%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : CSR020+1 : TPTP v8.1.2. Bugfixed v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 21:36:25 EDT 2023 % Result : Theorem 13.20s 2.47s % Output : Proof 22.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : CSR020+1 : TPTP v8.1.2. Bugfixed v3.1.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n007.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 % 0.12/0.34 % DateTime : Mon Aug 28 07:53:13 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.11/1.14 Prover 4: Preprocessing ... % 3.11/1.14 Prover 1: Preprocessing ... % 3.75/1.18 Prover 0: Preprocessing ... % 3.75/1.18 Prover 2: Preprocessing ... % 3.75/1.18 Prover 3: Preprocessing ... % 3.75/1.18 Prover 5: Preprocessing ... % 3.75/1.18 Prover 6: Preprocessing ... % 7.74/1.71 Prover 5: Proving ... % 8.64/1.86 Prover 1: Constructing countermodel ... % 9.04/1.94 Prover 3: Constructing countermodel ... % 9.48/1.97 Prover 6: Proving ... % 10.32/2.10 Prover 4: Constructing countermodel ... % 10.32/2.10 Prover 3: gave up % 10.65/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.65/2.11 Prover 1: gave up % 10.65/2.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.91/2.14 Prover 7: Preprocessing ... % 10.91/2.16 Prover 0: Proving ... % 10.91/2.16 Prover 8: Preprocessing ... % 10.91/2.20 Prover 6: gave up % 10.91/2.23 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 11.61/2.26 Prover 9: Preprocessing ... % 12.62/2.40 Prover 8: Warning: ignoring some quantifiers % 12.94/2.41 Prover 8: Constructing countermodel ... % 13.20/2.47 Prover 5: proved (1843ms) % 13.20/2.47 % 13.20/2.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.20/2.47 % 13.20/2.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.20/2.48 Prover 0: stopped % 13.20/2.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.20/2.52 Prover 10: Preprocessing ... % 13.85/2.55 Prover 2: Proving ... % 13.85/2.55 Prover 2: stopped % 13.85/2.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.85/2.59 Prover 11: Preprocessing ... % 13.85/2.59 Prover 13: Preprocessing ... % 13.85/2.59 Prover 8: gave up % 13.85/2.60 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.85/2.65 Prover 9: Constructing countermodel ... % 13.85/2.65 Prover 16: Preprocessing ... % 13.85/2.65 Prover 9: stopped % 13.85/2.66 Prover 7: Warning: ignoring some quantifiers % 13.85/2.66 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 14.85/2.70 Prover 7: Constructing countermodel ... % 14.85/2.70 Prover 19: Preprocessing ... % 16.03/2.90 Prover 11: Constructing countermodel ... % 16.03/2.92 Prover 10: Warning: ignoring some quantifiers % 16.72/2.97 Prover 19: Warning: ignoring some quantifiers % 17.12/2.99 Prover 10: Constructing countermodel ... % 17.12/3.02 Prover 13: Warning: ignoring some quantifiers % 17.12/3.02 Prover 19: Constructing countermodel ... % 17.12/3.04 Prover 13: Constructing countermodel ... % 17.12/3.04 Prover 16: Warning: ignoring some quantifiers % 17.62/3.06 Prover 16: Constructing countermodel ... % 22.28/3.69 Prover 10: Found proof (size 70) % 22.28/3.69 Prover 10: proved (1220ms) % 22.28/3.69 Prover 13: stopped % 22.28/3.69 Prover 16: stopped % 22.28/3.69 Prover 11: stopped % 22.28/3.69 Prover 19: stopped % 22.28/3.69 Prover 4: stopped % 22.28/3.70 Prover 7: stopped % 22.28/3.70 % 22.28/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.28/3.70 % 22.28/3.71 % SZS output start Proof for theBenchmark % 22.28/3.71 Assumptions after simplification: % 22.28/3.71 --------------------------------- % 22.28/3.71 % 22.28/3.71 (forwards_not_spinning) % 22.28/3.71 ~ (spinning = forwards) & $i(spinning) & $i(forwards) % 22.28/3.71 % 22.28/3.71 (happens_all_defn) % 22.28/3.73 $i(n2) & $i(pull) & $i(push) & $i(n1) & $i(n0) & happens(pull, n2) & % 22.28/3.73 happens(pull, n1) & happens(push, n2) & happens(push, n0) & ! [v0: $i] : ! % 22.28/3.73 [v1: $i] : (v1 = n2 | v1 = n1 | v1 = n0 | v0 = pull | ~ $i(v1) | ~ $i(v0) | % 22.28/3.73 ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n1 | v1 = % 22.28/3.73 n0 | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] : % 22.28/3.73 ! [v1: $i] : (v1 = n2 | v1 = n1 | v1 = n0 | ~ $i(v1) | ~ $i(v0) | ~ % 22.28/3.73 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n1 | v0 = % 22.28/3.73 pull | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] % 22.28/3.73 : ! [v1: $i] : (v1 = n2 | v1 = n1 | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ % 22.28/3.73 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n0 | v0 = % 22.28/3.73 pull | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] % 22.28/3.73 : ! [v1: $i] : (v1 = n2 | v1 = n0 | v0 = pull | ~ $i(v1) | ~ $i(v0) | ~ % 22.28/3.73 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v0 = pull | v0 = % 22.28/3.73 push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: % 22.28/3.73 $i] : (v1 = n1 | v1 = n0 | v0 = pull | v0 = push | ~ $i(v1) | ~ $i(v0) | % 22.28/3.73 ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n1 | v0 = pull | v0 = % 22.28/3.73 push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: % 22.28/3.73 $i] : (v1 = n0 | v0 = pull | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ % 22.28/3.73 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v0 = pull | v0 = push | ~ % 22.28/3.73 $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) % 22.28/3.73 % 22.28/3.73 (initiates_all_defn) % 22.67/3.74 $i(spinning) & $i(backwards) & $i(pull) & $i(forwards) & $i(push) & ! [v0: % 22.67/3.74 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = backwards | v1 = % 22.67/3.74 forwards | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2)) & % 22.67/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = backwards | v0 % 22.67/3.74 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2)) & ! % 22.67/3.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = backwards | ~ % 22.67/3.74 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ happens(pull, % 22.67/3.74 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = % 22.67/3.74 forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 22.67/3.74 v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = % 22.67/3.74 forwards | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ % 22.67/3.74 happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 22.67/3.74 spinning | v0 = pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 22.67/3.74 initiates(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 22.67/3.74 spinning | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 22.67/3.74 v1, v2) | ~ happens(pull, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.67/3.74 : (v1 = spinning | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 22.67/3.74 initiates(v0, v1, v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : % 22.67/3.74 ! [v2: $i] : (v1 = spinning | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 22.67/3.74 initiates(v0, v1, v2) | ~ happens(pull, v2) | ~ happens(push, v2)) & ! % 22.67/3.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v1 = forwards | v0 = % 22.67/3.74 pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2)) & ! % 22.67/3.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v1 = forwards | ~ % 22.67/3.74 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | happens(push, % 22.67/3.74 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v0 = % 22.67/3.74 pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, % 22.67/3.74 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v0 = % 22.67/3.74 pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ % 22.67/3.74 happens(pull, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 22.67/3.74 backwards | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 22.67/3.74 v1, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.67/3.74 (v1 = backwards | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) % 22.67/3.74 | ~ happens(pull, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! % 22.67/3.74 [v2: $i] : (v1 = forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 22.67/3.74 initiates(v0, v1, v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : % 22.67/3.74 ! [v2: $i] : (v1 = forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 22.67/3.74 ~ initiates(v0, v1, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : % 22.67/3.74 ! [v2: $i] : (v1 = forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 22.67/3.74 ~ initiates(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = % 22.67/3.74 pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, % 22.67/3.74 v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.67/3.74 (v0 = pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 22.67/3.74 v1, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.67/3.74 (v0 = pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 22.67/3.74 v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = pull | ~ % 22.67/3.74 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ happens(pull, % 22.67/3.74 v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.67/3.74 (v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ % 22.67/3.74 happens(pull, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.67/3.74 $i] : (v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, % 22.67/3.74 v2) | ~ happens(pull, v2)) & ! [v0: $i] : ( ~ $i(v0) | ~ happens(push, % 22.67/3.74 v0) | initiates(pull, spinning, v0)) & ? [v0: $i] : ( ~ $i(v0) | % 22.67/3.74 initiates(pull, backwards, v0) | happens(push, v0)) & ? [v0: $i] : ( ~ % 22.67/3.74 $i(v0) | initiates(push, forwards, v0) | happens(pull, v0)) % 22.67/3.74 % 22.67/3.74 (keep_not_holding) % 22.67/3.76 $i(n1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (plus(v1, n1) = v2) | % 22.67/3.76 ~ $i(v1) | ~ $i(v0) | ~ holdsAt(v0, v2) | releasedAt(v0, v2) | holdsAt(v0, % 22.67/3.76 v1) | ? [v3: $i] : ($i(v3) & initiates(v3, v0, v1) & happens(v3, v1))) % 22.67/3.76 % 22.67/3.76 (less2) % 22.67/3.76 $i(n2) & $i(n1) & ! [v0: $i] : ( ~ $i(v0) | ~ less_or_equal(v0, n1) | % 22.67/3.76 less(v0, n2)) & ! [v0: $i] : ( ~ $i(v0) | ~ less(v0, n2) | % 22.67/3.76 less_or_equal(v0, n1)) % 22.67/3.76 % 22.67/3.76 (not_releasedAt) % 22.67/3.76 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ releasedAt(v0, v1)) % 22.67/3.76 % 22.67/3.76 (not_spinning_2) % 22.67/3.76 $i(n2) & $i(spinning) & holdsAt(spinning, n2) % 22.67/3.76 % 22.67/3.76 (not_splinning_0) % 22.67/3.76 $i(spinning) & $i(n0) & ~ holdsAt(spinning, n0) % 22.67/3.76 % 22.67/3.76 (plus0_1) % 22.67/3.76 plus(n0, n1) = n1 & $i(n1) & $i(n0) % 22.67/3.76 % 22.67/3.76 (plus1_1) % 22.67/3.76 plus(n1, n1) = n2 & $i(n2) & $i(n1) % 22.67/3.76 % 22.67/3.76 (push_not_pull) % 22.67/3.76 ~ (pull = push) & $i(pull) & $i(push) % 22.67/3.76 % 22.67/3.76 (spinning_not_backwards) % 22.67/3.76 ~ (spinning = backwards) & $i(spinning) & $i(backwards) % 22.67/3.76 % 22.67/3.76 (function-axioms) % 22.67/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.67/3.76 (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) % 22.83/3.76 % 22.83/3.76 Further assumptions not needed in the proof: % 22.83/3.76 -------------------------------------------- % 22.83/3.76 antitrajectory, change_holding, forwards_not_backwards, happens_holds, % 22.83/3.76 happens_not_released, happens_releases, happens_terminates_not_holds, % 22.83/3.76 keep_holding, keep_not_released, keep_released, less0, less1, less3, less4, % 22.83/3.76 less5, less6, less7, less8, less9, less_or_equal, less_property, % 22.83/3.76 not_backwards_0, not_forwards_0, plus0_0, plus0_2, plus0_3, plus1_2, plus1_3, % 22.83/3.76 plus2_2, plus2_3, plus3_3, releases_all_defn, startedin_defn, stoppedin_defn, % 22.83/3.76 symmetry_of_plus, terminates_all_defn % 22.83/3.76 % 22.83/3.76 Those formulas are unsatisfiable: % 22.83/3.76 --------------------------------- % 22.83/3.76 % 22.83/3.76 Begin of proof % 22.83/3.77 | % 22.83/3.77 | ALPHA: (keep_not_holding) implies: % 22.83/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (plus(v1, n1) = v2) | ~ % 22.83/3.77 | $i(v1) | ~ $i(v0) | ~ holdsAt(v0, v2) | releasedAt(v0, v2) | % 22.83/3.77 | holdsAt(v0, v1) | ? [v3: $i] : ($i(v3) & initiates(v3, v0, v1) & % 22.83/3.77 | happens(v3, v1))) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (initiates_all_defn) implies: % 22.83/3.