%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : CSR004+2 : TPTP v8.1.2. Bugfixed v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 : Wed Aug 30 21:36:23 EDT 2023 % Result : Theorem 9.93s 2.14s % Output : Proof 12.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : CSR004+2 : TPTP v8.1.2. Bugfixed v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon Aug 28 13:05:25 EDT 2023 % 0.17/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.51/1.20 Prover 1: Preprocessing ... % 3.51/1.20 Prover 4: Preprocessing ... % 3.66/1.24 Prover 3: Preprocessing ... % 3.66/1.24 Prover 0: Preprocessing ... % 3.66/1.24 Prover 6: Preprocessing ... % 3.66/1.24 Prover 5: Preprocessing ... % 3.66/1.24 Prover 2: Preprocessing ... % 8.08/1.83 Prover 5: Proving ... % 8.08/1.91 Prover 6: Proving ... % 8.89/1.94 Prover 1: Constructing countermodel ... % 8.89/1.94 Prover 3: Constructing countermodel ... % 8.89/1.97 Prover 2: Proving ... % 9.50/2.08 Prover 0: Proving ... % 9.93/2.09 Prover 4: Constructing countermodel ... % 9.93/2.14 Prover 3: proved (1501ms) % 9.93/2.14 % 9.93/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.93/2.14 % 9.93/2.14 Prover 2: stopped % 9.93/2.14 Prover 5: stopped % 9.93/2.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.93/2.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.93/2.14 Prover 6: stopped % 9.93/2.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.93/2.15 Prover 0: stopped % 10.50/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.50/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.64/2.20 Prover 1: Found proof (size 27) % 10.64/2.20 Prover 1: proved (1573ms) % 10.64/2.20 Prover 4: stopped % 10.64/2.21 Prover 7: Preprocessing ... % 10.64/2.21 Prover 8: Preprocessing ... % 10.64/2.21 Prover 11: Preprocessing ... % 10.96/2.22 Prover 10: Preprocessing ... % 10.96/2.22 Prover 13: Preprocessing ... % 11.14/2.24 Prover 7: stopped % 11.14/2.27 Prover 10: stopped % 11.14/2.28 Prover 13: stopped % 11.14/2.30 Prover 11: stopped % 11.95/2.38 Prover 8: Warning: ignoring some quantifiers % 11.95/2.39 Prover 8: Constructing countermodel ... % 11.95/2.41 Prover 8: stopped % 11.95/2.41 % 11.95/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.95/2.41 % 11.95/2.42 % SZS output start Proof for theBenchmark % 11.95/2.42 Assumptions after simplification: % 11.95/2.42 --------------------------------- % 11.95/2.42 % 11.95/2.42 (filling_3) % 11.95/2.45 holdsAt(filling, n3) = 0 & $i(n3) & $i(filling) % 11.95/2.45 % 11.95/2.45 (happens_all_defn) % 11.95/2.45 $i(n3) & $i(overflow) & $i(filling) & $i(tapOn) & $i(n0) & ? [v0: $i] : % 11.95/2.45 (waterLevel(n3) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 % 11.95/2.45 = 0 | ~ (happens(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | (( ~ (v2 = n0) | % 11.95/2.45 ~ (v1 = tapOn)) & ( ~ (v1 = overflow) | ? [v4: any] : ? [v5: any] : % 11.95/2.45 (holdsAt(v0, v2) = v4 & holdsAt(filling, v2) = v5 & ( ~ (v5 = 0) | ~ % 11.95/2.45 (v4 = 0)))))) & ! [v1: $i] : ! [v2: $i] : ( ~ (happens(v1, v2) = % 11.95/2.45 0) | ~ $i(v2) | ~ $i(v1) | (v2 = n0 & v1 = tapOn) | (v1 = overflow & % 11.95/2.45 holdsAt(v0, v2) = 0 & holdsAt(filling, v2) = 0))) % 11.95/2.45 % 11.95/2.45 (overflow_3) % 11.95/2.45 $i(n3) & $i(overflow) & ? [v0: int] : ( ~ (v0 = 0) & happens(overflow, n3) = % 11.95/2.45 v0) % 11.95/2.45 % 11.95/2.45 (waterLevel_3) % 11.95/2.45 $i(n3) & ? [v0: $i] : (waterLevel(n3) = v0 & holdsAt(v0, n3) = 0 & $i(v0)) % 11.95/2.45 % 11.95/2.45 (function-axioms) % 12.32/2.