TSTP Solution File: SWC204+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC204+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 10:51:01 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   79 (  15 unt;   0 def)
%            Number of atoms       :  375 ( 146 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives :  482 ( 186   ~; 203   |;  69   &)
%                                         (   1 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   99 (   0 sgn  52   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax28) ).

fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax24) ).

fof(16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax22) ).

fof(22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax78) ).

fof(24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax15) ).

fof(26,axiom,
    ssList(nil),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax17) ).

fof(27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',ax18) ).

fof(29,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ( ~ neq(X2,nil)
                        | ? [X5] :
                            ( ssList(X5)
                            & X4 != X5
                            & ? [X6] :
                                ( ssList(X6)
                                & tl(X4) = X6
                                & app(X3,X6) = X5
                                & neq(nil,X4) ) )
                        | neq(X1,nil) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/tmp/tmpYyV4pP/sel_SWC204+1.p_1',co1) ).

fof(30,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X4 != X5
                              & ? [X6] :
                                  ( ssList(X6)
                                  & tl(X4) = X6
                                  & app(X3,X6) = X5
                                  & neq(nil,X4) ) )
                          | neq(X1,nil) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[29]) ).

fof(31,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X4 != X5
                              & ? [X6] :
                                  ( ssList(X6)
                                  & tl(X4) = X6
                                  & app(X3,X6) = X5
                                  & neq(nil,X4) ) )
                          | neq(X1,nil) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).

fof(62,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(63,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[62]) ).

cnf(64,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[63]) ).

fof(69,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ssList(tl(X1)) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(70,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | nil = X2
      | ssList(tl(X2)) ),
    inference(variable_rename,[status(thm)],[69]) ).

cnf(71,plain,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(95,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ssItem(hd(X1)) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(96,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | nil = X2
      | ssItem(hd(X2)) ),
    inference(variable_rename,[status(thm)],[95]) ).

cnf(97,plain,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[96]) ).

fof(125,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | cons(hd(X1),tl(X1)) = X1 ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(126,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | nil = X2
      | cons(hd(X2),tl(X2)) = X2 ),
    inference(variable_rename,[status(thm)],[125]) ).

cnf(127,plain,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[126]) ).

fof(132,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(133,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[132]) ).

fof(134,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[133]) ).

fof(135,plain,
    ! [X3,X4] :
      ( ( ~ neq(X3,X4)
        | X3 != X4
        | ~ ssList(X4)
        | ~ ssList(X3) )
      & ( X3 = X4
        | neq(X3,X4)
        | ~ ssList(X4)
        | ~ ssList(X3) ) ),
    inference(distribute,[status(thm)],[134]) ).

cnf(136,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(142,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(143,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) != X1 ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(144,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) != X3 ) ),
    inference(variable_rename,[status(thm)],[143]) ).

fof(145,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) != X3
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[144]) ).

cnf(146,plain,
    ( ~ ssList(X1)
    | cons(X2,X1) != X1
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[145]) ).

fof(153,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ( neq(X2,nil)
                      & ! [X5] :
                          ( ~ ssList(X5)
                          | X4 = X5
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | tl(X4) != X6
                              | app(X3,X6) != X5
                              | ~ neq(nil,X4) ) )
                      & ~ neq(X1,nil) )
                    | ( neq(X2,nil)
                      & ~ neq(X4,nil) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(154,negated_conjecture,
    ? [X7] :
      ( ssList(X7)
      & ? [X8] :
          ( ssList(X8)
          & ? [X9] :
              ( ssList(X9)
              & ? [X10] :
                  ( ssList(X10)
                  & X8 = X10
                  & X7 = X9
                  & ( ( neq(X8,nil)
                      & ! [X11] :
                          ( ~ ssList(X11)
                          | X10 = X11
                          | ! [X12] :
                              ( ~ ssList(X12)
                              | tl(X10) != X12
                              | app(X9,X12) != X11
                              | ~ neq(nil,X10) ) )
                      & ~ neq(X7,nil) )
                    | ( neq(X8,nil)
                      & ~ neq(X10,nil) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[153]) ).

