SET007 Axioms: SET007+303.ax


%------------------------------------------------------------------------------
% File     : SET007+303 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :  539 (  54 equality)
%            Maximal formula depth :   28 (   9 average)
%            Number of connectives :  532 (  51 ~  ;   0  |; 309  &)
%                                         (  13 <=>; 159 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   16 (   1 propositional; 0-3 arity)
%            Number of functors    :   33 (  12 constant; 0-5 arity)
%            Number of variables   :  164 (   0 singleton; 164 !;   0 ?)
%            Maximal term depth    :    8 (   1 average)
% 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) )).
%------------------------------------------------------------------------------