%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI686_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 : n012.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 17:48:48 EDT 2023 % Result : Theorem 3.43s 1.27s % Output : Proof 4.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ARI686_1 : TPTP v8.1.2. Released v6.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.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 18:43:09 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.24/1.03 Prover 1: Preprocessing ... % 2.24/1.03 Prover 3: Preprocessing ... % 2.24/1.03 Prover 0: Preprocessing ... % 2.24/1.04 Prover 6: Preprocessing ... % 2.24/1.04 Prover 4: Preprocessing ... % 2.24/1.04 Prover 5: Preprocessing ... % 2.24/1.05 Prover 2: Preprocessing ... % 2.65/1.12 Prover 0: Constructing countermodel ... % 2.65/1.12 Prover 2: Constructing countermodel ... % 2.65/1.12 Prover 3: Constructing countermodel ... % 2.65/1.12 Prover 6: Constructing countermodel ... % 2.65/1.12 Prover 4: Constructing countermodel ... % 2.65/1.12 Prover 1: Constructing countermodel ... % 2.65/1.13 Prover 5: Constructing countermodel ... % 3.43/1.27 Prover 2: proved (642ms) % 3.43/1.27 Prover 6: proved (637ms) % 3.43/1.27 % 3.43/1.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.43/1.27 % 3.43/1.27 % 3.43/1.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.43/1.27 % 3.43/1.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.43/1.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.43/1.28 Prover 0: proved (653ms) % 3.43/1.28 % 3.43/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.43/1.28 % 3.43/1.28 Prover 3: proved (653ms) % 3.43/1.28 % 3.43/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.43/1.28 % 3.43/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.43/1.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.43/1.28 Prover 5: proved (655ms) % 3.43/1.28 % 3.43/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.43/1.28 % 4.07/1.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.07/1.31 Prover 8: Preprocessing ... % 4.07/1.31 Prover 11: Preprocessing ... % 4.07/1.31 Prover 7: Preprocessing ... % 4.07/1.32 Prover 10: Preprocessing ... % 4.07/1.32 Prover 8: Constructing countermodel ... % 4.07/1.32 Prover 11: Constructing countermodel ... % 4.07/1.33 Prover 7: Constructing countermodel ... % 4.07/1.34 Prover 13: Preprocessing ... % 4.07/1.35 Prover 10: Constructing countermodel ... % 4.58/1.36 Prover 1: Found proof (size 20) % 4.58/1.36 Prover 1: proved (739ms) % 4.58/1.37 Prover 7: stopped % 4.58/1.37 Prover 10: stopped % 4.58/1.37 Prover 4: Found proof (size 20) % 4.58/1.37 Prover 4: proved (743ms) % 4.58/1.37 Prover 13: Constructing countermodel ... % 4.58/1.37 Prover 13: stopped % 4.58/1.39 Prover 11: stopped % 4.58/1.40 Prover 8: stopped % 4.58/1.40 % 4.58/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.58/1.40 % 4.58/1.40 % SZS output start Proof for theBenchmark % 4.58/1.41 Assumptions after simplification: % 4.58/1.41 --------------------------------- % 4.58/1.41 % 4.58/1.41 (conj) % 4.58/1.42 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ? % 4.58/1.42 [v5: int] : ? [v6: int] : ( ~ ($sum($sum($difference($sum($sum($product(2, % 4.58/1.42 v6), $product(2, v5)), $product(2, v4)), $product(2, v3)), % 4.58/1.42 $product(2, v1)), v0) = $product(612, a)) & $product(v5, a) = v6 & % 4.58/1.42 $product(v4, a) = v5 & $product(v3, a) = v4 & $product(v2, a) = v3 & % 4.58/1.42 $product(v1, a) = v2 & $product(v0, a) = v1 & $product(a, a) = v0) % 4.58/1.42 % 4.58/1.42 (eq1) % 4.58/1.42 $product($product(5, a), a) = $product(2, a) % 4.58/1.42 % 4.58/1.42 (eq2) % 4.58/1.42 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ? % 4.58/1.42 [v5: int] : ? [v6: int] : ($product($product(8, a), $sum(a, 9)) = v0 & % 4.58/1.42 $product($product(7, a), $difference(a, v0)) = v1 & $product($product(6, a), % 4.58/1.42 $sum(v1, a)) = v2 & $product($product(5, a), $difference(a, v2)) = v3 & % 4.58/1.42 $product($product(4, a), $sum(v3, a)) = v4 & $product($product(3, a), % 4.58/1.42 $difference(a, v4)) = v5 & $product($product(2, a), $sum(v5, a)) = v6 & % 4.58/1.42 $product(a, $difference(a, v6)) = 0) % 4.58/1.42 % 4.58/1.42 Those formulas are unsatisfiable: % 4.58/1.42 --------------------------------- % 4.58/1.42 % 4.58/1.42 Begin of proof % 4.58/1.42 | % 4.58/1.42 | DELTA: instantiating (conj) with fresh symbols all_3_0, all_3_1, all_3_2, % 4.58/1.42 | all_3_3, all_3_4, all_3_5, all_3_6 gives: % 4.58/1.42 | (1) ~ ($sum($sum($difference($sum($sum($product(2, all_3_0), $product(2, % 4.58/1.42 | all_3_1)), $product(2, all_3_2)), $product(2, all_3_3)), % 4.58/1.43 | $product(2, all_3_5)), all_3_6) = $product(612, a)) & % 4.58/1.43 | $product(all_3_1, a) = all_3_0 & $product(all_3_2, a) = all_3_1 & % 4.58/1.43 | $product(all_3_3, a) = all_3_2 & $product(all_3_4, a) = all_3_3 & % 4.58/1.43 | $product(all_3_5, a) = all_3_4 & $product(all_3_6, a) = all_3_5 & % 4.58/1.43 | $product(a, a) = all_3_6 % 4.58/1.43 | % 4.58/1.43 | ALPHA: (1) implies: % 4.58/1.43 | (2) ~ ($sum($sum($difference($sum($sum($product(2, all_3_0), $product(2, % 4.58/1.43 | all_3_1)), $product(2, all_3_2)), $product(2, all_3_3)), % 4.58/1.43 | $product(2, all_3_5)), all_3_6) = $product(612, a)) % 4.58/1.43 | (3) $product(a, a) = all_3_6 % 4.58/1.43 | (4) $product(all_3_6, a) = all_3_5 % 4.58/1.43 | (5) $product(all_3_4, a) = all_3_3 % 4.58/1.43 | (6) $product(all_3_3, a) = all_3_2 % 4.58/1.43 | (7) $product(all_3_2, a) = all_3_1 % 4.58/1.43 | (8) $product(all_3_1, a) = all_3_0 % 4.58/1.43 | % 4.58/1.43 | DELTA: instantiating (eq2) with fresh symbols all_5_0, all_5_1, all_5_2, % 4.58/1.43 | all_5_3, all_5_4, all_5_5, all_5_6 gives: % 4.58/1.43 | (9) $product($product(8, a), $sum(a, 9)) = all_5_6 & $product($product(7, % 4.58/1.43 | a), $difference(a, all_5_6)) = all_5_5 & $product($product(6, a), % 4.58/1.43 | $sum(all_5_5, a)) = all_5_4 & $product($product(5, a), $difference(a, % 4.58/1.43 | all_5_4)) = all_5_3 & $product($product(4, a), $sum(all_5_3, a)) = % 4.58/1.43 | all_5_2 & $product($product(3, a), $difference(a, all_5_2)) = all_5_1 & % 4.58/1.43 | $product($product(2, a), $sum(all_5_1, a)) = all_5_0 & $product(a, % 4.58/1.43 | $difference(a, all_5_0)) = 0 % 4.58/1.43 | % 4.58/1.43 | ALPHA: (9) implies: % 4.58/1.43 | (10) $product(a, $difference(a, all_5_0)) = 0 % 4.58/1.43 | (11) $product($product(2, a), $sum(all_5_1, a)) = all_5_0 % 4.58/1.43 | (12) $product($product(3, a), $difference(a, all_5_2)) = all_5_1 % 4.58/1.43 | (13) $product($product(4, a), $sum(all_5_3, a)) = all_5_2 % 4.58/1.43 | (14) $product($product(5, a), $difference(a, all_5_4)) = all_5_3 % 4.58/1.43 | (15) $product($product(6, a), $sum(all_5_5, a)) = all_5_4 % 4.58/1.43 | (16) $product($product(7, a), $difference(a, all_5_6)) = all_5_5 % 4.58/1.43 | (17) $product($product(8, a), $sum(a, 9)) = all_5_6 % 4.58/1.43 | % 4.58/1.43 | THEORY_AXIOM GroebnerMultiplication: % 4.58/1.44 | (18) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 4.58/1.44 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : (v0 = 0 | ~ % 4.58/1.44 | ($product($product(8, v0), $sum(v0, 9)) = v1) | ~ % 4.58/1.44 | ($product($product(7, v0), $difference(v0, v1)) = v2) | ~ % 4.58/1.44 | ($product($product(6, v0), $sum(v2, v0)) = v3) | ~ % 4.58/1.44 | ($product($product(5, v0), $difference(v0, v3)) = v4) | ~ % 4.58/1.44 | ($product($product(5, v0), v0) = $product(2, v0)) | ~ % 4.58/1.44 | ($product($product(4, v0), $sum(v4, v0)) = v5) | ~ % 4.58/1.44 | ($product($product(3, v0), $difference(v0, v5)) = v6) | ~ % 4.58/1.44 | ($product($product(2, v0), $sum(v6, v0)) = v7) | ~ ($product(v0, % 4.58/1.44 | $difference(v0, v7)) = 0)) % 4.58/1.44 | % 4.58/1.44 | GROUND_INST: instantiating (18) with a, all_5_6, all_5_5, all_5_4, all_5_3, % 4.58/1.44 | all_5_2, all_5_1, all_5_0, simplifying with (10), (11), (12), % 4.58/1.44 | (13), (14), (15), (16), (17), (eq1) gives: % 4.58/1.44 | (19) a = 0 % 4.58/1.44 | % 4.58/1.44 | THEORY_AXIOM GroebnerMultiplication: % 4.58/1.44 | (20) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 4.58/1.44 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : % 4.58/1.44 | (v1 = 0 | ~ ($product($product(8, v0), $sum(v0, 9)) = v2) | ~ % 4.58/1.44 | ($product($product(7, v0), $difference(v0, v2)) = v3) | ~ % 4.58/1.44 | ($product($product(6, v0), $sum(v3, v0)) = v4) | ~ % 4.58/1.44 | ($product($product(5, v0), $difference(v0, v4)) = v5) | ~ % 4.58/1.44 | ($product($product(5, v0), v0) = $product(2, v0)) | ~ % 4.58/1.44 | ($product($product(4, v0), $sum(v5, v0)) = v6) | ~ % 4.58/1.44 | ($product($product(3, v0), $difference(v0, v6)) = v7) | ~ % 4.58/1.44 | ($product($product(2, v0), $sum(v7, v0)) = v8) | ~ ($product(v0, % 4.58/1.44 | $difference(v0, v8)) = 0) | ~ ($product(v0, v0) = v1)) % 4.58/1.44 | % 4.58/1.44 | GROUND_INST: instantiating (20) with a, all_3_6, all_5_6, all_5_5, all_5_4, % 4.58/1.44 | all_5_3, all_5_2, all_5_1, all_5_0, simplifying with (3), (10), % 4.58/1.44 | (11), (12), (13), (14), (15), (16), (17), (eq1) gives: % 4.58/1.44 | (21) all_3_6 = 0 % 4.58/1.44 | % 4.58/1.44 | THEORY_AXIOM GroebnerMultiplication: % 4.58/1.45 | (22) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 4.58/1.45 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : % 4.58/1.45 | ! [v9: int] : (v2 = 0 | ~ ($product(v1, v0) = v2) | ~ % 4.58/1.45 | ($product($product(8, v0), $sum(v0, 9)) = v3) | ~ % 4.58/1.45 | ($product($product(7, v0), $difference(v0, v3)) = v4) | ~ % 4.58/1.45 | ($product($product(6, v0), $sum(v4, v0)) = v5) | ~ % 4.58/1.45 | ($product($product(5, v0), $difference(v0, v5)) = v6) | ~ % 4.58/1.45 | ($product($product(5, v0), v0) = $product(2, v0)) | ~ % 4.58/1.45 | ($product($product(4, v0), $sum(v6, v0)) = v7) | ~ % 4.58/1.45 | ($product($product(3, v0), $difference(v0, v7)) = v8) | ~ % 4.58/1.45 | ($product($product(2, v0), $sum(v8, v0)) = v9) | ~ ($product(v0, % 4.58/1.45 | $difference(v0, v9)) = 0)) % 4.58/1.45 | % 4.58/1.45 | GROUND_INST: instantiating (22) with a, all_3_6, all_3_5, all_5_6, all_5_5, % 4.58/1.45 | all_5_4, all_5_3, all_5_2, all_5_1, all_5_0, simplifying with % 4.58/1.45 | (4), (10), (11), (12), (13), (14), (15), (16), (17), (eq1) gives: % 4.58/1.45 | (23) all_3_5 = 0 % 4.58/1.45 | % 4.58/1.45 | GROUND_INST: instantiating (22) with a, all_3_4, all_3_3, all_5_6, all_5_5, % 4.58/1.45 | all_5_4, all_5_3, all_5_2, all_5_1, all_5_0, simplifying with % 4.58/1.45 | (5), (10), (11), (12), (13), (14), (15), (16), (17), (eq1) gives: % 4.58/1.45 | (24) all_3_3 = 0 % 4.58/1.45 | % 4.58/1.45 | GROUND_INST: instantiating (22) with a, all_3_3, all_3_2, all_5_6, all_5_5, % 4.58/1.45 | all_5_4, all_5_3, all_5_2, all_5_1, all_5_0, simplifying with % 4.58/1.45 | (6), (10), (11), (12), (13), (14), (15), (16), (17), (eq1) gives: % 4.58/1.45 | (25) all_3_2 = 0 % 4.58/1.45 | % 4.58/1.45 | GROUND_INST: instantiating (22) with a, all_3_2, all_3_1, all_5_6, all_5_5, % 4.58/1.45 | all_5_4, all_5_3, all_5_2, all_5_1, all_5_0, simplifying with % 4.58/1.45 | (7), (10), (11), (12), (13), (14), (15), (16), (17), (eq1) gives: % 4.58/1.45 | (26) all_3_1 = 0 % 4.58/1.45 | % 4.58/1.46 | GROUND_INST: instantiating (22) with a, all_3_1, all_3_0, all_5_6, all_5_5, % 4.58/1.46 | all_5_4, all_5_3, all_5_2, all_5_1, all_5_0, simplifying with % 4.58/1.46 | (8), (10), (11), (12), (13), (14), (15), (16), (17), (eq1) gives: % 4.58/1.46 | (27) all_3_0 = 0 % 4.58/1.46 | % 4.58/1.46 | REDUCE: (2), (19), (21), (23), (24), (25), (26), (27) imply: % 4.58/1.46 | (28) $false % 4.58/1.46 | % 4.58/1.46 | CLOSE: (28) is inconsistent. % 4.58/1.46 | % 4.58/1.46 End of proof % 4.58/1.46 % SZS output end Proof for theBenchmark % 4.58/1.46 % 4.58/1.46 851ms %------------------------------------------------------------------------------