%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI675_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 : n016.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 17:48:46 EDT 2023 % Result : Theorem 4.10s 1.31s % Output : Proof 4.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI675_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 : n016.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 18:53:01 EDT 2023 % 0.13/0.34 % CPUTime : % 0.63/0.62 ________ _____ % 0.63/0.62 ___ __ \_________(_)________________________________ % 0.63/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.63/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.63/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.63/0.62 % 0.63/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.63/0.62 (2023-06-19) % 0.63/0.62 % 0.63/0.62 (c) Philipp Rümmer, 2009-2023 % 0.63/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.63/0.62 Amanda Stjerna. % 0.63/0.62 Free software under BSD-3-Clause. % 0.63/0.62 % 0.63/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.63/0.62 % 0.63/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.64 Running up to 7 provers in parallel. % 0.67/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.87/1.00 Prover 2: Preprocessing ... % 1.87/1.00 Prover 4: Preprocessing ... % 1.87/1.00 Prover 5: Preprocessing ... % 1.87/1.00 Prover 0: Preprocessing ... % 1.87/1.00 Prover 6: Preprocessing ... % 1.87/1.00 Prover 3: Preprocessing ... % 1.87/1.00 Prover 1: Preprocessing ... % 2.31/1.05 Prover 5: Constructing countermodel ... % 2.31/1.05 Prover 3: Constructing countermodel ... % 2.31/1.05 Prover 6: Constructing countermodel ... % 2.31/1.05 Prover 1: Constructing countermodel ... % 2.31/1.05 Prover 0: Constructing countermodel ... % 2.31/1.05 Prover 2: Constructing countermodel ... % 2.31/1.05 Prover 4: Constructing countermodel ... % 4.10/1.31 Prover 5: proved (655ms) % 4.10/1.31 % 4.10/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.10/1.31 % 4.10/1.31 Prover 3: stopped % 4.10/1.32 Prover 0: stopped % 4.10/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.10/1.32 Prover 6: stopped % 4.10/1.32 Prover 2: stopped % 4.10/1.32 Prover 7: Preprocessing ... % 4.10/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.10/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.10/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.10/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.10/1.33 Prover 8: Preprocessing ... % 4.10/1.33 Prover 11: Preprocessing ... % 4.10/1.33 Prover 7: Constructing countermodel ... % 4.10/1.34 Prover 10: Preprocessing ... % 4.10/1.34 Prover 13: Preprocessing ... % 4.10/1.34 Prover 8: Constructing countermodel ... % 4.10/1.34 Prover 11: Constructing countermodel ... % 4.10/1.34 Prover 10: Constructing countermodel ... % 4.10/1.35 Prover 13: Constructing countermodel ... % 4.10/1.36 Prover 4: Found proof (size 53) % 4.10/1.36 Prover 4: proved (711ms) % 4.10/1.36 Prover 11: stopped % 4.10/1.36 Prover 8: stopped % 4.10/1.36 Prover 10: stopped % 4.10/1.37 Prover 13: stopped % 4.10/1.37 Prover 7: stopped % 4.10/1.37 Prover 1: Found proof (size 53) % 4.10/1.37 Prover 1: proved (719ms) % 4.10/1.37 % 4.10/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.10/1.37 % 4.10/1.38 % SZS output start Proof for theBenchmark % 4.10/1.38 Assumptions after simplification: % 4.10/1.38 --------------------------------- % 4.10/1.38 % 4.10/1.38 (conj) % 4.57/1.39 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($lesseq(11, % 4.57/1.39 $difference($product(-1, v2), v0)) & $product(v1, a) = v2 & $product(v0, % 4.57/1.39 