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.32/2.46 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (antitrajectory(v5, v4, % 12.32/2.46 v3, v2) = v1) | ~ (antitrajectory(v5, v4, v3, v2) = v0)) & ! [v0: % 12.32/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.32/2.46 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (trajectory(v5, v4, v3, v2) = v1) % 12.32/2.46 | ~ (trajectory(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.32/2.46 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 12.32/2.46 ~ (releases(v4, v3, v2) = v1) | ~ (releases(v4, v3, v2) = v0)) & ! [v0: % 12.32/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.32/2.46 : ! [v4: $i] : (v1 = v0 | ~ (startedIn(v4, v3, v2) = v1) | ~ (startedIn(v4, % 12.32/2.46 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 12.32/2.46 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (initiates(v4, v3, % 12.32/2.46 v2) = v1) | ~ (initiates(v4, v3, v2) = v0)) & ! [v0: % 12.32/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.32/2.46 : ! [v4: $i] : (v1 = v0 | ~ (stoppedIn(v4, v3, v2) = v1) | ~ (stoppedIn(v4, % 12.32/2.46 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 12.32/2.46 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (terminates(v4, v3, % 12.32/2.46 v2) = v1) | ~ (terminates(v4, v3, v2) = v0)) & ! [v0: % 12.32/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.32/2.46 : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ (less_or_equal(v3, v2) = % 12.32/2.46 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.32/2.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (releasedAt(v3, v2) = v1) | ~ % 12.32/2.46 (releasedAt(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 12.32/2.46 [v3: $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! % 12.32/2.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.32/2.46 $i] : (v1 = v0 | ~ (holdsAt(v3, v2) = v1) | ~ (holdsAt(v3, v2) = v0)) & ! % 12.32/2.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.32/2.46 $i] : (v1 = v0 | ~ (happens(v3, v2) = v1) | ~ (happens(v3, v2) = v0)) & ! % 12.32/2.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.32/2.46 $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 12.32/2.46 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (waterLevel(v2) = v1) | ~ % 12.32/2.46 (waterLevel(v2) = v0)) % 12.32/2.46 % 12.32/2.46 Further assumptions not needed in the proof: % 12.32/2.46 -------------------------------------------- % 12.32/2.46 antitrajectory, change_holding, change_of_waterLevel, distinct_waterLevels, % 12.32/2.46 filling_not_spilling, filling_not_waterLevel, happens_holds, % 12.32/2.46 happens_not_released, happens_releases, happens_terminates_not_holds, % 12.32/2.46 initiates_all_defn, keep_holding, keep_not_holding, keep_not_released, % 12.32/2.46 keep_released, less0, less1, less2, less3, less4, less5, less6, less7, less8, % 12.32/2.46 less9, less_or_equal, less_property, not_filling_0, not_released_filling_0, % 12.32/2.46 not_released_spilling_0, not_released_waterLevel_0, not_spilling_0, % 12.32/2.46 overflow_not_tapOn, plus0_0, plus0_1, plus0_2, plus0_3, plus1_1, plus1_2, % 12.32/2.46 plus1_3, plus2_2, plus2_3, plus3_3, releases_all_defn, same_waterLevel, % 12.32/2.46 spilling_not_waterLevel, startedin_defn, stoppedin_defn, symmetry_of_plus, % 