SET007 Axioms: SET007+414.ax
%------------------------------------------------------------------------------
% File : SET007+414 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Special Polygons
% 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 : sppol_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 92 ( 5 unt; 0 def)
% Number of atoms : 530 ( 65 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 481 ( 43 ~; 13 |; 193 &)
% ( 3 <=>; 229 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 7 con; 0-4 aty)
% Number of variables : 205 ( 195 !; 10 ?)
% 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(rc1_sppol_2,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v4_topreal1(A) ) ).
fof(cc1_sppol_2,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v4_topreal1(A)
=> ( v2_funct_1(A)
& ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A) ) ) ) ).
fof(cc2_sppol_2,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ( v2_funct_1(A)
& ~ v1_realset1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A) )
=> v4_topreal1(A) ) ) ).
fof(cc3_sppol_2,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v4_topreal1(A)
=> ~ v1_xboole_0(A) ) ) ).
fof(rc2_sppol_2,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& ~ v1_realset1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& v4_topreal1(A) ) ).
fof(fc1_sppol_2,axiom,
! [A,B] :
( ( v2_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v2_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc2_sppol_2,axiom,
! [A,B] :
( ( v2_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v2_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc3_sppol_2,axiom,
! [A,B] :
( ( v2_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v2_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc4_sppol_2,axiom,
! [A,B] :
( ( v3_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v3_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc5_sppol_2,axiom,
! [A,B] :
( ( v3_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v3_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc6_sppol_2,axiom,
! [A,B] :
( ( v3_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v3_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc7_sppol_2,axiom,
( v1_xboole_0(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v1_relat_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v1_funct_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v1_realset1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v1_finset_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v1_finseq_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v1_topreal1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v1_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v2_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v3_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v4_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
& v5_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(fc8_sppol_2,axiom,
! [A,B] :
( ( v1_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc9_sppol_2,axiom,
! [A,B] :
( ( v1_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(fc10_sppol_2,axiom,
! [A,B] :
( ( v1_topreal1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
& v1_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ).
fof(rc3_sppol_2,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& ~ v1_xboole_0(A)
& v5_topreal1(A) ) ).
fof(fc11_sppol_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
=> ( ~ v1_xboole_0(k1_topreal1(A,B,C))
& v6_compts_1(k1_topreal1(A,B,C),k15_euclid(A)) ) ) ).
fof(fc12_sppol_2,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( ~ v1_xboole_0(k1_sppol_2(A,B,C,D))
& v6_compts_1(k1_sppol_2(A,B,C,D),k15_euclid(np__2)) ) ) ).
fof(rc4_sppol_2,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& v1_topreal4(A) ) ).
fof(rc5_sppol_2,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& v1_topreal4(A) ) ).
fof(cc4_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal4(A)
=> ~ v1_xboole_0(A) ) ) ).
fof(cc5_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal4(A)
=> ~ v1_realset1(A) ) ) ).
fof(t1_sppol_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( k23_euclid(A,B) = k23_euclid(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t2_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k1_nat_1(B,C) = k3_finseq_1(A)
=> k4_topreal1(np__2,A,B) = k4_topreal1(np__2,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),C) ) ) ) ) ).
fof(t3_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,C)))
=> k4_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,C),B) = k4_topreal1(np__2,A,B) ) ) ) ) ).
fof(t4_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C) )
=> k4_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B),C) = k4_topreal1(np__2,A,k1_nat_1(B,C)) ) ) ) ) ).
fof(t5_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k5_real_1(k3_finseq_1(A),C)) )
=> k4_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,C),B) = k4_topreal1(np__2,A,k1_nat_1(C,B)) ) ) ) ) ).
fof(t6_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
=> k4_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),C) = k4_topreal1(np__2,A,C) ) ) ) ) ).
fof(t7_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,C)
=> k4_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k1_nat_1(k3_finseq_1(A),C)) = k4_topreal1(np__2,B,C) ) ) ) ) ).
fof(t8_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& k4_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k3_finseq_1(A)) != k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) ) ) ) ).
fof(t9_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)))
=> k4_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B),C) = k4_topreal1(np__2,A,C) ) ) ) ) ).
fof(t10_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_relat_1(A))
=> k4_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B),k1_nat_1(C,np__1)) = k4_topreal1(np__2,A,k1_nat_1(C,k5_finseq_4(A,B))) ) ) ) ) ).
fof(t11_sppol_2,axiom,
k5_topreal1(np__2,k6_finseq_1(u1_struct_0(k15_euclid(np__2)))) = k1_xboole_0 ).
