%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI670_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 : n028.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 17:48:45 EDT 2023 % Result : Theorem 3.29s 1.18s % Output : Proof 3.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI670_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 : n028.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 18:54:26 EDT 2023 % 0.14/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.52/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.99/0.98 Prover 1: Preprocessing ... % 1.99/0.98 Prover 5: Preprocessing ... % 1.99/0.98 Prover 3: Preprocessing ... % 1.99/0.98 Prover 2: Preprocessing ... % 1.99/0.98 Prover 6: Preprocessing ... % 1.99/0.98 Prover 0: Preprocessing ... % 1.99/0.98 Prover 4: Preprocessing ... % 2.40/1.03 Prover 5: Constructing countermodel ... % 2.40/1.03 Prover 1: Constructing countermodel ... % 2.40/1.03 Prover 6: Constructing countermodel ... % 2.40/1.03 Prover 2: Constructing countermodel ... % 2.40/1.03 Prover 3: Constructing countermodel ... % 2.40/1.03 Prover 4: Constructing countermodel ... % 2.40/1.03 Prover 0: Constructing countermodel ... % 3.29/1.18 Prover 6: proved (544ms) % 3.29/1.18 Prover 0: proved (552ms) % 3.29/1.18 Prover 2: proved (549ms) % 3.29/1.18 % 3.29/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.29/1.18 % 3.29/1.18 Prover 3: proved (550ms) % 3.29/1.18 % 3.29/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.29/1.18 % 3.29/1.18 % 3.29/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.29/1.18 % 3.29/1.18 % 3.29/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.29/1.19 % 3.29/1.19 Prover 5: proved (547ms) % 3.29/1.19 % 3.29/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.29/1.19 % 3.29/1.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.29/1.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.29/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.29/1.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.29/1.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.29/1.19 Prover 7: Preprocessing ... % 3.29/1.19 Prover 8: Preprocessing ... % 3.29/1.20 Prover 7: Constructing countermodel ... % 3.29/1.20 Prover 11: Preprocessing ... % 3.29/1.20 Prover 8: Constructing countermodel ... % 3.29/1.20 Prover 10: Preprocessing ... % 3.29/1.20 Prover 13: Preprocessing ... % 3.29/1.20 Prover 11: Constructing countermodel ... % 3.29/1.20 Prover 10: Constructing countermodel ... % 3.29/1.20 Prover 13: Constructing countermodel ... % 3.29/1.21 Prover 1: Found proof (size 26) % 3.29/1.21 Prover 1: proved (581ms) % 3.29/1.21 Prover 7: stopped % 3.29/1.21 Prover 10: stopped % 3.29/1.21 Prover 4: Found proof (size 26) % 3.29/1.21 Prover 4: proved (578ms) % 3.29/1.21 Prover 11: stopped % 3.29/1.21 Prover 13: stopped % 3.29/1.21 Prover 8: stopped % 3.29/1.21 % 3.29/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.29/1.21 % 3.29/1.22 % SZS output start Proof for theBenchmark % 3.29/1.22 Assumptions after simplification: % 3.29/1.22 --------------------------------- % 3.29/1.22 % 3.29/1.22 (conj) % 3.29/1.23 ? [v0: int] : ($lesseq(1, $difference(a, v0)) & $product(a, a) = v0) % 3.29/1.23 % 3.29/1.23 Those formulas are unsatisfiable: % 3.29/1.23 --------------------------------- % 3.29/1.23 % 3.29/1.23 Begin of proof % 3.29/1.23 | % 3.29/1.23 | DELTA: instantiating (conj) with fresh symbol all_2_0 gives: % 3.29/1.23 | (1) $lesseq(1, $difference(a, all_2_0)) & $product(a, a) = all_2_0 % 3.29/1.23 | % 3.29/1.23 | ALPHA: (1) implies: % 3.29/1.23 | (2) $lesseq(1, $difference(a, all_2_0)) % 3.29/1.24 | (3) $product(a, a) = all_2_0 % 3.29/1.24 | % 3.29/1.24 | THEORY_AXIOM GroebnerMultiplication: % 3.29/1.24 | (4) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v0, v1))) | % 3.29/1.24 | ~ ($lesseq(v1, 458328)) | ~ ($product(v0, v0) = v1)) % 3.29/1.24 | % 3.29/1.24 | GROUND_INST: instantiating (4) with a, all_2_0, simplifying with (3) gives: % 3.29/1.24 | (5) ~ ($lesseq(1, $difference(a, all_2_0))) | ~ ($lesseq(all_2_0, % 