TSTP Solution File: SWV050+1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SWV050+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 : 300s
% DateTime : Tue May 7 10:57:08 EDT 2024
% Result : Theorem 194.00s 28.55s
% Output : Refutation 194.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 65 ( 30 unt; 24 typ; 0 def)
% Number of atoms : 66 ( 65 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 747 ( 26 ~; 13 |; 9 &; 696 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 17 con; 0-3 aty)
% Number of variables : 19 ( 0 ^ 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(pv86_type,type,
pv86: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(n5_type,type,
n5: $i ).
thf(n1_type,type,
n1: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(abs_type,type,
abs: $i > $i ).
thf(a_select2_type,type,
a_select2: $i > $i > $i ).
thf(mu_type,type,
mu: $i ).
thf(pv87_type,type,
pv87: $i ).
thf(muold_type,type,
muold: $i ).
thf(plus_type,type,
plus: $i > $i > $i ).
thf(pv88_type,type,
pv88: $i ).
thf(rho_type,type,
rho: $i ).
thf(pv89_type,type,
pv89: $i ).
thf(rhoold_type,type,
rhoold: $i ).
thf(sigma_type,type,
sigma: $i ).
thf(pv91_type,type,
pv91: $i ).
thf(sigmaold_type,type,
sigmaold: $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(pred_type,type,
pred: $i > $i ).
thf(tptp_minus_1_type,type,
tptp_minus_1: $i ).
thf(tptp_float_0_0_type,type,
tptp_float_0_0: $i ).
thf(48,axiom,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(370,plain,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(371,plain,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
inference(cnf,[status(esa)],[370]) ).
thf(372,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= tptp_float_0_0 ),
inference(lifteq,[status(thm)],[371]) ).
thf(1,conjecture,
( ( ( pv86
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) )
& ( pv88
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ) )
=> ( ( n0
= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) ) )
& ( pv86
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) )
& ( pv88
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0022) ).
thf(2,negated_conjecture,
~ ( ( ( pv86
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) )
& ( pv88
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ) )
=> ( ( n0
= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) ) )
& ( pv86
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) )
& ( pv88
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(85,plain,
~ ( ( ( pv86
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) )
& ( pv88
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ) )
=> ( ( n0
= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) ) )
& ( pv86
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) )
& ( pv88
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,plain,
( ( n0
!= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) ) )
| ( pv86
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) )
| ( pv88
!= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(89,plain,
( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) )
!= n0 )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) )
!= pv86 )
| ( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) )
!= pv88 ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(87,plain,
( pv88
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(90,plain,
( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ rho @ pv89 ) @ ( a_select2 @ rhoold @ pv89 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ rho @ pv89 ) ) @ ( abs @ ( a_select2 @ rhoold @ pv89 ) ) ) ) )
= pv88 ),
inference(lifteq,[status(thm)],[87]) ).
thf(88,plain,
( pv86
= ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(91,plain,
( ( sum @ n0 @ ( minus @ n5 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ mu @ pv87 ) @ ( a_select2 @ muold @ pv87 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ mu @ pv87 ) ) @ ( abs @ ( a_select2 @ muold @ pv87 ) ) ) ) )
= pv86 ),
inference(lifteq,[status(thm)],[88]) ).
thf(553,plain,
( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) )
!= n0 )
| ( pv86 != pv86 )
| ( pv88 != pv88 ) ),
inference(rewrite,[status(thm)],[89,90,91]) ).
thf(554,plain,
( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) )
!= n0 ),
inference(simp,[status(thm)],[553]) ).
thf(4255,plain,
! [A: $i] :
( ( tptp_float_0_0 != n0 )
| ( ( sum @ n0 @ tptp_minus_1 @ A )
!= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[372,554]) ).
thf(4272,plain,
! [A: $i] :
( ( tptp_float_0_0 != n0 )
| ( n0 != n0 )
| ( ( minus @ n0 @ n1 )
!= tptp_minus_1 )
| ( A
!= ( divide @ ( abs @ ( minus @ ( a_select2 @ sigma @ pv91 ) @ ( a_select2 @ sigmaold @ pv91 ) ) ) @ ( plus @ ( abs @ ( a_select2 @ sigma @ pv91 ) ) @ ( abs @ ( a_select2 @ sigmaold @ pv91 ) ) ) ) ) ),
inference(simp,[status(thm)],[4255]) ).
thf(4277,plain,
( ( tptp_float_0_0 != n0 )
| ( ( minus @ n0 @ n1 )
!= tptp_minus_1 ) ),
inference(simp,[status(thm)],[4272]) ).
thf(79,axiom,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
thf(516,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(517,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(cnf,[status(esa)],[516]) ).
thf(518,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(lifteq,[status(thm)],[517]) ).
thf(4403,plain,
tptp_float_0_0 = n0,
inference(rewrite,[status(thm)],[518,372]) ).
thf(4405,plain,
( ( n0 != n0 )
| ( ( minus @ n0 @ n1 )
!= tptp_minus_1 ) ),
inference(rewrite,[status(thm)],[4277,4403]) ).
thf(4406,plain,
( ( minus @ n0 @ n1 )
!= tptp_minus_1 ),
inference(simp,[status(thm)],[4405]) ).
thf(41,axiom,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(218,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(219,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(cnf,[status(esa)],[218]) ).
thf(220,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(33532,plain,
( ( pred @ n0 )
!= tptp_minus_1 ),
inference(rewrite,[status(thm)],[4406,220]) ).
thf(46,axiom,
( ( succ @ tptp_minus_1 )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(317,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(318,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(lifteq,[status(thm)],[317]) ).
thf(21,axiom,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
thf(140,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(141,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(lifteq,[status(thm)],[141]) ).
thf(6719,plain,
! [A: $i] :
( ( ( pred @ n0 )
= A )
| ( ( succ @ tptp_minus_1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[318,142]) ).
thf(6720,plain,
( ( pred @ n0 )
= tptp_minus_1 ),
inference(pattern_uni,[status(thm)],[6719:[bind(A,$thf( tptp_minus_1 ))]]) ).
thf(33580,plain,
tptp_minus_1 != tptp_minus_1,
inference(rewrite,[status(thm)],[33532,6720]) ).
thf(33581,plain,
$false,
inference(simp,[status(thm)],[33580]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV050+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n014.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Tue May 7 00:17:54 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.04 % [INFO] Parsing done (165ms).
% 1.41/1.05 % [INFO] Running in sequential loop mode.
% 1.92/1.27 % [INFO] nitpick registered as external prover.
% 1.92/1.27 % [INFO] Scanning for conjecture ...
% 2.08/1.36 % [INFO] Found a conjecture and 84 axioms. Running axiom selection ...
% 2.27/1.42 % [INFO] Axiom selection finished. Selected 82 axioms (removed 2 axioms).
% 2.69/1.51 % [INFO] Problem is first-order (TPTP FOF).
% 2.69/1.53 % [INFO] Type checking passed.
% 2.69/1.53 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 194.00/28.54 % [INFO] Killing All external provers ...
% 194.00/28.54 % Time passed: 27993ms (effective reasoning time: 27487ms)
% 194.00/28.54 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 194.00/28.54 % Axioms used in derivation (5): pred_minus_1, succ_tptp_minus_1, sum_plus_base_float, sum_plus_base, pred_succ
% 194.00/28.54 % No. of inferences in proof: 41
% 194.00/28.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27993 ms resp. 27487 ms w/o parsing
% 194.00/28.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 194.00/28.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------