%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI679_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 : n018.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 3.84s 1.43s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : ARI679_1 : TPTP v8.1.2. Released v6.3.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n018.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 18:08:03 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.40/1.15 Prover 0: Preprocessing ... % 2.40/1.15 Prover 3: Preprocessing ... % 2.40/1.15 Prover 4: Preprocessing ... % 2.40/1.15 Prover 2: Preprocessing ... % 2.40/1.15 Prover 5: Preprocessing ... % 2.40/1.15 Prover 6: Preprocessing ... % 2.40/1.15 Prover 1: Preprocessing ... % 2.48/1.22 Prover 5: Constructing countermodel ... % 2.48/1.23 Prover 0: Constructing countermodel ... % 2.48/1.23 Prover 3: Constructing countermodel ... % 2.48/1.23 Prover 4: Constructing countermodel ... % 2.48/1.23 Prover 6: Constructing countermodel ... % 2.48/1.23 Prover 1: Constructing countermodel ... % 2.48/1.23 Prover 2: Constructing countermodel ... % 3.84/1.43 Prover 5: proved (787ms) % 3.84/1.43 Prover 6: proved (786ms) % 3.84/1.43 Prover 0: proved (791ms) % 3.84/1.43 % 3.84/1.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.84/1.43 % 3.84/1.43 Prover 3: proved (790ms) % 3.84/1.43 % 3.84/1.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.84/1.43 % 3.84/1.43 Prover 2: proved (790ms) % 3.84/1.44 % 3.84/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.84/1.44 % 3.84/1.44 % 3.84/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.84/1.44 % 3.84/1.44 % 3.84/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.84/1.44 % 3.84/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.84/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.84/1.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.84/1.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.84/1.45 Prover 10: Preprocessing ... % 3.84/1.45 Prover 7: Preprocessing ... % 3.84/1.45 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.84/1.45 Prover 11: Preprocessing ... % 3.84/1.45 Prover 8: Preprocessing ... % 3.84/1.46 Prover 10: Constructing countermodel ... % 3.84/1.46 Prover 11: Constructing countermodel ... % 3.84/1.46 Prover 8: Constructing countermodel ... % 3.84/1.46 Prover 7: Constructing countermodel ... % 3.84/1.47 Prover 13: Preprocessing ... % 3.84/1.47 Prover 4: Found proof (size 22) % 3.84/1.47 Prover 4: proved (829ms) % 3.84/1.47 Prover 1: Found proof (size 22) % 3.84/1.47 Prover 1: proved (833ms) % 3.84/1.47 Prover 7: stopped % 3.84/1.47 Prover 11: stopped % 3.84/1.47 Prover 10: stopped % 3.84/1.47 Prover 8: stopped % 4.39/1.48 Prover 13: Constructing countermodel ... % 4.39/1.48 Prover 13: stopped % 4.39/1.48 % 4.39/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.39/1.48 % 4.39/1.49 % SZS output start Proof for theBenchmark % 4.39/1.49 Assumptions after simplification: % 4.39/1.49 --------------------------------- % 4.39/1.49 % 4.39/1.49 (conj) % 4.39/1.49 $lesseq(3, d) % 4.39/1.49 % 4.39/1.49 (conj_001) % 4.39/1.49 $lesseq(2, c) % 4.39/1.49 % 4.39/1.49 (conj_002) % 4.47/1.50 ? [v0: int] : ? [v1: int] : ($product(c, $sum(d, -3)) = v1 & $product(c, d) % 4.47/1.50 = v0 & (($lesseq(7, $difference($product(2, d), v1)) & $lesseq(6, v0)) | % 4.47/1.50 ($lesseq(-6, $difference(v1, $product(2, d))) & $lesseq(v0, 5)))) % 4.47/1.50 % 4.47/1.50 Those formulas are unsatisfiable: % 4.47/1.50 --------------------------------- % 4.47/1.50 % 4.47/1.50 Begin of proof % 4.47/1.50 | % 4.47/1.50 | DELTA: instantiating (conj_002) with fresh symbols all_3_0, all_3_1 gives: % 4.47/1.50 | (1) $product(c, $sum(d, -3)) = all_3_0 & $product(c, d) = all_3_1 & % 4.47/1.50 | (($lesseq(7, $difference($product(2, d), all_3_0)) & $lesseq(6, % 4.47/1.50 | all_3_1)) | ($lesseq(-6, $difference(all_3_0, $product(2, d))) & % 4.47/1.50 | $lesseq(all_3_1, 5))) % 4.47/1.50 | % 4.47/1.50 | ALPHA: (1) implies: % 4.47/1.50 | (2) $product(c, d) = all_3_1 % 4.47/1.50 | (3) $product(c, $sum(d, -3)) = all_3_0 % 4.47/1.51 | (4) ($lesseq(7, $difference($product(2, d), all_3_0)) & $lesseq(6, % 4.47/1.51 | all_3_1)) | ($lesseq(-6, $difference(all_3_0, $product(2, d))) & % 4.47/1.51 | $lesseq(all_3_1, 5)) % 4.47/1.51 | % 4.47/1.51 | THEORY_AXIOM GroebnerMultiplication: % 4.47/1.51 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : % 4.47/1.51 | ($sum($difference(v3, v2), $product(3, v1)) = 0 | ~ ($product(v1, % 4.47/1.51 | $sum(v0, -3)) = v3) | ~ ($product(v1, v0) = v2)) % 4.47/1.51 | % 4.47/1.51 | GROUND_INST: instantiating (5) with d, c, all_3_1, all_3_0, simplifying with % 4.47/1.51 | (2), (3) gives: % 4.47/1.51 | (6) $sum($difference(all_3_0, all_3_1), $product(3, c)) = 0 % 4.47/1.51 | % 4.47/1.51 | THEORY_AXIOM GroebnerMultiplication: % 4.47/1.51 | (7) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(7, % 4.47/1.51 | $sum($difference($product(3, v1), v2), $product(2, v0)))) | ~ % 4.47/1.51 | ($lesseq(2, v1)) | ~ ($lesseq(3, v0)) | ~ ($product(v1, v0) = v2)) % 4.47/1.51 | % 4.47/1.51 | GROUND_INST: instantiating (7) with d, c, all_3_1, simplifying with (2) gives: % 4.47/1.51 | (8) ~ ($lesseq(7, $sum($difference($product(3, c), all_3_1), $product(2, % 4.47/1.51 | d)))) | ~ ($lesseq(2, c)) | ~ ($lesseq(3, d)) % 4.47/1.51 | % 4.47/1.51 | BETA: splitting (8) gives: % 4.47/1.51 | % 4.47/1.51 | Case 1: % 4.47/1.51 | | % 4.47/1.51 | | (9) $lesseq(c, 1) % 4.47/1.51 | | % 4.47/1.51 | | COMBINE_INEQS: (9), (conj_001) imply: % 4.47/1.51 | | (10) $false % 4.47/1.51 | | % 4.47/1.51 | | CLOSE: (10) is inconsistent. % 4.47/1.51 | | % 4.47/1.51 | Case 2: % 4.47/1.51 | | % 4.47/1.51 | | (11) ~ ($lesseq(7, $sum($difference($product(3, c), all_3_1), % 4.47/1.51 | | $product(2, d)))) | ~ ($lesseq(3, d)) % 4.47/1.51 | | % 4.47/1.51 | | BETA: splitting (11) gives: % 4.47/1.51 | | % 4.47/1.51 | | Case 1: % 4.47/1.51 | | | % 4.47/1.51 | | | (12) $lesseq(d, 2) % 4.47/1.51 | | | % 4.47/1.51 | | | COMBINE_INEQS: (12), (conj) imply: % 4.47/1.51 | | | (13) $false % 4.47/1.51 | | | % 4.54/1.51 | | | CLOSE: (13) is inconsistent. % 4.54/1.51 | | | % 4.54/1.51 | | Case 2: % 4.54/1.51 | | | % 4.54/1.51 | | | (14) $lesseq(-6, $difference($difference(all_3_1, $product(3, c)), % 4.54/1.51 | | | $product(2, d))) % 4.54/1.51 | | | % 4.54/1.51 | | | COMBINE_INEQS: (14), (conj_001) imply: % 4.54/1.51 | | | (15) $lesseq(0, $difference(all_3_1, $product(2, d))) % 4.54/1.51 | | | % 4.54/1.52 | | | COMBINE_INEQS: (15), (conj) imply: % 4.54/1.52 | | | (16) $lesseq(6, all_3_1) % 4.54/1.52 | | | % 4.54/1.52 | | | BETA: splitting (4) gives: % 4.54/1.52 | | | % 4.54/1.52 | | | Case 1: % 4.54/1.52 | | | | % 4.54/1.52 | | | | (17) $lesseq(7, $difference($product(2, d), all_3_0)) & $lesseq(6, % 4.54/1.52 | | | | all_3_1) % 4.54/1.52 | | | | % 4.54/1.52 | | | | ALPHA: (17) implies: % 4.54/1.52 | | | | (18) $lesseq(7, $difference($product(2, d), all_3_0)) % 4.54/1.52 | | | | % 4.54/1.52 | | | | REDUCE: (6), (18) imply: % 4.54/1.52 | | | | (19) $lesseq(7, $sum($difference($product(3, c), all_3_1), % 4.54/1.52 | | | | $product(2, d))) % 4.54/1.52 | | | | % 4.54/1.52 | | | | COMBINE_INEQS: (14), (19) imply: % 4.54/1.52 | | | | (20) $false % 4.54/1.52 | | | | % 4.54/1.52 | | | | CLOSE: (20) is inconsistent. % 4.54/1.52 | | | | % 4.54/1.52 | | | Case 2: % 4.54/1.52 | | | | % 4.54/1.52 | | | | (21) $lesseq(-6, $difference(all_3_0, $product(2, d))) & % 4.54/1.52 | | | | $lesseq(all_3_1, 5) % 4.54/1.52 | | | | % 4.54/1.52 | | | | ALPHA: (21) implies: % 4.54/1.52 | | | | (22) $lesseq(all_3_1, 5) % 4.54/1.52 | | | | % 4.54/1.52 | | | | COMBINE_INEQS: (16), (22) imply: % 4.54/1.52 | | | | (23) $false % 4.54/1.52 | | | | % 4.54/1.52 | | | | CLOSE: (23) is inconsistent. % 4.54/1.52 | | | | % 4.54/1.52 | | | End of split % 4.54/1.52 | | | % 4.54/1.52 | | End of split % 4.54/1.52 | | % 4.54/1.52 | End of split % 4.54/1.52 | % 4.54/1.52 End of proof % 4.54/1.52 % SZS output end Proof for theBenchmark % 4.54/1.52 % 4.54/1.52 897ms %------------------------------------------------------------------------------