12.32/2.46 tapOff_not_overflow, tapOff_not_tapOn, terminates_all_defn, waterLevel_0 % 12.32/2.46 % 12.32/2.46 Those formulas are unsatisfiable: % 12.32/2.46 --------------------------------- % 12.32/2.46 % 12.32/2.46 Begin of proof % 12.32/2.46 | % 12.32/2.46 | ALPHA: (happens_all_defn) implies: % 12.32/2.47 | (1) ? [v0: $i] : (waterLevel(n3) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] % 12.32/2.47 | : ! [v3: int] : (v3 = 0 | ~ (happens(v1, v2) = v3) | ~ $i(v2) | ~ % 12.32/2.47 | $i(v1) | (( ~ (v2 = n0) | ~ (v1 = tapOn)) & ( ~ (v1 = overflow) | % 12.32/2.47 | ? [v4: any] : ? [v5: any] : (holdsAt(v0, v2) = v4 & % 12.32/2.47 | holdsAt(filling, v2) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & % 12.32/2.47 | ! [v1: $i] : ! [v2: $i] : ( ~ (happens(v1, v2) = 0) | ~ $i(v2) | % 12.32/2.47 | ~ $i(v1) | (v2 = n0 & v1 = tapOn) | (v1 = overflow & holdsAt(v0, % 12.32/2.47 | v2) = 0 & holdsAt(filling, v2) = 0))) % 12.32/2.47 | % 12.32/2.47 | ALPHA: (waterLevel_3) implies: % 12.32/2.47 | (2) ? [v0: $i] : (waterLevel(n3) = v0 & holdsAt(v0, n3) = 0 & $i(v0)) % 12.32/2.47 | % 12.32/2.47 | ALPHA: (filling_3) implies: % 12.32/2.47 | (3) holdsAt(filling, n3) = 0 % 12.32/2.47 | % 12.32/2.47 | ALPHA: (overflow_3) implies: % 12.32/2.47 | (4) $i(overflow) % 12.32/2.47 | (5) $i(n3) % 12.32/2.47 | (6) ? [v0: int] : ( ~ (v0 = 0) & happens(overflow, n3) = v0) % 12.32/2.47 | % 12.32/2.47 | ALPHA: (function-axioms) implies: % 12.32/2.47 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (waterLevel(v2) % 12.32/2.47 | = v1) | ~ (waterLevel(v2) = v0)) % 12.32/2.47 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.32/2.47 | ! [v3: $i] : (v1 = v0 | ~ (holdsAt(v3, v2) = v1) | ~ (holdsAt(v3, % 12.32/2.47 | v2) = v0)) % 12.32/2.47 | % 12.32/2.47 | DELTA: instantiating (6) with fresh symbol all_46_0 gives: % 12.32/2.47 | (9) ~ (all_46_0 = 0) & happens(overflow, n3) = all_46_0 % 12.32/2.47 | % 12.32/2.47 | ALPHA: (9) implies: % 12.32/2.47 | (10) ~ (all_46_0 = 0) % 12.32/2.47 | (11) happens(overflow, n3) = all_46_0 % 12.32/2.47 | % 12.32/2.47 | DELTA: instantiating (2) with fresh symbol all_50_0 gives: % 12.32/2.47 | (12) waterLevel(n3) = all_50_0 & holdsAt(all_50_0, n3) = 0 & $i(all_50_0) % 12.32/2.47 | % 12.32/2.47 | ALPHA: (12) implies: % 12.32/2.47 | (13) holdsAt(all_50_0, n3) = 0 % 12.32/2.47 | (14) waterLevel(n3) = all_50_0 % 12.32/2.47 | % 12.32/2.47 | DELTA: instantiating (1) with fresh symbol all_52_0 gives: % 12.42/2.48 | (15) waterLevel(n3) = all_52_0 & $i(all_52_0) & ! [v0: $i] : ! [v1: $i] : % 12.42/2.48 | ! [v2: int] : (v2 = 0 | ~ (happens(v0, v1) = v2) | ~ $i(v1) | ~ % 12.42/2.48 | $i(v0) | (( ~ (v1 = n0) | ~ (v0 = tapOn)) & ( ~ (v0 = overflow) | % 12.42/2.48 | ? [v3: any] : ? [v4: any] : (holdsAt(all_52_0, v1) = v3 & % 12.42/2.48 | holdsAt(filling, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0)))))) & % 12.42/2.48 | ! [v0: $i] : ! [v1: $i] : ( ~ (happens(v0, v1) = 0) | ~ $i(v1) | ~ % 12.42/2.48 | $i(v0) | (v1 = n0 & v0 = tapOn) | (v0 = overflow & holdsAt(all_52_0, % 12.42/2.48 | v1) = 0 & holdsAt(filling, v1) = 0)) % 12.42/2.48 | % 12.42/2.48 | ALPHA: (15) implies: % 12.42/2.48 | (16) waterLevel(n3) = all_52_0 % 12.42/2.48 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (happens(v0, % 12.42/2.48 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | (( ~ (v1 = n0) | ~ (v0 = % 12.42/2.48 | tapOn)) & ( ~ (v0 = overflow) | ? [v3: any] : ? [v4: any] : % 12.42/2.48 | (holdsAt(all_52_0, v1) = v3 & holdsAt(filling, v1) = v4 & ( ~ % 12.42/2.48 | (v4 = 0) | ~ (v3 = 0)))))) % 12.42/2.48 | % 12.42/2.48 | GROUND_INST: instantiating (7) with all_50_0, all_52_0, n3, simplifying with % 12.42/2.48 | (14), (16) gives: % 12.42/2.48 | (18) all_52_0 = all_50_0 % 12.42/2.48 | % 12.42/2.48 | GROUND_INST: instantiating (17) with overflow, n3, all_46_0, simplifying with % 12.42/2.48 | (4), (5), (11) gives: % 12.42/2.48 | (19) all_46_0 = 0 | ( ? [v0: any] : ? [v1: any] : (holdsAt(all_52_0, n3) = % 12.42/2.48 | v0 & holdsAt(filling, n3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) & ( % 12.42/2.48 | ~ (n3 = n0) | ~ (overflow = tapOn))) % 12.42/2.48 | % 12.42/2.48 | BETA: splitting (19) gives: % 12.42/2.48 | % 12.42/2.48 | Case 1: % 12.42/2.48 | | % 12.42/2.48 | | (20) all_46_0 = 0 % 12.42/2.48 | | % 12.42/2.48 | | REDUCE: (10), (20) imply: % 12.42/2.48 | | (21) $false % 12.42/2.48 | | % 12.42/2.48 | | CLOSE: (21) is inconsistent. % 12.42/2.48 | | % 12.42/2.48 | Case 2: % 12.42/2.48 | | % 12.42/2.48 | | (22) ? [v0: any] : ? [v1: any] : (holdsAt(all_52_0, n3) = v0 & % 12.42/2.48 | | holdsAt(filling, n3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) & ( ~ (n3 % 12.42/2.48 | | = n0) | ~ (overflow = tapOn)) % 12.42/2.48 | | % 12.42/2.48 | | ALPHA: (22) implies: % 12.42/2.48 | | (23) ? [v0: any] : ? [v1: any] : (holdsAt(all_52_0, n3) = v0 & % 12.42/2.48 | | holdsAt(filling, n3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 12.42/2.48 | | % 12.42/2.48 | | DELTA: instantiating (23) with fresh symbols all_73_0, all_73_1 gives: % 12.42/2.48 | | (24) holdsAt(all_52_0, n3) = all_73_1 & holdsAt(filling, n3) = all_73_0 & % 12.42/2.48 | | ( ~ (all_73_0 = 0) | ~ (all_73_1 = 0)) % 12.42/2.48 | | % 12.42/2.48 | | ALPHA: (24) implies: % 12.42/2.48 | | (25) holdsAt(filling, n3) = all_73_0 % 12.42/2.48 | | (26) holdsAt(all_52_0, n3) = all_73_1 % 12.42/2.48 | | (27) ~ (all_73_0 = 0) | ~ (all_73_1 = 0) % 12.42/2.48 | | % 12.42/2.48 | | REDUCE: (18), (26) imply: % 12.42/2.48 | | (28) holdsAt(all_50_0, n3) = all_73_1 % 12.42/2.48 | | % 12.42/2.49 | | GROUND_INST: instantiating (8) with 0, all_73_0, n3, filling, simplifying % 12.42/2.49 | | with (3), (25) gives: % 12.42/2.49 | | (29) all_73_0 = 0 % 12.42/2.49 | | % 12.42/2.49 | | GROUND_INST: instantiating (8) with 0, all_73_1, n3, all_50_0, simplifying % 12.42/2.49 | | with (13), (28) gives: % 12.42/2.49 | | (30) all_73_1 = 0 % 12.42/2.49 | | % 12.42/2.49 | | BETA: splitting (27) gives: % 12.42/2.49 | | % 12.42/2.49 | | Case 1: % 12.42/2.49 | | | % 12.42/2.49 | | | (31) ~ (all_73_0 = 0) % 12.42/2.49 | | | % 12.42/2.49 | | | REDUCE: (29), (31) imply: % 12.42/2.49 | | | (32) $false % 12.42/2.49 | | | % 12.42/2.49 | | | CLOSE: (32) is inconsistent. % 12.42/2.49 | | | % 12.42/2.49 | | Case 2: % 12.42/2.49 | | | % 12.42/2.49 | | | (33) ~ (all_73_1 = 0) % 12.42/2.49 | | | % 12.42/2.49 | | | REDUCE: (30), (33) imply: % 12.42/2.49 | | | (34) $false % 12.42/2.49 | | | % 12.42/2.49 | | | CLOSE: (34) is inconsistent. % 12.42/2.49 | | | % 12.42/2.49 | | End of split % 12.42/2.49 | | % 12.42/2.49 | End of split % 12.42/2.49 | % 12.42/2.49 End of proof % 12.42/2.49 % SZS output end Proof for theBenchmark % 12.42/2.49 % 12.42/2.49 1879ms %------------------------------------------------------------------------------