SET007 Axioms: SET007+813.ax
%------------------------------------------------------------------------------
% File : SET007+813 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Series on Banach Algebra
% 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 : lopban_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 85 ( 1 unt; 0 def)
% Number of atoms : 1304 ( 95 equ)
% Maximal formula atoms : 56 ( 15 avg)
% Number of connectives : 1324 ( 105 ~; 6 |; 929 &)
% ( 16 <=>; 268 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 5 con; 0-4 aty)
% Number of variables : 277 ( 265 !; 12 ?)
% 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_lopban_3,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_normsp_1(A)
& l1_normsp_1(A) )
=> ? [B] :
( m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v1_lopban_3(B,A) ) ) ).
fof(rc2_lopban_3,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_normsp_1(A)
& l1_normsp_1(A) )
=> ? [B] :
( m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v2_lopban_3(B,A) ) ) ).
fof(fc1_lopban_3,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_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v2_lopban_3(B,A)
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_relat_1(k7_normsp_1(A,B))
& v1_funct_1(k7_normsp_1(A,B))
& v1_funct_2(k7_normsp_1(A,B),k5_numbers,k1_numbers)
& v1_series_1(k7_normsp_1(A,B)) ) ) ).
fof(cc1_lopban_3,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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_relset_1(B,k5_numbers,u1_struct_0(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v1_lopban_3(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v4_normsp_1(B,A) ) ) ) ) ).
fof(fc2_lopban_3,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_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v1_lopban_3(B,A)
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& v1_lopban_3(C,A)
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_relat_1(k3_normsp_1(A,B,C))
& v1_funct_1(k3_normsp_1(A,B,C))
& v1_funct_2(k3_normsp_1(A,B,C),k5_numbers,u1_struct_0(A))
& v4_normsp_1(k3_normsp_1(A,B,C),A)
& v1_lopban_3(k3_normsp_1(A,B,C),A) ) ) ).
fof(fc3_lopban_3,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_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v1_lopban_3(B,A)
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& v1_lopban_3(C,A)
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_relat_1(k4_normsp_1(A,B,C))
& v1_funct_1(k4_normsp_1(A,B,C))
& v1_funct_2(k4_normsp_1(A,B,C),k5_numbers,u1_struct_0(A))
& v4_normsp_1(k4_normsp_1(A,B,C),A)
& v1_lopban_3(k4_normsp_1(A,B,C),A) ) ) ).
fof(fc4_lopban_3,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_normsp_1(A)
& l1_normsp_1(A)
& m1_subset_1(B,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& v1_lopban_3(C,A)
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_relat_1(k6_normsp_1(A,C,B))
& v1_funct_1(k6_normsp_1(A,C,B))
& v1_funct_2(k6_normsp_1(A,C,B),k5_numbers,u1_struct_0(A))
& v4_normsp_1(k6_normsp_1(A,C,B),A)
& v1_lopban_3(k6_normsp_1(A,C,B),A) ) ) ).
fof(fc5_lopban_3,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_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v1_lopban_3(B,A)
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,k5_numbers) )
=> ( v1_relat_1(k3_lopban_3(A,B,C))
& v1_funct_1(k3_lopban_3(A,B,C))
& v1_funct_2(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& v4_normsp_1(k3_lopban_3(A,B,C),A)
& v1_lopban_3(k3_lopban_3(A,B,C),A) ) ) ).
fof(fc6_lopban_3,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_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v2_lopban_3(B,A)
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_relat_1(k1_series_1(k7_normsp_1(A,B)))
& v1_funct_1(k1_series_1(k7_normsp_1(A,B)))
& v1_funct_2(k1_series_1(k7_normsp_1(A,B)),k5_numbers,k1_numbers)
& v1_seq_2(k1_series_1(k7_normsp_1(A,B))) ) ) ).
