SET007 Axioms: SET007+303.ax
%------------------------------------------------------------------------------
% File : SET007+303 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Metrics in the Cartesian Product - 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 : metric_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 58 ( 11 unt; 0 def)
% Number of atoms : 539 ( 54 equ)
% Maximal formula atoms : 33 ( 9 avg)
% Number of connectives : 532 ( 51 ~; 0 |; 309 &)
% ( 13 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 12 con; 0-5 aty)
% Number of variables : 164 ( 164 !; 0 ?)
% 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_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k1_numbers)
& m2_relset_1(C,k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k1_numbers) )
=> ( C = k1_metric_4(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ! [I] :
( m1_subset_1(I,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ( ( H = k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,F)
& I = k1_domain_1(u1_struct_0(A),u1_struct_0(B),E,G) )
=> k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),C,H,I) = k9_square_1(k3_real_1(k7_square_1(k4_metric_1(A,D,E)),k7_square_1(k4_metric_1(B,F,G)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_metric_4,axiom,
$true ).
fof(t2_metric_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__0,B) )
=> ( k8_square_1(k2_xcmplx_0(A,B)) = np__0
<=> ( A = np__0
& B = np__0 ) ) ) ) ) ).
fof(t3_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ( k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B),C,D) = np__0
<=> C = D ) ) ) ) ) ).
fof(t4_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B),C,D) = k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B),D,C) ) ) ) ) ).
fof(t5_metric_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__0,B)
& r1_xreal_0(np__0,C)
& r1_xreal_0(np__0,D) )
=> r1_xreal_0(k8_square_1(k2_xcmplx_0(k5_square_1(k2_xcmplx_0(A,C)),k5_square_1(k2_xcmplx_0(B,D)))),k2_xcmplx_0(k8_square_1(k2_xcmplx_0(k5_square_1(A),k5_square_1(B))),k8_square_1(k2_xcmplx_0(k5_square_1(C),k5_square_1(D))))) ) ) ) ) ) ).
fof(t6_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> r1_xreal_0(k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B),C,E),k3_real_1(k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B),C,D),k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B),D,E))) ) ) ) ) ) ).
fof(d2_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
=> k2_metric_4(A,B,C,D) = k1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B),C,D) ) ) ) ) ).
fof(d3_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> k3_metric_4(A,B) = g1_metric_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k1_metric_4(A,B)) ) ) ).
fof(d4_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))),k1_numbers)
& m2_relset_1(D,k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))),k1_numbers) )
=> ( D = k4_metric_4(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(C))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(C))
=> ! [K] :
( m1_subset_1(K,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ! [L] :
( m1_subset_1(L,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ( ( K = k3_mcart_1(E,G,I)
& L = k3_mcart_1(F,H,J) )
=> k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),D,K,L) = k9_square_1(k3_real_1(k3_real_1(k7_square_1(k4_metric_1(A,E,F)),k7_square_1(k4_metric_1(B,G,H))),k7_square_1(k4_metric_1(C,I,J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_metric_4,axiom,
$true ).
fof(t8_metric_4,axiom,
$true ).
fof(t9_metric_4,axiom,
$true ).
fof(t10_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ( k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C),D,E) = np__0
<=> D = E ) ) ) ) ) ) ).
fof(t11_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C),D,E) = k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C),E,D) ) ) ) ) ) ).
fof(t12_metric_4,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k5_square_1(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k5_square_1(B)),k5_square_1(C)),k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,A),B),k3_xcmplx_0(k3_xcmplx_0(np__2,A),C)),k3_xcmplx_0(k3_xcmplx_0(np__2,B),C))) ) ) ) ).
fof(t13_metric_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__2,k3_xcmplx_0(A,D)),k3_xcmplx_0(C,B)),k3_xcmplx_0(k3_xcmplx_0(np__2,k3_xcmplx_0(A,F)),k3_xcmplx_0(E,C))),k3_xcmplx_0(k3_xcmplx_0(np__2,k3_xcmplx_0(B,F)),k3_xcmplx_0(E,D))),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k5_square_1(k3_xcmplx_0(A,D)),k5_square_1(k3_xcmplx_0(C,B))),k5_square_1(k3_xcmplx_0(A,F))),k5_square_1(k3_xcmplx_0(E,C))),k5_square_1(k3_xcmplx_0(B,F))),k5_square_1(k3_xcmplx_0(E,D)))) ) ) ) ) ) ) ).
fof(t14_metric_4,axiom,
$true ).
fof(t15_metric_4,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ! [F] :
( v1_xreal_0(F)
=> r1_xreal_0(k5_square_1(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)),k3_xcmplx_0(E,F))),k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k5_square_1(B)),k5_square_1(E)),k2_xcmplx_0(k2_xcmplx_0(k5_square_1(C),k5_square_1(D)),k5_square_1(F)))) ) ) ) ) ) ) ).
