%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI699_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 : n025.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 17:48:51 EDT 2023 % Result : Unsatisfiable 3.77s 1.28s % Output : Proof 4.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI699_1 : TPTP v8.1.2. Released v6.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.34 % Computer : n025.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Aug 29 18:06:10 EDT 2023 % 0.15/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.04/1.00 Prover 4: Preprocessing ... % 2.04/1.00 Prover 1: Preprocessing ... % 2.04/1.00 Prover 5: Preprocessing ... % 2.04/1.00 Prover 6: Preprocessing ... % 2.04/1.00 Prover 3: Preprocessing ... % 2.04/1.00 Prover 2: Preprocessing ... % 2.04/1.00 Prover 0: Preprocessing ... % 2.54/1.05 Prover 2: Constructing countermodel ... % 2.54/1.05 Prover 4: Constructing countermodel ... % 2.54/1.05 Prover 0: Constructing countermodel ... % 2.54/1.05 Prover 1: Constructing countermodel ... % 2.54/1.05 Prover 3: Constructing countermodel ... % 2.54/1.05 Prover 6: Constructing countermodel ... % 2.54/1.05 Prover 5: Constructing countermodel ... % 3.77/1.28 Prover 6: proved (651ms) % 3.77/1.28 Prover 5: proved (653ms) % 3.77/1.28 % 3.77/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.77/1.28 % 3.77/1.28 Prover 2: proved (657ms) % 3.77/1.28 % 3.77/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.77/1.28 % 3.77/1.28 Prover 0: proved (658ms) % 3.77/1.28 % 3.77/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.77/1.28 % 3.77/1.28 % 3.77/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.77/1.28 % 3.77/1.30 Prover 3: proved (658ms) % 3.77/1.30 % 3.77/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.77/1.30 % 3.77/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.77/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.77/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.77/1.31 Prover 10: Preprocessing ... % 3.77/1.31 Prover 7: Preprocessing ... % 3.77/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.77/1.31 Prover 8: Preprocessing ... % 3.77/1.31 Prover 1: Found proof (size 25) % 3.77/1.31 Prover 1: proved (681ms) % 3.77/1.31 Prover 10: Constructing countermodel ... % 3.77/1.31 Prover 4: Found proof (size 25) % 3.77/1.31 Prover 4: proved (681ms) % 3.77/1.31 Prover 8: Constructing countermodel ... % 3.77/1.31 Prover 7: Constructing countermodel ... % 3.77/1.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.77/1.32 Prover 7: stopped % 3.77/1.32 Prover 11: Preprocessing ... % 3.77/1.32 Prover 8: stopped % 3.77/1.32 Prover 13: Preprocessing ... % 3.77/1.33 Prover 11: Constructing countermodel ... % 3.77/1.33 Prover 11: stopped % 3.77/1.33 Prover 10: stopped % 3.77/1.34 Prover 13: Constructing countermodel ... % 3.77/1.34 Prover 13: stopped % 3.77/1.34 % 3.77/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.77/1.34 % 4.32/1.36 % SZS output start Proof for theBenchmark % 4.32/1.36 Assumptions after simplification: % 4.32/1.36 --------------------------------- % 4.32/1.36 % 4.32/1.36 (eq) % 4.32/1.37 $product($product(2, z), z) = y % 4.32/1.37 % 4.32/1.37 (ineq1) % 4.32/1.37 $lesseq(1, x) % 4.32/1.37 % 4.32/1.37 (ineq2) % 4.32/1.37 $lesseq(1, y) % 4.32/1.37 % 4.32/1.37 (ineq3) % 4.32/1.37 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($lesseq(v2, v1) & $product(v0, % 4.32/1.37 x) = v1 & $product(y, x) = v2 & $product(z, z) = v0) % 4.32/1.37 % 4.32/1.37 Those formulas are unsatisfiable: % 4.32/1.37 --------------------------------- % 4.32/1.37 % 4.32/1.37 Begin of proof % 4.32/1.38 | % 4.32/1.38 | DELTA: instantiating (ineq3) with fresh symbols all_4_0, all_4_1, all_4_2 % 4.32/1.38 | gives: % 4.32/1.38 | (1) $lesseq(all_4_0, all_4_1) & $product(all_4_2, x) = all_4_1 & % 4.32/1.38 | $product(y, x) = all_4_0 & $product(z, z) = all_4_2 % 4.32/1.38 | % 4.32/1.38 | ALPHA: (1) implies: % 4.32/1.38 | (2) $lesseq(all_4_0, all_4_1) % 4.32/1.38 | (3) $product(z, z) = all_4_2 % 4.32/1.38 | (4) $product(y, x) = all_4_0 % 4.32/1.38 | (5) $product(all_4_2, x) = all_4_1 % 4.32/1.38 | % 4.32/1.38 | THEORY_AXIOM GroebnerMultiplication: % 4.32/1.38 | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 4.32/1.38 | int] : ! [v5: int] : (v5 = $product(2, v4) | ~ ($product(v3, v1) = % 4.32/1.38 | v4) | ~ ($product(v2, v1) = v5) | ~ ($product($product(2, v0), % 4.32/1.38 | v0) = v2) | ~ ($product(v0, v0) = v3)) % 4.32/1.38 | % 4.32/1.39 | GROUND_INST: instantiating (6) with z, x, y, all_4_2, all_4_1, all_4_0, % 4.32/1.39 | simplifying with (3), (4), (5), (eq) gives: % 4.32/1.39 | (7) all_4_0 = $product(2, all_4_1) % 4.32/1.39 | % 4.32/1.39 | THEORY_AXIOM GroebnerMultiplication: % 4.32/1.39 | (8) ! [v0: int] : ! [v1: int] : ! [v2: int] : ($product(2, v2) = v1 | ~ % 4.32/1.39 | ($product($product(2, v0), v0) = v1) | ~ ($product(v0, v0) = v2)) % 4.32/1.39 | % 4.32/1.39 | GROUND_INST: instantiating (8) with z, y, all_4_2, simplifying with (3), (eq) % 4.32/1.39 | gives: % 4.32/1.39 | (9) $product(2, all_4_2) = y % 4.32/1.39 | % 4.32/1.39 | COL_REDUCE: introducing fresh symbol sc_10_0_0 defined by: % 4.32/1.39 | (10) $difference(all_4_2, y) = sc_10_0_0 % 4.32/1.39 | % 4.32/1.39 | COMBINE_EQS: (9), (10) imply: % 4.32/1.39 | (11) $sum(y, $product(2, sc_10_0_0)) = 0 % 4.32/1.39 | % 4.32/1.39 | COMBINE_EQS: (10), (11) imply: % 4.32/1.39 | (12) $sum(all_4_2, sc_10_0_0) = 0 % 4.32/1.39 | % 4.32/1.39 | REDUCE: (2), (7) imply: % 4.32/1.39 | (13) $lesseq(all_4_1, 0) % 4.32/1.39 | % 4.32/1.39 | REDUCE: (11), (ineq2) imply: % 4.32/1.39 | (14) $lesseq(sc_10_0_0, -1) % 4.32/1.39 | % 4.32/1.39 | SIMP: (14) implies: % 4.32/1.39 | (15) $lesseq(sc_10_0_0, -1) % 4.32/1.39 | % 4.32/1.39 | REDUCE: (5), (12) imply: % 4.32/1.39 | (16) $product($product(-1, sc_10_0_0), x) = all_4_1 % 4.32/1.39 | % 4.32/1.39 | THEORY_AXIOM GroebnerMultiplication: % 4.48/1.39 | (17) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(2, % 4.48/1.39 | $sum($difference($product(-1, v2), v1), v0))) | ~ ($lesseq(v1, % 4.48/1.39 | -1)) | ~ ($lesseq(1, v0)) | ~ ($product($product(-1, v1), v0) % 4.48/1.39 | = v2)) % 4.48/1.39 | % 4.48/1.39 | GROUND_INST: instantiating (17) with x, sc_10_0_0, all_4_1, simplifying with % 4.48/1.39 | (16) gives: % 4.48/1.39 | (18) ~ ($lesseq(2, $sum($difference($product(-1, all_4_1), sc_10_0_0), % 4.48/1.39 | x))) | ~ ($lesseq(sc_10_0_0, -1)) | ~ ($lesseq(1, x)) % 4.48/1.39 | % 4.48/1.39 | BETA: splitting (18) gives: % 4.48/1.39 | % 4.48/1.39 | Case 1: % 4.48/1.39 | | % 4.48/1.39 | | (19) $lesseq(0, sc_10_0_0) % 4.48/1.39 | | % 4.48/1.39 | | COMBINE_INEQS: (15), (19) imply: % 4.48/1.39 | | (20) $false % 4.48/1.39 | | % 4.48/1.39 | | CLOSE: (20) is inconsistent. % 4.48/1.39 | | % 4.48/1.39 | Case 2: % 4.48/1.39 | | % 4.48/1.39 | | (21) ~ ($lesseq(2, $sum($difference($product(-1, all_4_1), sc_10_0_0), % 4.48/1.40 | | x))) | ~ ($lesseq(1, x)) % 4.48/1.40 | | % 4.48/1.40 | | BETA: splitting (21) gives: % 4.48/1.40 | | % 4.48/1.40 | | Case 1: % 4.48/1.40 | | | % 4.48/1.40 | | | (22) $lesseq(x, 0) % 4.48/1.40 | | | % 4.48/1.40 | | | COMBINE_INEQS: (22), (ineq1) imply: % 4.48/1.40 | | | (23) $false % 4.48/1.40 | | | % 4.48/1.40 | | | CLOSE: (23) is inconsistent. % 4.48/1.40 | | | % 4.48/1.40 | | Case 2: % 4.48/1.40 | | | % 4.48/1.40 | | | (24) $lesseq(-1, $difference($sum(all_4_1, sc_10_0_0), x)) % 4.48/1.40 | | | % 4.48/1.40 | | | COMBINE_INEQS: (13), (24) imply: % 4.48/1.40 | | | (25) $lesseq(-1, $difference(sc_10_0_0, x)) % 4.48/1.40 | | | % 4.48/1.40 | | | COMBINE_INEQS: (15), (25) imply: % 4.48/1.40 | | | (26) $lesseq(x, 0) % 4.48/1.40 | | | % 4.48/1.40 | | | COMBINE_INEQS: (26), (ineq1) imply: % 4.48/1.40 | | | (27) $false % 4.48/1.40 | | | % 4.48/1.40 | | | CLOSE: (27) is inconsistent. % 4.48/1.40 | | | % 4.48/1.40 | | End of split % 4.48/1.40 | | % 4.48/1.40 | End of split % 4.48/1.40 | % 4.48/1.40 End of proof % 4.48/1.40 % SZS output end Proof for theBenchmark % 4.48/1.40 % 4.48/1.40 793ms %------------------------------------------------------------------------------