fof(cc2_lopban_3,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_normsp_1(A)
& v4_lopban_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_relset_1(B,k5_numbers,u1_struct_0(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v2_lopban_3(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v4_normsp_1(B,A)
& v1_lopban_3(B,A) ) ) ) ) ).
fof(d1_lopban_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_normsp_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)) )
=> ( C = k1_lopban_3(A,B)
<=> ( k2_normsp_1(A,C,np__0) = k2_normsp_1(A,B,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,k1_nat_1(D,np__1)) = k2_rlvect_1(A,k2_normsp_1(A,C,D),k2_normsp_1(A,B,k1_nat_1(D,np__1))) ) ) ) ) ) ) ).
fof(t1_lopban_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) = k1_rlvect_1(A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,k1_lopban_3(A,B),C) = k1_rlvect_1(A) ) ) ) ) ).
fof(d2_lopban_3,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_normsp_1(A)
& l1_normsp_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_lopban_3(B,A)
<=> v4_normsp_1(k1_lopban_3(A,B),A) ) ) ) ).
fof(d3_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> k2_lopban_3(A,B) = k8_normsp_1(A,k1_lopban_3(A,B)) ) ) ).
fof(d4_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( v2_lopban_3(B,A)
<=> v1_series_1(k7_normsp_1(A,B)) ) ) ) ).
fof(t2_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),C)) ) ) ) ).
fof(t3_lopban_3,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_normsp_1(A)
& l1_normsp_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))
=> k1_normsp_1(A,k6_rlvect_1(A,B,C)) = k1_normsp_1(A,k4_rlvect_1(A,k6_rlvect_1(A,B,D),k6_rlvect_1(A,D,C))) ) ) ) ) ).
fof(t4_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( v4_normsp_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(C,k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,B,D)))) ) ) ) ) ) ) ) ).
fof(t5_lopban_3,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_normsp_1(A)
& l1_normsp_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_rsspace3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(C,k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,B,D)))) ) ) ) ) ) ) ) ).
fof(t6_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) = k1_rlvect_1(A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k7_normsp_1(A,B)),C) = np__0 ) ) ) ) ).
fof(d5_lopban_3,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_normsp_1(A)
& l1_normsp_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)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,D) = C ) ) ) ) ) ).
fof(d6_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_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)) )
=> ( D = k3_lopban_3(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k2_normsp_1(A,B,k1_nat_1(E,C)) ) ) ) ) ) ) ).
fof(t7_lopban_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(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)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,k5_lopban_3(A,C,B),D) = k2_normsp_1(A,B,k2_seqm_3(C,D)) ) ) ) ) ).
fof(t8_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> k3_lopban_3(A,B,np__0) = B ) ) ).
fof(t9_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k3_lopban_3(A,k3_lopban_3(A,B,C),D) = k3_lopban_3(A,k3_lopban_3(A,B,D),C) ) ) ) ) ).
fof(t10_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k3_lopban_3(A,k3_lopban_3(A,B,C),D) = k3_lopban_3(A,B,k1_nat_1(C,D)) ) ) ) ) ).
fof(t11_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( ( m1_bhsp_3(C,A,B)
& v4_normsp_1(B,A) )
=> v4_normsp_1(C,A) ) ) ) ) ).
fof(t12_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( ( m1_bhsp_3(C,A,B)
& v4_normsp_1(B,A) )
=> k8_normsp_1(A,C) = k8_normsp_1(A,B) ) ) ) ) ).
fof(t13_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> m1_bhsp_3(k3_lopban_3(A,B,C),A,B) ) ) ) ).
fof(t14_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v4_normsp_1(B,A)
=> ( v4_normsp_1(k3_lopban_3(A,B,D),A)
& k8_normsp_1(A,k3_lopban_3(A,B,D)) = k8_normsp_1(A,B) ) ) ) ) ) ) ).
fof(t15_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( v4_normsp_1(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> B != k3_lopban_3(A,C,D) )
| v4_normsp_1(C,A) ) ) ) ) ) ).
