TSTP Solution File: MGT004+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT004+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 : Thu Aug 31 09:16:07 EDT 2023
% Result : Theorem 5.43s 1.45s
% Output : Proof 8.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT004+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 06:24:25 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.12/1.01 Prover 1: Preprocessing ...
% 2.12/1.01 Prover 4: Preprocessing ...
% 2.61/1.05 Prover 3: Preprocessing ...
% 2.61/1.05 Prover 0: Preprocessing ...
% 2.61/1.05 Prover 2: Preprocessing ...
% 2.61/1.05 Prover 5: Preprocessing ...
% 2.61/1.06 Prover 6: Preprocessing ...
% 3.41/1.21 Prover 5: Constructing countermodel ...
% 3.41/1.21 Prover 2: Constructing countermodel ...
% 3.96/1.27 Prover 1: Constructing countermodel ...
% 3.96/1.29 Prover 6: Constructing countermodel ...
% 3.96/1.29 Prover 3: Constructing countermodel ...
% 5.43/1.45 Prover 5: proved (835ms)
% 5.43/1.45
% 5.43/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.43/1.45
% 5.43/1.45 Prover 2: proved (840ms)
% 5.43/1.45
% 5.43/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.43/1.45
% 5.43/1.45 Prover 6: stopped
% 5.43/1.45 Prover 0: stopped
% 5.43/1.46 Prover 3: stopped
% 5.43/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.43/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.43/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.43/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.43/1.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.60/1.50 Prover 8: Preprocessing ...
% 5.60/1.50 Prover 7: Preprocessing ...
% 5.60/1.51 Prover 10: Preprocessing ...
% 5.60/1.51 Prover 11: Preprocessing ...
% 5.98/1.53 Prover 13: Preprocessing ...
% 5.98/1.53 Prover 7: Constructing countermodel ...
% 6.16/1.59 Prover 10: Constructing countermodel ...
% 6.16/1.60 Prover 13: Constructing countermodel ...
% 6.16/1.62 Prover 8: Warning: ignoring some quantifiers
% 6.77/1.63 Prover 8: Constructing countermodel ...
% 7.12/1.70 Prover 10: Found proof (size 19)
% 7.12/1.70 Prover 7: Found proof (size 19)
% 7.12/1.70 Prover 10: proved (240ms)
% 7.12/1.70 Prover 7: proved (249ms)
% 7.12/1.70 Prover 1: stopped
% 7.12/1.70 Prover 13: stopped
% 7.12/1.70 Prover 8: stopped
% 7.12/1.70 Prover 11: stopped
% 8.05/1.88 Prover 4: Constructing countermodel ...
% 8.05/1.89 Prover 4: stopped
% 8.05/1.89
% 8.05/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.05/1.89
% 8.05/1.90 % SZS output start Proof for theBenchmark
% 8.05/1.91 Assumptions after simplification:
% 8.05/1.91 ---------------------------------
% 8.05/1.91
% 8.05/1.91 (a1_FOL)
% 8.05/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.05/1.92 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) |
% 8.05/1.92 ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 8.05/1.92 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ greater(v5, v4) | ~ greater(v3, v2) |
% 8.05/1.92 ~ survival_chance(v1, v7, v9) | ~ survival_chance(v0, v6, v8) | ~
% 8.05/1.92 accountability(v1, v5, v9) | ~ accountability(v0, v4, v8) | ~
% 8.05/1.92 reliability(v1, v3, v9) | ~ reliability(v0, v2, v8) | ~ organization(v1,
% 8.05/1.92 v9) | ~ organization(v0, v8) | greater(v7, v6))
% 8.05/1.92
% 8.05/1.93 (a6_FOL)
% 8.05/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.05/1.93 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~
% 8.05/1.93 $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.05/1.93 $i(v0) | ~ reorganization(v0, v7, v8) | ~ greater(v6, v5) | ~
% 8.05/1.93 accountability(v0, v4, v6) | ~ accountability(v0, v3, v5) | ~
% 8.05/1.93 reliability(v0, v2, v6) | ~ reliability(v0, v1, v5) | ~ organization(v0,
% 8.05/1.93 v6) | ~ organization(v0, v5) | greater(v7, v5) | greater(v6, v8) |
