%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI669_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 : n014.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 3.56s 1.30s % Output : Proof 4.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI669_1 : TPTP v8.1.2. Released v6.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n014.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 18:28:30 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.92/1.01 Prover 1: Preprocessing ... % 1.92/1.01 Prover 6: Preprocessing ... % 1.92/1.01 Prover 0: Preprocessing ... % 1.92/1.01 Prover 5: Preprocessing ... % 1.92/1.01 Prover 4: Preprocessing ... % 1.92/1.01 Prover 2: Preprocessing ... % 1.92/1.01 Prover 3: Preprocessing ... % 2.41/1.07 Prover 5: Constructing countermodel ... % 2.41/1.07 Prover 6: Constructing countermodel ... % 2.41/1.07 Prover 4: Constructing countermodel ... % 2.41/1.07 Prover 2: Constructing countermodel ... % 2.41/1.07 Prover 0: Constructing countermodel ... % 2.41/1.07 Prover 3: Constructing countermodel ... % 2.41/1.07 Prover 1: Constructing countermodel ... % 3.56/1.30 Prover 3: proved (645ms) % 3.56/1.30 Prover 2: proved (656ms) % 3.56/1.30 % 3.56/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.56/1.30 % 3.56/1.31 % 3.56/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.56/1.31 % 3.56/1.31 Prover 0: stopped % 3.56/1.31 Prover 5: stopped % 3.56/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.56/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.56/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.56/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.56/1.31 Prover 6: stopped % 3.56/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.56/1.32 Prover 8: Preprocessing ... % 3.56/1.32 Prover 10: Preprocessing ... % 3.56/1.32 Prover 8: Constructing countermodel ... % 3.56/1.32 Prover 7: Preprocessing ... % 3.56/1.32 Prover 13: Preprocessing ... % 3.56/1.33 Prover 10: Constructing countermodel ... % 4.22/1.33 Prover 7: Constructing countermodel ... % 4.22/1.33 Prover 13: Constructing countermodel ... % 4.22/1.34 Prover 11: Preprocessing ... % 4.22/1.36 Prover 11: Constructing countermodel ... % 4.22/1.39 Prover 4: Found proof (size 34) % 4.22/1.39 Prover 4: proved (726ms) % 4.22/1.39 Prover 13: stopped % 4.22/1.39 Prover 11: stopped % 4.22/1.39 Prover 10: stopped % 4.22/1.39 Prover 8: stopped % 4.22/1.39 Prover 1: Found proof (size 34) % 4.22/1.39 Prover 1: proved (743ms) % 4.22/1.39 Prover 7: stopped % 4.22/1.39 % 4.22/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.22/1.39 % 4.22/1.39 % SZS output start Proof for theBenchmark % 4.22/1.40 Assumptions after simplification: % 4.22/1.40 --------------------------------- % 4.22/1.40 % 4.22/1.40 (conj) % 4.22/1.41 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($product(v1, c) = v2 & % 4.22/1.41 $product(v0, b) = v1 & $product(a, b) = v0 & ((v2 = 0 & ~ (c = 0) & ~ (b = % 4.22/1.41 0) & ~ (a = 0)) | ( ~ (v2 = 0) & (c = 0 | b = 0 | a = 0)))) % 4.22/1.41 % 