%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : CSR023+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 : n006.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 21:36:26 EDT 2023 % Result : Theorem 14.61s 2.71s % Output : Proof 17.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : CSR023+1 : TPTP v8.1.2. Bugfixed v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 07:17:21 EDT 2023 % 0.20/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.11/1.16 Prover 4: Preprocessing ... % 3.11/1.16 Prover 1: Preprocessing ... % 3.60/1.19 Prover 5: Preprocessing ... % 3.60/1.19 Prover 0: Preprocessing ... % 3.60/1.19 Prover 3: Preprocessing ... % 3.60/1.19 Prover 2: Preprocessing ... % 3.60/1.19 Prover 6: Preprocessing ... % 7.39/1.77 Prover 5: Proving ... % 8.08/1.86 Prover 1: Constructing countermodel ... % 8.08/1.86 Prover 6: Proving ... % 8.08/1.87 Prover 3: Constructing countermodel ... % 8.85/2.04 Prover 1: gave up % 8.85/2.04 Prover 3: gave up % 8.85/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.85/2.07 Prover 4: Constructing countermodel ... % 8.85/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.10/2.14 Prover 6: gave up % 10.10/2.15 Prover 7: Preprocessing ... % 10.10/2.16 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 10.10/2.17 Prover 0: Proving ... % 10.10/2.17 Prover 8: Preprocessing ... % 10.10/2.21 Prover 9: Preprocessing ... % 11.78/2.35 Prover 2: Proving ... % 12.29/2.43 Prover 8: Warning: ignoring some quantifiers % 12.29/2.45 Prover 8: Constructing countermodel ... % 13.27/2.53 Prover 9: Constructing countermodel ... % 13.27/2.61 Prover 8: gave up % 13.27/2.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.98/2.65 Prover 7: Warning: ignoring some quantifiers % 13.98/2.68 Prover 10: Preprocessing ... % 14.61/2.71 Prover 7: Constructing countermodel ... % 14.61/2.71 Prover 2: proved (2086ms) % 14.61/2.71 % 14.61/2.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.61/2.71 % 14.61/2.71 Prover 9: stopped % 14.61/2.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.61/2.71 Prover 5: stopped % 14.61/2.71 Prover 0: stopped % 14.61/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.61/2.73 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.61/2.74 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 14.61/2.76 Prover 11: Preprocessing ... % 14.61/2.77 Prover 16: Preprocessing ... % 15.22/2.78 Prover 13: Preprocessing ... % 15.22/2.80 Prover 19: Preprocessing ... % 16.87/3.02 Prover 19: Warning: ignoring some quantifiers % 17.04/3.05 Prover 11: Constructing countermodel ... % 17.04/3.06 Prover 19: Constructing countermodel ... % 17.04/3.08 Prover 13: Warning: ignoring some quantifiers % 17.04/3.10 Prover 7: Found proof (size 14) % 17.04/3.10 Prover 16: Warning: ignoring some quantifiers % 17.04/3.10 Prover 10: Warning: ignoring some quantifiers % 17.04/3.10 Prover 7: proved (1039ms) % 17.04/3.10 Prover 19: stopped % 17.04/3.10 Prover 4: stopped % 17.04/3.10 Prover 13: Constructing countermodel ... % 17.04/3.11 Prover 16: Constructing countermodel ... % 17.04/3.11 Prover 13: stopped % 17.04/3.11 Prover 10: Constructing countermodel ... % 17.04/3.11 Prover 11: stopped % 17.04/3.12 Prover 16: stopped % 17.61/3.12 Prover 10: stopped % 17.61/3.12 % 17.61/3.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.61/3.12 % 17.61/3.12 % SZS output start Proof for theBenchmark % 17.61/3.13 Assumptions after simplification: % 17.61/3.13 --------------------------------- % 17.61/3.13 % 17.61/3.13 (happens_all_defn) % 17.61/3.14 $i(n2) & $i(pull) & $i(push) & $i(n1) & $i(n0) & happens(pull, n2) & % 17.61/3.14 happens(pull, n1) & happens(push, n2) & happens(push, n0) & ! [v0: $i] : ! % 17.61/3.15 [v1: $i] : (v1 = n2 | v1 = n1 | v1 = n0 | v0 = pull | ~ $i(v1) | ~ $i(v0) | % 17.61/3.15 ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n1 | v1 = % 17.61/3.15 n0 | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] : % 17.61/3.15 ! [v1: $i] : (v1 = n2 | v1 = n1 | v1 = n0 | ~ $i(v1) | ~ $i(v0) | ~ % 17.61/3.15 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n1 | v0 = % 17.61/3.15 pull | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] % 17.61/3.15 : ! [v1: $i] : (v1 = n2 | v1 = n1 | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ % 17.61/3.15 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v1 = n0 | v0 = % 17.61/3.15 pull | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] % 17.61/3.15 : ! [v1: $i] : (v1 = n2 | v1 = n0 | v0 = pull | ~ $i(v1) | ~ $i(v0) | ~ % 17.61/3.15 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n2 | v0 = pull | v0 = % 17.61/3.15 push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: % 17.61/3.15 $i] : (v1 = n1 | v1 = n0 | v0 = pull | v0 = push | ~ $i(v1) | ~ $i(v0) | % 17.61/3.15 ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v1 = n1 | v0 = pull | v0 = % 17.61/3.15 push | ~ $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) & ! [v0: $i] : ! [v1: % 17.61/3.15 $i] : (v1 = n0 | v0 = pull | v0 = push | ~ $i(v1) | ~ $i(v0) | ~ % 17.61/3.15 happens(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (v0 = pull | v0 = push | ~ % 17.61/3.15 $i(v1) | ~ $i(v0) | ~ happens(v0, v1)) % 17.61/3.15 % 17.61/3.15 (happens_holds) % 17.61/3.17 $i(n1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (plus(v1, % 17.61/3.17 n1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v2, v1) % 17.61/3.17 | ~ happens(v0, v1) | holdsAt(v2, v3)) % 17.61/3.17 % 17.61/3.17 (initiates_all_defn) % 17.90/3.18 $i(spinning) & $i(backwards) & $i(pull) & $i(forwards) & $i(push) & ! [v0: % 17.90/3.18 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = backwards | v1 = % 17.90/3.18 forwards | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2)) & % 17.90/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = backwards | v0 % 17.90/3.18 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2)) & ! % 17.90/3.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = backwards | ~ % 17.90/3.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ happens(pull, % 17.90/3.18 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = % 17.90/3.18 forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 17.90/3.18 v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = spinning | v1 = % 17.90/3.18 forwards | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ % 17.90/3.18 happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 17.90/3.18 spinning | v0 = pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 17.90/3.18 initiates(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 17.90/3.18 spinning | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 17.90/3.18 v1, v2) | ~ happens(pull, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 17.90/3.18 : (v1 = spinning | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 17.90/3.18 initiates(v0, v1, v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : % 17.90/3.18 ! [v2: $i] : (v1 = spinning | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 17.90/3.18 initiates(v0, v1, v2) | ~ happens(pull, v2) | ~ happens(push, v2)) & ! % 17.90/3.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v1 = forwards | v0 = % 17.90/3.18 pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2)) & ! % 17.90/3.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v1 = forwards | ~ % 17.90/3.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | happens(push, % 17.90/3.18 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v0 = % 17.90/3.18 pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, % 17.90/3.18 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = backwards | v0 = % 17.90/3.18 pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ % 17.90/3.18 happens(pull, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 17.90/3.18 backwards | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 17.90/3.18 v1, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.90/3.18 (v1 = backwards | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) % 17.90/3.18 | ~ happens(pull, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! % 17.90/3.18 [v2: $i] : (v1 = forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 17.90/3.18 initiates(v0, v1, v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : % 17.90/3.18 ! [v2: $i] : (v1 = forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.90/3.18 ~ initiates(v0, v1, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : % 17.90/3.18 ! [v2: $i] : (v1 = forwards | v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.90/3.18 ~ initiates(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = % 17.90/3.18 pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, % 17.90/3.18 v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.90/3.18 (v0 = pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 17.90/3.18 v1, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.90/3.18 (v0 = pull | v0 = push | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 17.90/3.18 v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = pull | ~ % 17.90/3.