TSTP Solution File: CSR023+1 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------