SET007 Axioms: SET007+306.ax
%------------------------------------------------------------------------------
% File : SET007+306 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Banach and Hilbert Spaces - Part II
% 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 : bhsp_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 72 ( 0 unt; 0 def)
% Number of atoms : 1101 ( 71 equ)
% Maximal formula atoms : 22 ( 15 avg)
% Number of connectives : 1117 ( 88 ~; 3 |; 725 &)
% ( 15 <=>; 286 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 12 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 0 prp; 1-3 aty)
% Number of functors : 34 ( 34 usr; 4 con; 0-4 aty)
% Number of variables : 270 ( 259 !; 11 ?)
% 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(d1_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k5_bhsp_1(A,k2_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) ).
fof(t1_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(B)
=> v1_bhsp_2(B,A) ) ) ) ).
fof(t2_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& k2_normsp_1(A,C,E) != k2_normsp_1(A,B,E) ) )
| v1_bhsp_2(C,A) ) ) ) ) ) ).
fof(t3_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(B,A)
& v1_bhsp_2(C,A) )
=> v1_bhsp_2(k3_normsp_1(A,B,C),A) ) ) ) ) ).
fof(t4_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(B,A)
& v1_bhsp_2(C,A) )
=> v1_bhsp_2(k4_normsp_1(A,B,C),A) ) ) ) ) ).
fof(t5_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(C,A)
=> v1_bhsp_2(k6_normsp_1(A,C,B),A) ) ) ) ) ).
fof(t6_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
=> v1_bhsp_2(k6_bhsp_1(A,B),A) ) ) ) ).
fof(t7_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(C,A)
=> v1_bhsp_2(k7_bhsp_1(A,C,B),A) ) ) ) ) ).
fof(t8_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(C,A)
=> v1_bhsp_2(k5_normsp_1(A,C,B),A) ) ) ) ) ).
fof(t9_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k3_bhsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) ).
fof(d2_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k1_bhsp_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k5_bhsp_1(A,k2_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) ) ).
fof(t10_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v5_seqm_3(C)
& r2_hidden(B,k2_relat_1(C)) )
=> k1_bhsp_2(A,C) = B ) ) ) ) ).
fof(t11_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(C)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,D) != B )
| k1_bhsp_2(A,C) = B ) ) ) ) ) ).
fof(t12_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& k2_normsp_1(A,C,E) != k2_normsp_1(A,B,E) ) )
| k1_bhsp_2(A,B) = k1_bhsp_2(A,C) ) ) ) ) ) ).
fof(t13_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(B,A)
& v1_bhsp_2(C,A) )
=> k1_bhsp_2(A,k3_normsp_1(A,B,C)) = k4_rlvect_1(A,k1_bhsp_2(A,B),k1_bhsp_2(A,C)) ) ) ) ) ).
fof(t14_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(B,A)
& v1_bhsp_2(C,A) )
=> k1_bhsp_2(A,k4_normsp_1(A,B,C)) = k6_rlvect_1(A,k1_bhsp_2(A,B),k1_bhsp_2(A,C)) ) ) ) ) ).
fof(t15_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(C,A)
=> k1_bhsp_2(A,k6_normsp_1(A,C,B)) = k3_rlvect_1(A,k1_bhsp_2(A,C),B) ) ) ) ) ).
fof(t16_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
=> k1_bhsp_2(A,k6_bhsp_1(A,B)) = k5_rlvect_1(A,k1_bhsp_2(A,B)) ) ) ) ).
fof(t17_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(C,A)
=> k1_bhsp_2(A,k7_bhsp_1(A,C,B)) = k4_rlvect_1(A,k1_bhsp_2(A,C),B) ) ) ) ) ).
fof(t18_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(C,A)
=> k1_bhsp_2(A,k5_normsp_1(A,C,B)) = k6_rlvect_1(A,k1_bhsp_2(A,C),B) ) ) ) ) ).
fof(t19_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(C,A)
=> ( k1_bhsp_2(A,C) = B
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k3_bhsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,C,F),B))) ) ) ) ) ) ) ) ) ) ).
fof(d3_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( C = k2_bhsp_2(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k3_bhsp_1(A,k2_normsp_1(A,B,D)) ) ) ) ) ) ).
fof(t20_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_bhsp_2(B,A)
=> v4_seq_2(k2_bhsp_2(A,B)) ) ) ) ).
fof(t21_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(C,A)
& k1_bhsp_2(A,C) = B )
=> ( v4_seq_2(k2_bhsp_2(A,C))
& k2_seq_2(k2_bhsp_2(A,C)) = k3_bhsp_1(A,B) ) ) ) ) ) ).
fof(t22_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(C,A)
& k1_bhsp_2(A,C) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,C,B)))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,C,B))) = np__0 ) ) ) ) ) ).
