_euclid(np__2) ) ).
fof(t16_jgraph_2,axiom,
$true ).
fof(t17_jgraph_2,axiom,
$true ).
fof(t18_jgraph_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> A = k23_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) ) ).
fof(t19_jgraph_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( A = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
=> ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) != k1_xboole_0
& k4_xboole_0(u1_struct_0(k15_euclid(np__2)),A) != k1_xboole_0 ) ) ) ).
fof(t20_jgraph_2,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] :
( ( 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)) )
=> ( v5_pre_topc(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ~ ( r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),E)
& v3_pre_topc(E,B)
& ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(D,F)
& v3_pre_topc(F,A)
& r1_tarski(k4_pre_topc(A,B,C,F),E) ) ) ) ) ) ) ) ) ) ).
fof(t22_jgraph_2,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] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
=> ! [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)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k3_pre_topc(B,D)),u1_struct_0(k3_pre_topc(C,E)))
& m2_relset_1(G,u1_struct_0(k3_pre_topc(B,D)),u1_struct_0(k3_pre_topc(C,E))) )
=> ~ ( v5_pre_topc(F,A,B)
& v5_pre_topc(G,k3_pre_topc(B,D),k3_pre_topc(C,E))
& r1_tarski(k1_pscomp_1(u1_struct_0(A),u1_struct_0(B),F),D)
& D != k1_xboole_0
& E != k1_xboole_0
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(H,u1_struct_0(A),u1_struct_0(C)) )
=> ~ ( v5_pre_topc(H,A,C)
& H = k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(k3_pre_topc(B,D)),u1_struct_0(k3_pre_topc(C,E)),F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_jgraph_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))))
& m2_relset_1(A,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) )
=> ( A = k1_jgraph_2
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( B != k16_euclid(np__2)
=> ( ( ( ( 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))) ) )
=> k1_funct_1(A,B) = k23_euclid(k6_real_1(np__1,k21_euclid(B)),k6_real_1(k6_real_1(k22_euclid(B),k21_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))) )
& k1_funct_1(A,B) != k23_euclid(k6_real_1(k6_real_1(k21_euclid(B),k22_euclid(B)),k22_euclid(B)),k6_real_1(np__1,k22_euclid(B))) ) ) ) ) ) ) ).
fof(t23_jgraph_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_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))) )
& ~ ( 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))) ) ) ) ).
fof(t24_jgraph_2,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(k1_jgraph_2,A) = k23_euclid(k6_real_1(k6_real_1(k21_euclid(A),k22_euclid(A)),k22_euclid(A)),k6_real_1(np__1,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(k1_jgraph_2,A) != k23_euclid(k6_real_1(np__1,k21_euclid(A)),k6_real_1(k6_real_1(k22_euclid(A),k21_euclid(A)),k21_euclid(A))) ) ) ) ) ).
fof(t29_jgraph_2,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] :
( ( 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(F,G) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t30_jgraph_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( v1_xreal_0(B)
=> ? [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))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) = B )
& v5_pre_topc(C,A,k3_topmetr) ) ) ) ).
fof(t31_jgraph_2,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] :
( ( 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) = k6_xcmplx_0(F,G) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t32_jgraph_2,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] :
( ( 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) = k3_xcmplx_0(E,E) ) ) )
& v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) ).
fof(t33_jgraph_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k3_xcmplx_0(C,F) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t34_jgraph_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( v1_xreal_0(F)
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k2_xcmplx_0(F,C) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t35_jgraph_2,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] :
( ( 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,G) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t36_jgraph_2,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))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C) != np__0 )
& ! [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) = k7_xcmplx_0(np__1,E) ) ) )
& v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) ).
fof(t37_jgraph_2,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,G) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t38_jgraph_2,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(k7_xcmplx_0(F,G),G) ) ) ) )
& v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) ).
fof(t39_jgraph_2,axiom,
! [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(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k1_funct_1(k16_pscomp_1,C) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t40_jgraph_2,axiom,
! [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(k3_pre_topc(k15_euclid(np__2),A)))
=> k1_funct_1(B,C) = k1_funct_1(k17_pscomp_1,C) )
=> v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) ).
