SET007 Axioms: SET007+713.ax
%------------------------------------------------------------------------------
% File : SET007+713 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Fan Homeomorphisms in the Plane
% 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 192 ( 4 unt; 0 def)
% Number of atoms : 1766 ( 327 equ)
% Maximal formula atoms : 26 ( 9 avg)
% Number of connectives : 1928 ( 354 ~; 160 |; 733 &)
% ( 28 <=>; 653 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 78 ( 78 usr; 12 con; 0-4 aty)
% Number of variables : 596 ( 547 !; 49 ?)
% 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_4,axiom,
$true ).
fof(t2_jgraph_4,axiom,
$true ).
fof(t3_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ ( ~ r1_xreal_0(k2_xcmplx_0(np__1,A),np__0)
& ~ r1_xreal_0(k6_xcmplx_0(np__1,A),np__0) ) ) ) ).
fof(t4_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(k5_square_1(A),np__1)
=> ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) ) ) ) ).
fof(t5_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(np__1,k5_square_1(A))
=> ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A) ) ) ) ).
fof(t8_jgraph_4,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))) )
=> ( ( v5_pre_topc(A,k15_euclid(np__2),k15_euclid(np__2))
& v2_funct_1(A)
& k1_pscomp_1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A) = k2_pre_topc(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 = k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),A,C)
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& r2_hidden(B,D)
& v3_pre_topc(D,k15_euclid(np__2))
& r1_tarski(D,C)
& r2_hidden(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A,B),D) ) ) ) )
=> v3_tops_2(A,k15_euclid(np__2),k15_euclid(np__2)) ) ) ).
fof(t9_jgraph_4,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)) )
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& E != np__0
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != np__0 )
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( v1_xreal_0(I)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,G) = H
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,G) = I )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),F,G) = k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(H,I),D),E) ) ) ) )
& v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) ).
fof(t10_jgraph_4,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)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& E != np__0
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != np__0 )
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,G) = H
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,G) = I )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),F,G) = k4_real_1(I,k6_real_1(k5_real_1(k6_real_1(H,I),D),E)) ) ) ) )
& v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) ).
fof(t11_jgraph_4,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) = k5_square_1(E) ) ) )
& v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) ).
fof(t12_jgraph_4,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) = k18_complex1(E) ) ) )
& v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) ).
fof(t13_jgraph_4,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) = k4_xcmplx_0(E) ) ) )
& v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) ).
fof(t14_jgraph_4,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)) )
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& E != np__0
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != np__0 )
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( v1_xreal_0(I)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,G) = H
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,G) = I )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),F,G) = k3_xcmplx_0(I,k1_real_1(k9_square_1(k18_complex1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(H,I),D),E))))))) ) ) ) )
& v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) ).
fof(t15_jgraph_4,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)) )
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ~ ( v5_pre_topc(B,A,k3_topmetr)
& v5_pre_topc(C,A,k3_topmetr)
& E != np__0
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != np__0 )
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( v1_xreal_0(H)
=> ! [I] :
( v1_xreal_0(I)
=> ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,G) = H
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,G) = I )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),F,G) = k3_xcmplx_0(I,k9_square_1(k18_complex1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(H,I),D),E)))))) ) ) ) )
& v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) ).
fof(d1_jgraph_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr)) )
=> ( B = k1_jgraph_4(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr),B,C) = k5_toprns_1(A,C) ) ) ) ) ).
fof(t16_jgraph_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k1_relat_1(k1_jgraph_4(A)) = u1_struct_0(k15_euclid(A))
& k1_relat_1(k1_jgraph_4(A)) = k1_euclid(A) ) ) ).
fof(t17_jgraph_4,axiom,
$true ).
fof(t18_jgraph_4,axiom,
$true ).
fof(t19_jgraph_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr)) )
=> ( B = k1_jgraph_4(A)
=> v5_pre_topc(B,k15_euclid(A),k3_topmetr) ) ) ) ).
fof(t20_jgraph_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(A),B)),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(A),B)),u1_struct_0(k3_topmetr)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
=> k1_funct_1(C,D) = k1_funct_1(k1_jgraph_4(A),D) )
=> v5_pre_topc(C,k3_pre_topc(k15_euclid(A),B),k3_topmetr) ) ) ) ) ).