fof(d4_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& m2_relset_1(D,k5_numbers,k1_numbers) )
=> ( D = k3_bhsp_2(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,D,E) = k5_bhsp_1(A,k2_normsp_1(A,B,E),C) ) ) ) ) ) ) ).
fof(t23_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(C,A)
& k1_bhsp_2(A,C) = B )
=> v4_seq_2(k3_bhsp_2(A,C,B)) ) ) ) ) ).
fof(t24_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(C,A)
& k1_bhsp_2(A,C) = B )
=> ( v4_seq_2(k3_bhsp_2(A,C,B))
& k2_seq_2(k3_bhsp_2(A,C,B)) = np__0 ) ) ) ) ) ).
fof(t25_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B
& v1_bhsp_2(E,A)
& k1_bhsp_2(A,E) = C )
=> ( v4_seq_2(k2_bhsp_2(A,k3_normsp_1(A,D,E)))
& k2_seq_2(k2_bhsp_2(A,k3_normsp_1(A,D,E))) = k3_bhsp_1(A,k4_rlvect_1(A,B,C)) ) ) ) ) ) ) ) ).
fof(t26_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B
& v1_bhsp_2(E,A)
& k1_bhsp_2(A,E) = C )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k3_normsp_1(A,D,E),k4_rlvect_1(A,B,C))))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k3_normsp_1(A,D,E),k4_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ) ).
fof(t27_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B
& v1_bhsp_2(E,A)
& k1_bhsp_2(A,E) = C )
=> ( v4_seq_2(k2_bhsp_2(A,k4_normsp_1(A,D,E)))
& k2_seq_2(k2_bhsp_2(A,k4_normsp_1(A,D,E))) = k3_bhsp_1(A,k6_rlvect_1(A,B,C)) ) ) ) ) ) ) ) ).
fof(t28_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B
& v1_bhsp_2(E,A)
& k1_bhsp_2(A,E) = C )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k4_normsp_1(A,D,E),k6_rlvect_1(A,B,C))))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k4_normsp_1(A,D,E),k6_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ) ).
fof(t29_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k6_normsp_1(A,D,C)))
& k2_seq_2(k2_bhsp_2(A,k6_normsp_1(A,D,C))) = k3_bhsp_1(A,k3_rlvect_1(A,B,C)) ) ) ) ) ) ) ).
fof(t30_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k6_normsp_1(A,D,C),k3_rlvect_1(A,B,C))))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k6_normsp_1(A,D,C),k3_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ).
fof(t31_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(C,A)
& k1_bhsp_2(A,C) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k6_bhsp_1(A,C)))
& k2_seq_2(k2_bhsp_2(A,k6_bhsp_1(A,C))) = k3_bhsp_1(A,k5_rlvect_1(A,B)) ) ) ) ) ) ).
fof(t32_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(C,A)
& k1_bhsp_2(A,C) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k6_bhsp_1(A,C),k5_rlvect_1(A,B))))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k6_bhsp_1(A,C),k5_rlvect_1(A,B)))) = np__0 ) ) ) ) ) ).
fof(t33_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k7_bhsp_1(A,D,C),k4_rlvect_1(A,B,C))))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k7_bhsp_1(A,D,C),k4_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ).
fof(t34_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,D,C)))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,D,C))) = k3_bhsp_1(A,k6_rlvect_1(A,B,C)) ) ) ) ) ) ) ).
fof(t35_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B )
=> ( v4_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k5_normsp_1(A,D,C),k6_rlvect_1(A,B,C))))
& k2_seq_2(k2_bhsp_2(A,k5_normsp_1(A,k5_normsp_1(A,D,C),k6_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ).
fof(t36_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B
& v1_bhsp_2(E,A)
& k1_bhsp_2(A,E) = C )
=> ( v4_seq_2(k3_bhsp_2(A,k3_normsp_1(A,D,E),k4_rlvect_1(A,B,C)))
& k2_seq_2(k3_bhsp_2(A,k3_normsp_1(A,D,E),k4_rlvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ) ).
fof(t37_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B
& v1_bhsp_2(E,A)
& k1_bhsp_2(A,E) = C )
=> ( v4_seq_2(k3_bhsp_2(A,k4_normsp_1(A,D,E),k6_rlvect_1(A,B,C)))
& k2_seq_2(k3_bhsp_2(A,k4_normsp_1(A,D,E),k6_rlvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ) ).
fof(t38_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B )
=> ( v4_seq_2(k3_bhsp_2(A,k6_normsp_1(A,D,C),k3_rlvect_1(A,B,C)))
& k2_seq_2(k3_bhsp_2(A,k6_normsp_1(A,D,C),k3_rlvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ).
fof(t39_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_bhsp_2(D,A)
& k1_bhsp_2(A,D) = B )
=> ( v4_seq_2(k3_bhsp_2(A,k7_bhsp_1(A,D,C),k4_rlvect_1(A,B,C)))
& k2_seq_2(k3_bhsp_2(A,k7_bhsp_1(A,D,C),k4_rlvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ).