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = forwards | v0 = pull | % 22.83/3.77 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2)) % 22.83/3.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | ~ $i(v2) | % 22.83/3.77 | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ happens(pull, % 22.83/3.77 | v2) | happens(push, v2)) % 22.83/3.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v0 = push | % 22.83/3.77 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | % 22.83/3.77 | happens(push, v2)) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (happens_all_defn) implies: % 22.83/3.77 | (5) happens(pull, n1) % 22.83/3.77 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n0 | v0 = pull | ~ $i(v1) % 22.83/3.77 | | ~ $i(v0) | ~ happens(v0, v1)) % 22.83/3.77 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n1 | v0 = push | ~ $i(v1) % 22.83/3.77 | | ~ $i(v0) | ~ happens(v0, v1)) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (push_not_pull) implies: % 22.83/3.77 | (8) ~ (pull = push) % 22.83/3.77 | (9) $i(push) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (forwards_not_spinning) implies: % 22.83/3.77 | (10) ~ (spinning = forwards) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (spinning_not_backwards) implies: % 22.83/3.77 | (11) ~ (spinning = backwards) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (plus0_1) implies: % 22.83/3.77 | (12) plus(n0, n1) = n1 % 22.83/3.77 | % 22.83/3.77 | ALPHA: (plus1_1) implies: % 22.83/3.77 | (13) plus(n1, n1) = n2 % 22.83/3.77 | % 22.83/3.77 | ALPHA: (less2) implies: % 22.83/3.77 | (14) $i(n1) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (not_splinning_0) implies: % 22.83/3.77 | (15) ~ holdsAt(spinning, n0) % 22.83/3.77 | (16) $i(n0) % 22.83/3.77 | % 22.83/3.77 | ALPHA: (not_spinning_2) implies: % 22.83/3.77 | (17) holdsAt(spinning, n2) % 22.83/3.77 | (18) $i(spinning) % 22.83/3.77 | (19) $i(n2) % 22.83/3.77 | % 22.83/3.77 | GROUND_INST: instantiating (1) with spinning, n1, n2, simplifying with (13), % 22.83/3.77 | (14), (17), (18) gives: % 22.83/3.77 | (20) releasedAt(spinning, n2) | holdsAt(spinning, n1) | ? [v0: $i] : % 22.83/3.77 | ($i(v0) & initiates(v0, spinning, n1) & happens(v0, n1)) % 22.83/3.77 | % 22.83/3.77 | BETA: splitting (20) gives: % 22.83/3.77 | % 22.83/3.77 | Case 1: % 22.83/3.77 | | % 22.83/3.77 | | (21) releasedAt(spinning, n2) % 22.83/3.77 | | % 22.83/3.78 | | GROUND_INST: instantiating (not_releasedAt) with spinning, n2, simplifying % 22.83/3.78 | | with (18), (19), (21) gives: % 22.83/3.78 | | (22) $false % 22.83/3.78 | | % 22.83/3.78 | | CLOSE: (22) is inconsistent. % 22.83/3.78 | | % 22.83/3.78 | Case 2: % 22.83/3.78 | | % 22.83/3.78 | | (23) holdsAt(spinning, n1) | ? [v0: $i] : ($i(v0) & initiates(v0, % 22.83/3.78 | | spinning, n1) & happens(v0, n1)) % 22.83/3.78 | | % 22.83/3.78 | | BETA: splitting (23) gives: % 22.83/3.78 | | % 22.83/3.78 | | Case 1: % 22.83/3.78 | | | % 22.83/3.78 | | | (24) holdsAt(spinning, n1) % 22.83/3.78 | | | % 22.83/3.78 | | | GROUND_INST: instantiating (1) with spinning, n0, n1, simplifying with % 22.83/3.78 | | | (12), (15), (16), (18), (24) gives: % 22.83/3.78 | | | (25) releasedAt(spinning, n1) | ? [v0: $i] : ($i(v0) & initiates(v0, % 22.83/3.78 | | | spinning, n0) & happens(v0, n0)) % 22.83/3.78 | | | % 22.83/3.78 | | | BETA: splitting (25) gives: % 22.83/3.78 | | | % 22.83/3.78 | | | Case 1: % 22.83/3.78 | | | | % 22.83/3.78 | | | | (26) releasedAt(spinning, n1) % 22.83/3.78 | | | | % 22.83/3.78 | | | | GROUND_INST: instantiating (not_releasedAt) with spinning, n1, % 22.83/3.78 | | | | simplifying with (14), (18), (26) gives: % 22.83/3.78 | | | | (27) $false % 22.83/3.78 | | | | % 22.83/3.78 | | | | CLOSE: (27) is inconsistent. % 22.83/3.78 | | | | % 22.83/3.78 | | | Case 2: % 22.83/3.78 | | | | % 22.83/3.78 | | | | (28) ? [v0: $i] : ($i(v0) & initiates(v0, spinning, n0) & % 22.83/3.78 | | | | happens(v0, n0)) % 22.83/3.78 | | | | % 22.83/3.78 | | | | DELTA: instantiating (28) with fresh symbol all_186_0 gives: % 22.83/3.78 | | | | (29) $i(all_186_0) & initiates(all_186_0, spinning, n0) & % 22.83/3.78 | | | | happens(all_186_0, n0) % 22.83/3.78 | | | | % 22.83/3.78 | | | | ALPHA: (29) implies: % 22.83/3.78 | | | | (30) happens(all_186_0, n0) % 22.83/3.78 | | | | (31) initiates(all_186_0, spinning, n0) % 22.83/3.78 | | | | (32) $i(all_186_0) % 22.83/3.78 | | | | % 22.83/3.78 | | | | GROUND_INST: instantiating (7) with all_186_0, n0, simplifying with % 22.83/3.78 | | | | (16), (30), (32) gives: % 22.83/3.78 | | | | (33) all_186_0 = push | n2 = n0 | n1 = n0 % 22.83/3.78 | | | | % 22.83/3.78 | | | | GROUND_INST: instantiating (2) with all_186_0, spinning, n0, simplifying % 22.83/3.78 | | | | with (16), (18), (31), (32) gives: % 22.83/3.78 | | | | (34) all_186_0 = pull | spinning = forwards % 22.83/3.78 | | | | % 22.83/3.78 | | | | BETA: splitting (34) gives: % 22.83/3.78 | | | | % 22.83/3.78 | | | | Case 1: % 22.83/3.78 | | | | | % 22.83/3.78 | | | | | (35) all_186_0 = pull % 22.83/3.78 | | | | | % 22.83/3.78 | | | | | BETA: splitting (33) gives: % 22.83/3.78 | | | | | % 22.83/3.78 | | | | | Case 1: % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | | (36) all_186_0 = push % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | | COMBINE_EQS: (35), (36) imply: % 22.83/3.78 | | | | | | (37) pull = push % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | | REDUCE: (8), (37) imply: % 22.83/3.78 | | | | | | (38) $false % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | | CLOSE: (38) is inconsistent. % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | Case 2: % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | | (39) n2 = n0 | n1 = n0 % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | | BETA: splitting (39) gives: % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | | Case 1: % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | (40) n1 = n0 % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | REDUCE: (24), (40) imply: % 22.83/3.78 | | | | | | | (41) holdsAt(spinning, n0) % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | PRED_UNIFY: (15), (41) imply: % 22.83/3.78 | | | | | | | (42) $false % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | CLOSE: (42) is inconsistent. % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | Case 2: % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | (43) n2 = n0 % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | REDUCE: (17), (43) imply: % 22.83/3.78 | | | | | | | (44) holdsAt(spinning, n0) % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | PRED_UNIFY: (15), (44) imply: % 22.83/3.78 | | | | | | | (45) $false % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | | CLOSE: (45) is inconsistent. % 22.83/3.78 | | | | | | | % 22.83/3.78 | | | | | | End of split % 22.83/3.78 | | | | | | % 22.83/3.78 | | | | | End of split % 22.83/3.78 | | | | | % 22.83/3.78 | | | | Case 2: % 22.83/3.78 | | | | | % 22.83/3.78 | | | | | (46) spinning = forwards % 22.83/3.78 | | | | | % 22.83/3.78 | | | | | REDUCE: (10), (46) imply: % 22.83/3.78 | | | | | (47) $false % 22.83/3.78 | | | | | % 22.83/3.78 | | | | | CLOSE: (47) is inconsistent. % 22.83/3.78 | | | | | % 22.83/3.78 | | | | End of split % 22.83/3.78 | | | | % 22.83/3.78 | | | End of split % 22.83/3.78 | | | % 22.83/3.78 | | Case 2: % 22.83/3.78 | | | % 22.83/3.78 | | | (48) ~ holdsAt(spinning, n1) % 22.83/3.78 | | | (49) ? [v0: $i] : ($i(v0) & initiates(v0, spinning, n1) & happens(v0, % 22.83/3.78 | | | n1)) % 22.83/3.78 | | | % 22.83/3.78 | | | DELTA: instantiating (49) with fresh symbol all_151_0 gives: % 22.83/3.78 | | | (50) $i(all_151_0) & initiates(all_151_0, spinning, n1) & % 22.83/3.78 | | | happens(all_151_0, n1) % 22.83/3.78 | | | % 22.83/3.78 | | | ALPHA: (50) implies: % 22.83/3.79 | | | (51) initiates(all_151_0, spinning, n1) % 22.83/3.79 | | | (52) $i(all_151_0) % 22.83/3.79 | | | % 22.83/3.79 | | | GROUND_INST: instantiating (3) with all_151_0, spinning, n1, simplifying % 22.83/3.79 | | | with (5), (14), (18), (51), (52) gives: % 22.83/3.79 | | | (53) spinning = backwards | happens(push, n1) % 