TSTP Solution File: CSR002+2 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : CSR002+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 07:30:22 EDT 2024
% Result : Theorem 8.29s 2.76s
% Output : Refutation 8.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 85
% Syntax : Number of formulae : 202 ( 96 unt; 29 typ; 0 def)
% Number of atoms : 436 ( 162 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 1185 ( 109 ~; 41 |; 132 &; 819 @)
% ( 18 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 16 con; 0-4 aty)
% Number of variables : 211 ( 0 ^ 177 !; 34 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(holdsAt_type,type,
holdsAt: $i > $i > $o ).
thf(filling_type,type,
filling: $i ).
thf(n4_type,type,
n4: $i ).
thf(plus_type,type,
plus: $i > $i > $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(n1_type,type,
n1: $i ).
thf(less_or_equal_type,type,
less_or_equal: $i > $i > $o ).
thf(n0_type,type,
n0: $i ).
thf(n3_type,type,
n3: $i ).
thf(n2_type,type,
n2: $i ).
thf(stoppedIn_type,type,
stoppedIn: $i > $i > $i > $o ).
thf(happens_type,type,
happens: $i > $i > $o ).
thf(terminates_type,type,
terminates: $i > $i > $i > $o ).
thf(releasedAt_type,type,
releasedAt: $i > $i > $o ).
thf(initiates_type,type,
initiates: $i > $i > $i > $o ).
thf(tapOff_type,type,
tapOff: $i ).
thf(tapOn_type,type,
tapOn: $i ).
thf(n6_type,type,
n6: $i ).
thf(overflow_type,type,
overflow: $i ).
thf(n5_type,type,
n5: $i ).
thf(releases_type,type,
releases: $i > $i > $i > $o ).
thf(n7_type,type,
n7: $i ).
thf(waterLevel_type,type,
waterLevel: $i > $i ).
thf(n8_type,type,
n8: $i ).
thf(n9_type,type,
n9: $i ).
thf(spilling_type,type,
spilling: $i ).
thf(startedIn_type,type,
startedIn: $i > $i > $i > $o ).
thf(antitrajectory_type,type,
antitrajectory: $i > $i > $i > $i > $o ).
thf(trajectory_type,type,
trajectory: $i > $i > $i > $i > $o ).
thf(12,axiom,
( ( plus @ n2 @ n3 )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus2_3) ).
thf(101,plain,
( ( plus @ n2 @ n3 )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i] :
( ( less @ A @ n8 )
<=> ( less_or_equal @ A @ n7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less8) ).
thf(129,plain,
! [A: $i] :
( ( ( less @ A @ n8 )
=> ( less_or_equal @ A @ n7 ) )
& ( ( less_or_equal @ A @ n7 )
=> ( less @ A @ n8 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
~ ( holdsAt @ filling @ n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_4) ).
thf(2,negated_conjecture,
~ ~ ( holdsAt @ filling @ n4 ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(58,plain,
~ ~ ( holdsAt @ filling @ n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(59,plain,
holdsAt @ filling @ n4,
inference(polarity_switch,[status(thm)],[58]) ).
thf(39,axiom,
~ ( holdsAt @ filling @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_0) ).
thf(205,plain,
~ ( holdsAt @ filling @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(206,plain,
~ ( holdsAt @ filling @ n0 ),
inference(polarity_switch,[status(thm)],[205]) ).
thf(312,plain,
( ( holdsAt @ filling @ n0 )
!= ( holdsAt @ filling @ n4 ) ),
inference(paramod_ordered,[status(thm)],[59,206]) ).
thf(313,plain,
( ( filling != filling )
| ( n0 != n4 ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
n0 != n4,
inference(simp,[status(thm)],[313]) ).
thf(31,axiom,
~ ? [A: $i] : ( less @ A @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less0) ).
thf(183,plain,
~ ? [A: $i] : ( less @ A @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(55,axiom,
filling != spilling,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',filling_not_spilling) ).