fof(t40_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k4_bhsp_2(A,C,D))
<=> ~ r1_xreal_0(D,k3_bhsp_1(A,k6_rlvect_1(A,C,B))) ) ) ) ) ) ).
fof(t41_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k4_bhsp_2(A,C,D))
<=> ~ r1_xreal_0(D,k5_bhsp_1(A,C,B)) ) ) ) ) ) ).
fof(t42_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ r1_xreal_0(C,np__0)
=> r2_hidden(B,k4_bhsp_2(A,B,C)) ) ) ) ) ).
fof(t43_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(B,k4_bhsp_2(A,C,E))
& r2_hidden(D,k4_bhsp_2(A,C,E))
& r1_xreal_0(k4_real_1(np__2,E),k5_bhsp_1(A,B,D)) ) ) ) ) ) ) ).
fof(t44_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(B,k4_bhsp_2(A,C,E))
=> r2_hidden(k6_rlvect_1(A,B,D),k4_bhsp_2(A,k6_rlvect_1(A,C,D),E)) ) ) ) ) ) ) ).
fof(t45_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k4_bhsp_2(A,C,D))
=> r2_hidden(k6_rlvect_1(A,B,C),k4_bhsp_2(A,k1_rlvect_1(A),D)) ) ) ) ) ) ).
fof(t46_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ( r2_hidden(B,k4_bhsp_2(A,C,D))
& r1_xreal_0(D,E) )
=> r2_hidden(B,k4_bhsp_2(A,C,E)) ) ) ) ) ) ) ).
fof(t47_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k5_bhsp_2(A,C,D))
<=> r1_xreal_0(k3_bhsp_1(A,k6_rlvect_1(A,C,B)),D) ) ) ) ) ) ).
fof(t48_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k5_bhsp_2(A,C,D))
<=> r1_xreal_0(k5_bhsp_1(A,C,B),D) ) ) ) ) ) ).
fof(t49_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(np__0,C)
=> r2_hidden(B,k5_bhsp_2(A,B,C)) ) ) ) ) ).
fof(t50_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k4_bhsp_2(A,C,D))
=> r2_hidden(B,k5_bhsp_2(A,C,D)) ) ) ) ) ) ).
fof(t51_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k6_bhsp_2(A,C,D))
<=> k3_bhsp_1(A,k6_rlvect_1(A,C,B)) = D ) ) ) ) ) ).
fof(t52_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k6_bhsp_2(A,C,D))
<=> k5_bhsp_1(A,C,B) = D ) ) ) ) ) ).
fof(t53_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(B,k6_bhsp_2(A,C,D))
=> r2_hidden(B,k5_bhsp_2(A,C,D)) ) ) ) ) ) ).
fof(t54_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r1_tarski(k4_bhsp_2(A,B,C),k5_bhsp_2(A,B,C)) ) ) ) ).
fof(t55_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r1_tarski(k6_bhsp_2(A,B,C),k5_bhsp_2(A,B,C)) ) ) ) ).
fof(t56_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k4_subset_1(u1_struct_0(A),k4_bhsp_2(A,B,C),k6_bhsp_2(A,B,C)) = k5_bhsp_2(A,B,C) ) ) ) ).
fof(dt_k1_bhsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> m1_subset_1(k1_bhsp_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_bhsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k2_bhsp_2(A,B))
& v1_funct_2(k2_bhsp_2(A,B),k5_numbers,k1_numbers)
& m2_relset_1(k2_bhsp_2(A,B),k5_numbers,k1_numbers) ) ) ).
fof(dt_k3_bhsp_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_funct_1(k3_bhsp_2(A,B,C))
& v1_funct_2(k3_bhsp_2(A,B,C),k5_numbers,k1_numbers)
& m2_relset_1(k3_bhsp_2(A,B,C),k5_numbers,k1_numbers) ) ) ).
fof(dt_k4_bhsp_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k4_bhsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_bhsp_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k5_bhsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_bhsp_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k6_bhsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(d5_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k4_bhsp_2(A,B,C) = a_3_0_bhsp_2(A,B,C) ) ) ) ).
fof(d6_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k5_bhsp_2(A,B,C) = a_3_1_bhsp_2(A,B,C) ) ) ) ).
fof(d7_bhsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k6_bhsp_2(A,B,C) = a_3_2_bhsp_2(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_bhsp_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_0_bhsp_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& ~ r1_xreal_0(D,k3_bhsp_1(B,k6_rlvect_1(B,C,E))) ) ) ) ).
fof(fraenkel_a_3_1_bhsp_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_1_bhsp_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r1_xreal_0(k3_bhsp_1(B,k6_rlvect_1(B,C,E)),D) ) ) ) ).
fof(fraenkel_a_3_2_bhsp_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_2_bhsp_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& k3_bhsp_1(B,k6_rlvect_1(B,C,E)) = D ) ) ) ).
%------------------------------------------------------------------------------