fof(t21_jgraph_4,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,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( D = k10_metric_1(k14_euclid(A),B,C)
=> ( v1_jordan2c(D,A)
& v4_pre_topc(D,k15_euclid(A)) ) ) ) ) ) ) ).
fof(t22_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k14_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( C = k10_metric_1(k14_euclid(np__2),A,B)
=> v6_compts_1(C,k15_euclid(np__2)) ) ) ) ) ).
fof(d2_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
=> ( r1_xreal_0(np__0,k21_euclid(B))
| k2_jgraph_4(A,B) = k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k4_xcmplx_0(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A)))))),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A)))) ) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k21_euclid(B))
& k2_jgraph_4(A,B) != k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k4_xcmplx_0(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A)))))),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A)))) )
& ~ ( ~ ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k21_euclid(B)) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k21_euclid(B)) )
& k2_jgraph_4(A,B) != B ) ) ) ) ).
fof(d3_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( B = k3_jgraph_4(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,C) = k2_jgraph_4(A,C) ) ) ) ) ).
fof(t23_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(B,k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)))
=> ( r1_xreal_0(np__0,k21_euclid(A))
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(B),A) = k23_euclid(k3_xcmplx_0(k5_toprns_1(np__2,A),k4_xcmplx_0(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B))))))),k3_xcmplx_0(k5_toprns_1(np__2,A),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B)))) ) )
& ( r1_xreal_0(np__0,k21_euclid(A))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(B),A) = A ) ) ) ) ).
fof(t24_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r1_xreal_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B)
=> ( r1_xreal_0(np__0,k21_euclid(A))
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))))))),k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))) ) ) ) ) ).
fof(t25_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,B)
& ~ ( ( ( r1_xreal_0(B,k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)))
& r1_xreal_0(k21_euclid(A),np__0) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B))))))),k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B)))) ) )
& ( ( r1_xreal_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B)
& r1_xreal_0(k21_euclid(A),np__0) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))))))),k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))) ) ) ) ) ) ) ).
fof(t26_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k21_euclid(D),np__0)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t27_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k21_euclid(D),np__0)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t28_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A))))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k21_euclid(D),np__0)
& r1_xreal_0(A,k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t29_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A))))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k21_euclid(D),np__0)
& r1_xreal_0(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t40_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,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)),k3_jgraph_4(A),B)) = k5_toprns_1(np__2,B) ) ) ).
fof(t43_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_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),B)))
& 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),B))) )
=> ~ ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),B)
& v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ).
fof(t44_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k3_jgraph_4(A)
& v5_pre_topc(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t45_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ v2_funct_1(k3_jgraph_4(A)) ) ) ).
fof(t46_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ ( v1_funct_1(k3_jgraph_4(A))
& v1_funct_2(k3_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k3_jgraph_4(A),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)),k3_jgraph_4(A)) = u1_struct_0(k15_euclid(np__2)) ) ) ) ).
fof(t47_jgraph_4,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)
& ! [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 = k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k3_jgraph_4(A),C)
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& r2_hidden(B,D)
& v3_pre_topc(D,k15_euclid(np__2))
& r1_tarski(D,C)
& r2_hidden(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),B),D) ) ) ) ) ) ) ).
fof(t48_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k3_jgraph_4(A)
& v3_tops_2(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t49_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_xreal_0(np__0,k21_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)),k3_jgraph_4(A),B)
=> ( ~ r1_xreal_0(np__0,k21_euclid(C))
& r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ) ) ).
fof(t50_jgraph_4,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,k21_euclid(B))
& ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,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)),k3_jgraph_4(A),B)
& ~ ( ~ r1_xreal_0(np__0,k21_euclid(C))
& ~ r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ).
fof(t51_jgraph_4,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(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& r1_xreal_0(A,k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C))) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_xreal_0(np__0,k21_euclid(B))
| r1_xreal_0(np__0,k21_euclid(C))
| 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)),k3_jgraph_4(A),B)
& E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_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(t52_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(np__0,k21_euclid(B))
& ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k21_euclid(C))
& ~ r1_xreal_0(A,k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)))
& ~ 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)),k3_jgraph_4(A),B)
& E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_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(t53_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(np__0,k21_euclid(B))
& ~ r1_xreal_0(np__0,k21_euclid(C))
& ~ 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)),k3_jgraph_4(A),B)
& E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_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(t54_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)) = A
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_xreal_0(np__0,k21_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)),k3_jgraph_4(A),B)
=> ( ~ r1_xreal_0(np__0,k21_euclid(C))
& k22_euclid(C) = np__0 ) ) ) ) ) ) ) ).
