TSTP Solution File: LCL712^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL712^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:10:32 EDT 2022
% Result : Theorem 36.68s 36.92s
% Output : Proof 36.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 79
% Syntax : Number of formulae : 89 ( 43 unt; 5 typ; 36 def)
% Number of atoms : 232 ( 41 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 490 ( 80 ~; 23 |; 0 &; 274 @)
% ( 20 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 60 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 157 ( 52 ^ 105 !; 0 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__28,type,
eigen__28: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( $i > $i > $o ) > $o,X2: $i > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( eigen__0 @ eigen__1 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__1 @ eigen__28 )
=> ( eigen__0 @ eigen__1 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__0 @ eigen__1 @ X1 ) )
=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__1 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP11
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP10
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0 @ eigen__1 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP16
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( ~ ( ~ ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(conj,conjecture,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ~ ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ).
thf(h2,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[conj]) ).
thf(1,plain,
( sP3
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP12
| ~ sP11
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).
thf(6,plain,
( ~ sP6
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP20
| ~ sP16
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| ~ sP8
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP10
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP10
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP15
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP2
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(16,plain,
( sP9
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(17,plain,
( sP19
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(18,plain,
( sP1
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP1
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP14
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h2]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[21,h1]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ~ ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[21,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL712^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 11:22:43 EDT 2022
% 0.13/0.33 % CPUTime :
% 36.68/36.92 % SZS status Theorem
% 36.68/36.92 % Mode: mode485
% 36.68/36.92 % Inferences: 316
% 36.68/36.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------