22.83/3.79 | | | % 22.83/3.79 | | | GROUND_INST: instantiating (4) with all_151_0, spinning, n1, simplifying % 22.83/3.79 | | | with (14), (18), (51), (52) gives: % 22.83/3.79 | | | (54) all_151_0 = push | spinning = backwards | happens(push, n1) % 22.83/3.79 | | | % 22.83/3.79 | | | BETA: splitting (54) gives: % 22.83/3.79 | | | % 22.83/3.79 | | | Case 1: % 22.83/3.79 | | | | % 22.83/3.79 | | | | (55) happens(push, n1) % 22.83/3.79 | | | | % 22.83/3.79 | | | | GROUND_INST: instantiating (6) with push, n1, simplifying with (9), % 22.83/3.79 | | | | (14), (55) gives: % 22.83/3.79 | | | | (56) n2 = n1 | pull = push | n1 = n0 % 22.83/3.79 | | | | % 22.83/3.79 | | | | BETA: splitting (56) gives: % 22.83/3.79 | | | | % 22.83/3.79 | | | | Case 1: % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | (57) pull = push % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | REDUCE: (8), (57) imply: % 22.83/3.79 | | | | | (58) $false % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | CLOSE: (58) is inconsistent. % 22.83/3.79 | | | | | % 22.83/3.79 | | | | Case 2: % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | (59) n2 = n1 | n1 = n0 % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | BETA: splitting (59) gives: % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | Case 1: % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | (60) n2 = n1 % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | REDUCE: (17), (60) imply: % 22.83/3.79 | | | | | | (61) holdsAt(spinning, n1) % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | PRED_UNIFY: (48), (61) imply: % 22.83/3.79 | | | | | | (62) $false % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | CLOSE: (62) is inconsistent. % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | Case 2: % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | (63) n1 = n0 % 22.83/3.79 | | | | | | (64) ~ (n2 = n1) % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | REDUCE: (63), (64) imply: % 22.83/3.79 | | | | | | (65) ~ (n2 = n0) % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | REDUCE: (13), (63) imply: % 22.83/3.79 | | | | | | (66) plus(n0, n0) = n2 % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | REDUCE: (12), (63) imply: % 22.83/3.79 | | | | | | (67) plus(n0, n0) = n0 % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | GROUND_INST: instantiating (function-axioms) with n0, n2, n0, n0, % 22.83/3.79 | | | | | | simplifying with (66), (67) gives: % 22.83/3.79 | | | | | | (68) n2 = n0 % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | REDUCE: (65), (68) imply: % 22.83/3.79 | | | | | | (69) $false % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | | CLOSE: (69) is inconsistent. % 22.83/3.79 | | | | | | % 22.83/3.79 | | | | | End of split % 22.83/3.79 | | | | | % 22.83/3.79 | | | | End of split % 22.83/3.79 | | | | % 22.83/3.79 | | | Case 2: % 22.83/3.79 | | | | % 22.83/3.79 | | | | (70) ~ happens(push, n1) % 22.83/3.79 | | | | % 22.83/3.79 | | | | BETA: splitting (53) gives: % 22.83/3.79 | | | | % 22.83/3.79 | | | | Case 1: % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | (71) happens(push, n1) % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | PRED_UNIFY: (70), (71) imply: % 22.83/3.79 | | | | | (72) $false % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | CLOSE: (72) is inconsistent. % 22.83/3.79 | | | | | % 22.83/3.79 | | | | Case 2: % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | (73) spinning = backwards % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | REDUCE: (11), (73) imply: % 22.83/3.79 | | | | | (74) $false % 22.83/3.79 | | | | | % 22.83/3.79 | | | | | CLOSE: (74) is inconsistent. % 22.83/3.79 | | | | | % 22.83/3.79 | | | | End of split % 22.83/3.79 | | | | % 22.83/3.79 | | | End of split % 22.83/3.79 | | | % 22.83/3.79 | | End of split % 22.83/3.79 | | % 22.83/3.79 | End of split % 22.83/3.79 | % 22.83/3.79 End of proof % 22.83/3.79 % SZS output end Proof for theBenchmark % 22.83/3.79 % 22.83/3.79 3191ms %------------------------------------------------------------------------------