TSTP Solution File: DAT031_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT031_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.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 22:18:56 EDT 2023
% Result : Theorem 4.82s 1.40s
% Output : Proof 6.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT031_1 : TPTP v8.1.2. Released v5.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.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 : Thu Aug 24 14:11:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.29/1.03 Prover 4: Preprocessing ...
% 2.29/1.03 Prover 1: Preprocessing ...
% 2.29/1.07 Prover 6: Preprocessing ...
% 2.29/1.07 Prover 2: Preprocessing ...
% 2.29/1.07 Prover 5: Preprocessing ...
% 2.29/1.07 Prover 0: Preprocessing ...
% 2.29/1.07 Prover 3: Preprocessing ...
% 3.84/1.22 Prover 1: Constructing countermodel ...
% 3.84/1.23 Prover 3: Constructing countermodel ...
% 3.84/1.23 Prover 5: Proving ...
% 3.84/1.23 Prover 6: Proving ...
% 3.84/1.24 Prover 0: Proving ...
% 3.84/1.24 Prover 4: Constructing countermodel ...
% 3.84/1.25 Prover 2: Proving ...
% 3.84/1.31 Prover 1: gave up
% 3.84/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.84/1.31 Prover 3: gave up
% 3.84/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.84/1.34 Prover 7: Preprocessing ...
% 3.84/1.35 Prover 8: Preprocessing ...
% 4.82/1.37 Prover 4: gave up
% 4.82/1.38 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.82/1.39 Prover 9: Preprocessing ...
% 4.82/1.40 Prover 2: proved (783ms)
% 4.82/1.40
% 4.82/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.82/1.40
% 4.82/1.40 Prover 6: stopped
% 4.82/1.40 Prover 5: stopped
% 4.82/1.40 Prover 0: stopped
% 4.82/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.82/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.82/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.82/1.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.82/1.41 Prover 7: Constructing countermodel ...
% 4.82/1.42 Prover 8: Warning: ignoring some quantifiers
% 4.82/1.43 Prover 13: Preprocessing ...
% 4.82/1.43 Prover 11: Preprocessing ...
% 4.82/1.43 Prover 8: Constructing countermodel ...
% 4.82/1.43 Prover 16: Preprocessing ...
% 4.82/1.44 Prover 10: Preprocessing ...
% 5.51/1.47 Prover 8: gave up
% 5.51/1.47 Prover 9: Constructing countermodel ...
% 5.51/1.47 Prover 16: Warning: ignoring some quantifiers
% 5.51/1.47 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.51/1.48 Prover 16: Constructing countermodel ...
% 5.51/1.48 Prover 9: stopped
% 5.51/1.48 Prover 13: Warning: ignoring some quantifiers
% 5.51/1.48 Prover 11: Constructing countermodel ...
% 5.51/1.49 Prover 19: Preprocessing ...
% 5.51/1.49 Prover 10: Constructing countermodel ...
% 5.51/1.49 Prover 13: Constructing countermodel ...
% 5.89/1.51 Prover 7: Found proof (size 8)
% 5.89/1.51 Prover 7: proved (201ms)
% 5.89/1.52 Prover 11: stopped
% 5.89/1.52 Prover 13: stopped
% 5.89/1.52 Prover 10: Found proof (size 8)
% 5.89/1.52 Prover 10: proved (117ms)
% 5.89/1.52 Prover 16: stopped
% 5.89/1.54 Prover 19: Warning: ignoring some quantifiers
% 6.16/1.55 Prover 19: Constructing countermodel ...