thf(276,plain,
filling != spilling,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(16,axiom,
( ( plus @ n0 @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).
thf(119,plain,
( ( plus @ n0 @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(120,plain,
( ( plus @ n0 @ n1 )
= n1 ),
inference(lifteq,[status(thm)],[119]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( holdsAt @ A @ B )
& ~ ( releasedAt @ A @ ( plus @ B @ n1 ) )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( terminates @ C @ A @ B ) ) )
=> ( holdsAt @ A @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_holding) ).
thf(247,plain,
! [A: $i,B: $i] :
( ( ( holdsAt @ A @ B )
& ~ ( releasedAt @ A @ ( plus @ B @ n1 ) )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( terminates @ C @ A @ B ) ) )
=> ( holdsAt @ A @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(184,plain,
~ ? [A: $i] : ( less @ A @ n0 ),
inference(polarity_switch,[status(thm)],[183]) ).
thf(185,plain,
! [A: $i] :
~ ( less @ A @ n0 ),
inference(cnf,[status(esa)],[184]) ).
thf(46,axiom,
holdsAt @ ( waterLevel @ n0 ) @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_0) ).
thf(225,plain,
holdsAt @ ( waterLevel @ n0 ) @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(561,plain,
( ( holdsAt @ ( waterLevel @ n0 ) @ n0 )
!= ( holdsAt @ filling @ n0 ) ),
inference(paramod_ordered,[status(thm)],[225,206]) ).
thf(563,plain,
( ( ( waterLevel @ n0 )
!= filling )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[561]) ).
thf(565,plain,
( ( waterLevel @ n0 )
!= filling ),
inference(simp,[status(thm)],[563]) ).
thf(53,axiom,
( ( plus @ n2 @ n2 )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus2_2) ).
thf(257,plain,
( ( plus @ n2 @ n2 )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( less_or_equal @ A @ B )
<=> ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( less_or_equal @ A @ B )
=> ( ( less @ A @ B )
| ( A = B ) ) )
& ( ( ( less @ A @ B )
| ( A = B ) )
=> ( less_or_equal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(35,axiom,
( ( plus @ n1 @ n2 )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_2) ).
thf(195,plain,
( ( plus @ n1 @ n2 )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(196,plain,
( ( plus @ n1 @ n2 )
= n3 ),
inference(lifteq,[status(thm)],[195]) ).
thf(25,axiom,
( ( plus @ n0 @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_0) ).
thf(157,plain,
( ( plus @ n0 @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
tapOff != tapOn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tapOff_not_tapOn) ).
thf(93,plain,
tapOff != tapOn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ~ ( releasedAt @ A @ B )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( releases @ C @ A @ B ) ) )
=> ~ ( releasedAt @ A @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_not_released) ).
thf(152,plain,
! [A: $i,B: $i] :
( ( ~ ( releasedAt @ A @ B )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( releases @ C @ A @ B ) ) )
=> ~ ( releasedAt @ A @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( happens @ A @ B )
<=> ( ( ( A = tapOn )
& ( B = n0 ) )
| ( ( holdsAt @ ( waterLevel @ n3 ) @ B )
& ( holdsAt @ filling @ B )
& ( A = overflow ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_all_defn) ).
thf(228,plain,
! [A: $i,B: $i] :
( ( ( happens @ A @ B )
=> ( ( ( A = tapOn )
& ( B = n0 ) )
| ( ( holdsAt @ ( waterLevel @ n3 ) @ B )
& ( holdsAt @ filling @ B )
& ( A = overflow ) ) ) )
& ( ( ( ( A = tapOn )
& ( B = n0 ) )
| ( ( holdsAt @ ( waterLevel @ n3 ) @ B )
& ( holdsAt @ filling @ B )
& ( A = overflow ) ) )
=> ( happens @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(43,axiom,
! [A: $i] :
( ( less @ A @ n5 )
<=> ( less_or_equal @ A @ n4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less5) ).