4.22/1.41 Those formulas are unsatisfiable: % 4.22/1.41 --------------------------------- % 4.22/1.41 % 4.22/1.41 Begin of proof % 4.22/1.41 | % 4.22/1.41 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1, all_2_2 % 4.22/1.41 | gives: % 4.22/1.41 | (1) $product(all_2_1, c) = all_2_0 & $product(all_2_2, b) = all_2_1 & % 4.22/1.41 | $product(a, b) = all_2_2 & ((all_2_0 = 0 & ~ (c = 0) & ~ (b = 0) & ~ % 4.22/1.41 | (a = 0)) | ( ~ (all_2_0 = 0) & (c = 0 | b = 0 | a = 0))) % 4.22/1.41 | % 4.22/1.41 | ALPHA: (1) implies: % 4.22/1.41 | (2) $product(a, b) = all_2_2 % 4.22/1.41 | (3) $product(all_2_2, b) = all_2_1 % 4.22/1.41 | (4) $product(all_2_1, c) = all_2_0 % 4.22/1.41 | (5) (all_2_0 = 0 & ~ (c = 0) & ~ (b = 0) & ~ (a = 0)) | ( ~ (all_2_0 = % 4.22/1.41 | 0) & (c = 0 | b = 0 | a = 0)) % 4.22/1.41 | % 4.22/1.42 | BETA: splitting (5) gives: % 4.22/1.42 | % 4.22/1.42 | Case 1: % 4.22/1.42 | | % 4.22/1.42 | | (6) all_2_0 = 0 & ~ (c = 0) & ~ (b = 0) & ~ (a = 0) % 4.22/1.42 | | % 4.22/1.42 | | ALPHA: (6) implies: % 4.22/1.42 | | (7) all_2_0 = 0 % 4.22/1.42 | | (8) ~ (a = 0) % 4.22/1.42 | | (9) ~ (b = 0) % 4.22/1.42 | | (10) ~ (c = 0) % 4.22/1.42 | | % 4.22/1.42 | | REDUCE: (4), (7) imply: % 4.22/1.42 | | (11) $product(all_2_1, c) = 0 % 4.22/1.42 | | % 4.22/1.42 | | THEORY_AXIOM GroebnerMultiplication: % 4.22/1.42 | | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 4.22/1.42 | | int] : (v2 = 0 | v1 = 0 | v0 = 0 | ~ ($product(v4, v2) = 0) | ~ % 4.22/1.42 | | ($product(v3, v1) = v4) | ~ ($product(v0, v1) = v3)) % 4.22/1.42 | | % 4.22/1.42 | | GROUND_INST: instantiating (12) with a, b, c, all_2_2, all_2_1, simplifying % 4.22/1.42 | | with (2), (3), (11) gives: % 4.22/1.42 | | (13) c = 0 | b = 0 | a = 0 % 4.22/1.42 | | % 4.22/1.42 | | BETA: splitting (13) gives: % 4.22/1.42 | | % 4.22/1.42 | | Case 1: % 4.22/1.42 | | | % 4.22/1.42 | | | (14) b = 0 % 4.22/1.42 | | | % 4.22/1.42 | | | REDUCE: (9), (14) imply: % 4.22/1.42 | | | (15) $false % 4.22/1.42 | | | % 4.22/1.42 | | | CLOSE: (15) is inconsistent. % 4.22/1.42 | | | % 4.22/1.42 | | Case 2: % 4.22/1.42 | | | % 4.22/1.42 | | | (16) c = 0 | a = 0 % 4.22/1.42 | | | % 4.22/1.42 | | | BETA: splitting (16) gives: % 4.22/1.42 | | | % 4.22/1.42 | | | Case 1: % 4.22/1.42 | | | | % 4.22/1.42 | | | | (17) c = 0 % 4.22/1.42 | | | | % 4.22/1.42 | | | | REDUCE: (10), (17) imply: % 4.22/1.42 | | | | (18) $false % 4.22/1.42 | | | | % 4.22/1.42 | | | | CLOSE: (18) is inconsistent. % 4.22/1.42 | | | | % 4.22/1.42 | | | Case 2: % 4.22/1.42 | | | | % 4.22/1.42 | | | | (19) a = 0 % 4.22/1.42 | | | | % 4.22/1.42 | | | | REDUCE: (8), (19) imply: % 4.22/1.42 | | | | (20) $false % 4.22/1.42 | | | | % 4.22/1.42 | | | | CLOSE: (20) is inconsistent. % 4.22/1.42 | | | | % 4.22/1.42 | | | End of split % 4.22/1.42 | | | % 4.22/1.42 | | End of split % 4.22/1.42 | | % 4.22/1.42 | Case 2: % 4.22/1.42 | | % 4.22/1.42 | | (21) ~ (all_2_0 = 0) & (c = 0 | b = 0 | a = 0) % 4.22/1.42 | | % 4.22/1.42 | | ALPHA: (21) implies: % 4.22/1.43 | | (22) ~ (all_2_0 = 0) % 