fof(t16_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ! [F] :
( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> r1_xreal_0(k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C),D,F),k3_real_1(k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C),D,E),k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C),E,F))) ) ) ) ) ) ) ).
fof(d5_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
=> k5_metric_4(A,B,C,D,E) = k1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C),D,E) ) ) ) ) ) ).
fof(d6_metric_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> k6_metric_4(A,B,C) = g1_metric_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k4_metric_4(A,B,C)) ) ) ) ).
fof(t17_metric_4,axiom,
$true ).
fof(t18_metric_4,axiom,
$true ).
fof(d7_metric_4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers) )
=> ( A = k7_metric_4
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [G] :
( m1_subset_1(G,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ( ( F = k1_domain_1(k1_numbers,k1_numbers,B,D)
& G = k1_domain_1(k1_numbers,k1_numbers,C,E) )
=> k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),A,F,G) = k3_real_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,C),k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,D,E)) ) ) ) ) ) ) ) ) ) ).
fof(t19_metric_4,axiom,
! [A] :
( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ( k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k7_metric_4,A,B) = np__0
<=> A = B ) ) ) ).
fof(t20_metric_4,axiom,
! [A] :
( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers))
=> k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k7_metric_4,A,B) = k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k7_metric_4,B,A) ) ) ).
fof(t21_metric_4,axiom,
! [A] :
( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(k1_numbers,k1_numbers))
=> r1_xreal_0(k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k7_metric_4,A,C),k3_real_1(k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k7_metric_4,A,B),k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k7_metric_4,B,C))) ) ) ) ).
fof(d8_metric_4,axiom,
k8_metric_4 = g1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k7_metric_4) ).
fof(d9_metric_4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers) )
=> ( A = k9_metric_4
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [G] :
( m1_subset_1(G,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ( ( F = k1_domain_1(k1_numbers,k1_numbers,B,D)
& G = k1_domain_1(k1_numbers,k1_numbers,C,E) )
=> k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),A,F,G) = k9_square_1(k3_real_1(k7_square_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,C)),k7_square_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,D,E)))) ) ) ) ) ) ) ) ) ) ).
fof(t22_metric_4,axiom,
! [A] :
( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ( k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k9_metric_4,A,B) = np__0
<=> A = B ) ) ) ).
fof(t23_metric_4,axiom,
! [A] :
( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers))
=> k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k9_metric_4,A,B) = k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k9_metric_4,B,A) ) ) ).
fof(t24_metric_4,axiom,
! [A] :
( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(k1_numbers,k1_numbers))
=> r1_xreal_0(k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k9_metric_4,A,C),k3_real_1(k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k9_metric_4,A,B),k1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k9_metric_4,B,C))) ) ) ) ).
fof(d10_metric_4,axiom,
k10_metric_4 = g1_metric_1(k2_zfmisc_1(k1_numbers,k1_numbers),k9_metric_4) ).
fof(d11_metric_4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers) )
=> ( A = k11_metric_4
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [I] :
( m1_subset_1(I,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ( ( H = k3_mcart_1(B,D,F)
& I = k3_mcart_1(C,E,G) )
=> k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),A,H,I) = k3_real_1(k3_real_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,C),k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,D,E)),k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,F,G)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_metric_4,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ( k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k11_metric_4,A,B) = np__0
<=> A = B ) ) ) ).
fof(t26_metric_4,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k11_metric_4,A,B) = k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k11_metric_4,B,A) ) ) ).
fof(t27_metric_4,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> r1_xreal_0(k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k11_metric_4,A,C),k3_real_1(k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k11_metric_4,A,B),k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k11_metric_4,B,C))) ) ) ) ).
fof(d12_metric_4,axiom,
k12_metric_4 = g1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k11_metric_4) ).
fof(d13_metric_4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers) )
=> ( A = k13_metric_4
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [I] :
( m1_subset_1(I,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ( ( H = k3_mcart_1(B,D,F)
& I = k3_mcart_1(C,E,G) )
=> k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),A,H,I) = k9_square_1(k3_real_1(k3_real_1(k7_square_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,C)),k7_square_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,D,E))),k7_square_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,F,G)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_metric_4,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ( k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k13_metric_4,A,B) = np__0
<=> A = B ) ) ) ).
fof(t29_metric_4,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k13_metric_4,A,B) = k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k13_metric_4,B,A) ) ) ).
fof(t30_metric_4,axiom,
! [A] :
( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [B] :
( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers))
=> r1_xreal_0(k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k13_metric_4,A,C),k3_real_1(k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k13_metric_4,A,B),k1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k13_metric_4,B,C))) ) ) ) ).