thf(216,plain,
! [A: $i] :
( ( ( less @ A @ n5 )
=> ( less_or_equal @ A @ n4 ) )
& ( ( less_or_equal @ A @ n4 )
=> ( less @ A @ n5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(17,axiom,
! [A: $i] :
( ( less @ A @ n7 )
<=> ( less_or_equal @ A @ n6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less7) ).
thf(121,plain,
! [A: $i] :
( ( ( less @ A @ n7 )
=> ( less_or_equal @ A @ n6 ) )
& ( ( less_or_equal @ A @ n6 )
=> ( less @ A @ n7 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
<=> ( ~ ( less @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( ( less @ A @ B )
=> ( ~ ( less @ B @ A )
& ( B != A ) ) )
& ( ( ~ ( less @ B @ A )
& ( B != A ) )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
! [A: $i] :
( ( less @ A @ n6 )
<=> ( less_or_equal @ A @ n5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less6) ).
thf(147,plain,
! [A: $i] :
( ( ( less @ A @ n6 )
=> ( less_or_equal @ A @ n5 ) )
& ( ( less_or_equal @ A @ n5 )
=> ( less @ A @ n6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( initiates @ A @ B @ C )
<=> ( ( ( A = tapOn )
& ( B = filling ) )
| ( ( A = overflow )
& ( B = spilling ) )
| ? [D: $i] :
( ( holdsAt @ ( waterLevel @ D ) @ C )
& ( A = tapOff )
& ( B
= ( waterLevel @ D ) ) )
| ? [D: $i] :
( ( holdsAt @ ( waterLevel @ D ) @ C )
& ( A = overflow )
& ( B
= ( waterLevel @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initiates_all_defn) ).
thf(280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( initiates @ A @ B @ C )
=> ( ( ( A = tapOn )
& ( B = filling ) )
| ( ( A = overflow )
& ( B = spilling ) )
| ? [D: $i] :
( ( holdsAt @ ( waterLevel @ D ) @ C )
& ( A = tapOff )
& ( B
= ( waterLevel @ D ) ) )
| ? [D: $i] :
( ( holdsAt @ ( waterLevel @ D ) @ C )
& ( A = overflow )
& ( B
= ( waterLevel @ D ) ) ) ) )
& ( ( ( ( A = tapOn )
& ( B = filling ) )
| ( ( A = overflow )
& ( B = spilling ) )
| ? [D: $i] :
( ( holdsAt @ ( waterLevel @ D ) @ C )
& ( A = tapOff )
& ( B
= ( waterLevel @ D ) ) )
| ? [D: $i] :
( ( holdsAt @ ( waterLevel @ D ) @ C )
& ( A = overflow )
& ( B
= ( waterLevel @ D ) ) ) )
=> ( initiates @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( initiates @ A @ C @ B ) )
=> ( holdsAt @ C @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_holds) ).
thf(221,plain,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( initiates @ A @ C @ B ) )
=> ( holdsAt @ C @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(102,plain,
( ( plus @ n2 @ n3 )
= n5 ),
inference(lifteq,[status(thm)],[101]) ).
thf(26,axiom,
~ ( releasedAt @ spilling @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_released_spilling_0) ).
thf(159,plain,
~ ( releasedAt @ spilling @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(160,plain,
~ ( releasedAt @ spilling @ n0 ),
inference(polarity_switch,[status(thm)],[159]) ).
thf(34,axiom,
overflow != tapOn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',overflow_not_tapOn) ).
thf(192,plain,
overflow != tapOn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(52,axiom,
~ ( holdsAt @ spilling @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_spilling_0) ).
thf(255,plain,
~ ( holdsAt @ spilling @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(256,plain,
~ ( holdsAt @ spilling @ n0 ),
inference(polarity_switch,[status(thm)],[255]) ).
thf(562,plain,
( ( holdsAt @ ( waterLevel @ n0 ) @ n0 )
!= ( holdsAt @ spilling @ n0 ) ),
inference(paramod_ordered,[status(thm)],[225,256]) ).