fof(t16_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( v4_normsp_1(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> B != k3_lopban_3(A,C,D) )
| k8_normsp_1(A,C) = k8_normsp_1(A,B) ) ) ) ) ) ).
fof(t17_lopban_3,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_normsp_1(A)
& l1_normsp_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)
=> v4_normsp_1(B,A) ) ) ) ).
fof(t18_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) = k1_rlvect_1(A) )
=> v2_lopban_3(B,A) ) ) ) ).
fof(t19_lopban_3,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_normsp_1(A)
& l1_normsp_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_lopban_3(B,A)
=> ( v4_normsp_1(B,A)
& k8_normsp_1(A,B) = k1_rlvect_1(A) ) ) ) ) ).
fof(t20_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> k3_normsp_1(A,k1_lopban_3(A,B),k1_lopban_3(A,C)) = k1_lopban_3(A,k3_normsp_1(A,B,C)) ) ) ) ).
fof(t21_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> k4_normsp_1(A,k1_lopban_3(A,B),k1_lopban_3(A,C)) = k1_lopban_3(A,k4_normsp_1(A,B,C)) ) ) ) ).
fof(t22_lopban_3,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_normsp_1(A)
& l1_normsp_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_lopban_3(B,A)
& v1_lopban_3(C,A) )
=> ( v1_lopban_3(k3_normsp_1(A,B,C),A)
& k2_lopban_3(A,k3_normsp_1(A,B,C)) = k4_rlvect_1(A,k2_lopban_3(A,B),k2_lopban_3(A,C)) ) ) ) ) ) ).
fof(t23_lopban_3,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_normsp_1(A)
& l1_normsp_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_lopban_3(B,A)
& v1_lopban_3(C,A) )
=> ( v1_lopban_3(k4_normsp_1(A,B,C),A)
& k2_lopban_3(A,k4_normsp_1(A,B,C)) = k6_rlvect_1(A,k2_lopban_3(A,B),k2_lopban_3(A,C)) ) ) ) ) ) ).
fof(t24_lopban_3,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_normsp_1(A)
& l1_normsp_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,k1_numbers)
=> k1_lopban_3(A,k6_normsp_1(A,B,C)) = k6_normsp_1(A,k1_lopban_3(A,B),C) ) ) ) ).
fof(t25_lopban_3,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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v1_lopban_3(B,A)
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( v1_lopban_3(k6_normsp_1(A,B,C),A)
& k2_lopban_3(A,k6_normsp_1(A,B,C)) = k3_rlvect_1(A,k2_lopban_3(A,B),C) ) ) ) ) ).
fof(t26_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,D) = k2_normsp_1(A,B,np__0) )
=> k1_lopban_3(A,k3_lopban_3(A,B,np__1)) = k4_normsp_1(A,k3_lopban_3(A,k1_lopban_3(A,B),np__1),C) ) ) ) ) ).
fof(t27_lopban_3,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_normsp_1(A)
& l1_normsp_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_lopban_3(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> v1_lopban_3(k3_lopban_3(A,B,C),A) ) ) ) ) ).
fof(t28_lopban_3,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_normsp_1(A)
& l1_normsp_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_seq_2(k1_series_1(k7_normsp_1(A,B)))
<=> v2_lopban_3(B,A) ) ) ) ).
fof(t29_lopban_3,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_normsp_1(A)
& v4_lopban_1(A)
& l1_normsp_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_lopban_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(C,k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,k1_lopban_3(A,B),E),k2_normsp_1(A,k1_lopban_3(A,B),D)))) ) ) ) ) ) ) ) ).
fof(t30_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,D)
=> r1_xreal_0(k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,k1_lopban_3(A,B),D),k2_normsp_1(A,k1_lopban_3(A,B),C))),k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k7_normsp_1(A,B)),D),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k7_normsp_1(A,B)),C)))) ) ) ) ) ) ).