3.29/1.24 | 458328)) % 3.29/1.24 | % 3.29/1.24 | BETA: splitting (5) gives: % 3.29/1.24 | % 3.29/1.24 | Case 1: % 3.29/1.24 | | % 3.29/1.24 | | (6) $lesseq(a, all_2_0) % 3.29/1.24 | | % 3.29/1.24 | | COMBINE_INEQS: (2), (6) imply: % 3.29/1.24 | | (7) $false % 3.29/1.24 | | % 3.29/1.24 | | CLOSE: (7) is inconsistent. % 3.29/1.24 | | % 3.29/1.24 | Case 2: % 3.29/1.24 | | % 3.29/1.24 | | (8) $lesseq(458329, all_2_0) % 3.29/1.24 | | % 3.29/1.24 | | COMBINE_INEQS: (2), (8) imply: % 3.29/1.24 | | (9) $lesseq(458330, a) % 3.29/1.24 | | % 3.29/1.24 | | THEORY_AXIOM GroebnerMultiplication: % 3.29/1.24 | | (10) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v0, v1))) % 3.29/1.24 | | | ~ ($lesseq(v1, 999999999999)) | ~ ($lesseq(458330, v0)) | ~ % 3.29/1.24 | | ($product(v0, v0) = v1)) % 3.29/1.24 | | % 3.29/1.24 | | GROUND_INST: instantiating (10) with a, all_2_0, simplifying with (3) gives: % 3.29/1.25 | | (11) ~ ($lesseq(1, $difference(a, all_2_0))) | ~ ($lesseq(all_2_0, % 3.29/1.25 | | 999999999999)) | ~ ($lesseq(458330, a)) % 3.29/1.25 | | % 3.29/1.25 | | BETA: splitting (11) gives: % 3.29/1.25 | | % 3.29/1.25 | | Case 1: % 3.29/1.25 | | | % 3.29/1.25 | | | (12) $lesseq(a, all_2_0) % 3.29/1.25 | | | % 3.29/1.25 | | | COMBINE_INEQS: (2), (12) imply: % 3.29/1.25 | | | (13) $false % 3.29/1.25 | | | % 3.29/1.25 | | | CLOSE: (13) is inconsistent. % 3.29/1.25 | | | % 3.29/1.25 | | Case 2: % 3.29/1.25 | | | % 3.29/1.25 | | | (14) ~ ($lesseq(all_2_0, 999999999999)) | ~ ($lesseq(458330, a)) % 3.29/1.25 | | | % 3.29/1.25 | | | BETA: splitting (14) gives: % 3.29/1.25 | | | % 3.29/1.25 | | | Case 1: % 3.29/1.25 | | | | % 3.29/1.25 | | | | (15) $lesseq(a, 458329) % 3.29/1.25 | | | | % 3.29/1.25 | | | | COMBINE_INEQS: (9), (15) imply: % 3.29/1.25 | | | | (16) $false % 3.29/1.25 | | | | % 3.29/1.25 | | | | CLOSE: (16) is inconsistent. % 3.29/1.25 | | | | % 3.29/1.25 | | | Case 2: % 3.29/1.25 | | | | % 3.29/1.25 | | | | (17) $lesseq(1000000000000, all_2_0) % 3.29/1.25 | | | | % 3.29/1.25 | | | | THEORY_AXIOM GroebnerMultiplication: % 3.29/1.25 | | | | (18) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(210066388901, % 3.29/1.25 | | | | $difference($product(916660, v0), v1))) | ~ % 3.29/1.25 | | | | ($lesseq(458330, v0)) | ~ ($product(v0, v0) = v1)) % 3.29/1.25 | | | | % 3.29/1.25 | | | | GROUND_INST: instantiating (18) with a, all_2_0, simplifying with (3) % 3.29/1.25 | | | | gives: % 3.29/1.25 | | | | (19) ~ ($lesseq(210066388901, $difference($product(916660, a), % 3.29/1.25 | | | | all_2_0))) | ~ ($lesseq(458330, a)) % 3.29/1.25 | | | | % 3.29/1.25 | | | | BETA: splitting (19) gives: % 3.29/1.25 | | | | % 3.29/1.25 | | | | Case 1: % 3.29/1.25 | | | | | % 3.29/1.25 | | | | | (20) $lesseq(a, 458329) % 3.29/1.25 | | | | | % 3.29/1.25 | | | | | COMBINE_INEQS: (9), (20) imply: % 3.29/1.25 | | | | | (21) $false % 3.29/1.25 | | | | | % 3.29/1.25 | | | | | CLOSE: (21) is inconsistent. % 3.29/1.25 | | | | | % 3.29/1.25 | | | | Case 2: % 3.29/1.25 | | | | | % 3.29/1.25 | | | | | (22) $lesseq(-210066388900, $difference(all_2_0, $product(916660, % 3.29/1.25 | | | | | a))) % 3.29/1.25 | | | | | % 3.29/1.25 | | | | | COMBINE_INEQS: (2), (22) imply: % 3.29/1.25 | | | | | (23) $lesseq(a, 229165) % 3.29/1.25 | | | | | % 3.29/1.25 | | | | | SIMP: (23) implies: % 3.29/1.25 | | | | | (24) $lesseq(a, 229165) % 3.29/1.25 | | | | | % 3.29/1.25 | | | | | COMBINE_INEQS: (2), (17) imply: % 3.29/1.25 | | | | | (25) $lesseq(1000000000001, a) % 3.29/1.25 | | | | | % 3.29/1.26 | | | | | COMBINE_INEQS: (24), (25) imply: % 3.29/1.26 | | | | | (26) $false % 3.29/1.26 | | | | | % 3.29/1.26 | | | | | CLOSE: (26) is inconsistent. % 3.29/1.26 | | | | | % 3.29/1.26 | | | | End of split % 3.29/1.26 | | | | % 3.29/1.26 | | | End of split % 3.29/1.26 | | | % 3.29/1.26 | | End of split % 3.29/1.26 | | % 3.29/1.26 | End of split % 3.29/1.26 | % 3.29/1.26 End of proof % 3.29/1.26 % SZS output end Proof for theBenchmark % 3.29/1.26 % 3.29/1.26 647ms %------------------------------------------------------------------------------