fof(155,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & ( ( neq(esk8_0,nil)
        & ! [X11] :
            ( ~ ssList(X11)
            | esk10_0 = X11
            | ! [X12] :
                ( ~ ssList(X12)
                | tl(esk10_0) != X12
                | app(esk9_0,X12) != X11
                | ~ neq(nil,esk10_0) ) )
        & ~ neq(esk7_0,nil) )
      | ( neq(esk8_0,nil)
        & ~ neq(esk10_0,nil) ) ) ),
    inference(skolemize,[status(esa)],[154]) ).

fof(156,negated_conjecture,
    ! [X11,X12] :
      ( ( ( ( ~ ssList(X12)
            | tl(esk10_0) != X12
            | app(esk9_0,X12) != X11
            | ~ neq(nil,esk10_0)
            | ~ ssList(X11)
            | esk10_0 = X11 )
          & neq(esk8_0,nil)
          & ~ neq(esk7_0,nil) )
        | ( neq(esk8_0,nil)
          & ~ neq(esk10_0,nil) ) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(shift_quantors,[status(thm)],[155]) ).

fof(157,negated_conjecture,
    ! [X11,X12] :
      ( ( neq(esk8_0,nil)
        | ~ ssList(X12)
        | tl(esk10_0) != X12
        | app(esk9_0,X12) != X11
        | ~ neq(nil,esk10_0)
        | ~ ssList(X11)
        | esk10_0 = X11 )
      & ( ~ neq(esk10_0,nil)
        | ~ ssList(X12)
        | tl(esk10_0) != X12
        | app(esk9_0,X12) != X11
        | ~ neq(nil,esk10_0)
        | ~ ssList(X11)
        | esk10_0 = X11 )
      & ( neq(esk8_0,nil)
        | neq(esk8_0,nil) )
      & ( ~ neq(esk10_0,nil)
        | neq(esk8_0,nil) )
      & ( neq(esk8_0,nil)
        | ~ neq(esk7_0,nil) )
      & ( ~ neq(esk10_0,nil)
        | ~ neq(esk7_0,nil) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(distribute,[status(thm)],[156]) ).

cnf(158,negated_conjecture,
    ssList(esk7_0),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(159,negated_conjecture,
    ssList(esk8_0),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(162,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(163,negated_conjecture,
    esk8_0 = esk10_0,
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(164,negated_conjecture,
    ( ~ neq(esk7_0,nil)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(167,negated_conjecture,
    ( neq(esk8_0,nil)
    | neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(168,negated_conjecture,
    ( esk10_0 = X1
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0)
    | app(esk9_0,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(172,negated_conjecture,
    ssList(esk10_0),
    inference(rw,[status(thm)],[159,163,theory(equality)]) ).

cnf(173,negated_conjecture,
    neq(esk10_0,nil),
    inference(rw,[status(thm)],[167,163,theory(equality)]) ).

cnf(178,negated_conjecture,
    ( ~ neq(esk7_0,nil)
    | $false ),
    inference(rw,[status(thm)],[164,173,theory(equality)]) ).

cnf(179,negated_conjecture,
    ~ neq(esk7_0,nil),
    inference(cn,[status(thm)],[178,theory(equality)]) ).

cnf(187,negated_conjecture,
    ( esk7_0 = nil
    | ~ ssList(nil)
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[179,136,theory(equality)]) ).

cnf(188,negated_conjecture,
    ( esk7_0 = nil
    | $false
    | ~ ssList(esk7_0) ),
    inference(rw,[status(thm)],[187,142,theory(equality)]) ).

cnf(189,negated_conjecture,
    ( esk7_0 = nil
    | $false
    | $false ),
    inference(rw,[status(thm)],[188,158,theory(equality)]) ).

cnf(190,negated_conjecture,
    esk7_0 = nil,
    inference(cn,[status(thm)],[189,theory(equality)]) ).

cnf(213,plain,
    ( nil = X1
    | X1 != tl(X1)
    | ~ ssItem(hd(X1))
    | ~ ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[146,127,theory(equality)]) ).