thf(564,plain,
( ( ( waterLevel @ n0 )
!= spilling )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[562]) ).
thf(566,plain,
( ( waterLevel @ n0 )
!= spilling ),
inference(simp,[status(thm)],[564]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( happens @ A @ B )
& ( terminates @ A @ C @ B )
& ( less @ n0 @ D )
& ( antitrajectory @ C @ B @ E @ D )
& ~ ( startedIn @ B @ C @ ( plus @ B @ D ) ) )
=> ( holdsAt @ E @ ( plus @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antitrajectory) ).
thf(197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( happens @ A @ B )
& ( terminates @ A @ C @ B )
& ( less @ n0 @ D )
& ( antitrajectory @ C @ B @ E @ D )
& ~ ( startedIn @ B @ C @ ( plus @ B @ D ) ) )
=> ( holdsAt @ E @ ( plus @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(10,axiom,
( ( plus @ n3 @ n3 )
= n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus3_3) ).
thf(96,plain,
( ( plus @ n3 @ n3 )
= n6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(97,plain,
( ( plus @ n3 @ n3 )
= n6 ),
inference(lifteq,[status(thm)],[96]) ).
thf(45,axiom,
~ ( releasedAt @ filling @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_released_filling_0) ).
thf(223,plain,
~ ( releasedAt @ filling @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(224,plain,
~ ( releasedAt @ filling @ n0 ),
inference(polarity_switch,[status(thm)],[223]) ).
thf(24,axiom,
( ( plus @ n0 @ n3 )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_3) ).
thf(155,plain,
( ( plus @ n0 @ n3 )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(156,plain,
( ( plus @ n0 @ n3 )
= n3 ),
inference(lifteq,[status(thm)],[155]) ).
thf(33,axiom,
! [A: $i] :
( spilling
!= ( waterLevel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spilling_not_waterLevel) ).
thf(188,plain,
! [A: $i] :
( spilling
!= ( waterLevel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(41,axiom,
! [A: $i] :
( filling
!= ( waterLevel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',filling_not_waterLevel) ).
thf(209,plain,
! [A: $i] :
( filling
!= ( waterLevel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(210,plain,
~ ? [A: $i] :
( filling
= ( waterLevel @ A ) ),
inference(miniscope,[status(thm)],[209]) ).
thf(211,plain,
! [A: $i] :
( filling
!= ( waterLevel @ A ) ),
inference(cnf,[status(esa)],[210]) ).
thf(212,plain,
! [A: $i] :
( ( waterLevel @ A )
!= filling ),
inference(lifteq,[status(thm)],[211]) ).
thf(20,axiom,
! [A: $i] :
( ( less @ A @ n9 )
<=> ( less_or_equal @ A @ n8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less9) ).
thf(134,plain,
! [A: $i] :
( ( ( less @ A @ n9 )
=> ( less_or_equal @ A @ n8 ) )
& ( ( less_or_equal @ A @ n8 )
=> ( less @ A @ n9 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( stoppedIn @ A @ B @ C )
<=> ? [D: $i,E: $i] :
( ( happens @ D @ E )
& ( less @ A @ E )
& ( less @ E @ C )
& ( terminates @ D @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stoppedin_defn) ).
thf(73,plain,
! [A: $i,B: $i,C: $i] :
( ( ( stoppedIn @ A @ B @ C )
=> ? [D: $i,E: $i] :
( ( happens @ D @ E )
& ( less @ A @ E )
& ( less @ E @ C )
& ( terminates @ D @ B @ E ) ) )
& ( ? [D: $i,E: $i] :
( ( happens @ D @ E )
& ( less @ A @ E )
& ( less @ E @ C )
& ( terminates @ D @ B @ E ) )
=> ( stoppedIn @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ~ ( holdsAt @ A @ B )
& ~ ( releasedAt @ A @ ( plus @ B @ n1 ) )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( initiates @ C @ A @ B ) ) )
=> ~ ( holdsAt @ A @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_not_holding) ).