fof(t55_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> k16_euclid(np__2) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),k16_euclid(np__2)) ) ).
fof(d4_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
=> ( r1_xreal_0(k22_euclid(B),np__0)
| k4_jgraph_4(A,B) = k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A)),k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A))))))) ) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k22_euclid(B),np__0)
& k4_jgraph_4(A,B) != k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A)),k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A))))))) )
& ~ ( ~ ( r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k22_euclid(B),np__0) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k22_euclid(B),np__0) )
& k4_jgraph_4(A,B) != B ) ) ) ) ).
fof(d5_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( B = k5_jgraph_4(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,C) = k4_jgraph_4(A,C) ) ) ) ) ).
fof(t56_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(B,k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)))
=> ( r1_xreal_0(k22_euclid(A),np__0)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(B),A) = k23_euclid(k3_xcmplx_0(k5_toprns_1(np__2,A),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B))),k3_xcmplx_0(k5_toprns_1(np__2,A),k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B))))))) ) )
& ( r1_xreal_0(k22_euclid(A),np__0)
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(B),A) = A ) ) ) ) ).
fof(t57_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r1_xreal_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B)
=> ( r1_xreal_0(k22_euclid(A),np__0)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))),k4_real_1(k5_toprns_1(np__2,A),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))))))) ) ) ) ) ).
fof(t58_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,B)
& ~ ( ( ( r1_xreal_0(B,k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)))
& r1_xreal_0(np__0,k22_euclid(A)) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B))),k4_real_1(k5_toprns_1(np__2,A),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B))))))) ) )
& ( ( r1_xreal_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B)
& r1_xreal_0(np__0,k22_euclid(A)) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))),k4_real_1(k5_toprns_1(np__2,A),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))))))) ) ) ) ) ) ) ).
fof(t59_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k22_euclid(D))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t60_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k22_euclid(D))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t61_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A)))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k22_euclid(D))
& r1_xreal_0(A,k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t62_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A)))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k22_euclid(D))
& r1_xreal_0(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t73_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,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)),k5_jgraph_4(A),B)) = k5_toprns_1(np__2,B) ) ) ).
fof(t76_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_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),B)))
& 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),B))) )
=> ~ ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
& v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ).
fof(t77_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k5_jgraph_4(A)
& v5_pre_topc(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t78_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ v2_funct_1(k5_jgraph_4(A)) ) ) ).
fof(t79_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ ( v1_funct_1(k5_jgraph_4(A))
& v1_funct_2(k5_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k5_jgraph_4(A),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)),k5_jgraph_4(A)) = u1_struct_0(k15_euclid(np__2)) ) ) ) ).
fof(t80_jgraph_4,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)
& ! [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 = k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k5_jgraph_4(A),C)
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& r2_hidden(B,D)
& v3_pre_topc(D,k15_euclid(np__2))
& r1_tarski(D,C)
& r2_hidden(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B),D) ) ) ) ) ) ) ).
fof(t81_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k5_jgraph_4(A)
& v3_tops_2(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t82_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
=> ( 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)
& r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ) ) ) ) ).
fof(t83_jgraph_4,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)
& ~ r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,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)),k5_jgraph_4(A),B)
& ~ ( ~ r1_xreal_0(k22_euclid(C),np__0)
& ~ r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ) ) ).
fof(t84_jgraph_4,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(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& r1_xreal_0(A,k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C))) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_xreal_0(k22_euclid(B),np__0)
| r1_xreal_0(k22_euclid(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(t85_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k22_euclid(B),np__0)
& ~ r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k22_euclid(C),np__0)
& ~ r1_xreal_0(A,k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)))
& ~ 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(t86_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k22_euclid(B),np__0)
& ~ r1_xreal_0(k22_euclid(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(t87_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)) = A
=> ( 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)
& k21_euclid(C) = np__0 ) ) ) ) ) ) ) ).
fof(t88_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> k16_euclid(np__2) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),k16_euclid(np__2)) ) ).