cnf(244,negated_conjecture,
    ( esk10_0 = X1
    | tl(esk10_0) != X2
    | app(esk7_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0)
    | ~ neq(esk10_0,nil) ),
    inference(rw,[status(thm)],[168,162,theory(equality)]) ).

cnf(245,negated_conjecture,
    ( esk10_0 = X1
    | tl(esk10_0) != X2
    | app(esk7_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0)
    | $false ),
    inference(rw,[status(thm)],[244,173,theory(equality)]) ).

cnf(246,negated_conjecture,
    ( esk10_0 = X1
    | tl(esk10_0) != X2
    | app(esk7_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0) ),
    inference(cn,[status(thm)],[245,theory(equality)]) ).

cnf(325,negated_conjecture,
    ~ neq(nil,nil),
    inference(rw,[status(thm)],[179,190,theory(equality)]) ).

cnf(326,negated_conjecture,
    ( esk10_0 = X1
    | app(nil,X2) != X1
    | tl(esk10_0) != X2
    | ~ neq(nil,esk10_0)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[246,190,theory(equality)]) ).

cnf(335,plain,
    ( nil = X1
    | tl(X1) != X1
    | ~ ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[213,71]) ).

cnf(336,plain,
    ( nil = X1
    | tl(X1) != X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[335,97]) ).

cnf(366,negated_conjecture,
    ( esk10_0 = X1
    | nil = esk10_0
    | app(nil,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(esk10_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[326,136,theory(equality)]) ).

cnf(368,negated_conjecture,
    ( esk10_0 = X1
    | nil = esk10_0
    | app(nil,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[366,172,theory(equality)]) ).

cnf(369,negated_conjecture,
    ( esk10_0 = X1
    | nil = esk10_0
    | app(nil,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[368,142,theory(equality)]) ).

cnf(370,negated_conjecture,
    ( esk10_0 = X1
    | nil = esk10_0
    | app(nil,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[369,theory(equality)]) ).

cnf(371,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(nil,tl(esk10_0)) != X1
    | ~ ssList(tl(esk10_0))
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[370,theory(equality)]) ).

cnf(372,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(nil,tl(esk10_0)) != X1
    | ~ ssList(X1)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[371,71,theory(equality)]) ).

cnf(373,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(nil,tl(esk10_0)) != X1
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[372,172,theory(equality)]) ).

cnf(374,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(nil,tl(esk10_0)) != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[373,theory(equality)]) ).

cnf(375,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = app(nil,tl(esk10_0))
    | ~ ssList(app(nil,tl(esk10_0))) ),
    inference(er,[status(thm)],[374,theory(equality)]) ).

cnf(377,negated_conjecture,
    ( tl(esk10_0) = esk10_0
    | esk10_0 = nil
    | ~ ssList(tl(esk10_0)) ),
    inference(spm,[status(thm)],[375,64,theory(equality)]) ).

cnf(381,negated_conjecture,
    ( tl(esk10_0) = esk10_0
    | esk10_0 = nil
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[377,71,theory(equality)]) ).

cnf(382,negated_conjecture,
    ( tl(esk10_0) = esk10_0
    | esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[381,172,theory(equality)]) ).

cnf(383,negated_conjecture,
    ( tl(esk10_0) = esk10_0
    | esk10_0 = nil ),
    inference(cn,[status(thm)],[382,theory(equality)]) ).

cnf(388,negated_conjecture,
    ( nil = esk10_0
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[336,383,theory(equality)]) ).

cnf(401,negated_conjecture,
    ( nil = esk10_0
    | $false ),
    inference(rw,[status(thm)],[388,172,theory(equality)]) ).

cnf(402,negated_conjecture,
    nil = esk10_0,
    inference(cn,[status(thm)],[401,theory(equality)]) ).

cnf(405,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[173,402,theory(equality)]) ).

cnf(406,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[405,325,theory(equality)]) ).

cnf(407,negated_conjecture,
    $false,
    406,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC204+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpYyV4pP/sel_SWC204+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC204+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC204+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC204+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------