% 8.05/1.93 greater(v3, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 8.05/1.93 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 8.05/1.93 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 8.05/1.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ reorganization(v0, v7, v8) | ~
% 8.05/1.94 greater(v6, v5) | ~ accountability(v0, v4, v6) | ~ accountability(v0, v3,
% 8.05/1.94 v5) | ~ reliability(v0, v2, v6) | ~ reliability(v0, v1, v5) | ~
% 8.05/1.94 organization(v0, v6) | ~ organization(v0, v5) | greater(v7, v5) |
% 8.05/1.94 greater(v6, v8) | greater(v1, v2))
% 8.05/1.94
% 8.05/1.94 (mp1)
% 8.05/1.94 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ organization(v0, v1) |
% 8.05/1.94 ? [v2: $i] : ($i(v2) & reliability(v0, v2, v1)))
% 8.05/1.94
% 8.05/1.94 (mp2)
% 8.05/1.94 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ organization(v0, v1) |
% 8.05/1.94 ? [v2: $i] : ($i(v2) & accountability(v0, v2, v1)))
% 8.05/1.94
% 8.05/1.94 (t4_FOL)
% 8.05/1.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.05/1.94 $i] : ? [v6: $i] : ($i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 8.05/1.94 $i(v0) & reorganization(v0, v5, v6) & greater(v4, v3) & survival_chance(v0,
% 8.05/1.94 v2, v4) & survival_chance(v0, v1, v3) & organization(v0, v4) &
% 8.05/1.94 organization(v0, v3) & ~ greater(v5, v3) & ~ greater(v4, v6) & ~
% 8.05/1.94 greater(v1, v2))
% 8.05/1.94
% 8.05/1.94 Those formulas are unsatisfiable:
% 8.05/1.94 ---------------------------------
% 8.05/1.94
% 8.05/1.94 Begin of proof
% 8.05/1.94 |
% 8.05/1.94 | ALPHA: (a6_FOL) implies:
% 8.05/1.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 8.05/1.95 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~
% 8.05/1.95 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 8.05/1.95 | ~ $i(v1) | ~ $i(v0) | ~ reorganization(v0, v7, v8) | ~ greater(v6,
% 8.05/1.95 | v5) | ~ accountability(v0, v4, v6) | ~ accountability(v0, v3, v5)
% 8.05/1.95 | | ~ reliability(v0, v2, v6) | ~ reliability(v0, v1, v5) | ~
% 8.05/1.95 | organization(v0, v6) | ~ organization(v0, v5) | greater(v7, v5) |
% 8.05/1.95 | greater(v6, v8) | greater(v1, v2))
% 8.05/1.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 8.05/1.95 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~
% 8.05/1.95 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 8.05/1.95 | ~ $i(v1) | ~ $i(v0) | ~ reorganization(v0, v7, v8) | ~ greater(v6,
% 8.05/1.95 | v5) | ~ accountability(v0, v4, v6) | ~ accountability(v0, v3, v5)
% 8.05/1.95 | | ~ reliability(v0, v2, v6) | ~ reliability(v0, v1, v5) | ~
% 8.05/1.95 | organization(v0, v6) | ~ organization(v0, v5) | greater(v7, v5) |
% 8.05/1.95 | greater(v6, v8) | greater(v3, v4))
% 8.05/1.95 |
% 8.05/1.95 | DELTA: instantiating (t4_FOL) with fresh symbols all_6_0, all_6_1, all_6_2,
% 8.05/1.95 | all_6_3, all_6_4, all_6_5, all_6_6 gives:
% 8.05/1.96 | (3) $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & $i(all_6_4) &
% 8.05/1.96 | $i(all_6_5) & $i(all_6_6) & reorganization(all_6_6, all_6_1, all_6_0) &
% 8.05/1.96 | greater(all_6_2, all_6_3) & survival_chance(all_6_6, all_6_4, all_6_2)
% 8.05/1.96 | & survival_chance(all_6_6, all_6_5, all_6_3) & organization(all_6_6,
% 8.05/1.96 | all_6_2) & organization(all_6_6, all_6_3) & ~ greater(all_6_1,
% 8.05/1.96 | all_6_3) & ~ greater(all_6_2, all_6_0) & ~ greater(all_6_5,
% 8.05/1.96 | all_6_4)
% 8.05/1.96 |
% 8.05/1.96 | ALPHA: (3) implies:
% 8.05/1.96 | (4) ~ greater(all_6_5, all_6_4)
% 8.05/1.96 | (5) ~ greater(all_6_2, all_6_0)
% 8.05/1.96 | (6) ~ greater(all_6_1, all_6_3)
% 8.05/1.96 | (7) organization(all_6_6, all_6_3)
% 8.05/1.96 | (8) organization(all_6_6, all_6_2)
% 8.05/1.96 | (9) survival_chance(all_6_6, all_6_5, all_6_3)
% 8.05/1.96 | (10) survival_chance(all_6_6, all_6_4, all_6_2)
