%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI682_1 : TPTP v8.1.2. Released v6.3.0. % 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 17:48:47 EDT 2023 % Result : Theorem 3.11s 1.21s % Output : Proof 3.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI682_1 : TPTP v8.1.2. Released v6.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n007.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 18:10:14 EDT 2023 % 0.14/0.34 % CPUTime : % 0.48/0.62 ________ _____ % 0.48/0.62 ___ __ \_________(_)________________________________ % 0.48/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.48/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.48/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.48/0.62 % 0.48/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.48/0.62 (2023-06-19) % 0.48/0.62 % 0.48/0.62 (c) Philipp Rümmer, 2009-2023 % 0.48/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.48/0.62 Amanda Stjerna. % 0.48/0.62 Free software under BSD-3-Clause. % 0.48/0.62 % 0.48/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.48/0.62 % 0.48/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.48/0.63 Running up to 7 provers in parallel. % 0.69/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.20/1.02 Prover 4: Preprocessing ... % 2.20/1.02 Prover 6: Preprocessing ... % 2.20/1.02 Prover 2: Preprocessing ... % 2.20/1.02 Prover 5: Preprocessing ... % 2.20/1.02 Prover 1: Preprocessing ... % 2.20/1.02 Prover 0: Preprocessing ... % 2.20/1.02 Prover 3: Preprocessing ... % 2.65/1.07 Prover 4: Constructing countermodel ... % 2.65/1.07 Prover 6: Constructing countermodel ... % 2.65/1.07 Prover 5: Constructing countermodel ... % 2.65/1.07 Prover 2: Constructing countermodel ... % 2.65/1.07 Prover 0: Constructing countermodel ... % 2.65/1.07 Prover 3: Constructing countermodel ... % 2.65/1.07 Prover 1: Constructing countermodel ... % 3.11/1.21 Prover 6: proved (567ms) % 3.11/1.21 Prover 5: proved (569ms) % 3.11/1.21 Prover 3: proved (571ms) % 3.11/1.21 Prover 0: proved (571ms) % 3.11/1.21 % 3.11/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.21 % 3.11/1.21 Prover 2: proved (572ms) % 3.11/1.21 % 3.11/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.21 % 3.11/1.21 % 3.11/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.21 % 3.11/1.22 % 3.11/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.22 % 3.11/1.22 % 3.11/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.22 % 3.11/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.11/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.11/1.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.11/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.11/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.11/1.23 Prover 7: Preprocessing ... % 3.11/1.23 Prover 8: Preprocessing ... % 3.62/1.23 Prover 11: Preprocessing ... % 3.62/1.24 Prover 10: Preprocessing ... % 3.62/1.24 Prover 8: Constructing countermodel ... % 3.62/1.24 Prover 7: Constructing countermodel ... % 3.62/1.24 Prover 11: Constructing countermodel ... % 3.62/1.24 Prover 13: Preprocessing ... % 3.62/1.24 Prover 10: Constructing countermodel ... % 3.62/1.24 Prover 1: Found proof (size 20) % 3.62/1.24 Prover 1: proved (605ms) % 3.62/1.25 Prover 10: stopped % 3.62/1.25 Prover 11: stopped % 3.62/1.25 Prover 8: stopped % 3.62/1.25 Prover 7: stopped % 3.62/1.25 Prover 4: Found proof (size 20) % 3.62/1.25 Prover 4: proved (607ms) % 3.62/1.25 Prover 13: Constructing countermodel ... % 3.62/1.25 Prover 13: stopped % 3.62/1.25 % 3.62/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.62/1.25 % 3.62/1.26 % SZS output start Proof for theBenchmark % 3.62/1.26 Assumptions after simplification: % 3.62/1.26 --------------------------------- % 3.62/1.26 % 3.62/1.26 (conj) % 3.62/1.26 $lesseq(1, $difference(b, a)) % 3.62/1.26 % 3.62/1.26 (conj_001) % 3.62/1.27 $lesseq(0, a) % 3.62/1.27 % 3.62/1.27 (conj_002) % 3.62/1.27 ? [v0: int] : ($lesseq(b, $difference(a, v0)) & $product(a, b) = v0) % 3.62/1.27 % 3.62/1.27 Those formulas are unsatisfiable: % 3.62/1.27 --------------------------------- % 3.62/1.27 % 3.62/1.27 Begin of proof % 3.62/1.27 | % 3.62/1.27 | DELTA: instantiating (conj_002) with fresh symbol all_3_0 gives: % 3.62/1.27 | (1) $lesseq(b, $difference(a, all_3_0)) & $product(a, b) = all_3_0 % 3.62/1.27 | % 3.62/1.27 | ALPHA: (1) implies: % 3.85/1.27 | (2) $lesseq(b, $difference(a, all_3_0)) % 3.85/1.28 | (3) $product(a, b) = all_3_0 % 3.85/1.28 | % 3.85/1.28 | COMBINE_INEQS: (conj), (conj_001) imply: % 3.85/1.28 | (4) $lesseq(1, b) % 3.85/1.28 | % 3.85/1.28 | THEORY_AXIOM GroebnerMultiplication: % 3.85/1.28 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v0, % 3.85/1.28 | $difference(v1, v2))) | ~ ($lesseq(v2, 457651)) | ~ ($lesseq(1, % 3.85/1.28 | $difference(v0, v1))) | ~ ($lesseq(0, v1)) | ~ ($product(v1, % 3.85/1.28 | v0) = v2)) % 3.85/1.28 | % 3.85/1.28 | GROUND_INST: instantiating (5) with b, a, all_3_0, simplifying with (3) gives: % 3.85/1.28 | (6) ~ ($lesseq(b, $difference(a, all_3_0))) | ~ ($lesseq(all_3_0, % 3.85/1.28 | 457651)) | ~ ($lesseq(1, $difference(b, a))) | ~ ($lesseq(0, a)) % 3.85/1.28 | % 3.85/1.28 | BETA: splitting (6) gives: % 3.85/1.28 | % 3.85/1.28 | Case 1: % 3.85/1.28 | | % 3.85/1.28 | | (7) ~ ($lesseq(b, $difference(a, all_3_0))) | ~ ($lesseq(1, % 3.85/1.28 | | $difference(b, a))) % 3.85/1.28 | | % 3.85/1.28 | | BETA: splitting (7) gives: % 3.85/1.28 | | % 3.85/1.28 | | Case 1: % 3.85/1.28 | | | % 3.85/1.28 | | | (8) $lesseq(1, $sum($difference(all_3_0, a), b)) % 3.85/1.28 | | | % 3.85/1.28 | | | COMBINE_INEQS: (2), (8) imply: % 3.85/1.28 | | | (9) $false % 3.85/1.28 | | | % 3.85/1.28 | | | CLOSE: (9) is inconsistent. % 3.85/1.28 | | | % 3.85/1.28 | | Case 2: % 3.85/1.28 | | | % 3.85/1.28 | | | (10) $lesseq(b, a) % 3.85/1.28 | | | % 3.85/1.29 | | | COMBINE_INEQS: (10), (conj) imply: % 3.85/1.29 | | | (11) $false % 3.85/1.29 | | | % 3.85/1.29 | | | CLOSE: (11) is inconsistent. % 3.85/1.29 | | | % 3.85/1.29 | | End of split % 3.85/1.29 | | % 3.85/1.29 | Case 2: % 3.85/1.29 | | % 3.85/1.29 | | (12) ~ ($lesseq(all_3_0, 457651)) | ~ ($lesseq(0, a)) | ~ ($lesseq(1, % 3.85/1.29 | | b)) % 3.85/1.29 | | % 3.85/1.29 | | BETA: splitting (12) gives: % 3.85/1.29 | | % 3.85/1.29 | | Case 1: % 3.85/1.29 | | | % 3.85/1.29 | | | (13) $lesseq(a, -1) % 3.85/1.29 | | | % 3.85/1.29 | | | COMBINE_INEQS: (13), (conj_001) imply: % 3.85/1.29 | | | (14) $false % 3.85/1.29 | | | % 3.85/1.29 | | | CLOSE: (14) is inconsistent. % 3.85/1.29 | | | % 3.85/1.29 | | Case 2: % 3.85/1.29 | | | % 3.85/1.29 | | | (15) ~ ($lesseq(all_3_0, 457651)) | ~ ($lesseq(1, b)) % 3.85/1.29 | | | % 3.85/1.29 | | | BETA: splitting (15) gives: % 3.85/1.29 | | | % 3.85/1.29 | | | Case 1: % 3.85/1.29 | | | | % 3.85/1.29 | | | | (16) $lesseq(b, 0) % 3.85/1.29 | | | | % 3.85/1.29 | | | | COMBINE_INEQS: (4), (16) imply: % 3.85/1.29 | | | | (17) $false % 3.85/1.29 | | | | % 3.85/1.29 | | | | CLOSE: (17) is inconsistent. % 3.85/1.29 | | | | % 3.85/1.29 | | | Case 2: % 3.85/1.29 | | | | % 3.85/1.29 | | | | (18) $lesseq(457652, all_3_0) % 3.85/1.29 | | | | % 3.85/1.29 | | | | COMBINE_INEQS: (2), (18) imply: % 3.85/1.29 | | | | (19) $lesseq(457652, $difference(a, b)) % 3.85/1.29 | | | | % 3.85/1.29 | | | | COMBINE_INEQS: (19), (conj) imply: % 3.85/1.29 | | | | (20) $false % 3.85/1.29 | | | | % 3.85/1.29 | | | | CLOSE: (20) is inconsistent. % 3.85/1.29 | | | | % 3.85/1.29 | | | End of split % 3.85/1.29 | | | % 3.85/1.29 | | End of split % 3.85/1.29 | | % 3.85/1.29 | End of split % 3.85/1.29 | % 3.85/1.29 End of proof % 3.85/1.29 % SZS output end Proof for theBenchmark % 3.85/1.29 % 3.85/1.29 670ms %------------------------------------------------------------------------------