4.22/1.43 | | (23) c = 0 | b = 0 | a = 0 % 4.22/1.43 | | % 4.22/1.43 | | BETA: splitting (23) gives: % 4.22/1.43 | | % 4.22/1.43 | | Case 1: % 4.22/1.43 | | | % 4.22/1.43 | | | (24) b = 0 % 4.22/1.43 | | | % 4.22/1.43 | | | REDUCE: (3), (24) imply: % 4.22/1.43 | | | (25) $product(all_2_2, 0) = all_2_1 % 4.22/1.43 | | | % 4.22/1.43 | | | THEORY_AXIOM GroebnerMultiplication: % 4.22/1.43 | | | (26) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 = % 4.22/1.43 | | | 0 | ~ ($product(v2, v0) = v3) | ~ ($product(v1, 0) = v2)) % 4.22/1.43 | | | % 4.22/1.43 | | | GROUND_INST: instantiating (26) with c, all_2_2, all_2_1, all_2_0, % 4.22/1.43 | | | simplifying with (4), (25) gives: % 4.22/1.43 | | | (27) all_2_0 = 0 % 4.22/1.43 | | | % 4.22/1.43 | | | REDUCE: (22), (27) imply: % 4.22/1.43 | | | (28) $false % 4.22/1.43 | | | % 4.22/1.43 | | | CLOSE: (28) is inconsistent. % 4.22/1.43 | | | % 4.22/1.43 | | Case 2: % 4.22/1.43 | | | % 4.22/1.43 | | | (29) c = 0 | a = 0 % 4.22/1.43 | | | % 4.22/1.43 | | | BETA: splitting (29) gives: % 4.22/1.43 | | | % 4.22/1.43 | | | Case 1: % 4.22/1.43 | | | | % 4.22/1.43 | | | | (30) c = 0 % 4.22/1.43 | | | | % 4.22/1.43 | | | | REDUCE: (4), (30) imply: % 4.22/1.43 | | | | (31) $product(all_2_1, 0) = all_2_0 % 4.22/1.43 | | | | % 4.22/1.43 | | | | THEORY_AXIOM GroebnerMultiplication: % 4.22/1.43 | | | | (32) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($product(v0, 0) = % 4.22/1.43 | | | | v1)) % 4.22/1.43 | | | | % 4.22/1.43 | | | | GROUND_INST: instantiating (32) with all_2_1, all_2_0, simplifying with % 4.22/1.43 | | | | (31) gives: % 4.22/1.43 | | | | (33) all_2_0 = 0 % 4.22/1.43 | | | | % 4.22/1.43 | | | | REDUCE: (22), (33) imply: % 4.22/1.43 | | | | (34) $false % 4.22/1.43 | | | | % 4.22/1.43 | | | | CLOSE: (34) is inconsistent. % 4.22/1.43 | | | | % 4.22/1.43 | | | Case 2: % 4.22/1.43 | | | | % 4.22/1.43 | | | | (35) a = 0 % 4.22/1.43 | | | | % 4.22/1.43 | | | | REDUCE: (2), (35) imply: % 4.22/1.43 | | | | (36) $product(0, b) = all_2_2 % 4.22/1.43 | | | | % 4.22/1.43 | | | | THEORY_AXIOM GroebnerMultiplication: % 4.22/1.43 | | | | (37) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! % 4.22/1.43 | | | | [v4: int] : (v4 = 0 | ~ ($product(v3, v1) = v4) | ~ % 4.22/1.43 | | | | ($product(v2, v0) = v3) | ~ ($product(0, v0) = v2)) % 4.22/1.43 | | | | % 4.22/1.43 | | | | GROUND_INST: instantiating (37) with b, c, all_2_2, all_2_1, all_2_0, % 4.22/1.43 | | | | simplifying with (3), (4), (36) gives: % 4.22/1.43 | | | | (38) all_2_0 = 0 % 4.22/1.43 | | | | % 4.22/1.43 | | | | REDUCE: (22), (38) imply: % 4.22/1.43 | | | | (39) $false % 4.22/1.43 | | | | % 4.22/1.43 | | | | CLOSE: (39) is inconsistent. % 4.22/1.43 | | | | % 4.22/1.43 | | | End of split % 4.22/1.43 | | | % 4.22/1.43 | | End of split % 4.22/1.43 | | % 4.22/1.43 | End of split % 4.22/1.43 | % 4.22/1.43 End of proof % 4.22/1.43 % SZS output end Proof for theBenchmark % 4.22/1.43 % 4.22/1.43 807ms %------------------------------------------------------------------------------