%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : CSR309_1 : TPTP v9.0.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 Apr 1 01:53:41 AM UTC 2025 % Result : Theorem 10.96s 2.26s % Output : Proof 14.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : CSR309_1 : TPTP v9.0.0. Released v9.1.0. % 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n008.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 : 300 % 0.13/0.33 % DateTime : Mon Mar 31 16:20:33 EDT 2025 % 0.13/0.34 % CPUTime : % 0.70/0.67 ________ _____ % 0.70/0.67 ___ __ \_________(_)________________________________ % 0.70/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.70/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.70/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.70/0.67 % 0.70/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.70/0.67 (2023-06-19) % 0.70/0.67 % 0.70/0.67 (c) Philipp Rümmer, 2009-2023 % 0.70/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.70/0.67 Amanda Stjerna. % 0.70/0.67 Free software under BSD-3-Clause. % 0.70/0.67 % 0.70/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.70/0.67 % 0.70/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.68 Running up to 7 provers in parallel. % 0.70/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.11/1.33 Prover 1: Preprocessing ... % 4.11/1.34 Prover 4: Preprocessing ... % 4.48/1.38 Prover 6: Preprocessing ... % 4.48/1.38 Prover 0: Preprocessing ... % 4.48/1.38 Prover 5: Preprocessing ... % 4.48/1.38 Prover 2: Preprocessing ... % 4.48/1.38 Prover 3: Preprocessing ... % 9.06/1.99 Prover 6: Proving ... % 9.06/1.99 Prover 1: Constructing countermodel ... % 9.06/2.00 Prover 3: Constructing countermodel ... % 9.06/2.00 Prover 5: Proving ... % 9.06/2.03 Prover 4: Constructing countermodel ... % 9.77/2.10 Prover 0: Proving ... % 10.08/2.14 Prover 2: Proving ... % 10.96/2.25 Prover 3: proved (1557ms) % 10.96/2.25 % 10.96/2.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.96/2.26 % 10.96/2.26 Prover 2: stopped % 10.96/2.26 Prover 5: stopped % 10.96/2.26 Prover 0: stopped % 10.96/2.27 Prover 6: stopped % 10.96/2.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.96/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.96/2.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.96/2.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.96/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.42/2.35 Prover 13: Preprocessing ... % 11.42/2.35 Prover 8: Preprocessing ... % 11.42/2.35 Prover 7: Preprocessing ... % 12.03/2.37 Prover 10: Preprocessing ... % 12.03/2.38 Prover 11: Preprocessing ... % 12.58/2.50 Prover 13: Warning: ignoring some quantifiers % 12.58/2.51 Prover 8: Warning: ignoring some quantifiers % 12.58/2.51 Prover 13: Constructing countermodel ... % 13.33/2.54 Prover 7: Warning: ignoring some quantifiers % 13.33/2.54 Prover 8: Constructing countermodel ... % 13.33/2.55 Prover 10: Warning: ignoring some quantifiers % 13.33/2.56 Prover 7: Constructing countermodel ... % 13.33/2.56 Prover 10: Constructing countermodel ... % 13.80/2.63 Prover 1: Found proof (size 50) % 13.80/2.63 Prover 1: proved (1939ms) % 13.80/2.63 Prover 13: stopped % 13.80/2.63 Prover 4: stopped % 13.80/2.63 Prover 10: stopped % 13.80/2.63 Prover 8: stopped % 13.80/2.63 Prover 7: stopped % 14.25/2.69 Prover 11: Constructing countermodel ... % 14.25/2.70 Prover 11: stopped % 14.25/2.70 % 14.25/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.25/2.70 % 14.48/2.71 % SZS output start Proof for theBenchmark % 14.48/2.72 Assumptions after simplification: % 14.48/2.72 --------------------------------- % 14.48/2.72 % 14.48/2.72 (distinct_waterLevels) % 14.48/2.73 ! [v0: int] : ! [v1: fluent] : ! [v2: fluent] : (v2 = v1 | ~ % 14.48/2.73 (waterLevel(v0) = v2) | ~ (waterLevel(v0) = v1)) & ! [v0: int] : ! [v1: % 14.48/2.73 int] : ! [v2: fluent] : (v1 = v0 | ~ (waterLevel(v1) = v2) | ~ % 14.48/2.73 (waterLevel(v0) = v2)) % 14.48/2.73 % 14.48/2.73 (happens_all_defn) % 14.48/2.74 event(overflow) & event(tapOn) & fluent(filling) & ? [v0: fluent] : % 14.48/2.74 (waterLevel(3) = v0 & fluent(v0) & ! [v1: event] : ! [v2: int] : ! [v3: % 14.48/2.74 time] : ! [v4: int] : (v4 = 0 | ~ (at_time(v2) = v3) | ~ (happens(v1, % 14.48/2.74 v3) = v4) | ~ event(v1) | (( ~ (v2 = 0) | ~ (v1 = tapOn)) & ( ~ (v1 % 14.48/2.74 = overflow) | ? [v5: any] : ? [v6: any] : (holdsAt(v0, v3) = v5 & % 14.48/2.74 holdsAt(filling, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ! % 14.48/2.74 [v1: event] : ! [v2: int] : ! [v3: time] : ( ~ (at_time(v2) = v3) | ~ % 14.48/2.74 (happens(v1, v3) = 0) | ~ event(v1) | (v2 = 0 & v1 = tapOn) | (v1 = % 14.48/2.74 overflow & holdsAt(v0, v3) = 0 & holdsAt(filling, v3) = 0))) % 14.48/2.74 % 14.48/2.74 (keep_holding) % 14.48/2.74 ! [v0: fluent] : ! [v1: int] : ! [v2: time] : ! [v3: int] : (v3 = 0 | ~ % 14.48/2.74 (releasedAt(v0, v2) = v3) | ~ (at_time($sum(v1, 1)) = v2) | ~ fluent(v0) | % 14.48/2.74 ? [v4: time] : ? [v5: any] : ? [v6: any] : (holdsAt(v0, v4) = v5 & % 14.48/2.74 holdsAt(v0, v2) = v6 & at_time(v1) = v4 & time(v4) & ( ~ (v5 = 0) | v6 = 0 % 14.48/2.74 | ? [v7: event] : (happens(v7, v4) = 0 & terminates(v7, v0, v4) = 0 & % 14.48/2.74 event(v7))))) % 14.48/2.74 % 14.48/2.74 (keep_released) % 14.48/2.74 ! [v0: fluent] : ! [v1: int] : ! [v2: time] : ! [v3: int] : (v3 = 0 | ~ % 14.48/2.74 (releasedAt(v0, v2) = v3) | ~ (at_time($sum(v1, 1)) = v2) | ~ fluent(v0) | % 14.48/2.74 ? [v4: time] : ? [v5: any] : (releasedAt(v0, v4) = v5 & at_time(v1) = v4 & % 14.48/2.74 time(v4) & ( ~ (v5 = 0) | ? [v6: event] : ? [v7: any] : ? [v8: any] : % 14.48/2.74 (initiates(v6, v0, v4) = v7 & happens(v6, v4) = 0 & terminates(v6, v0, % 14.48/2.74 v4) = v8 & event(v6) & (v8 = 0 | v7 = 0))))) % 14.48/2.74 % 14.48/2.74 (release_hold) % 14.66/2.74 ? [v0: time] : ? [v1: time] : ? [v2: fluent] : ? [v3: any] : % 14.66/2.74 (waterLevel(3) = v2 & holdsAt(v2, v0) = v3 & at_time(4) = v1 & at_time(3) = v0 % 14.66/2.74 & fluent(v2) & time(v1) & time(v0) & ? [v4: fluent] : ? [v5: int] : ? % 14.66/2.74 [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & ~ (v3 = 0) & releasedAt(v4, v1) = % 14.66/2.74 v5 & holdsAt(v4, v1) = v6 & holdsAt(v4, v0) = 0 & fluent(v4))) % 14.66/2.74 % 14.66/2.75 (function-axioms) % 14.66/2.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! % 14.66/2.75 [v3: fluent] : ! [v4: time] : ! [v5: fluent] : (v1 = v0 | ~ % 14.66/2.75 (antitrajectory(v5, v4, v3, v2) = v1) | ~ (antitrajectory(v5, v4, v3, v2) = % 14.66/2.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.66/2.75 int] : ! [v3: fluent] : ! [v4: time] : ! [v5: fluent] : (v1 = v0 | ~ % 14.66/2.75 (trajectory(v5, v4, v3, v2) = v1) | ~ (trajectory(v5, v4, v3, v2) = v0)) & % 14.66/2.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! % 14.66/2.75 [v3: fluent] : ! [v4: event] : (v1 = v0 | ~ (releases(v4, v3, v2) = v1) | ~ % 14.66/2.75 (releases(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.66/2.75 MultipleValueBool] : ! [v2: time] : ! [v3: fluent] : ! [v4: time] : (v1 = % 14.66/2.75 v0 | ~ (startedIn(v4, v3, v2) = v1) | ~ (startedIn(v4, v3, v2) = v0)) & ! % 14.66/2.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! [v3: % 14.66/2.75 fluent] : ! [v4: event] : (v1 = v0 | ~ (initiates(v4, v3, v2) = v1) | ~ % 14.66/2.75 (initiates(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.66/2.75 MultipleValueBool] : ! [v2: time] : ! [v3: fluent] : ! [v4: time] : (v1 = % 14.66/2.75 v0 | ~ (stoppedIn(v4, v3, v2) = v1) | ~ (stoppedIn(v4, v3, v2) = v0)) & ! % 14.66/2.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! [v3: % 14.66/2.75 fluent] : ! [v4: event] : (v1 = v0 | ~ (terminates(v4, v3, v2) = v1) | ~ % 14.66/2.75 (terminates(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.66/2.75 MultipleValueBool] : ! [v2: time] : ! [v3: fluent] : (v1 = v0 | ~ % 14.66/2.75 (releasedAt(v3, v2) = v1) | ~ (releasedAt(v3, v2) = v0)) & ! [v0: % 14.66/2.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! [v3: % 14.66/2.75 fluent] : (v1 = v0 | ~ (holdsAt(v3, v2) = v1) | ~ (holdsAt(v3, v2) = v0)) % 14.66/2.75 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! % 14.66/2.75 [v3: event] : (v1 = v0 | ~ (happens(v3, v2) = v1) | ~ (happens(v3, v2) = % 14.66/2.75 v0)) & ! [v0: fluent] : ! [v1: fluent] : ! [v2: int] : (v1 = v0 | ~ % 14.66/2.75 (waterLevel(v2) = v1) | ~ (waterLevel(v2) = v0)) & ! [v0: time] : ! [v1: % 14.66/2.75 time] : ! [v2: int] : (v1 = v0 | ~ (at_time(v2) = v1) | ~ (at_time(v2) = % 14.66/2.75 v0)) % 14.66/2.75 % 14.66/2.75 Further assumptions not needed in the proof: % 14.66/2.75 -------------------------------------------- % 14.66/2.75 antitrajectory, change_holding, change_of_waterLevel, filling_not_spilling, % 14.66/2.75 filling_not_waterLevel, happens_holds, happens_not_released, happens_releases, % 14.66/2.75 happens_terminates_not_holds, initiates_all_defn, keep_not_holding, % 14.66/2.75 keep_not_released, not_filling_0, not_released_filling_0, % 14.66/2.75 not_released_spilling_0, not_released_waterLevel_0, not_spilling_0, % 14.66/2.75 releases_all_defn, same_waterLevel, spilling_not_waterLevel, startedin_defn, % 14.66/2.75 stoppedin_defn, tapOff_overflow, tapOn_overflow, tapOn_tapOff, % 14.66/2.75 terminates_all_defn, waterLevel_0 % 14.66/2.75 % 14.66/2.75 Those formulas are unsatisfiable: % 14.66/2.75 --------------------------------- % 14.66/2.75 % 14.66/2.75 Begin of proof % 14.66/2.75 | % 14.66/2.75 | ALPHA: (distinct_waterLevels) implies: % 14.66/2.75 | (1) ! [v0: int] : ! [v1: fluent] : ! [v2: fluent] : (v2 = v1 | ~ % 14.66/2.75 | (waterLevel(v0) = v2) | ~ (waterLevel(v0) = v1)) % 14.66/2.75 | % 14.66/2.76 | ALPHA: (happens_all_defn) implies: % 14.66/2.76 | (2) ? [v0: fluent] : (waterLevel(3) = v0 & fluent(v0) & ! [v1: event] : % 14.66/2.76 | ! [v2: int] : ! [v3: time] : ! [v4: int] : (v4 = 0 | ~ % 14.66/2.76 | (at_time(v2) = v3) | ~ (happens(v1, v3) = v4) | ~ event(v1) | (( % 14.66/2.76 | ~ (v2 = 0) | ~ (v1 = tapOn)) & ( ~ (v1 = overflow) | ? [v5: % 14.66/2.76 | any] : ? [v6: any] : (holdsAt(v0, v3) = v5 & % 14.66/2.76 | holdsAt(filling, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & % 14.66/2.76 | ! [v1: event] : ! [v2: int] : ! [v3: time] : ( ~ (at_time(v2) = % 14.66/2.76 | v3) | ~ (happens(v1, v3) = 0) | ~ event(v1) | (v2 = 0 & v1 = % 14.66/2.76 | tapOn) | (v1 = overflow & holdsAt(v0, v3) = 0 & holdsAt(filling, % 14.66/2.76 | v3) = 0))) % 14.66/2.76 | % 14.66/2.76 | ALPHA: (function-axioms) implies: % 14.66/2.76 | (3) ! [v0: time] : ! [v1: time] : ! [v2: int] : (v1 = v0 | ~ % 14.66/2.76 | (at_time(v2) = v1) | ~ (at_time(v2) = v0)) % 14.66/2.76 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] % 14.66/2.76 | : ! [v3: fluent] : (v1 = v0 | ~ (holdsAt(v3, v2) = v1) | ~ % 14.66/2.76 | (holdsAt(v3, v2) = v0)) % 14.66/2.76 | % 14.66/2.76 | DELTA: instantiating (release_hold) with fresh symbols all_43_0, all_43_1, % 14.66/2.76 | all_43_2, all_43_3 gives: % 14.66/2.76 | (5) waterLevel(3) = all_43_1 & holdsAt(all_43_1, all_43_3) = all_43_0 & % 14.66/2.76 | at_time(4) = all_43_2 & at_time(3) = all_43_3 & fluent(all_43_1) & % 14.66/2.76 | time(all_43_2) & time(all_43_3) & ? [v0: fluent] : ? [v1: int] : ? % 14.66/2.76 | [v2: int] : ( ~ (v2 = 0) & ~ (v1 = 0) & ~ (all_43_0 = 0) & % 14.66/2.76 | releasedAt(v0, all_43_2) = v1 & holdsAt(v0, all_43_2) = v2 & % 14.66/2.76 | holdsAt(v0, all_43_3) = 0 & fluent(v0)) % 14.66/2.76 | % 14.66/2.76 | ALPHA: (5) implies: % 14.66/2.76 | (6) at_time(3) = all_43_3 % 14.66/2.76 | (7) at_time(4) = all_43_2 % 14.66/2.76 | (8) holdsAt(all_43_1, all_43_3) = all_43_0 % 14.66/2.76 | (9) waterLevel(3) = all_43_1 % 14.66/2.76 | (10) ? [v0: fluent] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = 0) & ~ (v1 % 14.66/2.76 | = 0) & ~ (all_43_0 = 0) & releasedAt(v0, all_43_2) = v1 & % 14.66/2.76 | holdsAt(v0, all_43_2) = v2 & holdsAt(v0, all_43_3) = 0 & fluent(v0)) % 14.66/2.76 | % 14.66/2.76 | DELTA: instantiating (2) with fresh symbol all_45_0 gives: % 14.66/2.76 | (11) waterLevel(3) = all_45_0 & fluent(all_45_0) & ! [v0: event] : ! [v1: % 14.66/2.76 | int] : ! [v2: time] : ! [v3: int] : (v3 = 0 | ~ (at_time(v1) = % 14.66/2.76 | v2) | ~ (happens(v0, v2) = v3) | ~ event(v0) | (( ~ (v1 = 0) | % 14.66/2.76 | ~ (v0 = tapOn)) & ( ~ (v0 = overflow) | ? [v4: any] : ? [v5: % 14.66/2.76 | any] : (holdsAt(all_45_0, v2) = v4 & holdsAt(filling, v2) = v5 % 14.66/2.76 | & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ! [v0: event] : ! [v1: % 14.66/2.76 | int] : ! [v2: time] : ( ~ (at_time(v1) = v2) | ~ (happens(v0, v2) % 14.66/2.76 | = 0) | ~ event(v0) | (v1 = 0 & v0 = tapOn) | (v0 = overflow & % 14.66/2.76 | holdsAt(all_45_0, v2) = 0 & holdsAt(filling, v2) = 0)) % 14.66/2.76 | % 14.66/2.76 | ALPHA: (11) implies: % 14.66/2.76 | (12) waterLevel(3) = all_45_0 % 14.66/2.76 | (13) ! [v0: event] : ! [v1: int] : ! [v2: time] : ( ~ (at_time(v1) = v2) % 14.66/2.76 | | ~ (happens(v0, v2) = 0) | ~ event(v0) | (v1 = 0 & v0 = tapOn) | % 14.66/2.76 | (v0 = overflow & holdsAt(all_45_0, v2) = 0 & holdsAt(filling, v2) = % 14.66/2.76 | 0)) % 14.66/2.76 | % 14.66/2.76 | DELTA: instantiating (10) with fresh symbols all_48_0, all_48_1, all_48_2 % 14.66/2.77 | gives: % 14.66/2.77 | (14) ~ (all_48_0 = 0) & ~ (all_48_1 = 0) & ~ (all_43_0 = 0) & % 14.66/2.77 | releasedAt(all_48_2, all_43_2) = all_48_1 & holdsAt(all_48_2, % 14.66/2.77 | all_43_2) = all_48_0 & holdsAt(all_48_2, all_43_3) = 0 & % 14.66/2.77 | fluent(all_48_2) % 14.66/2.77 | % 14.66/2.77 | ALPHA: (14) implies: % 14.66/2.77 | (15) ~ (all_43_0 = 0) % 14.66/2.77 | (16) ~ (all_48_1 = 0) % 14.66/2.77 | (17) ~ (all_48_0 = 0) % 14.66/2.77 | (18) fluent(all_48_2) % 14.66/2.77 | (19) holdsAt(all_48_2, all_43_3) = 0 % 14.66/2.77 | (20) holdsAt(all_48_2, all_43_2) = all_48_0 % 14.66/2.77 | (21) releasedAt(all_48_2, all_43_2) = all_48_1 % 14.66/2.77 | % 14.66/2.77 | GROUND_INST: instantiating (1) with 3, all_43_1, all_45_0, simplifying with % 14.66/2.77 | (9), (12) gives: % 14.66/2.77 | (22) all_45_0 = all_43_1 % 14.66/2.77 | % 14.66/2.77 | GROUND_INST: instantiating (keep_holding) with all_48_2, 3, all_43_2, % 