TSTP Solution File: ARI601_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI601_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 17:48:32 EDT 2023
% Result : Theorem 2.89s 1.13s
% Output : Proof 3.48s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI601_1 : TPTP v8.1.2. Released v5.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n001.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 : Tue Aug 29 19:20:23 EDT 2023
% 0.13/0.34 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 1.75/0.97 Prover 4: Preprocessing ...
% 1.75/0.97 Prover 1: Preprocessing ...
% 2.29/1.01 Prover 3: Preprocessing ...
% 2.29/1.01 Prover 2: Preprocessing ...
% 2.29/1.01 Prover 5: Preprocessing ...
% 2.29/1.01 Prover 6: Preprocessing ...
% 2.29/1.01 Prover 0: Preprocessing ...
% 2.29/1.06 Prover 4: Constructing countermodel ...
% 2.29/1.06 Prover 1: Constructing countermodel ...
% 2.29/1.06 Prover 3: Constructing countermodel ...
% 2.29/1.06 Prover 5: Proving ...
% 2.29/1.06 Prover 2: Proving ...
% 2.29/1.06 Prover 6: Proving ...
% 2.29/1.06 Prover 0: Proving ...
% 2.89/1.13 Prover 3: proved (498ms)
% 2.89/1.13
% 2.89/1.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.89/1.13
% 2.89/1.13 Prover 6: stopped
% 2.89/1.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.89/1.14 Prover 0: proved (512ms)
% 2.89/1.14
% 2.89/1.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.89/1.14
% 2.89/1.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.89/1.14 Prover 2: proved (511ms)
% 2.89/1.14
% 2.89/1.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.89/1.14
% 2.89/1.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.89/1.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.89/1.14 Prover 4: Found proof (size 6)
% 2.89/1.14 Prover 4: proved (514ms)
% 2.89/1.15 Prover 7: Preprocessing ...
% 2.89/1.15 Prover 8: Preprocessing ...
% 2.89/1.15 Prover 10: Preprocessing ...
% 2.89/1.15 Prover 1: Found proof (size 6)
% 2.89/1.15 Prover 1: proved (521ms)
% 2.89/1.15 Prover 11: Preprocessing ...
% 2.89/1.15 Prover 5: proved (502ms)
% 2.89/1.16 Prover 8: Warning: ignoring some quantifiers
% 2.89/1.16 Prover 10: Constructing countermodel ...
% 2.89/1.16 Prover 7: Constructing countermodel ...
% 2.89/1.16 Prover 10: stopped
% 2.89/1.16 Prover 7: stopped
% 2.89/1.16 Prover 11: Constructing countermodel ...
% 2.89/1.16 Prover 11: stopped
% 2.89/1.17 Prover 8: Constructing countermodel ...
% 2.89/1.17 Prover 8: stopped
% 2.89/1.17
% 2.89/1.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.89/1.17
% 2.89/1.17 % SZS output start Proof for theBenchmark
% 2.89/1.17 Assumptions after simplification:
% 2.89/1.17 ---------------------------------
% 2.89/1.17
% 2.89/1.17 (fX_gt_X_implies_ineq)
% 3.48/1.20 ? [v0: int] : ($lesseq(v0, 4) & $lesseq(4, a) & f($sum(a, 1)) = v0 & ! [v1:
% 3.48/1.21 int] : ! [v2: int] : ( ~ ($lesseq(v2, v1)) | ~ (f(v1) = v2)))
% 3.48/1.21
% 3.48/1.21 Those formulas are unsatisfiable:
% 3.48/1.21 ---------------------------------
% 3.48/1.21
% 3.48/1.21 Begin of proof
% 3.48/1.21 |
% 3.48/1.21 | DELTA: instantiating (fX_gt_X_implies_ineq) with fresh symbol all_3_0 gives:
% 3.48/1.21 | (1) $lesseq(all_3_0, 4) & $lesseq(4, a) & f($sum(a, 1)) = all_3_0 & ! [v0:
% 3.48/1.21 | int] : ! [v1: int] : ( ~ ($lesseq(v1, v0)) | ~ (f(v0) = v1))
% 3.48/1.21 |
% 3.48/1.21 | ALPHA: (1) implies:
% 3.48/1.21 | (2) $lesseq(4, a)
% 3.48/1.21 | (3) $lesseq(all_3_0, 4)
% 3.48/1.21 | (4) f($sum(a, 1)) = all_3_0
% 3.48/1.21 | (5) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, v0)) | ~ (f(v0) = v1))
% 3.48/1.21 |
% 3.48/1.21 | GROUND_INST: instantiating (5) with $sum(a, 1), all_3_0, simplifying with (4)
% 3.48/1.21 | gives:
% 3.48/1.22 | (6) $lesseq(2, $difference(all_3_0, a))
% 3.48/1.22 |
% 3.48/1.22 | COMBINE_INEQS: (3), (6) imply:
% 3.48/1.22 | (7) $lesseq(a, 2)
% 3.48/1.22 |
% 3.48/1.22 | COMBINE_INEQS: (2), (7) imply:
% 3.48/1.22 | (8) $false
% 3.48/1.22 |
% 3.48/1.22 | CLOSE: (8) is inconsistent.
% 3.48/1.22 |
% 3.48/1.22 End of proof
% 3.48/1.22 % SZS output end Proof for theBenchmark
% 3.48/1.22
% 3.48/1.22 610ms
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