fof(t12_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k5_topreal1(np__2,k12_finseq_1(u1_struct_0(k15_euclid(np__2)),A)) = k1_xboole_0 ) ).
fof(t13_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k5_topreal1(np__2,A))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(B,k4_topreal1(np__2,A,C)) ) ) ) ) ) ).
fof(t14_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k5_topreal1(np__2,A))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(B,k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)))) ) ) ) ) ) ).
fof(t15_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(B,k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)))) )
=> r2_hidden(B,k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t16_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A)) )
=> r1_tarski(k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k5_topreal1(np__2,A)) ) ) ) ).
fof(t17_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k4_topreal1(np__2,A,C))
=> r2_hidden(B,k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t18_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(np__2,k3_finseq_1(A))
=> r1_tarski(k2_relat_1(A),k5_topreal1(np__2,A)) ) ) ).
fof(t19_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(A)
=> k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B))) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B)) ) ) ) ).
fof(t20_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(A)
=> k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B),A)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)),k5_topreal1(np__2,A)) ) ) ) ).
fof(t21_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> k5_topreal1(np__2,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) = k3_topreal1(np__2,A,B) ) ) ).
fof(t22_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> k5_topreal1(np__2,A) = k5_topreal1(np__2,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ).
fof(t23_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) != k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))),k5_topreal1(np__2,B)) ) ) ) ).
fof(t24_sppol_2,axiom,
$true ).
fof(t25_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k2_relat_1(A))
=> k5_topreal1(np__2,A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)),k5_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ).
fof(t26_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k4_topreal1(np__2,A,C))
=> k5_topreal1(np__2,A) = k5_topreal1(np__2,k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ).
fof(t27_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k3_finseq_1(A),np__2)
=> v2_topreal1(A) ) ) ).
fof(t28_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k2_relat_1(A))
& v2_topreal1(A) )
=> v2_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t29_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v2_topreal1(A)
=> v2_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ) ).
fof(t30_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v2_topreal1(A)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)),k4_topreal1(np__2,A,np__1)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) )
=> v2_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B),A)) ) ) ) ).
fof(t31_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v2_topreal1(A)
& k1_nat_1(C,np__1) = k3_finseq_1(A)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) )
=> v2_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B))) ) ) ) ) ).
fof(t32_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v2_topreal1(A)
& v2_topreal1(B)
& k1_nat_1(C,np__1) = k3_finseq_1(A)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)),k4_topreal1(np__2,B,np__1)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
=> v2_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t33_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v2_topreal1(A)
& r2_hidden(B,k4_topreal1(np__2,A,C)) )
=> v2_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ).
fof(t34_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k3_finseq_1(A),np__2)
=> v3_topreal1(A) ) ) ).
fof(t35_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k2_relat_1(A))
& v3_topreal1(A) )
=> v3_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t36_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v3_topreal1(A)
=> v3_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ) ).
fof(t37_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v3_topreal1(A)
& v3_topreal1(B)
& r1_xboole_0(k5_topreal1(np__2,A),k5_topreal1(np__2,B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(A)) )
=> r1_xboole_0(k4_topreal1(np__2,A,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__2,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
=> r1_xboole_0(k4_topreal1(np__2,B,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))) ) ) )
=> v3_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t38_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k4_topreal1(np__2,A,C)) )
=> ( r2_hidden(B,k2_relat_1(A))
| v3_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ) ).
fof(t39_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v1_topreal1(k12_finseq_1(u1_struct_0(k15_euclid(np__2)),A)) ) ).
fof(t40_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( k21_euclid(A) = k21_euclid(B)
| k22_euclid(A) = k22_euclid(B) )
=> v1_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t41_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k2_relat_1(A))
& v1_topreal1(A) )
=> v1_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t42_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_topreal1(A)
=> v1_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ) ).
fof(t43_sppol_2,axiom,
$true ).
fof(t44_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v1_topreal1(A)
& r2_hidden(B,k4_topreal1(np__2,A,C)) )
=> v1_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ).
fof(t45_sppol_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k2_relat_1(A))
& v2_topreal1(A)
& v3_topreal1(A) )
=> ( np__1 = k5_finseq_4(A,B)
| k5_finseq_4(A,B) = k3_finseq_1(A)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)),k5_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) ).
fof(t46_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( A != B
& ( k21_euclid(A) = k21_euclid(B)
| k22_euclid(A) = k22_euclid(B) )
& ~ v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t47_sppol_2,axiom,
! [A] :
( ( v4_topreal1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> v4_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ).