fof(d6_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
=> ( r1_xreal_0(k21_euclid(B),np__0)
| k6_jgraph_4(A,B) = k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A))))),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A)))) ) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k21_euclid(B),np__0)
& k6_jgraph_4(A,B) != k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A))))),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A)))) )
& ~ ( ~ ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k21_euclid(B),np__0) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k21_euclid(B),np__0) )
& k6_jgraph_4(A,B) != B ) ) ) ) ).
fof(d7_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( B = k7_jgraph_4(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,C) = k6_jgraph_4(A,C) ) ) ) ) ).
fof(t89_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(B,k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)))
=> ( r1_xreal_0(k21_euclid(A),np__0)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(B),A) = k23_euclid(k3_xcmplx_0(k5_toprns_1(np__2,A),k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B)))))),k3_xcmplx_0(k5_toprns_1(np__2,A),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B)))) ) )
& ( r1_xreal_0(k21_euclid(A),np__0)
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(B),A) = A ) ) ) ) ).
fof(t90_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r1_xreal_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B)
=> ( r1_xreal_0(k21_euclid(A),np__0)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))))),k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))) ) ) ) ) ).
fof(t91_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,B)
& ~ ( ( ( r1_xreal_0(B,k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)))
& r1_xreal_0(np__0,k21_euclid(A)) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B)))))),k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B)))) ) )
& ( ( r1_xreal_0(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B)
& r1_xreal_0(np__0,k21_euclid(A)) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))))),k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k22_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))) ) ) ) ) ) ) ).
fof(t92_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k21_euclid(D))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t93_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k21_euclid(D))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t94_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A)))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k21_euclid(D))
& r1_xreal_0(A,k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t95_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A)))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(np__0,k21_euclid(D))
& r1_xreal_0(k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D)),A)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t104_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,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)),k7_jgraph_4(A),B)) = k5_toprns_1(np__2,B) ) ) ).
fof(t107_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_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),B)))
& 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),B))) )
=> ~ ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
& v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ).
fof(t108_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k7_jgraph_4(A)
& v5_pre_topc(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t109_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ v2_funct_1(k7_jgraph_4(A)) ) ) ).
fof(t110_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ ( v1_funct_1(k7_jgraph_4(A))
& v1_funct_2(k7_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k7_jgraph_4(A),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)),k7_jgraph_4(A)) = u1_struct_0(k15_euclid(np__2)) ) ) ) ).
fof(t111_jgraph_4,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)
& ! [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 = k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k7_jgraph_4(A),C)
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& r2_hidden(B,D)
& v3_pre_topc(D,k15_euclid(np__2))
& r1_tarski(D,C)
& r2_hidden(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B),D) ) ) ) ) ) ) ).
fof(t112_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k7_jgraph_4(A)
& v3_tops_2(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t113_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
=> ( 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)
& r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ) ) ).
fof(t114_jgraph_4,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)
& ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,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)),k7_jgraph_4(A),B)
& ~ ( ~ r1_xreal_0(k21_euclid(C),np__0)
& ~ r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ).
fof(t115_jgraph_4,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(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& r1_xreal_0(A,k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C))) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r1_xreal_0(k21_euclid(B),np__0)
| r1_xreal_0(k21_euclid(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(t116_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k21_euclid(B),np__0)
& ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(k21_euclid(C),np__0)
& ~ r1_xreal_0(A,k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)))
& ~ 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(t117_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k21_euclid(B),np__0)
& ~ r1_xreal_0(k21_euclid(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(t118_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)) = A
=> ( 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)
& k22_euclid(C) = np__0 ) ) ) ) ) ) ) ).
fof(t119_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> k16_euclid(np__2) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),k16_euclid(np__2)) ) ).
fof(d8_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
=> ( r1_xreal_0(np__0,k22_euclid(B))
| k8_jgraph_4(A,B) = k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A)),k4_xcmplx_0(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k6_xcmplx_0(np__1,A)))))))) ) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k22_euclid(B))
& k8_jgraph_4(A,B) != k18_euclid(k5_toprns_1(np__2,B),np__2,k23_euclid(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A)),k4_xcmplx_0(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A),k2_xcmplx_0(np__1,A)))))))) )
& ~ ( ~ ( r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k22_euclid(B)) )
& ~ ( ~ r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k22_euclid(B)) )
& k8_jgraph_4(A,B) != B ) ) ) ) ).