fof(t41_jgraph_2,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(np__1,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(t42_jgraph_2,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(np__1,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(t43_jgraph_2,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(k6_real_1(k22_euclid(C),k21_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_2,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(k6_real_1(k21_euclid(C),k22_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(t45_jgraph_2,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))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
& m2_relset_1(E,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
=> ( ( v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr)
& v5_pre_topc(E,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr)
& ! [F] :
( v1_xreal_0(F)
=> ! [G] :
( v1_xreal_0(G)
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( v1_xreal_0(I)
=> ( ( r2_hidden(k23_euclid(F,G),A)
& H = k1_funct_1(D,k23_euclid(F,G))
& I = k1_funct_1(E,k23_euclid(F,G)) )
=> k1_funct_1(C,k23_euclid(F,G)) = k23_euclid(H,I) ) ) ) ) ) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ) ).
fof(t50_jgraph_2,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 = k1_jgraph_2
& v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ).
fof(t53_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,F) = k23_euclid(k2_xcmplx_0(k3_xcmplx_0(A,k21_euclid(F)),B),k2_xcmplx_0(k3_xcmplx_0(C,k22_euclid(F)),D)) )
=> v5_pre_topc(E,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ) ) ).
fof(d2_jgraph_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( E = k2_jgraph_2(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,F) = k23_euclid(k2_xcmplx_0(k3_xcmplx_0(A,k21_euclid(F)),B),k2_xcmplx_0(k3_xcmplx_0(C,k22_euclid(F)),D)) ) ) ) ) ) ) ) ).
fof(t54_jgraph_2,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,np__0)
& ~ r1_xreal_0(C,np__0)
& ~ v2_funct_1(k2_jgraph_2(A,B,C,D)) ) ) ) ) ) ).
fof(t55_jgraph_2,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] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> ! [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)
& k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)) = C
& 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,G)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)),F)
& 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
& 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,G)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)),D)
& 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)
& ~ r1_xreal_0(D,C)
& ~ r1_xreal_0(F,E)
& ! [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))) ) )
& ! [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)),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(dt_k1_jgraph_2,axiom,
( v1_funct_1(k1_jgraph_2)
& v1_funct_2(k1_jgraph_2,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))))
& m2_relset_1(k1_jgraph_2,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) ) ).
fof(dt_k2_jgraph_2,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( v1_funct_1(k2_jgraph_2(A,B,C,D))
& v1_funct_2(k2_jgraph_2(A,B,C,D),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k2_jgraph_2(A,B,C,D),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ) ).
fof(t10_jgraph_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( v1_xreal_0(D)
=> ( C = B
=> k9_metric_1(k14_euclid(A),B,D) = a_3_0_jgraph_2(A,C,D) ) ) ) ) ) ).
fof(t21_jgraph_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( v3_pre_topc(B,k15_euclid(np__2))
& r2_hidden(A,B)
& ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,np__0)
& r1_tarski(a_2_0_jgraph_2(A,C),B) ) ) ) ) ) ).
fof(t25_jgraph_2,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))))
=> ( B = a_0_0_jgraph_2
=> r1_tarski(k2_relat_1(k2_partfun1(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,B)),u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B))) ) ) ) ).
fof(t26_jgraph_2,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))))
=> ( B = a_0_1_jgraph_2
=> r1_tarski(k2_relat_1(k2_partfun1(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,B)),u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B))) ) ) ) ).
fof(t27_jgraph_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( A = a_0_0_jgraph_2
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)) )
=> ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))))
& ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ) ).
fof(t28_jgraph_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( A = a_0_1_jgraph_2
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)) )
=> ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))))
& ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ) ).
fof(t46_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
=> v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ).
fof(t47_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
=> v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ).
fof(t48_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
=> ( 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(t49_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
=> ( 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(t51_jgraph_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( A = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
& B = a_0_2_jgraph_2
& C = a_0_3_jgraph_2
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A))),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A))))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A))),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))) )
=> ~ ( v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))
& v2_funct_1(D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(E,B)
& E != k16_euclid(np__2)
& r2_hidden(k1_funct_1(D,E),k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ~ r2_hidden(E,k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C))
=> r2_hidden(k1_funct_1(D,E),B) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(E,C)
=> k1_funct_1(D,E) = E ) ) ) ) ) ) ) ) ).