fof(t48_sppol_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,k4_finseq_1(B))
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k5_topreal1(np__2,B)) ) ) ) ).
fof(t49_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( A != B
& ( k21_euclid(A) = k21_euclid(B)
| k22_euclid(A) = k22_euclid(B) )
& ~ v5_topreal1(k3_topreal1(np__2,A,B)) ) ) ) ).
fof(t50_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,k2_relat_1(B))
=> ( k5_finseq_4(B,A) = np__1
| v4_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ) ) ).
fof(t51_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,k2_relat_1(B))
=> ( k5_finseq_4(B,A) = k3_finseq_1(B)
| v4_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ) ) ).
fof(t52_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v4_topreal1(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,k4_topreal1(np__2,C,B))
=> ( r2_hidden(A,k2_relat_1(C))
| v4_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),C,A,B)) ) ) ) ) ) ).
fof(t53_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal4(A,B,C)
=> r1_topreal4(A,C,B) ) ) ) ) ).
fof(d1_sppol_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_sppol_2(A,B,C)
<=> ( A != B
& ? [D] :
( v4_topreal1(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
& ? [E] :
( v4_topreal1(E)
& m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
& A = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,np__1)
& A = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,np__1)
& B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D))
& B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k2_struct_0(k15_euclid(np__2),A,B)
& C = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) ) ) ) ) ) ) ) ).
fof(t54_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sppol_2(B,C,A)
=> r1_sppol_2(C,B,A) ) ) ) ) ).
fof(t55_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sppol_2(B,C,A)
& r2_hidden(D,A) )
=> ( D = B
| r1_sppol_2(B,D,A) ) ) ) ) ) ) ).
fof(t56_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sppol_2(B,C,A)
& r2_hidden(D,A) )
=> ( D = C
| r1_sppol_2(D,C,A) ) ) ) ) ) ) ).
fof(t57_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sppol_2(B,C,A)
& r2_hidden(D,A)
& r2_hidden(E,A) )
=> ( D = E
| r1_sppol_2(D,E,A) ) ) ) ) ) ) ) ).
fof(d2_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal4(A)
<=> ? [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_sppol_2(B,C,A) ) ) ) ) ).
fof(d3_sppol_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k1_sppol_2(A,B,C,D) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))) ) ) ) ) ).
fof(t59_sppol_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( A != B
& C != D
& ~ v1_topreal4(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ).
fof(t60_sppol_2,axiom,
k2_topreal1 = k1_sppol_2(np__0,np__1,np__0,np__1) ).
fof(t61_sppol_2,axiom,
v1_topreal4(k2_topreal1) ).
fof(t62_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v5_topreal1(A)
=> v6_compts_1(A,k15_euclid(np__2)) ) ) ).
fof(t63_sppol_2,axiom,
! [A] :
( ( v1_topreal4(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v6_compts_1(A,k15_euclid(np__2)) ) ).
fof(t64_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal4(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> ( B = C
| r1_sppol_2(B,C,A) ) ) ) ) ) ) ).
fof(t65_sppol_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal4(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( B != C
& r2_hidden(B,A)
& r2_hidden(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( r1_topreal4(D,B,C)
& r1_topreal4(E,B,C)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),D,E) = k2_struct_0(k15_euclid(np__2),B,C)
& A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),D,E) ) ) ) ) ) ) ) ) ).
fof(dt_k1_sppol_2,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> m1_subset_1(k1_sppol_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t58_sppol_2,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k1_sppol_2(A,B,C,D) = a_4_0_sppol_2(A,B,C,D) ) ) ) ) ) ).
fof(fraenkel_a_4_0_sppol_2,axiom,
! [A,B,C,D,E] :
( ( v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D)
& v1_xreal_0(E) )
=> ( r2_hidden(A,a_4_0_sppol_2(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
& A = F
& ~ ( ~ ( k21_euclid(F) = B
& r1_xreal_0(k22_euclid(F),E)
& r1_xreal_0(D,k22_euclid(F)) )
& ~ ( r1_xreal_0(k21_euclid(F),C)
& r1_xreal_0(B,k21_euclid(F))
& k22_euclid(F) = E )
& ~ ( r1_xreal_0(k21_euclid(F),C)
& r1_xreal_0(B,k21_euclid(F))
& k22_euclid(F) = D )
& ~ ( k21_euclid(F) = C
& r1_xreal_0(k22_euclid(F),E)
& r1_xreal_0(D,k22_euclid(F)) ) ) ) ) ) ).
%------------------------------------------------------------------------------