fof(t31_lopban_3,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_normsp_1(A)
& v4_lopban_1(A)
& l1_normsp_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)) )
=> ( v2_lopban_3(B,A)
=> v1_lopban_3(B,A) ) ) ) ).
fof(t32_lopban_3,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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,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_series_1(B)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& ~ r1_xreal_0(k1_normsp_1(A,k2_normsp_1(A,C,E)),k2_seq_1(k5_numbers,k1_numbers,B,E)) ) )
| v2_lopban_3(C,A) ) ) ) ) ) ).
fof(t33_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D))
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,C),D)) ) )
& v2_lopban_3(C,A) )
=> ( v2_lopban_3(B,A)
& r1_xreal_0(k2_series_1(k7_normsp_1(A,B)),k2_series_1(k7_normsp_1(A,C))) ) ) ) ) ) ).
fof(t34_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),C),np__0) )
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,D)
=> r1_xreal_0(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k1_nat_1(D,np__1)),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D))) ) ) )
& v2_lopban_3(B,A) ) ) ) ).
fof(t35_lopban_3,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_normsp_1(A)
& l1_normsp_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) )
=> ( ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) )
& v4_seq_2(C) )
=> ( r1_xreal_0(np__1,k2_seq_2(C))
| v2_lopban_3(B,A) ) ) ) ) ) ).
fof(t36_lopban_3,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_normsp_1(A)
& l1_normsp_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) )
=> ~ ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) )
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,E)
=> r1_xreal_0(np__1,k2_seq_1(k5_numbers,k1_numbers,C,E)) ) ) )
& v1_series_1(k7_normsp_1(A,B)) ) ) ) ) ).
fof(t37_lopban_3,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_normsp_1(A)
& l1_normsp_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) )
=> ~ ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) )
& v4_seq_2(C)
& ~ r1_xreal_0(k2_seq_2(C),np__1)
& v2_lopban_3(B,A) ) ) ) ) ).
fof(t38_lopban_3,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_normsp_1(A)
& l1_normsp_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) )
=> ( ( v4_seqm_3(k7_normsp_1(A,B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k4_real_1(k4_power(np__2,D),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k4_power(np__2,D))) ) )
=> ( v2_lopban_3(B,A)
<=> v1_series_1(C) ) ) ) ) ) ).
fof(t39_lopban_3,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_normsp_1(A)
& l1_normsp_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,k1_numbers)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,D)
=> k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D) = k6_real_1(np__1,k4_power(D,C)) ) )
=> ( r1_xreal_0(C,np__1)
| v2_lopban_3(B,A) ) ) ) ) ) ).
fof(t40_lopban_3,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_normsp_1(A)
& l1_normsp_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,k1_numbers)
=> ~ ( r1_xreal_0(C,np__1)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,D)
=> k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D) = k6_real_1(np__1,k4_power(D,C)) ) )
& v2_lopban_3(B,A) ) ) ) ) ).
fof(t41_lopban_3,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_normsp_1(A)
& l1_normsp_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) )
=> ( ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k2_normsp_1(A,B,D) != k1_rlvect_1(A)
& k2_seq_1(k5_numbers,k1_numbers,C,D) = k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k1_nat_1(D,np__1)),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) ) )
& v4_seq_2(C) )
=> ( r1_xreal_0(np__1,k2_seq_2(C))
| v2_lopban_3(B,A) ) ) ) ) ) ).
fof(t42_lopban_3,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_normsp_1(A)
& l1_normsp_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) != k1_rlvect_1(A) )
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,D)
=> r1_xreal_0(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k1_nat_1(D,np__1)),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D))) ) ) )
& v2_lopban_3(B,A) ) ) ) ).