% 6.16/1.55 Prover 19: stopped
% 6.16/1.55
% 6.16/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.16/1.55
% 6.16/1.56 % SZS output start Proof for theBenchmark
% 6.16/1.56 Assumptions after simplification:
% 6.16/1.56 ---------------------------------
% 6.16/1.56
% 6.16/1.56 (ax4)
% 6.16/1.58 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2
% 6.16/1.58 = v0 | ~ (add(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v3) | in(v0,
% 6.16/1.58 v1)) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3:
% 6.16/1.58 collection] : ( ~ (add(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v1) |
% 6.16/1.58 in(v0, v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 6.16/1.58 (add(v0, v1) = v2) | ~ collection(v1) | in(v0, v2))
% 6.16/1.58
% 6.16/1.58 (co1)
% 6.16/1.58 collection(empty) & ? [v0: collection] : ? [v1: collection] : ? [v2:
% 6.16/1.58 collection] : (add(50, empty) = v0 & add(30, v0) = v1 & add(10, v1) = v2 &
% 6.16/1.58 collection(v2) & collection(v1) & collection(v0) & ! [v3: int] : ( ~
% 6.16/1.59 ($lesseq(v3, 40)) | ~ ($lesseq(20, v3)) | ~ in(v3, v2)))
% 6.16/1.59
% 6.16/1.59 Further assumptions not needed in the proof:
% 6.16/1.59 --------------------------------------------
% 6.16/1.59 ax1, ax2, ax3, ax5
% 6.16/1.59
% 6.16/1.59 Those formulas are unsatisfiable:
% 6.16/1.59 ---------------------------------
% 6.16/1.59
% 6.16/1.59 Begin of proof
% 6.16/1.59 |
% 6.16/1.59 | ALPHA: (ax4) implies:
% 6.16/1.59 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 6.16/1.59 | v1) = v2) | ~ collection(v1) | in(v0, v2))
% 6.16/1.59 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 6.16/1.59 | : ( ~ (add(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v1) | in(v0,
% 6.16/1.59 | v3))
% 6.16/1.59 |
% 6.16/1.59 | ALPHA: (co1) implies:
% 6.16/1.59 | (3) ? [v0: collection] : ? [v1: collection] : ? [v2: collection] :
% 6.16/1.59 | (add(50, empty) = v0 & add(30, v0) = v1 & add(10, v1) = v2 &
% 6.16/1.59 | collection(v2) & collection(v1) & collection(v0) & ! [v3: int] : ( ~
% 6.16/1.59 | ($lesseq(v3, 40)) | ~ ($lesseq(20, v3)) | ~ in(v3, v2)))
% 6.16/1.59 |
% 6.16/1.59 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2
% 6.16/1.59 | gives:
% 6.16/1.60 | (4) add(50, empty) = all_11_2 & add(30, all_11_2) = all_11_1 & add(10,
% 6.16/1.60 | all_11_1) = all_11_0 & collection(all_11_0) & collection(all_11_1) &
% 6.16/1.60 | collection(all_11_2) & ! [v0: int] : ( ~ ($lesseq(v0, 40)) | ~
% 6.16/1.60 | ($lesseq(20, v0)) | ~ in(v0, all_11_0))
% 6.16/1.60 |
% 6.16/1.60 | ALPHA: (4) implies:
% 6.16/1.60 | (5) collection(all_11_2)
% 6.16/1.60 | (6) collection(all_11_1)
% 6.16/1.60 | (7) add(10, all_11_1) = all_11_0
% 6.16/1.60 | (8) add(30, all_11_2) = all_11_1
% 6.16/1.60 | (9) ! [v0: int] : ( ~ ($lesseq(v0, 40)) | ~ ($lesseq(20, v0)) | ~ in(v0,
% 6.16/1.60 | all_11_0))
% 6.16/1.60 |
% 6.16/1.60 | GROUND_INST: instantiating (1) with 30, all_11_2, all_11_1, simplifying with
% 6.16/1.60 | (5), (8) gives:
% 6.16/1.60 | (10) in(30, all_11_1)
% 6.16/1.60 |
% 6.16/1.60 | GROUND_INST: instantiating (9) with 30 gives:
% 6.16/1.60 | (11) ~ in(30, all_11_0)
% 6.16/1.60 |
% 6.16/1.60 | GROUND_INST: instantiating (2) with 30, all_11_1, 10, all_11_0, simplifying
% 6.16/1.60 | with (6), (7), (10), (11) gives:
% 6.16/1.60 | (12) $false
% 6.16/1.60 |
% 6.16/1.60 | CLOSE: (12) is inconsistent.
% 6.16/1.60 |
% 6.16/1.60 End of proof
% 6.16/1.60 % SZS output end Proof for theBenchmark
% 6.16/1.60
% 6.16/1.60 1009ms
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