14.66/2.77 | all_48_1, simplifying with (7), (18), (21) gives: % 14.66/2.77 | (23) all_48_1 = 0 | ? [v0: time] : ? [v1: any] : ? [v2: any] : % 14.66/2.77 | (holdsAt(all_48_2, v0) = v1 & holdsAt(all_48_2, all_43_2) = v2 & % 14.66/2.77 | at_time(3) = v0 & time(v0) & ( ~ (v1 = 0) | v2 = 0 | ? [v3: event] % 14.66/2.77 | : (happens(v3, v0) = 0 & terminates(v3, all_48_2, v0) = 0 & % 14.66/2.77 | event(v3)))) % 14.66/2.77 | % 14.66/2.77 | GROUND_INST: instantiating (keep_released) with all_48_2, 3, all_43_2, % 14.66/2.77 | all_48_1, simplifying with (7), (18), (21) gives: % 14.66/2.77 | (24) all_48_1 = 0 | ? [v0: time] : ? [v1: any] : (releasedAt(all_48_2, % 14.66/2.77 | v0) = v1 & at_time(3) = v0 & time(v0) & ( ~ (v1 = 0) | ? [v2: % 14.66/2.77 | event] : ? [v3: any] : ? [v4: any] : (initiates(v2, all_48_2, % 14.66/2.77 | v0) = v3 & happens(v2, v0) = 0 & terminates(v2, all_48_2, v0) % 14.66/2.77 | = v4 & event(v2) & (v4 = 0 | v3 = 0)))) % 14.66/2.77 | % 14.66/2.77 | BETA: splitting (23) gives: % 14.66/2.77 | % 14.66/2.77 | Case 1: % 14.66/2.77 | | % 14.66/2.77 | | (25) all_48_1 = 0 % 14.66/2.77 | | % 14.66/2.77 | | REDUCE: (16), (25) imply: % 14.66/2.77 | | (26) $false % 14.66/2.77 | | % 14.66/2.77 | | CLOSE: (26) is inconsistent. % 14.66/2.77 | | % 14.66/2.77 | Case 2: % 14.66/2.77 | | % 14.66/2.77 | | (27) ? [v0: time] : ? [v1: any] : ? [v2: any] : (holdsAt(all_48_2, v0) % 14.66/2.77 | | = v1 & holdsAt(all_48_2, all_43_2) = v2 & at_time(3) = v0 & % 14.66/2.77 | | time(v0) & ( ~ (v1 = 0) | v2 = 0 | ? [v3: event] : (happens(v3, % 14.66/2.77 | | v0) = 0 & terminates(v3, all_48_2, v0) = 0 & event(v3)))) % 14.66/2.77 | | % 14.66/2.77 | | DELTA: instantiating (27) with fresh symbols all_67_0, all_67_1, all_67_2 % 14.66/2.77 | | gives: % 14.66/2.77 | | (28) holdsAt(all_48_2, all_67_2) = all_67_1 & holdsAt(all_48_2, all_43_2) % 14.66/2.77 | | = all_67_0 & at_time(3) = all_67_2 & time(all_67_2) & ( ~ (all_67_1 % 14.66/2.77 | | = 0) | all_67_0 = 0 | ? [v0: event] : (happens(v0, all_67_2) = % 14.66/2.77 | | 0 & terminates(v0, all_48_2, all_67_2) = 0 & event(v0))) % 14.66/2.77 | | % 14.66/2.77 | | ALPHA: (28) implies: % 14.66/2.77 | | (29) at_time(3) = all_67_2 % 14.66/2.77 | | (30) holdsAt(all_48_2, all_43_2) = all_67_0 % 14.66/2.77 | | (31) holdsAt(all_48_2, all_67_2) = all_67_1 % 14.66/2.78 | | (32) ~ (all_67_1 = 0) | all_67_0 = 0 | ? [v0: event] : (happens(v0, % 14.66/2.78 | | all_67_2) = 0 & terminates(v0, all_48_2, all_67_2) = 0 & % 14.66/2.78 | | event(v0)) % 14.66/2.78 | | % 14.66/2.78 | | BETA: splitting (24) gives: % 14.66/2.78 | | % 14.66/2.78 | | Case 1: % 14.66/2.78 | | | % 14.66/2.78 | | | (33) all_48_1 = 0 % 14.66/2.78 | | | % 14.66/2.78 | | | REDUCE: (16), (33) imply: % 14.66/2.78 | | | (34) $false % 14.66/2.78 | | | % 14.66/2.78 | | | CLOSE: (34) is inconsistent. % 