%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI617_1 : TPTP v8.1.2. Released v5.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 17:48:35 EDT 2023 % Result : Theorem 3.41s 1.23s % Output : Proof 4.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI617_1 : TPTP v8.1.2. Released v5.1.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n027.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 18:44:38 EDT 2023 % 0.14/0.35 % CPUTime : % 0.53/0.62 ________ _____ % 0.53/0.62 ___ __ \_________(_)________________________________ % 0.53/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.53/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.53/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.53/0.62 % 0.53/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.53/0.62 (2023-06-19) % 0.53/0.62 % 0.53/0.62 (c) Philipp Rümmer, 2009-2023 % 0.53/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.53/0.62 Amanda Stjerna. % 0.53/0.62 Free software under BSD-3-Clause. % 0.53/0.62 % 0.53/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.53/0.62 % 0.53/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.53/0.64 Running up to 7 provers in parallel. % 0.53/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.53/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.53/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.85/0.99 Prover 4: Preprocessing ... % 1.85/0.99 Prover 1: Preprocessing ... % 2.35/1.03 Prover 3: Preprocessing ... % 2.35/1.03 Prover 0: Preprocessing ... % 2.35/1.03 Prover 5: Preprocessing ... % 2.35/1.03 Prover 2: Preprocessing ... % 2.35/1.03 Prover 6: Preprocessing ... % 3.06/1.10 Prover 4: Constructing countermodel ... % 3.06/1.10 Prover 6: Proving ... % 3.06/1.10 Prover 3: Constructing countermodel ... % 3.06/1.11 Prover 1: Constructing countermodel ... % 3.06/1.11 Prover 0: Proving ... % 3.06/1.11 Prover 5: Proving ... % 3.06/1.12 Prover 2: Proving ... % 3.41/1.23 Prover 3: proved (583ms) % 3.41/1.23 % 3.41/1.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.41/1.23 % 3.41/1.23 Prover 5: stopped % 3.41/1.23 Prover 2: stopped % 3.41/1.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.41/1.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.41/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.41/1.23 Prover 0: stopped % 3.41/1.23 Prover 6: stopped % 3.41/1.24 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.41/1.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.41/1.26 Prover 7: Preprocessing ... % 3.41/1.26 Prover 10: Preprocessing ... % 3.41/1.26 Prover 8: Preprocessing ... % 3.41/1.27 Prover 13: Preprocessing ... % 3.41/1.27 Prover 11: Preprocessing ... % 4.24/1.29 Prover 8: Warning: ignoring some quantifiers % 4.24/1.29 Prover 7: Constructing countermodel ... % 4.24/1.29 Prover 8: Constructing countermodel ... % 4.24/1.29 Prover 4: Found proof (size 31) % 4.24/1.29 Prover 4: proved (646ms) % 4.24/1.29 Prover 7: stopped % 4.24/1.29 Prover 1: Found proof (size 32) % 4.24/1.30 Prover 1: proved (651ms) % 4.24/1.30 Prover 8: stopped % 4.24/1.30 Prover 11: Constructing countermodel ... % 4.24/1.30 Prover 11: stopped % 4.24/1.30 Prover 10: Constructing countermodel ... % 4.24/1.30 Prover 10: stopped % 4.24/1.31 Prover 13: Warning: ignoring some quantifiers % 4.24/1.31 Prover 13: Constructing countermodel ... % 4.24/1.31 Prover 13: stopped % 4.24/1.32 % 4.24/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.24/1.32 % 4.24/1.32 % SZS output start Proof for theBenchmark % 4.24/1.32 Assumptions after simplification: % 4.24/1.32 --------------------------------- % 4.24/1.33 % 4.24/1.33 (absolute_value_defs) % 4.67/1.35 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & g(v0) = v2 & % 4.67/1.35 f(v0) = v1 & ! [v3: int] : ! [v4: int] : (v4 = v3 | $sum(v4, v3) = 0 | ~ % 4.67/1.35 (g(v3) = v4)) & ! [v3: int] : ! [v4: int] : ( ~ ($lesseq(1, % 4.67/1.35 $difference($product(-1, v4), v3))) | ~ (f(v3) = v4)) & ! [v3: int] % 4.67/1.35 : ! [v4: int] : ( ~ ($lesseq(1, $difference(v3, v4))) | ~ (f(v3) = v4)) & % 4.67/1.35 ! [v3: int] : ! [v4: int] : ( ~ ($lesseq(v4, -1)) | ~ (g(v3) = v4)) & ! % 4.67/1.35 [v3: int] : ! [v4: int] : ( ~ ($lesseq(1, $difference(v4, v3))) | ~ % 4.67/1.35 ($lesseq(1, $sum(v4, v3))) | ~ (f(v3) = v4))) % 4.67/1.35 % 4.67/1.35 Those formulas are unsatisfiable: % 4.67/1.35 --------------------------------- % 4.67/1.35 % 4.67/1.35 Begin of proof % 4.67/1.36 | % 4.67/1.36 | DELTA: instantiating (absolute_value_defs) with fresh symbols all_3_0, % 4.67/1.36 | all_3_1, all_3_2 gives: % 4.67/1.36 | (1) ~ (all_3_0 = all_3_1) & g(all_3_2) = all_3_0 & f(all_3_2) = all_3_1 & % 4.67/1.36 | ! [v0: int] : ! [v1: int] : (v1 = v0 | $sum(v1, v0) = 0 | ~ (g(v0) = % 4.67/1.36 | v1)) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, % 4.67/1.36 | $difference($product(-1, v1), v0))) | ~ (f(v0) = v1)) & ! [v0: % 4.67/1.36 | int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v0, v1))) | ~ % 4.67/1.36 | (f(v0) = v1)) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | % 4.67/1.36 | ~ (g(v0) = v1)) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, % 4.67/1.36 | $difference(v1, v0))) | ~ ($lesseq(1, $sum(v1, v0))) | ~ (f(v0) % 4.67/1.36 | = v1)) % 4.67/1.36 | % 4.67/1.36 | ALPHA: (1) implies: % 4.67/1.36 | (2) ~ (all_3_0 = all_3_1) % 4.67/1.36 | (3) f(all_3_2) = all_3_1 % 4.67/1.36 | (4) g(all_3_2) = all_3_0 % 4.67/1.37 | (5) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v1, v0))) | % 4.67/1.37 | ~ ($lesseq(1, $sum(v1, v0))) | ~ (f(v0) = v1)) % 4.67/1.37 | (6) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ (g(v0) = v1)) % 4.67/1.37 | (7) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v0, v1))) | % 4.67/1.37 | ~ (f(v0) = v1)) % 4.67/1.37 | (8) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(-1, % 4.67/1.37 | v1), v0))) | ~ (f(v0) = v1)) % 4.67/1.37 | (9) ! [v0: int] : ! [v1: int] : (v1 = v0 | $sum(v1, v0) = 0 | ~ (g(v0) = % 4.67/1.37 | v1)) % 4.67/1.37 | % 4.67/1.37 | GROUND_INST: instantiating (8) with all_3_2, all_3_1, simplifying with (3) % 4.67/1.37 | gives: % 4.79/1.37 | (10) $lesseq(0, $sum(all_3_1, all_3_2)) % 4.79/1.37 | % 4.79/1.37 | GROUND_INST: instantiating (7) with all_3_2, all_3_1, simplifying with (3) % 4.79/1.37 | gives: % 4.79/1.37 | (11) $lesseq(all_3_2, all_3_1) % 4.79/1.37 | % 4.79/1.37 | GROUND_INST: instantiating (5) with all_3_2, all_3_1, simplifying with (3) % 4.79/1.37 | gives: % 4.79/1.37 | (12) ~ ($lesseq(1, $difference(all_3_1, all_3_2))) | ~ ($lesseq(1, % 4.79/1.37 | $sum(all_3_1, all_3_2))) % 4.79/1.37 | % 4.79/1.37 | GROUND_INST: instantiating (9) with all_3_2, all_3_0, simplifying with (4) % 4.79/1.37 | gives: % 4.79/1.37 | (13) all_3_0 = all_3_2 | $sum(all_3_0, all_3_2) = 0 % 4.79/1.37 | % 4.79/1.37 | GROUND_INST: instantiating (6) with all_3_2, all_3_0, simplifying with (4) % 4.79/1.37 | gives: % 4.79/1.37 | (14) $lesseq(0, all_3_0) % 4.79/1.37 | % 4.79/1.37 | BETA: splitting (12) gives: % 4.79/1.37 | % 4.79/1.37 | Case 1: % 4.79/1.37 | | % 4.79/1.37 | | (15) $lesseq(all_3_1, all_3_2) % 4.79/1.37 | | % 4.79/1.37 | | ANTI_SYMM: (11), (15) imply: % 4.79/1.37 | | (16) all_3_1 = all_3_2 % 4.79/1.37 | | % 4.79/1.37 | | REDUCE: (10), (16) imply: % 4.79/1.37 | | (17) $lesseq(0, all_3_2) % 4.79/1.37 | | % 4.79/1.37 | | SIMP: (17) implies: % 4.79/1.37 | | (18) $lesseq(0, all_3_2) % 4.79/1.37 | | % 4.79/1.37 | | REDUCE: (2), (16) imply: % 4.79/1.37 | | (19) ~ (all_3_0 = all_3_2) % 4.79/1.37 | | % 4.79/1.37 | | BETA: splitting (13) gives: % 4.79/1.37 | | % 4.79/1.37 | | Case 1: % 4.79/1.37 | | | % 4.79/1.38 | | | (20) all_3_0 = all_3_2 % 4.79/1.38 | | | % 4.79/1.38 | | | REDUCE: (19), (20) imply: % 4.79/1.38 | | | (21) $false % 4.79/1.38 | | | % 4.79/1.38 | | | CLOSE: (21) is inconsistent. % 4.79/1.38 | | | % 4.79/1.38 | | Case 2: % 4.79/1.38 | | | % 4.79/1.38 | | | (22) $sum(all_3_0, all_3_2) = 0 % 4.79/1.38 | | | % 4.79/1.38 | | | REDUCE: (14), (22) imply: % 4.79/1.38 | | | (23) $lesseq(all_3_2, 0) % 4.79/1.38 | | | % 4.79/1.38 | | | REDUCE: (19), (22) imply: % 4.79/1.38 | | | (24) ~ (all_3_2 = 0) % 4.79/1.38 | | | % 4.79/1.38 | | | SIMP: (24) implies: % 4.79/1.38 | | | (25) ~ (all_3_2 = 0) % 4.79/1.38 | | | % 4.79/1.38 | | | STRENGTHEN: (18), (25) imply: % 4.79/1.38 | | | (26) $lesseq(1, all_3_2) % 4.79/1.38 | | | % 4.79/1.38 | | | COMBINE_INEQS: (23), (26) imply: % 4.79/1.38 | | | (27) $false % 4.79/1.38 | | | % 4.79/1.38 | | | CLOSE: (27) is inconsistent. % 4.79/1.38 | | | % 4.79/1.38 | | End of split % 4.79/1.38 | | % 4.79/1.38 | Case 2: % 4.79/1.38 | | % 4.79/1.38 | | (28) $lesseq(1, $difference(all_3_1, all_3_2)) % 4.79/1.38 | | (29) $lesseq(all_3_2, $product(-1, all_3_1)) % 4.79/1.38 | | % 4.79/1.38 | | ANTI_SYMM: (10), (29) imply: % 4.79/1.38 | | (30) $sum(all_3_1, all_3_2) = 0 % 4.79/1.38 | | % 4.79/1.38 | | REDUCE: (28), (30) imply: % 4.79/1.38 | | (31) $lesseq(all_3_2, -1) % 4.79/1.38 | | % 4.79/1.38 | | SIMP: (31) implies: % 4.79/1.38 | | (32) $lesseq(all_3_2, -1) % 4.79/1.38 | | % 4.79/1.38 | | REDUCE: (2), (30) imply: % 4.79/1.38 | | (33) ~ ($sum(all_3_0, all_3_2) = 0) % 4.79/1.38 | | % 4.79/1.38 | | BETA: splitting (13) gives: % 4.79/1.38 | | % 4.79/1.38 | | Case 1: % 4.79/1.38 | | | % 4.79/1.38 | | | (34) all_3_0 = all_3_2 % 4.79/1.38 | | | % 4.79/1.38 | | | REDUCE: (14), (34) imply: % 4.79/1.38 | | | (35) $lesseq(0, all_3_2) % 4.79/1.38 | | | % 4.79/1.38 | | | COMBINE_INEQS: (32), (35) imply: % 4.79/1.38 | | | (36) $false % 4.79/1.38 | | | % 4.79/1.38 | | | CLOSE: (36) is inconsistent. % 4.79/1.38 | | | % 4.79/1.38 | | Case 2: % 4.79/1.38 | | | % 4.79/1.38 | | | (37) $sum(all_3_0, all_3_2) = 0 % 4.79/1.38 | | | % 4.79/1.38 | | | REDUCE: (33), (37) imply: % 4.79/1.38 | | | (38) $false % 4.79/1.38 | | | % 4.79/1.38 | | | CLOSE: (38) is inconsistent. % 4.79/1.38 | | | % 4.79/1.38 | | End of split % 4.79/1.38 | | % 4.79/1.38 | End of split % 4.79/1.38 | % 4.79/1.38 End of proof % 4.79/1.38 % SZS output end Proof for theBenchmark % 4.79/1.38 % 4.79/1.38 757ms %------------------------------------------------------------------------------