fof(t52_jgraph_2,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,u1_struct_0(k5_topmetr))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_topmetr))
=> ~ ( D = np__0
& E = 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_2_jgraph_2
& k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,D)) = k1_real_1(np__1)
& k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,E)) = np__1
& r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,D)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,D)),np__1)
& r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,E)))
& r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,E)),np__1)
& k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,D)) = k1_real_1(np__1)
& k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,E)) = np__1
& r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,D)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,D)),np__1)
& r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,E)))
& r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,E)),np__1)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
& r1_xboole_0(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(t56_jgraph_2,axiom,
( v4_pre_topc(a_0_4_jgraph_2,k15_euclid(np__2))
& m1_subset_1(a_0_4_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& v4_pre_topc(a_0_5_jgraph_2,k15_euclid(np__2))
& m1_subset_1(a_0_5_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t57_jgraph_2,axiom,
( v4_pre_topc(a_0_6_jgraph_2,k15_euclid(np__2))
& m1_subset_1(a_0_6_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& v4_pre_topc(a_0_7_jgraph_2,k15_euclid(np__2))
& m1_subset_1(a_0_7_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t58_jgraph_2,axiom,
( v4_pre_topc(a_0_8_jgraph_2,k15_euclid(np__2))
& m1_subset_1(a_0_8_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& v4_pre_topc(a_0_9_jgraph_2,k15_euclid(np__2))
& m1_subset_1(a_0_9_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(s1_jgraph_2,axiom,
m1_subset_1(a_0_10_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ).
fof(s2_jgraph_2,axiom,
( f1_s2_jgraph_2 = a_0_11_jgraph_2
=> k3_subset_1(u1_struct_0(k15_euclid(np__2)),f1_s2_jgraph_2) = a_0_12_jgraph_2 ) ).
fof(s3_jgraph_2,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)))
=> ( f1_s3_jgraph_2(k20_euclid(np__2,A,B)) = k6_xcmplx_0(f1_s3_jgraph_2(A),f1_s3_jgraph_2(B))
& f2_s3_jgraph_2(k20_euclid(np__2,A,B)) = k6_xcmplx_0(f2_s3_jgraph_2(A),f2_s3_jgraph_2(B)) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> k7_square_1(k5_toprns_1(np__2,k20_euclid(np__2,A,B))) = k2_xcmplx_0(k5_square_1(f1_s3_jgraph_2(k20_euclid(np__2,A,B))),k5_square_1(f2_s3_jgraph_2(k20_euclid(np__2,A,B)))) ) ) )
=> ( v4_pre_topc(a_0_13_jgraph_2,k15_euclid(np__2))
& m1_subset_1(a_0_13_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ).
fof(fraenkel_a_3_0_jgraph_2,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,u1_struct_0(k15_euclid(B)))
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_0_jgraph_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
& A = E
& ~ r1_xreal_0(D,k5_toprns_1(B,k20_euclid(B,C,E))) ) ) ) ).
fof(fraenkel_a_2_0_jgraph_2,axiom,
! [A,B,C] :
( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_0_jgraph_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& A = D
& ~ r1_xreal_0(k21_euclid(D),k6_xcmplx_0(k21_euclid(B),C))
& ~ r1_xreal_0(k2_xcmplx_0(k21_euclid(B),C),k21_euclid(D))
& ~ r1_xreal_0(k22_euclid(D),k6_xcmplx_0(k22_euclid(B),C))
& ~ r1_xreal_0(k2_xcmplx_0(k22_euclid(B),C),k22_euclid(D)) ) ) ) ).
fof(fraenkel_a_0_0_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_0_jgraph_2)
<=> ? [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_2,axiom,
! [A] :
( r2_hidden(A,a_0_1_jgraph_2)
<=> ? [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_2,axiom,
! [A] :
( r2_hidden(A,a_0_2_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ r1_xreal_0(k21_euclid(B),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k21_euclid(B))
& ~ r1_xreal_0(k22_euclid(B),k1_real_1(np__1))
& ~ r1_xreal_0(np__1,k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_3_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_3_jgraph_2)
<=> ? [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_4_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_4_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k22_euclid(B),k21_euclid(B)) ) ) ).
fof(fraenkel_a_0_5_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_5_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k21_euclid(B),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_6_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_6_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ).
fof(fraenkel_a_0_7_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_7_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ).
fof(fraenkel_a_0_8_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_8_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k1_real_1(k22_euclid(B)),k21_euclid(B)) ) ) ).
fof(fraenkel_a_0_9_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_9_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k21_euclid(B),k1_real_1(k22_euclid(B))) ) ) ).
fof(fraenkel_a_0_10_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_10_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& p1_s1_jgraph_2(B) ) ) ).
fof(fraenkel_a_0_11_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_11_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& p1_s2_jgraph_2(B) ) ) ).
fof(fraenkel_a_0_12_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_12_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& ~ p1_s2_jgraph_2(B) ) ) ).
fof(fraenkel_a_0_13_jgraph_2,axiom,
! [A] :
( r2_hidden(A,a_0_13_jgraph_2)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(f1_s3_jgraph_2(B),f2_s3_jgraph_2(B)) ) ) ).
%------------------------------------------------------------------------------