thf(244,plain,
! [A: $i,B: $i] :
( ( ~ ( holdsAt @ A @ B )
& ~ ( releasedAt @ A @ ( plus @ B @ n1 ) )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( initiates @ C @ A @ B ) ) )
=> ~ ( holdsAt @ A @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(27,axiom,
( ( plus @ n0 @ n2 )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_2) ).
thf(161,plain,
( ( plus @ n0 @ n2 )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(56,axiom,
holdsAt @ ( waterLevel @ n3 ) @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_3) ).
thf(279,plain,
holdsAt @ ( waterLevel @ n3 ) @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( ( initiates @ A @ C @ B )
| ( terminates @ A @ C @ B ) ) )
=> ~ ( releasedAt @ C @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_not_released) ).
thf(180,plain,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( ( initiates @ A @ C @ B )
| ( terminates @ A @ C @ B ) ) )
=> ~ ( releasedAt @ C @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(189,plain,
~ ? [A: $i] :
( spilling
= ( waterLevel @ A ) ),
inference(miniscope,[status(thm)],[188]) ).
thf(190,plain,
! [A: $i] :
( spilling
!= ( waterLevel @ A ) ),
inference(cnf,[status(esa)],[189]) ).
thf(191,plain,
! [A: $i] :
( ( waterLevel @ A )
!= spilling ),
inference(lifteq,[status(thm)],[190]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( terminates @ A @ B @ C )
<=> ( ( ( A = tapOff )
& ( B = filling ) )
| ( ( A = overflow )
& ( B = filling ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',terminates_all_defn) ).
thf(259,plain,
! [A: $i,B: $i,C: $i] :
( ( ( terminates @ A @ B @ C )
=> ( ( ( A = tapOff )
& ( B = filling ) )
| ( ( A = overflow )
& ( B = filling ) ) ) )
& ( ( ( ( A = tapOff )
& ( B = filling ) )
| ( ( A = overflow )
& ( B = filling ) ) )
=> ( terminates @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(5,axiom,
! [A: $i] :
( ( less @ A @ n3 )
<=> ( less_or_equal @ A @ n2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less3) ).
thf(68,plain,
! [A: $i] :
( ( ( less @ A @ n3 )
=> ( less_or_equal @ A @ n2 ) )
& ( ( less_or_equal @ A @ n2 )
=> ( less @ A @ n3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(69,plain,
( ! [A: $i] :
( ( less @ A @ n3 )
=> ( less_or_equal @ A @ n2 ) )
& ! [A: $i] :
( ( less_or_equal @ A @ n2 )
=> ( less @ A @ n3 ) ) ),
inference(miniscope,[status(thm)],[68]) ).
thf(71,plain,
! [A: $i] :
( ~ ( less @ A @ n3 )
| ( less_or_equal @ A @ n2 ) ),
inference(cnf,[status(esa)],[69]) ).
thf(32,axiom,
( ( plus @ n1 @ n1 )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_1) ).
thf(186,plain,
( ( plus @ n1 @ n1 )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(187,plain,
( ( plus @ n1 @ n1 )
= n2 ),
inference(lifteq,[status(thm)],[186]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( releasedAt @ A @ B )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( ( initiates @ C @ A @ B )
| ( terminates @ C @ A @ B ) ) ) )
=> ( releasedAt @ A @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_released) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( ( releasedAt @ A @ B )
& ~ ? [C: $i] :
( ( happens @ C @ B )
& ( ( initiates @ C @ A @ B )
| ( terminates @ C @ A @ B ) ) ) )
=> ( releasedAt @ A @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
tapOff != overflow,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tapOff_not_overflow) ).
thf(98,plain,
tapOff != overflow,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
( ( plus @ n1 @ n3 )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_3) ).
thf(207,plain,
( ( plus @ n1 @ n3 )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(208,plain,
( ( plus @ n1 @ n3 )
= n4 ),
inference(lifteq,[status(thm)],[207]) ).