fof(d14_metric_4,axiom,
k14_metric_4 = g1_metric_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k13_metric_4) ).
fof(dt_k1_metric_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ( v1_funct_1(k1_metric_4(A,B))
& v1_funct_2(k1_metric_4(A,B),k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k1_numbers)
& m2_relset_1(k1_metric_4(A,B),k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k1_numbers) ) ) ).
fof(dt_k2_metric_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B)
& m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))
& m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) )
=> m1_subset_1(k2_metric_4(A,B,C,D),k1_numbers) ) ).
fof(dt_k3_metric_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B) )
=> ( ~ v3_struct_0(k3_metric_4(A,B))
& v1_metric_1(k3_metric_4(A,B))
& v6_metric_1(k3_metric_4(A,B))
& v7_metric_1(k3_metric_4(A,B))
& v8_metric_1(k3_metric_4(A,B))
& v9_metric_1(k3_metric_4(A,B))
& l1_metric_1(k3_metric_4(A,B)) ) ) ).
fof(dt_k4_metric_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B)
& ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> ( v1_funct_1(k4_metric_4(A,B,C))
& v1_funct_2(k4_metric_4(A,B,C),k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))),k1_numbers)
& m2_relset_1(k4_metric_4(A,B,C),k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))),k1_numbers) ) ) ).
fof(dt_k5_metric_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B)
& ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C)
& m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C)))
& m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) )
=> m1_subset_1(k5_metric_4(A,B,C,D,E),k1_numbers) ) ).
fof(dt_k6_metric_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& ~ v3_struct_0(B)
& v6_metric_1(B)
& v7_metric_1(B)
& v8_metric_1(B)
& v9_metric_1(B)
& l1_metric_1(B)
& ~ v3_struct_0(C)
& v6_metric_1(C)
& v7_metric_1(C)
& v8_metric_1(C)
& v9_metric_1(C)
& l1_metric_1(C) )
=> ( ~ v3_struct_0(k6_metric_4(A,B,C))
& v1_metric_1(k6_metric_4(A,B,C))
& v6_metric_1(k6_metric_4(A,B,C))
& v7_metric_1(k6_metric_4(A,B,C))
& v8_metric_1(k6_metric_4(A,B,C))
& v9_metric_1(k6_metric_4(A,B,C))
& l1_metric_1(k6_metric_4(A,B,C)) ) ) ).
fof(dt_k7_metric_4,axiom,
( v1_funct_1(k7_metric_4)
& v1_funct_2(k7_metric_4,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(k7_metric_4,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers) ) ).
fof(dt_k8_metric_4,axiom,
( ~ v3_struct_0(k8_metric_4)
& v1_metric_1(k8_metric_4)
& v6_metric_1(k8_metric_4)
& v7_metric_1(k8_metric_4)
& v8_metric_1(k8_metric_4)
& v9_metric_1(k8_metric_4)
& l1_metric_1(k8_metric_4) ) ).
fof(dt_k9_metric_4,axiom,
( v1_funct_1(k9_metric_4)
& v1_funct_2(k9_metric_4,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(k9_metric_4,k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers)),k1_numbers) ) ).
fof(dt_k10_metric_4,axiom,
( ~ v3_struct_0(k10_metric_4)
& v1_metric_1(k10_metric_4)
& v6_metric_1(k10_metric_4)
& v7_metric_1(k10_metric_4)
& v8_metric_1(k10_metric_4)
& v9_metric_1(k10_metric_4)
& l1_metric_1(k10_metric_4) ) ).
fof(dt_k11_metric_4,axiom,
( v1_funct_1(k11_metric_4)
& v1_funct_2(k11_metric_4,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(k11_metric_4,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers) ) ).
fof(dt_k12_metric_4,axiom,
( ~ v3_struct_0(k12_metric_4)
& v1_metric_1(k12_metric_4)
& v6_metric_1(k12_metric_4)
& v7_metric_1(k12_metric_4)
& v8_metric_1(k12_metric_4)
& v9_metric_1(k12_metric_4)
& l1_metric_1(k12_metric_4) ) ).
fof(dt_k13_metric_4,axiom,
( v1_funct_1(k13_metric_4)
& v1_funct_2(k13_metric_4,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers)
& m2_relset_1(k13_metric_4,k2_zfmisc_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)),k1_numbers) ) ).
fof(dt_k14_metric_4,axiom,
( ~ v3_struct_0(k14_metric_4)
& v1_metric_1(k14_metric_4)
& v6_metric_1(k14_metric_4)
& v7_metric_1(k14_metric_4)
& v8_metric_1(k14_metric_4)
& v9_metric_1(k14_metric_4)
& l1_metric_1(k14_metric_4) ) ).
%------------------------------------------------------------------------------