% 8.05/1.96 | (11) greater(all_6_2, all_6_3)
% 8.05/1.96 | (12) reorganization(all_6_6, all_6_1, all_6_0)
% 8.05/1.96 | (13) $i(all_6_6)
% 8.05/1.96 | (14) $i(all_6_5)
% 8.05/1.96 | (15) $i(all_6_4)
% 8.05/1.96 | (16) $i(all_6_3)
% 8.05/1.96 | (17) $i(all_6_2)
% 8.05/1.96 | (18) $i(all_6_1)
% 8.05/1.96 | (19) $i(all_6_0)
% 8.05/1.96 |
% 8.05/1.96 | GROUND_INST: instantiating (mp2) with all_6_6, all_6_3, simplifying with (7),
% 8.05/1.96 | (13), (16) gives:
% 8.05/1.96 | (20) ? [v0: $i] : ($i(v0) & accountability(all_6_6, v0, all_6_3))
% 8.05/1.96 |
% 8.05/1.96 | GROUND_INST: instantiating (mp1) with all_6_6, all_6_3, simplifying with (7),
% 8.05/1.96 | (13), (16) gives:
% 8.05/1.96 | (21) ? [v0: $i] : ($i(v0) & reliability(all_6_6, v0, all_6_3))
% 8.05/1.96 |
% 8.05/1.96 | GROUND_INST: instantiating (mp2) with all_6_6, all_6_2, simplifying with (8),
% 8.05/1.96 | (13), (17) gives:
% 8.05/1.96 | (22) ? [v0: $i] : ($i(v0) & accountability(all_6_6, v0, all_6_2))
% 8.05/1.96 |
% 8.05/1.96 | GROUND_INST: instantiating (mp1) with all_6_6, all_6_2, simplifying with (8),
% 8.05/1.96 | (13), (17) gives:
% 8.05/1.96 | (23) ? [v0: $i] : ($i(v0) & reliability(all_6_6, v0, all_6_2))
% 8.05/1.96 |
% 8.05/1.96 | DELTA: instantiating (23) with fresh symbol all_17_0 gives:
% 8.05/1.97 | (24) $i(all_17_0) & reliability(all_6_6, all_17_0, all_6_2)
% 8.05/1.97 |
% 8.05/1.97 | ALPHA: (24) implies:
% 8.05/1.97 | (25) reliability(all_6_6, all_17_0, all_6_2)
% 8.05/1.97 | (26) $i(all_17_0)
% 8.05/1.97 |
% 8.05/1.97 | DELTA: instantiating (21) with fresh symbol all_19_0 gives:
% 8.05/1.97 | (27) $i(all_19_0) & reliability(all_6_6, all_19_0, all_6_3)
% 8.05/1.97 |
% 8.05/1.97 | ALPHA: (27) implies:
% 8.05/1.97 | (28) reliability(all_6_6, all_19_0, all_6_3)
% 8.05/1.97 | (29) $i(all_19_0)
% 8.05/1.97 |
% 8.05/1.97 | DELTA: instantiating (20) with fresh symbol all_21_0 gives:
% 8.05/1.97 | (30) $i(all_21_0) & accountability(all_6_6, all_21_0, all_6_3)
% 8.05/1.97 |
% 8.05/1.97 | ALPHA: (30) implies:
% 8.05/1.97 | (31) accountability(all_6_6, all_21_0, all_6_3)
% 8.05/1.97 | (32) $i(all_21_0)
% 8.05/1.97 |
% 8.05/1.97 | DELTA: instantiating (22) with fresh symbol all_23_0 gives:
% 8.05/1.97 | (33) $i(all_23_0) & accountability(all_6_6, all_23_0, all_6_2)
% 8.05/1.97 |
% 8.05/1.97 | ALPHA: (33) implies:
% 8.05/1.97 | (34) accountability(all_6_6, all_23_0, all_6_2)
% 8.05/1.97 | (35) $i(all_23_0)
% 8.05/1.97 |
% 8.05/1.97 | GROUND_INST: instantiating (2) with all_6_6, all_19_0, all_17_0, all_21_0,
% 8.05/1.97 | all_23_0, all_6_3, all_6_2, all_6_1, all_6_0, simplifying with
% 8.05/1.97 | (5), (6), (7), (8), (11), (12), (13), (16), (17), (18), (19),
% 8.05/1.97 | (25), (26), (28), (29), (31), (32), (34), (35) gives:
% 8.05/1.97 | (36) greater(all_21_0, all_23_0)
% 8.05/1.97 |
% 8.05/1.97 | GROUND_INST: instantiating (1) with all_6_6, all_19_0, all_17_0, all_21_0,
% 8.05/1.97 | all_23_0, all_6_3, all_6_2, all_6_1, all_6_0, simplifying with
% 8.05/1.97 | (5), (6), (7), (8), (11), (12), (13), (16), (17), (18), (19),
% 8.05/1.97 | (25), (26), (28), (29), (31), (32), (34), (35) gives:
% 8.05/1.97 | (37) greater(all_19_0, all_17_0)
% 8.05/1.97 |
% 8.05/1.98 | GROUND_INST: instantiating (a1_FOL) with all_6_6, all_6_6, all_17_0, all_19_0,
% 8.05/1.98 | all_23_0, all_21_0, all_6_4, all_6_5, all_6_2, all_6_3,
% 8.05/1.98 | simplifying with (4), (7), (8), (9), (10), (13), (14), (15),
% 8.05/1.98 | (16), (17), (25), (26), (28), (29), (31), (32), (34), (35), (36),
% 8.05/1.98 | (37) gives:
% 8.05/1.98 | (38) $false
% 8.05/1.98 |
% 8.05/1.98 | CLOSE: (38) is inconsistent.
% 8.05/1.98 |
% 8.05/1.98 End of proof
% 8.05/1.98 % SZS output end Proof for theBenchmark
% 8.05/1.98
% 8.05/1.98 1386ms
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