14.66/2.78 | | | % 14.66/2.78 | | Case 2: % 14.66/2.78 | | | % 14.66/2.78 | | | (35) ? [v0: time] : ? [v1: any] : (releasedAt(all_48_2, v0) = v1 & % 14.66/2.78 | | | at_time(3) = v0 & time(v0) & ( ~ (v1 = 0) | ? [v2: event] : ? % 14.66/2.78 | | | [v3: any] : ? [v4: any] : (initiates(v2, all_48_2, v0) = v3 & % 14.66/2.78 | | | happens(v2, v0) = 0 & terminates(v2, all_48_2, v0) = v4 & % 14.66/2.78 | | | event(v2) & (v4 = 0 | v3 = 0)))) % 14.66/2.78 | | | % 14.66/2.78 | | | DELTA: instantiating (35) with fresh symbols all_92_0, all_92_1 gives: % 14.66/2.78 | | | (36) releasedAt(all_48_2, all_92_1) = all_92_0 & at_time(3) = all_92_1 % 14.66/2.78 | | | & time(all_92_1) & ( ~ (all_92_0 = 0) | ? [v0: event] : ? [v1: % 14.66/2.78 | | | any] : ? [v2: any] : (initiates(v0, all_48_2, all_92_1) = v1 % 14.66/2.78 | | | & happens(v0, all_92_1) = 0 & terminates(v0, all_48_2, % 14.66/2.78 | | | all_92_1) = v2 & event(v0) & (v2 = 0 | v1 = 0))) % 14.66/2.78 | | | % 14.66/2.78 | | | ALPHA: (36) implies: % 14.66/2.78 | | | (37) at_time(3) = all_92_1 % 14.66/2.78 | | | % 14.66/2.78 | | | GROUND_INST: instantiating (3) with all_43_3, all_92_1, 3, simplifying % 14.66/2.78 | | | with (6), (37) gives: % 14.66/2.78 | | | (38) all_92_1 = all_43_3 % 14.66/2.78 | | | % 14.66/2.78 | | | GROUND_INST: instantiating (3) with all_67_2, all_92_1, 3, simplifying % 14.66/2.78 | | | with (29), (37) gives: % 14.66/2.78 | | | (39) all_92_1 = all_67_2 % 14.66/2.78 | | | % 14.66/2.78 | | | GROUND_INST: instantiating (4) with all_48_0, all_67_0, all_43_2, % 14.66/2.78 | | | all_48_2, simplifying with (20), (30) gives: % 14.66/2.78 | | | (40) all_67_0 = all_48_0 % 14.66/2.78 | | | % 14.66/2.78 | | | COMBINE_EQS: (38), (39) imply: % 14.66/2.78 | | | (41) all_67_2 = all_43_3 % 14.66/2.78 | | | % 14.66/2.78 | | | SIMP: (41) implies: % 14.66/2.78 | | | (42) all_67_2 = all_43_3 % 14.66/2.78 | | | % 14.66/2.78 | | | REDUCE: (31), (42) imply: % 14.66/2.78 | | | (43) holdsAt(all_48_2, all_43_3) = all_67_1 % 14.66/2.78 | | | % 14.66/2.78 | | | GROUND_INST: instantiating (4) with 0, all_67_1, all_43_3, all_48_2, % 14.66/2.78 | | | simplifying with (19), (43) gives: % 14.66/2.78 | | | (44) all_67_1 = 0 % 14.66/2.78 | | | % 14.66/2.78 | | | BETA: splitting (32) gives: % 14.66/2.78 | | | % 14.66/2.78 | | | Case 1: % 14.66/2.78 | | | | % 14.66/2.78 | | | | (45) ~ (all_67_1 = 0) % 14.66/2.78 | | | | % 14.66/2.78 | | | | REDUCE: (44), (45) imply: % 14.66/2.78 | | | | (46) $false % 14.66/2.78 | | | | % 14.66/2.78 | | | | CLOSE: (46) is inconsistent. % 14.66/2.78 | | | | % 14.66/2.78 | | | Case 2: % 14.66/2.78 | | | | % 14.66/2.78 | | | | (47) all_67_0 = 0 | ? [v0: event] : (happens(v0, all_67_2) = 0 & % 14.66/2.78 | | | | terminates(v0, all_48_2, all_67_2) = 0 & event(v0)) % 14.66/2.78 | | | | % 14.66/2.78 | | | | BETA: splitting (47) gives: % 14.66/2.78 | | | | % 14.66/2.78 | | | | Case 1: % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | (48) all_67_0 = 0 % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | COMBINE_EQS: (40), (48) imply: % 14.66/2.78 | | | | | (49) all_48_0 = 0 % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | SIMP: (49) implies: % 14.66/2.78 | | | | | (50) all_48_0 = 0 % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | REDUCE: (17), (50) imply: % 14.66/2.78 | | | | | (51) $false % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | CLOSE: (51) is inconsistent. % 14.66/2.78 | | | | | % 14.66/2.78 | | | | Case 2: % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | (52) ? [v0: event] : (happens(v0, all_67_2) = 0 & terminates(v0, % 14.66/2.78 | | | | | all_48_2, all_67_2) = 0 & event(v0)) % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | DELTA: instantiating (52) with fresh symbol all_120_0 gives: % 14.66/2.78 | | | | | (53) happens(all_120_0, all_67_2) = 0 & terminates(all_120_0, % 14.66/2.78 | | | | | all_48_2, all_67_2) = 0 & event(all_120_0) % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | ALPHA: (53) implies: % 14.66/2.78 | | | | | (54) event(all_120_0) % 14.66/2.78 | | | | | (55) happens(all_120_0, all_67_2) = 0 % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | REDUCE: (42), (55) imply: % 14.66/2.78 | | | | | (56) happens(all_120_0, all_43_3) = 0 % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | GROUND_INST: instantiating (13) with all_120_0, 3, all_43_3, % 14.66/2.78 | | | | | simplifying with (6), (54), (56) gives: % 14.66/2.78 | | | | | (57) all_120_0 = overflow & holdsAt(all_45_0, all_43_3) = 0 & % 14.66/2.78 | | | | | holdsAt(filling, all_43_3) = 0 % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | ALPHA: (57) implies: % 14.66/2.78 | | | | | (58) holdsAt(all_45_0, all_43_3) = 0 % 14.66/2.78 | | | | | % 14.66/2.78 | | | | | REDUCE: (22), (58) imply: % 14.66/2.79 | | | | | (59) holdsAt(all_43_1, all_43_3) = 0 % 14.66/2.79 | | | | | % 14.66/2.79 | | | | | GROUND_INST: instantiating (4) with all_43_0, 0, all_43_3, all_43_1, % 14.66/2.79 | | | | | simplifying with (8), (59) gives: % 14.66/2.79 | | | | | (60) all_43_0 = 0 % 14.66/2.79 | | | | | % 14.66/2.79 | | | | | REDUCE: (15), (60) imply: % 14.66/2.79 | | | | | (61) $false % 14.66/2.79 | | | | | % 14.66/2.79 | | | | | CLOSE: (61) is inconsistent. % 14.66/2.79 | | | | | % 14.66/2.79 | | | | End of split % 14.66/2.79 | | | | % 14.66/2.79 | | | End of split % 14.66/2.79 | | | % 14.66/2.79 | | End of split % 14.66/2.79 | | % 14.66/2.79 | End of split % 14.66/2.79 | % 14.66/2.79 End of proof % 14.66/2.79 % SZS output end Proof for theBenchmark % 14.66/2.79 % 14.66/2.79 2115ms %------------------------------------------------------------------------------