thf(13,axiom,
! [A: $i] :
( ( less @ A @ n2 )
<=> ( less_or_equal @ A @ n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less2) ).
thf(103,plain,
! [A: $i] :
( ( ( less @ A @ n2 )
=> ( less_or_equal @ A @ n1 ) )
& ( ( less_or_equal @ A @ n1 )
=> ( less @ A @ n2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( holdsAt @ ( waterLevel @ B ) @ A )
& ( holdsAt @ ( waterLevel @ C ) @ A ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',same_waterLevel) ).
thf(213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( holdsAt @ ( waterLevel @ B ) @ A )
& ( holdsAt @ ( waterLevel @ C ) @ A ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(4,axiom,
! [A: $i] :
( ( less @ A @ n1 )
<=> ( less_or_equal @ A @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less1) ).
thf(63,plain,
! [A: $i] :
( ( ( less @ A @ n1 )
=> ( less_or_equal @ A @ n0 ) )
& ( ( less_or_equal @ A @ n0 )
=> ( less @ A @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,plain,
( ! [A: $i] :
( ( less @ A @ n1 )
=> ( less_or_equal @ A @ n0 ) )
& ! [A: $i] :
( ( less_or_equal @ A @ n0 )
=> ( less @ A @ n1 ) ) ),
inference(miniscope,[status(thm)],[63]) ).
thf(66,plain,
! [A: $i] :
( ~ ( less @ A @ n1 )
| ( less_or_equal @ A @ n0 ) ),
inference(cnf,[status(esa)],[64]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( releases @ A @ C @ B ) )
=> ( releasedAt @ C @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_releases) ).
thf(108,plain,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( releases @ A @ C @ B ) )
=> ( releasedAt @ C @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(277,plain,
filling != spilling,
inference(polarity_switch,[status(thm)],[276]) ).
thf(278,plain,
spilling != filling,
inference(lifteq,[status(thm)],[277]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( happens @ A @ B )
& ( initiates @ A @ C @ B )
& ( less @ n0 @ E )
& ( trajectory @ C @ B @ D @ E )
& ~ ( stoppedIn @ B @ C @ ( plus @ B @ E ) ) )
=> ( holdsAt @ D @ ( plus @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',change_holding) ).
thf(226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( happens @ A @ B )
& ( initiates @ A @ C @ B )
& ( less @ n0 @ E )
& ( trajectory @ C @ B @ D @ E )
& ~ ( stoppedIn @ B @ C @ ( plus @ B @ E ) ) )
=> ( holdsAt @ D @ ( plus @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(162,plain,
( ( plus @ n0 @ n2 )
= n2 ),
inference(lifteq,[status(thm)],[161]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( plus @ A @ B )
= ( plus @ B @ A ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( plus @ B @ A )
= n1 )
| ( ( plus @ n0 @ n1 )
!= ( plus @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[120,62]) ).
thf(342,plain,
( ( plus @ n1 @ n0 )
= n1 ),
inference(pattern_uni,[status(thm)],[341:[bind(A,$thf( n0 )),bind(B,$thf( n1 ))]]) ).
thf(193,plain,
overflow != tapOn,
inference(polarity_switch,[status(thm)],[192]) ).
thf(194,plain,
overflow != tapOn,
inference(lifteq,[status(thm)],[193]) ).
thf(94,plain,
tapOff != tapOn,
inference(polarity_switch,[status(thm)],[93]) ).
thf(95,plain,
tapOn != tapOff,
inference(lifteq,[status(thm)],[94]) ).
thf(65,plain,
! [A: $i] :
( ~ ( less_or_equal @ A @ n0 )
| ( less @ A @ n1 ) ),
inference(cnf,[status(esa)],[64]) ).
