%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 : Sun Apr 6 10:08:51 AM UTC 2025 % Result : Theorem 8.69s 1.87s % Output : Proof 10.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.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 : Sun Apr 6 02:56:45 EDT 2025 % 0.13/0.34 % CPUTime : % 0.56/0.62 ________ _____ % 0.56/0.62 ___ __ \_________(_)________________________________ % 0.56/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.56/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.56/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.56/0.62 % 0.56/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.56/0.62 (2023-06-19) % 0.56/0.62 % 0.56/0.62 (c) Philipp Rümmer, 2009-2023 % 0.56/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.56/0.62 Amanda Stjerna. % 0.56/0.62 Free software under BSD-3-Clause. % 0.56/0.62 % 0.56/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.56/0.62 % 0.56/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.56/0.63 Running up to 7 provers in parallel. % 0.70/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.70/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.54/1.17 Prover 2: Preprocessing ... % 3.54/1.17 Prover 1: Preprocessing ... % 3.54/1.17 Prover 5: Preprocessing ... % 3.54/1.18 Prover 3: Preprocessing ... % 3.54/1.18 Prover 4: Preprocessing ... % 3.54/1.18 Prover 0: Preprocessing ... % 3.54/1.18 Prover 6: Preprocessing ... % 7.05/1.63 Prover 4: Warning: ignoring some quantifiers % 7.05/1.63 Prover 1: Warning: ignoring some quantifiers % 7.05/1.66 Prover 3: Warning: ignoring some quantifiers % 7.05/1.67 Prover 6: Proving ... % 7.48/1.67 Prover 5: Proving ... % 7.48/1.67 Prover 1: Constructing countermodel ... % 7.48/1.68 Prover 3: Constructing countermodel ... % 7.48/1.68 Prover 4: Constructing countermodel ... % 7.48/1.69 Prover 2: Proving ... % 7.48/1.71 Prover 0: Proving ... % 8.69/1.87 Prover 3: proved (1231ms) % 8.69/1.87 % 8.69/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.69/1.87 % 8.69/1.87 Prover 6: stopped % 8.69/1.87 Prover 0: proved (1238ms) % 8.69/1.87 Prover 2: stopped % 8.69/1.87 % 8.69/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.69/1.87 % 8.69/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.69/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.69/1.88 Prover 5: stopped % 8.69/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.69/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.69/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.21/1.95 Prover 8: Preprocessing ... % 9.21/1.96 Prover 4: Found proof (size 14) % 9.21/1.96 Prover 4: proved (1325ms) % 9.21/1.96 Prover 10: Preprocessing ... % 9.21/1.96 Prover 1: stopped % 9.21/1.97 Prover 7: Preprocessing ... % 9.21/1.97 Prover 11: Preprocessing ... % 9.75/1.99 Prover 13: Preprocessing ... % 9.75/2.00 Prover 10: stopped % 9.75/2.01 Prover 7: stopped % 9.75/2.02 Prover 11: stopped % 9.75/2.03 Prover 13: stopped % 10.52/2.09 Prover 8: Warning: ignoring some quantifiers % 10.52/2.10 Prover 8: Constructing countermodel ... % 10.52/2.11 Prover 8: stopped % 10.52/2.11 % 10.52/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.52/2.11 % 10.52/2.11 % SZS output start Proof for theBenchmark % 10.52/2.12 Assumptions after simplification: % 10.52/2.12 --------------------------------- % 10.52/2.12 % 10.52/2.12 (formula_3_unnamed_formula) % 