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ happens(pull, % 17.90/3.18 v2) | ~ happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.90/3.18 (v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, v2) | ~ % 17.90/3.18 happens(pull, v2) | happens(push, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.90/3.18 $i] : (v0 = pull | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, v1, % 17.90/3.18 v2) | ~ happens(pull, v2)) & ! [v0: $i] : ( ~ $i(v0) | ~ happens(push, % 17.90/3.18 v0) | initiates(pull, spinning, v0)) & ? [v0: $i] : ( ~ $i(v0) | % 17.90/3.18 initiates(pull, backwards, v0) | happens(push, v0)) & ? [v0: $i] : ( ~ % 17.90/3.18 $i(v0) | initiates(push, forwards, v0) | happens(pull, v0)) % 17.90/3.18 % 17.90/3.18 (less2) % 17.90/3.18 $i(n2) & $i(n1) & ! [v0: $i] : ( ~ $i(v0) | ~ less_or_equal(v0, n1) | % 17.90/3.18 less(v0, n2)) & ! [v0: $i] : ( ~ $i(v0) | ~ less(v0, n2) | % 17.90/3.18 less_or_equal(v0, n1)) % 17.90/3.18 % 17.90/3.18 (less3) % 17.90/3.18 $i(n3) & $i(n2) & ! [v0: $i] : ( ~ $i(v0) | ~ less_or_equal(v0, n2) | % 17.90/3.18 less(v0, n3)) & ! [v0: $i] : ( ~ $i(v0) | ~ less(v0, n3) | % 17.90/3.18 less_or_equal(v0, n2)) % 17.90/3.18 % 17.90/3.18 (plus1_2) % 17.90/3.18 plus(n1, n2) = n3 & $i(n3) & $i(n2) & $i(n1) % 17.90/3.18 % 17.90/3.18 (push_not_pull) % 17.90/3.18 ~ (pull = push) & $i(pull) & $i(push) % 17.90/3.18 % 17.90/3.18 (spinning_3) % 17.90/3.18 $i(n3) & $i(spinning) & ~ holdsAt(spinning, n3) % 17.90/3.18 % 17.90/3.18 (symmetry_of_plus) % 17.90/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (plus(v1, v0) = v2) | ~ $i(v1) % 17.90/3.19 | ~ $i(v0) | (plus(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! % 17.90/3.19 [v2: $i] : ( ~ (plus(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (plus(v1, v0) = % 17.90/3.19 v2 & $i(v2))) % 17.90/3.19 % 17.90/3.19 Further assumptions not needed in the proof: % 17.90/3.19 -------------------------------------------- % 17.90/3.19 antitrajectory, change_holding, forwards_not_backwards, forwards_not_spinning, % 17.90/3.19 happens_not_released, happens_releases, happens_terminates_not_holds, % 17.90/3.19 keep_holding, keep_not_holding, keep_not_released, keep_released, less0, less1, % 17.90/3.19 less4, less5, less6, less7, less8, less9, less_or_equal, less_property, % 17.90/3.19 not_backwards_0, not_forwards_0, not_releasedAt, not_splinning_0, plus0_0, % 17.90/3.19 plus0_1, plus0_2, plus0_3, plus1_1, plus1_3, plus2_2, plus2_3, plus3_3, % 17.90/3.19 releases_all_defn, spinning_not_backwards, startedin_defn, stoppedin_defn, % 17.90/3.19 terminates_all_defn % 17.90/3.19 % 17.90/3.19 Those formulas are unsatisfiable: % 17.90/3.19 --------------------------------- % 17.90/3.19 % 17.90/3.19 Begin of proof % 17.90/3.19 | % 17.90/3.19 | ALPHA: (happens_holds) implies: % 17.90/3.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (plus(v1, % 17.90/3.19 | n1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ initiates(v0, % 17.90/3.19 | v2, v1) | ~ happens(v0, v1) | holdsAt(v2, v3)) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (initiates_all_defn) implies: % 17.90/3.19 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ happens(push, v0) | initiates(pull, % 17.90/3.19 | spinning, v0)) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (happens_all_defn) implies: % 17.90/3.19 | (3) happens(push, n2) % 17.90/3.19 | (4) happens(pull, n2) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (push_not_pull) implies: % 17.90/3.19 | (5) $i(pull) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (plus1_2) implies: % 17.90/3.19 | (6) plus(n1, n2) = n3 % 17.90/3.19 | % 17.90/3.19 | ALPHA: (symmetry_of_plus) implies: % 17.90/3.19 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (plus(v1, v0) = v2) | ~ % 17.90/3.19 | $i(v1) | ~ $i(v0) | (plus(v0, v1) = v2 & $i(v2))) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (less2) implies: % 17.90/3.19 | (8) $i(n1) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (less3) implies: % 17.90/3.19 | (9) $i(n2) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (spinning_3) implies: % 17.90/3.19 | (10) ~ holdsAt(spinning, n3) % 17.90/3.19 | (11) $i(spinning) % 17.90/3.19 | % 17.90/3.19 | GROUND_INST: instantiating (2) with n2, simplifying with (3), (9) gives: % 17.90/3.19 | (12) initiates(pull, spinning, n2) % 17.90/3.19 | % 17.90/3.19 | GROUND_INST: instantiating (7) with n2, n1, n3, simplifying with (6), (8), (9) % 17.90/3.19 | gives: % 17.90/3.19 | (13) plus(n2, n1) = n3 & $i(n3) % 17.90/3.19 | % 17.90/3.19 | ALPHA: (13) implies: % 17.90/3.19 | (14) plus(n2, n1) = n3 % 17.90/3.19 | % 17.90/3.20 | GROUND_INST: instantiating (1) with pull, n2, spinning, n3, simplifying with % 17.90/3.20 | (4), (5), (9), (10), (11), (12), (14) gives: % 17.90/3.20 | (15) $false % 17.90/3.20 | % 17.90/3.20 | CLOSE: (15) is inconsistent. % 17.90/3.20 | % 17.90/3.20 End of proof % 17.90/3.20 % SZS output end Proof for theBenchmark % 17.90/3.20 % 17.90/3.20 2589ms %------------------------------------------------------------------------------