fof(d9_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ( B = k9_jgraph_4(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,C) = k8_jgraph_4(A,C) ) ) ) ) ).
fof(t120_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(B,k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)))
=> ( r1_xreal_0(np__0,k22_euclid(A))
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(B),A) = k23_euclid(k3_xcmplx_0(k5_toprns_1(np__2,A),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B))),k3_xcmplx_0(k5_toprns_1(np__2,A),k4_xcmplx_0(k8_square_1(k6_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k6_xcmplx_0(np__1,B)))))))) ) )
& ( r1_xreal_0(np__0,k22_euclid(A))
=> k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(B),A) = A ) ) ) ) ).
fof(t121_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r1_xreal_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B)
=> ( r1_xreal_0(np__0,k22_euclid(A))
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))),k4_real_1(k5_toprns_1(np__2,A),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))))))) ) ) ) ) ).
fof(t122_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,B)
& ~ ( ( ( r1_xreal_0(B,k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)))
& r1_xreal_0(k22_euclid(A),np__0) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B))),k4_real_1(k5_toprns_1(np__2,A),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k5_real_1(np__1,B)))))))) ) )
& ( ( r1_xreal_0(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B)
& r1_xreal_0(k22_euclid(A),np__0) )
=> ( A = k16_euclid(np__2)
| k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(B),A) = k23_euclid(k4_real_1(k5_toprns_1(np__2,A),k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B))),k4_real_1(k5_toprns_1(np__2,A),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(A),k5_toprns_1(np__2,A)),B),k3_real_1(np__1,B)))))))) ) ) ) ) ) ) ).
fof(t123_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k22_euclid(D),np__0)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t124_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k22_euclid(D),np__0)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t125_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k5_real_1(np__1,A))))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k22_euclid(D),np__0)
& r1_xreal_0(A,k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)))
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t126_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(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_topmetr))
& m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_topmetr)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> k1_funct_1(C,D) = k4_real_1(k5_toprns_1(np__2,D),k1_real_1(k9_square_1(k5_real_1(np__1,k7_square_1(k6_real_1(k5_real_1(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A),k3_real_1(np__1,A))))))) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
=> ( r1_xreal_0(k22_euclid(D),np__0)
& r1_xreal_0(k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D)),A)
& D != k16_euclid(np__2) ) ) ) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_topmetr) ) ) ) ) ) ).
fof(t135_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,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)),k9_jgraph_4(A),B)) = k5_toprns_1(np__2,B) ) ) ).
fof(t138_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_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),B)))
& 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),B))) )
=> ~ ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ).
fof(t139_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k9_jgraph_4(A)
& v5_pre_topc(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t140_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ v2_funct_1(k9_jgraph_4(A)) ) ) ).
fof(t141_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ ( v1_funct_1(k9_jgraph_4(A))
& v1_funct_2(k9_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k9_jgraph_4(A),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)),k9_jgraph_4(A)) = u1_struct_0(k15_euclid(np__2)) ) ) ) ).
fof(t142_jgraph_4,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)
& ! [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 = k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k9_jgraph_4(A),C)
& ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& r2_hidden(B,D)
& v3_pre_topc(D,k15_euclid(np__2))
& r1_tarski(D,C)
& r2_hidden(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B),D) ) ) ) ) ) ) ).
fof(t143_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
=> ~ ( B = k9_jgraph_4(A)
& v3_tops_2(B,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ).
fof(t144_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
=> ( 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))
& r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ) ) ) ) ).
fof(t145_jgraph_4,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(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,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))
& ~ r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ) ) ).
fof(t146_jgraph_4,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(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& r1_xreal_0(A,k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C))) )
=> ( 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(np__0,k22_euclid(C))
| 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(t147_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(np__0,k22_euclid(B))
& ~ r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
& ~ r1_xreal_0(np__0,k22_euclid(C))
& ~ r1_xreal_0(A,k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)))
& ~ 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(t148_jgraph_4,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(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ r1_xreal_0(np__0,k22_euclid(B))
& ~ r1_xreal_0(np__0,k22_euclid(C))
& ~ 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(t149_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)) = A
=> ( 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))
& k21_euclid(C) = np__0 ) ) ) ) ) ) ) ).
fof(t150_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> k16_euclid(np__2) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),k16_euclid(np__2)) ) ).