thf(67,plain,
! [A: $i] :
( ~ ( less_or_equal @ A @ n0 )
| ( less @ A @ n1 ) ),
inference(simp,[status(thm)],[65]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( holdsAt @ ( waterLevel @ A ) @ B )
& ( C
= ( plus @ A @ D ) ) )
=> ( trajectory @ filling @ B @ ( waterLevel @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',change_of_waterLevel) ).
thf(199,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( holdsAt @ ( waterLevel @ A ) @ B )
& ( C
= ( plus @ A @ D ) ) )
=> ( trajectory @ filling @ B @ ( waterLevel @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(51,axiom,
! [A: $i] :
( ( less @ A @ n4 )
<=> ( less_or_equal @ A @ n3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less4) ).
thf(250,plain,
! [A: $i] :
( ( ( less @ A @ n4 )
=> ( less_or_equal @ A @ n3 ) )
& ( ( less_or_equal @ A @ n3 )
=> ( less @ A @ n4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( terminates @ A @ C @ B ) )
=> ~ ( holdsAt @ C @ ( plus @ B @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_terminates_not_holds) ).
thf(203,plain,
! [A: $i,B: $i,C: $i] :
( ( ( happens @ A @ B )
& ( terminates @ A @ C @ B ) )
=> ~ ( holdsAt @ C @ ( plus @ B @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(258,plain,
( ( plus @ n2 @ n2 )
= n4 ),
inference(lifteq,[status(thm)],[257]) ).
thf(158,plain,
( ( plus @ n0 @ n0 )
= n0 ),
inference(lifteq,[status(thm)],[157]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( releases @ A @ B @ C )
<=> ? [D: $i] :
( ( A = tapOn )
& ( B
= ( waterLevel @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',releases_all_defn) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( releases @ A @ B @ C )
=> ? [D: $i] :
( ( A = tapOn )
& ( B
= ( waterLevel @ D ) ) ) )
& ( ? [D: $i] :
( ( A = tapOn )
& ( B
= ( waterLevel @ D ) ) )
=> ( releases @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( waterLevel @ A )
= ( waterLevel @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct_waterLevels) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( ( waterLevel @ A )
= ( waterLevel @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( waterLevel @ A )
= ( waterLevel @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( ( plus @ B @ A )
= n5 )
| ( ( plus @ n2 @ n3 )
!= ( plus @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[102,62]) ).
thf(326,plain,
( ( plus @ n3 @ n2 )
= n5 ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( n2 )),bind(B,$thf( n3 ))]]) ).
thf(229,plain,
( ! [A: $i,B: $i] :
( ( happens @ A @ B )
=> ( ( ( A = tapOn )
& ( B = n0 ) )
| ( ( holdsAt @ ( waterLevel @ n3 ) @ B )
& ( holdsAt @ filling @ B )
& ( A = overflow ) ) ) )
& ! [A: $i,B: $i] :
( ( ( ( A = tapOn )
& ( B = n0 ) )
| ( ( holdsAt @ ( waterLevel @ n3 ) @ B )
& ( holdsAt @ filling @ B )
& ( A = overflow ) ) )
=> ( happens @ A @ B ) ) ),
inference(miniscope,[status(thm)],[228]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( A != tapOn )
| ( B != n0 )
| ( happens @ A @ B ) ),
inference(cnf,[status(esa)],[229]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A != tapOn )
| ( B != n0 )
| ( happens @ A @ B ) ),
inference(lifteq,[status(thm)],[231]) ).
thf(242,plain,
happens @ tapOn @ n0,
inference(simp,[status(thm)],[241]) ).
thf(18,axiom,
! [A: $i] :
~ ( releasedAt @ ( waterLevel @ A ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_released_waterLevel_0) ).