fof(t43_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(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)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B)
& k4_rlvect_1(A,k4_rlvect_1(A,B,C),D) = k4_rlvect_1(A,B,k4_rlvect_1(A,C,D))
& k4_rlvect_1(A,B,k1_rlvect_1(A)) = B
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& k4_rlvect_1(A,B,G) = k1_rlvect_1(A) )
& k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D))
& k3_rlvect_1(A,B,np__1) = B
& k3_rlvect_1(A,B,np__0) = k1_rlvect_1(A)
& k3_rlvect_1(A,k1_rlvect_1(A),E) = k1_rlvect_1(A)
& k3_rlvect_1(A,B,k1_real_1(np__1)) = k5_rlvect_1(A,B)
& k1_group_1(A,B,k2_group_1(A)) = B
& k1_group_1(A,k2_group_1(A),B) = B
& k1_group_1(A,B,k4_rlvect_1(A,C,D)) = k4_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))
& k1_group_1(A,k4_rlvect_1(A,C,D),B) = k4_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B))
& k3_rlvect_1(A,k1_group_1(A,B,C),E) = k1_group_1(A,k3_rlvect_1(A,B,E),C)
& k3_rlvect_1(A,k4_rlvect_1(A,B,C),E) = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,E))
& k3_rlvect_1(A,B,k3_real_1(E,F)) = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,B,F))
& k3_rlvect_1(A,B,k4_real_1(E,F)) = k3_rlvect_1(A,k3_rlvect_1(A,B,F),E)
& k3_rlvect_1(A,k1_group_1(A,B,C),k4_real_1(E,F)) = k1_group_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F))
& k3_rlvect_1(A,k1_group_1(A,B,C),E) = k1_group_1(A,B,k3_rlvect_1(A,C,E))
& k1_group_1(A,k1_rlvect_1(A),B) = k1_rlvect_1(A)
& k1_group_1(A,B,k1_rlvect_1(A)) = k1_rlvect_1(A)
& k1_group_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))
& k1_group_1(A,k6_rlvect_1(A,C,D),B) = k6_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B))
& k6_rlvect_1(A,k4_rlvect_1(A,B,C),D) = k4_rlvect_1(A,B,k6_rlvect_1(A,C,D))
& k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k6_rlvect_1(A,C,D))
& k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k4_rlvect_1(A,C,D))
& k4_rlvect_1(A,B,C) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),k4_rlvect_1(A,D,C))
& k6_rlvect_1(A,B,C) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),k6_rlvect_1(A,D,C))
& B = k4_rlvect_1(A,k6_rlvect_1(A,B,C),C)
& B = k6_rlvect_1(A,C,k6_rlvect_1(A,C,B))
& ( k1_normsp_1(A,B) = np__0
=> B = k1_rlvect_1(A) )
& ( B = k1_rlvect_1(A)
=> k1_normsp_1(A,B) = np__0 )
& k1_normsp_1(A,k3_rlvect_1(A,B,E)) = k4_real_1(k18_complex1(E),k1_normsp_1(A,B))
& r1_xreal_0(k1_normsp_1(A,k4_rlvect_1(A,B,C)),k3_real_1(k1_normsp_1(A,B),k1_normsp_1(A,C)))
& r1_xreal_0(k1_normsp_1(A,k1_group_1(A,B,C)),k4_real_1(k1_normsp_1(A,B),k1_normsp_1(A,C)))
& k1_normsp_1(A,k2_group_1(A)) = np__1
& v4_lopban_1(A) ) ) ) ) ) ) ) ).
fof(d7_lopban_3,axiom,
$true ).
fof(d8_lopban_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_lopban_3(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k1_group_1(A,B,C) = k2_group_1(A)
& k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) ).
fof(d9_lopban_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(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,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( D = k6_lopban_3(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k1_group_1(A,C,k2_normsp_1(A,B,E)) ) ) ) ) ) ) ).
fof(d10_lopban_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(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,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( D = k7_lopban_3(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k1_group_1(A,k2_normsp_1(A,B,E),C) ) ) ) ) ) ) ).
fof(d11_lopban_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(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)) )
=> ! [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)) )
=> ( D = k8_lopban_3(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k1_group_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,C,E)) ) ) ) ) ) ) ).