fof(dt_k1_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_funct_1(k1_jgraph_4(A))
& v1_funct_2(k1_jgraph_4(A),u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(k1_jgraph_4(A),u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr)) ) ) ).
fof(dt_k2_jgraph_4,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k2_jgraph_4(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k3_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( v1_funct_1(k3_jgraph_4(A))
& v1_funct_2(k3_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k3_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ) ).
fof(dt_k4_jgraph_4,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k4_jgraph_4(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k5_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( v1_funct_1(k5_jgraph_4(A))
& v1_funct_2(k5_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k5_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ) ).
fof(dt_k6_jgraph_4,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k6_jgraph_4(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k7_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( v1_funct_1(k7_jgraph_4(A))
& v1_funct_2(k7_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k7_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ) ).
fof(dt_k8_jgraph_4,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k8_jgraph_4(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k9_jgraph_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ( v1_funct_1(k9_jgraph_4(A))
& v1_funct_2(k9_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k9_jgraph_4(A),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ) ).
fof(t6_jgraph_4,axiom,
! [A] :
( ( ~ v3_struct_0(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] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( v1_xreal_0(D)
=> ( ( v5_pre_topc(B,A,k3_topmetr)
& C = a_3_0_jgraph_4(A,B,D) )
=> v3_pre_topc(C,A) ) ) ) ) ) ).
fof(t7_jgraph_4,axiom,
! [A] :
( ( ~ v3_struct_0(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] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( v5_pre_topc(B,A,k3_topmetr)
& C = a_3_1_jgraph_4(A,B,D) )
=> v3_pre_topc(C,A) ) ) ) ) ) ).
fof(t30_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),B)
& C = a_0_0_jgraph_4
& B = a_1_0_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t31_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),B)
& C = a_0_0_jgraph_4
& B = a_1_1_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t32_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_2_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t33_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_3_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t34_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),B)
& C = 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_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t35_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),B)
& C = 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_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t36_jgraph_4,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))))
=> ( ( 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_4 )
=> v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ).
fof(t37_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_0_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t38_jgraph_4,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))))
=> ( ( 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_4 )
=> v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ).
fof(t39_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k3_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_1_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t41_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_0_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k3_jgraph_4(A),B),C) ) ) ) ).
fof(t42_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_1_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k3_jgraph_4(A),B),C) ) ) ) ).
fof(t63_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
& C = a_0_2_jgraph_4
& B = a_1_4_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t64_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
& C = a_0_2_jgraph_4
& B = a_1_5_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t65_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_6_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t66_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_7_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t67_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
& C = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_2_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t68_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
& C = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_3_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t69_jgraph_4,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))))
=> ( ( 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_2_jgraph_4 )
=> v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ).
fof(t70_jgraph_4,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))))
=> ( ( 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_3_jgraph_4 )
=> v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ).
fof(t71_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_2_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t72_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_3_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t74_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_2_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k5_jgraph_4(A),B),C) ) ) ) ).
fof(t75_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_3_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k5_jgraph_4(A),B),C) ) ) ) ).
fof(t96_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
& C = a_0_1_jgraph_4
& B = a_1_8_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t97_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
& C = a_0_1_jgraph_4
& B = a_1_9_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t98_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_10_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t99_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_11_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t100_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
& C = 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_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t101_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
& C = 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_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t102_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_1_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t103_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_0_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t105_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_1_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k7_jgraph_4(A),B),C) ) ) ) ).
fof(t106_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_0_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k7_jgraph_4(A),B),C) ) ) ) ).
fof(t127_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& C = a_0_3_jgraph_4
& B = a_1_12_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t128_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& C = a_0_3_jgraph_4
& B = a_1_13_jgraph_4(A) )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t129_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_14_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t130_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = a_1_15_jgraph_4(A)
=> v4_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t131_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& C = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_3_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t132_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),C))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
& C = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& B = a_0_2_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),C)) ) ) ) ) ) ) ).
fof(t133_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_3_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t134_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [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(k3_pre_topc(k15_euclid(np__2),B))))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
& m2_relset_1(D,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
=> ( ( D = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),C)
& B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
& C = a_0_2_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| v5_pre_topc(D,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),B),C),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ).
fof(t136_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_3_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k9_jgraph_4(A),B),C) ) ) ) ).