a) = v1 & $product(a, a) = v0) % 4.57/1.39 % 4.57/1.39 Those formulas are unsatisfiable: % 4.57/1.39 --------------------------------- % 4.57/1.39 % 4.57/1.39 Begin of proof % 4.57/1.39 | % 4.57/1.39 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1, all_2_2 % 4.57/1.39 | gives: % 4.57/1.40 | (1) $lesseq(11, $difference($product(-1, all_2_0), all_2_2)) & % 4.57/1.40 | $product(all_2_1, a) = all_2_0 & $product(all_2_2, a) = all_2_1 & % 4.57/1.40 | $product(a, a) = all_2_2 % 4.57/1.40 | % 4.57/1.40 | ALPHA: (1) implies: % 4.57/1.40 | (2) $lesseq(11, $difference($product(-1, all_2_0), all_2_2)) % 4.57/1.40 | (3) $product(a, a) = all_2_2 % 4.57/1.40 | (4) $product(all_2_2, a) = all_2_1 % 4.57/1.40 | (5) $product(all_2_1, a) = all_2_0 % 4.57/1.40 | % 4.57/1.40 | THEORY_AXIOM GroebnerMultiplication: % 4.57/1.40 | (6) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ ($product(v0, % 4.57/1.40 | v0) = v1)) % 4.57/1.40 | % 4.57/1.40 | GROUND_INST: instantiating (6) with a, all_2_2, simplifying with (3) gives: % 4.57/1.40 | (7) $lesseq(0, all_2_2) % 4.57/1.40 | % 4.57/1.40 | CUT: with $lesseq(all_2_1, 0): % 4.57/1.40 | % 4.57/1.40 | Case 1: % 4.57/1.40 | | % 4.57/1.40 | | (8) $lesseq(all_2_1, 0) % 4.57/1.40 | | % 4.57/1.40 | | COMBINE_INEQS: (2), (7) imply: % 4.57/1.40 | | (9) $lesseq(all_2_0, -11) % 4.57/1.40 | | % 4.57/1.40 | | REF_CLOSE: (2), (4), (5), (7), (8), (9) are inconsistent by sub-proof #1. % 4.57/1.40 | | % 4.57/1.40 | Case 2: % 4.57/1.40 | | % 4.57/1.40 | | (10) $lesseq(1, all_2_1) % 4.57/1.40 | | % 4.57/1.40 | | COMBINE_INEQS: (2), (7) imply: % 4.57/1.41 | | (11) $lesseq(all_2_0, -11) % 4.57/1.41 | | % 4.57/1.41 | | THEORY_AXIOM GroebnerMultiplication: % 4.57/1.41 | | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ( ~ % 4.57/1.41 | | ($lesseq(v3, -11)) | ~ ($lesseq(1, v2)) | ~ ($lesseq(0, v1)) | % 4.57/1.41 | | ~ ($product(v2, v0) = v3) | ~ ($product(v1, v0) = v2)) % 4.57/1.41 | | % 4.57/1.41 | | GROUND_INST: instantiating (12) with a, all_2_2, all_2_1, all_2_0, % 4.57/1.41 | | simplifying with (4), (5) gives: % 4.57/1.41 | | (13) ~ ($lesseq(all_2_0, -11)) | ~ ($lesseq(1, all_2_1)) | ~ % 4.57/1.41 | | ($lesseq(0, all_2_2)) % 4.57/1.41 | | % 4.57/1.41 | | BETA: splitting (13) gives: % 4.57/1.41 | | % 4.57/1.41 | | Case 1: % 4.57/1.41 | | | % 4.57/1.41 | | | (14) ~ ($lesseq(all_2_0, -11)) | ~ ($lesseq(1, all_2_1)) % 4.57/1.41 | | | % 4.57/1.41 | | | BETA: splitting (14) gives: % 4.57/1.41 | | | % 4.57/1.41 | | | Case 1: % 4.57/1.41 | | | | % 4.57/1.41 | | | | (15) $lesseq(-10, all_2_0) % 4.57/1.41 | | | | % 4.57/1.41 | | | | COMBINE_INEQS: (11), (15) imply: % 4.57/1.41 | | | | (16) $false % 4.57/1.41 | | | | % 4.57/1.41 | | | | CLOSE: (16) is inconsistent. % 4.57/1.41 | | | | % 4.57/1.41 | | | Case 2: % 4.57/1.41 | | | | % 4.57/1.41 | | | | (17) $lesseq(all_2_1, 0) % 4.57/1.41 | | | | % 4.57/1.41 | | | | COMBINE_INEQS: (10), (17) imply: % 4.57/1.41 | | | | (18) $false % 4.57/1.41 | | | | % 4.57/1.41 | | | | CLOSE: (18) is inconsistent. % 4.57/1.41 | | | | % 4.57/1.41 | | | End of split % 4.57/1.41 | | | % 4.57/1.41 | | Case 2: % 4.57/1.41 | | | % 4.57/1.41 | | | (19) ~ ($lesseq(1, all_2_1)) | ~ ($lesseq(0, all_2_2)) % 4.57/1.41 | | | % 4.57/1.41 | | | BETA: splitting (19) gives: % 4.57/1.41 | | | % 4.57/1.41 | | | Case 1: % 4.57/1.41 | | | | % 4.57/1.41 | | | | (20) $lesseq(all_2_2, -1) % 4.57/1.41 | | | | % 4.57/1.41 | | | | COMBINE_INEQS: (7), (20) imply: % 4.57/1.41 | | | | (21) $false % 4.57/1.41 | | | | % 4.57/1.41 | | | | CLOSE: (21) is inconsistent. % 4.57/1.41 | | | | % 4.57/1.41 | | | Case 2: % 4.57/1.41 | | | | % 4.57/1.41 | | | | (22) $lesseq(all_2_1, 0) % 4.57/1.41 | | | | % 4.57/1.41 | | | | REF_CLOSE: (2), (4), (5), (7), (11), (22) are inconsistent by sub-proof % 4.57/1.41 | | | | #1. % 4.57/1.41 | | | | % 4.57/1.41 | | | End of split % 4.57/1.41 | | | % 4.57/1.41 | | End of split % 4.57/1.41 | | % 4.57/1.41 | End of split % 4.57/1.41 | % 4.57/1.41 End of proof % 4.57/1.42 % 4.57/1.42 Sub-proof #1 shows that the following formulas are inconsistent: % 4.57/1.42 ---------------------------------------------------------------- % 4.57/1.42 (1) $lesseq(11, $difference($product(-1, all_2_0), all_2_2)) % 4.57/1.42 (2) $lesseq(all_2_1, 0) % 4.57/1.42 (3) $lesseq(0, all_2_2) % 4.57/1.42 (4) $product(all_2_2, a) = all_2_1 % 4.57/1.42 (5) $lesseq(all_2_0, -11) % 4.57/1.42 (6) $product(all_2_1, a) = all_2_0 % 4.57/1.42 % 4.57/1.42 Begin of proof % 4.57/1.42 | % 4.57/1.42 | THEORY_AXIOM GroebnerMultiplication: % 4.57/1.42 | (7) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v2 = 0 | % 4.57/1.42 | ~ ($lesseq(v3, -11)) | ~ ($lesseq(v2, 0) | ~ ($lesseq(0, v1)) | ~ % 4.57/1.42 | ($product(v2, v0) = v3) | ~ ($product(v1, v0) = v2)) % 4.57/1.42 | % 4.57/1.42 | GROUND_INST: instantiating (7) with a, all_2_2, all_2_1, all_2_0, simplifying % 4.57/1.42 | with (4), (6) gives: % 4.57/1.42 | (8) all_2_1 = 0 | ~ ($lesseq(all_2_0, -11)) | ~ ($lesseq(all_2_1, 0) | ~ % 4.57/1.42 | ($lesseq(0, all_2_2)) % 4.57/1.42 | % 4.57/1.42 | BETA: splitting (8) gives: % 4.57/1.42 | % 4.57/1.42 | Case 1: % 4.57/1.42 | | % 4.57/1.42 | | (9) ~ ($lesseq(all_2_0, -11)) | ~ ($lesseq(all_2_1, 0) % 4.57/1.42 | | % 4.57/1.42 | | BETA: splitting (9) gives: % 4.57/1.42 | | % 4.57/1.42 | | Case 1: % 4.57/1.42 | | | % 4.57/1.42 | | | (10) $lesseq(-10, all_2_0) % 4.57/1.42 | | | % 4.57/1.42 | | | COMBINE_INEQS: (5), (10) imply: % 4.57/1.42 | | | (11) $false % 4.57/1.42 | | | % 4.57/1.42 | | | CLOSE: (11) is inconsistent. % 4.57/1.42 | | | % 4.57/1.42 | | Case 2: % 4.57/1.42 | | | % 4.57/1.42 | | | (12) $lesseq(1, all_2_1) % 4.57/1.42 | | | % 4.57/1.42 | | | COMBINE_INEQS: (2), (12) imply: % 4.57/1.42 | | | (13) $false % 4.57/1.42 | | | % 4.57/1.42 | | | CLOSE: (13) is inconsistent. % 4.57/1.42 | | | % 4.57/1.42 | | End of split % 4.57/1.42 | | % 4.57/1.42 | Case 2: % 4.57/1.42 | | % 4.57/1.42 | | (14) all_2_1 = 0 | ~ ($lesseq(0, all_2_2)) % 4.57/1.42 | | % 4.57/1.42 | | BETA: splitting (14) gives: % 4.57/1.42 | | % 4.57/1.42 | | Case 1: % 4.57/1.42 | | | % 4.57/1.42 | | | (15) $lesseq(all_2_2, -1) % 4.57/1.42 | | | % 4.57/1.42 | | | COMBINE_INEQS: (3), (15) imply: % 4.57/1.42 | | | (16) $false % 4.57/1.42 | | | % 4.57/1.42 | | | CLOSE: (16) is inconsistent. % 4.57/1.42 | | | % 4.57/1.42 | | Case 2: % 4.57/1.42 | | | % 4.57/1.42 | | | (17) all_2_1 = 0 % 4.57/1.42 | | | % 4.57/1.42 | | | REDUCE: (6), (17) imply: % 4.57/1.42 | | | (18) $product(0, a) = all_2_0 % 4.57/1.42 | | | % 4.57/1.42 | | | THEORY_AXIOM GroebnerMultiplication: % 4.57/1.42 | | | (19) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($product(0, v0) = v1)) % 4.57/1.42 | | | % 4.57/1.42 | | | GROUND_INST: instantiating (19) with a, all_2_0, simplifying with (18) % 4.57/1.42 | | | gives: % 4.57/1.42 | | | (20) all_2_0 = 0 % 4.57/1.42 | | | % 4.57/1.42 | | | REDUCE: (5), (20) imply: % 4.57/1.42 | | | (21) $false % 4.57/1.42 | | | % 4.57/1.42 | | | CLOSE: (21) is inconsistent. % 4.57/1.42 | | | % 4.57/1.42 | | End of split % 4.57/1.42 | | % 4.57/1.42 | End of split % 4.57/1.42 | % 4.57/1.42 End of proof % 4.57/1.42 % SZS output end Proof for theBenchmark % 4.57/1.43 % 4.57/1.43 802ms %------------------------------------------------------------------------------