fof(d12_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_lopban_3(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k9_lopban_3(A,B)
<=> ( k1_group_1(A,B,C) = k2_group_1(A)
& k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) ) ) ).
fof(d13_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(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)) )
=> ( C = k10_lopban_3(A,B)
<=> ( k2_normsp_1(A,C,np__0) = k2_group_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,k1_nat_1(D,np__1)) = k1_group_1(A,k2_normsp_1(A,C,D),B) ) ) ) ) ) ) ).
fof(d14_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k11_lopban_3(A,B,C) = k2_normsp_1(A,k10_lopban_3(A,B),C) ) ) ) ).
fof(t44_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k11_lopban_3(A,B,np__0) = k2_group_1(A) ) ) ).
fof(t45_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ r1_xreal_0(np__1,k1_normsp_1(A,B))
=> ( v1_lopban_3(k10_lopban_3(A,B),A)
& v2_lopban_3(k10_lopban_3(A,B),A) ) ) ) ) ).
fof(t46_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ r1_xreal_0(np__1,k1_normsp_1(A,k6_rlvect_1(A,k2_group_1(A),B)))
=> ( v1_lopban_3(k10_lopban_3(A,k6_rlvect_1(A,k2_group_1(A),B)),A)
& v2_lopban_3(k10_lopban_3(A,k6_rlvect_1(A,k2_group_1(A),B)),A) ) ) ) ) ).
fof(t47_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ r1_xreal_0(np__1,k1_normsp_1(A,k6_rlvect_1(A,k2_group_1(A),B)))
=> ( v4_lopban_3(B,A)
& k9_lopban_3(A,B) = k2_lopban_3(A,k10_lopban_3(A,k6_rlvect_1(A,k2_group_1(A),B))) ) ) ) ) ).
fof(redefinition_v3_lopban_3,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_normsp_1(A)
& l1_normsp_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)) )
=> ( v3_lopban_3(B,A)
<=> v5_seqm_3(B) ) ) ).
fof(dt_k1_lopban_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_normsp_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(k1_lopban_3(A,B))
& v1_funct_2(k1_lopban_3(A,B),k5_numbers,u1_struct_0(A))
& m2_relset_1(k1_lopban_3(A,B),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k2_lopban_3,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_normsp_1(A)
& l1_normsp_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(k2_lopban_3(A,B),u1_struct_0(A)) ) ).
fof(dt_k3_lopban_3,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_normsp_1(A)
& l1_normsp_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,k5_numbers) )
=> ( v1_funct_1(k3_lopban_3(A,B,C))
& v1_funct_2(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k4_lopban_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k4_lopban_3(A,B,C))
& v1_funct_2(k4_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k4_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(redefinition_k4_lopban_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k4_lopban_3(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k5_lopban_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k5_lopban_3(A,B,C))
& v1_funct_2(k5_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k5_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(redefinition_k5_lopban_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k5_lopban_3(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k6_lopban_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(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(k6_lopban_3(A,B,C))
& v1_funct_2(k6_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k6_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k7_lopban_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(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(k7_lopban_3(A,B,C))
& v1_funct_2(k7_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k7_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k8_lopban_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(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(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k8_lopban_3(A,B,C))
& v1_funct_2(k8_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k8_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k9_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k9_lopban_3(A,B),u1_struct_0(A)) ) ).
fof(dt_k10_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k10_lopban_3(A,B))
& v1_funct_2(k10_lopban_3(A,B),k5_numbers,u1_struct_0(A))
& m2_relset_1(k10_lopban_3(A,B),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k11_lopban_3,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_normsp_1(A)
& v4_group_1(A)
& v2_funcsdom(A)
& v5_lopban_2(A)
& l1_lopban_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k11_lopban_3(A,B,C),u1_struct_0(A)) ) ).
%------------------------------------------------------------------------------