fof(t137_jgraph_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B,C] :
( ( r2_hidden(B,C)
& C = a_0_2_jgraph_4 )
=> ( r1_xreal_0(A,k1_real_1(np__1))
| r1_xreal_0(np__1,A)
| r2_hidden(k1_funct_1(k9_jgraph_4(A),B),C) ) ) ) ).
fof(s1_jgraph_4,axiom,
( f1_s1_jgraph_4 = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
=> r1_tarski(a_0_4_jgraph_4,u1_struct_0(k3_pre_topc(k15_euclid(np__2),f1_s1_jgraph_4))) ) ).
fof(fraenkel_a_3_0_jgraph_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(k3_topmetr))
& v1_xreal_0(D) )
=> ( r2_hidden(A,a_3_0_jgraph_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& ~ r1_xreal_0(k6_jordan2c(B,k3_topmetr,C,E),D) ) ) ) ).
fof(fraenkel_a_3_1_jgraph_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(k3_topmetr))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_1_jgraph_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& ~ r1_xreal_0(D,k6_jordan2c(B,k3_topmetr,C,E)) ) ) ) ).
fof(fraenkel_a_0_0_jgraph_4,axiom,
! [A] :
( r2_hidden(A,a_0_0_jgraph_4)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k21_euclid(B),np__0)
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_1_0_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_0_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(B,k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)))
& r1_xreal_0(k21_euclid(C),np__0)
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_1_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_1_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)),B)
& r1_xreal_0(k21_euclid(C),np__0)
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_2_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_2_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k4_real_1(B,k5_toprns_1(np__2,C)),k22_euclid(C))
& r1_xreal_0(k21_euclid(C),np__0) ) ) ) ).
fof(fraenkel_a_1_3_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_3_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k22_euclid(C),k4_real_1(B,k5_toprns_1(np__2,C)))
& r1_xreal_0(k21_euclid(C),np__0) ) ) ) ).
fof(fraenkel_a_0_1_jgraph_4,axiom,
! [A] :
( r2_hidden(A,a_0_1_jgraph_4)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(np__0,k21_euclid(B))
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_0_2_jgraph_4,axiom,
! [A] :
( r2_hidden(A,a_0_2_jgraph_4)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(np__0,k22_euclid(B))
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_1_4_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_4_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(B,k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)))
& r1_xreal_0(np__0,k22_euclid(C))
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_5_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_5_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)),B)
& r1_xreal_0(np__0,k22_euclid(C))
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_6_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_6_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k4_real_1(B,k5_toprns_1(np__2,C)),k21_euclid(C))
& r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_7_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_7_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k21_euclid(C),k4_real_1(B,k5_toprns_1(np__2,C)))
& r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ).
fof(fraenkel_a_0_3_jgraph_4,axiom,
! [A] :
( r2_hidden(A,a_0_3_jgraph_4)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& r1_xreal_0(k22_euclid(B),np__0)
& B != k16_euclid(np__2) ) ) ).
fof(fraenkel_a_1_8_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_8_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(B,k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)))
& r1_xreal_0(np__0,k21_euclid(C))
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_9_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_9_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)),B)
& r1_xreal_0(np__0,k21_euclid(C))
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_10_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_10_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k4_real_1(B,k5_toprns_1(np__2,C)),k22_euclid(C))
& r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_11_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_11_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k22_euclid(C),k4_real_1(B,k5_toprns_1(np__2,C)))
& r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_12_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_12_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(B,k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)))
& r1_xreal_0(k22_euclid(C),np__0)
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_13_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_13_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)),B)
& r1_xreal_0(k22_euclid(C),np__0)
& C != k16_euclid(np__2) ) ) ) ).
fof(fraenkel_a_1_14_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_14_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k4_real_1(B,k5_toprns_1(np__2,C)),k21_euclid(C))
& r1_xreal_0(k22_euclid(C),np__0) ) ) ) ).
fof(fraenkel_a_1_15_jgraph_4,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_15_jgraph_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k21_euclid(C),k4_real_1(B,k5_toprns_1(np__2,C)))
& r1_xreal_0(k22_euclid(C),np__0) ) ) ) ).
fof(fraenkel_a_0_4_jgraph_4,axiom,
! [A] :
( r2_hidden(A,a_0_4_jgraph_4)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& A = B
& p1_s1_jgraph_4(B)
& B != k16_euclid(np__2) ) ) ).
%------------------------------------------------------------------------------