thf(126,plain,
! [A: $i] :
~ ( releasedAt @ ( waterLevel @ A ) @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( startedIn @ A @ C @ B )
<=> ? [D: $i,E: $i] :
( ( happens @ D @ E )
& ( less @ A @ E )
& ( less @ E @ B )
& ( initiates @ D @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',startedin_defn) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( ( startedIn @ A @ C @ B )
=> ? [D: $i,E: $i] :
( ( happens @ D @ E )
& ( less @ A @ E )
& ( less @ E @ B )
& ( initiates @ D @ C @ E ) ) )
& ( ? [D: $i,E: $i] :
( ( happens @ D @ E )
& ( less @ A @ E )
& ( less @ E @ B )
& ( initiates @ D @ C @ E ) )
=> ( startedIn @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(334,plain,
( ( n5 = n6 )
| ( ( plus @ n2 @ n3 )
!= ( plus @ n3 @ n3 ) ) ),
inference(paramod_ordered,[status(thm)],[97,102]) ).
thf(336,plain,
( ( n5 = n6 )
| ( n2 != n3 )
| ( n3 != n3 ) ),
inference(simp,[status(thm)],[334]) ).
thf(337,plain,
( ( n5 = n6 )
| ( n2 != n3 ) ),
inference(simp,[status(thm)],[336]) ).
thf(99,plain,
tapOff != overflow,
inference(polarity_switch,[status(thm)],[98]) ).
thf(100,plain,
overflow != tapOff,
inference(lifteq,[status(thm)],[99]) ).
thf(1095,plain,
$false,
inference(e,[status(thm)],[101,129,314,183,276,120,247,185,565,257,110,196,157,93,152,228,216,121,84,147,280,221,206,60,102,160,192,566,197,97,224,156,188,256,225,212,96,134,73,244,205,161,279,180,191,59,259,71,159,187,81,98,208,103,213,66,155,108,278,223,226,162,255,209,342,194,63,95,67,199,250,203,258,158,186,171,139,207,119,58,326,242,126,195,163,68,62,337,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : CSR002+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.16/0.17 % Command : run_Leo-III %s %d
% 0.18/0.38 % Computer : n029.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Mon May 6 15:48:54 EDT 2024
% 0.18/0.39 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.02 % [INFO] Parsing done (143ms).
% 1.26/1.03 % [INFO] Running in sequential loop mode.
% 1.91/1.24 % [INFO] eprover registered as external prover.
% 1.91/1.24 % [INFO] cvc4 registered as external prover.
% 1.91/1.25 % [INFO] Scanning for conjecture ...
% 1.95/1.31 % [INFO] Found a conjecture and 55 axioms. Running axiom selection ...
% 2.25/1.36 % [INFO] Axiom selection finished. Selected 55 axioms (removed 0 axioms).
% 2.25/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/1.44 % [INFO] Type checking passed.
% 2.57/1.44 % [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 ...
% 8.29/2.76 % External prover 'e' found a proof!
% 8.29/2.76 % [INFO] Killing All external provers ...
% 8.29/2.76 % Time passed: 2212ms (effective reasoning time: 1726ms)
% 8.29/2.76 % 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)>
% 8.29/2.76 % Axioms used in derivation (55): keep_not_holding, same_waterLevel, plus1_1, stoppedin_defn, happens_all_defn, plus3_3, happens_holds, plus2_2, less9, waterLevel_3, keep_holding, not_filling_0, releases_all_defn, spilling_not_waterLevel, less8, less_property, antitrajectory, tapOff_not_overflow, less0, plus0_0, happens_terminates_not_holds, waterLevel_0, distinct_waterLevels, less4, less1, keep_released, plus2_3, less3, filling_not_waterLevel, plus0_1, not_spilling_0, plus0_3, not_released_filling_0, plus1_2, overflow_not_tapOn, filling_not_spilling, tapOff_not_tapOn, symmetry_of_plus, less7, initiates_all_defn, keep_not_released, not_released_waterLevel_0, terminates_all_defn, less2, change_of_waterLevel, plus0_2, plus1_3, change_holding, less6, happens_releases, less5, startedin_defn, happens_not_released, less_or_equal, not_released_spilling_0
% 8.29/2.76 % No. of inferences in proof: 173
% 8.29/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2212 ms resp. 1726 ms w/o parsing
% 8.29/2.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.29/2.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------