10.67/2.13 ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 10.67/2.13 ($lesseq(0, v1)) | ~ ($lesseq(1, v0)) | ~ (f__integer__(v1) = v2) | ~ % 10.67/2.13 (f__integer__(v0) = v3) | ? [v4: int] : ? [v5: int] : ? [v6: general] : % 10.67/2.13 ? [v7: general] : (div(v2, v3, v6, v7) = 0 & f__integer__(v5) = v7 & % 10.67/2.13 f__integer__(v4) = v6 & general(v7) & general(v6))) % 10.67/2.13 % 10.67/2.13 (formula_4_unnamed_formula) % 10.67/2.14 ? [v0: int] : ? [v1: int] : ? [v2: general] : ? [v3: general] : % 10.67/2.14 ($lesseq(1, v1) & $lesseq(0, v0) & f__integer__(v1) = v3 & f__integer__(v0) = % 10.67/2.14 v2 & general(v3) & general(v2) & ! [v4: int] : ! [v5: int] : ! [v6: % 10.67/2.14 general] : ! [v7: general] : ( ~ (div(v2, v3, v6, v7) = 0) | ~ % 10.67/2.14 (f__integer__(v5) = v7) | ~ (f__integer__(v4) = v6))) % 10.67/2.14 % 10.67/2.14 Further assumptions not needed in the proof: % 10.67/2.14 -------------------------------------------- % 10.67/2.14 antisymmetric_ordering_ax, f__integer__def_ax, f__symbolic__def_ax, % 10.67/2.14 formula_0_completed_definition_of_div_4, formula_1_unnamed_formula, % 10.67/2.14 formula_2_unnamed_formula, general_universe_ax, maximal_element_ax, % 10.67/2.14 minimal_element_ax, numeral_ordering_ax, numerals_less_than_symbols_ax, % 10.67/2.14 p__greater__def_ax, p__greater_equal__def_ax, p__is_integer__def_ax, % 10.67/2.14 p__is_symbolic__def_ax, p__less__def_ax, strongly_connected_ordering_ax, % 10.67/2.14 transitive_ordering_ax % 10.67/2.14 % 10.67/2.14 Those formulas are unsatisfiable: % 10.67/2.14 --------------------------------- % 10.67/2.14 % 10.67/2.14 Begin of proof % 10.67/2.14 | % 10.75/2.14 | DELTA: instantiating (formula_4_unnamed_formula) with fresh symbols all_25_0, % 10.75/2.14 | all_25_1, all_25_2, all_25_3 gives: % 10.75/2.14 | (1) $lesseq(1, all_25_2) & $lesseq(0, all_25_3) & f__integer__(all_25_2) = % 10.75/2.14 | all_25_0 & f__integer__(all_25_3) = all_25_1 & general(all_25_0) & % 10.75/2.14 | general(all_25_1) & ! [v0: int] : ! [v1: int] : ! [v2: general] : ! % 10.75/2.14 | [v3: general] : ( ~ (div(all_25_1, all_25_0, v2, v3) = 0) | ~ % 10.75/2.14 | (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2)) % 10.75/2.14 | % 10.75/2.14 | ALPHA: (1) implies: % 10.75/2.14 | (2) $lesseq(0, all_25_3) % 10.75/2.14 | (3) $lesseq(1, all_25_2) % 10.75/2.14 | (4) f__integer__(all_25_3) = all_25_1 % 10.75/2.14 | (5) f__integer__(all_25_2) = all_25_0 % 10.75/2.14 | (6) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 10.75/2.14 | (div(all_25_1, all_25_0, v2, v3) = 0) | ~ (f__integer__(v1) = v3) | % 10.75/2.14 | ~ (f__integer__(v0) = v2)) % 10.75/2.14 | % 10.75/2.14 | GROUND_INST: instantiating (formula_3_unnamed_formula) with all_25_2, % 10.75/2.14 | all_25_3, all_25_1, all_25_0, simplifying with (4), (5) gives: % 10.75/2.15 | (7) ~ ($lesseq(1, all_25_2)) | ~ ($lesseq(0, all_25_3)) | ? [v0: int] : % 10.75/2.15 | ? [v1: int] : ? [v2: general] : ? [v3: general] : (div(all_25_1, % 10.75/2.15 | all_25_0, v2, v3) = 0 & f__integer__(v1) = v3 & f__integer__(v0) = % 10.75/2.15 | v2 & general(v3) & general(v2)) % 10.75/2.15 | % 10.75/2.15 | BETA: splitting (7) gives: % 10.75/2.15 | % 10.75/2.15 | Case 1: % 10.75/2.15 | | % 10.75/2.15 | | (8) $lesseq(all_25_3, -1) % 10.75/2.15 | | % 10.75/2.15 | | COMBINE_INEQS: (2), (8) imply: % 10.75/2.15 | | (9) $false % 10.75/2.15 | | % 10.75/2.15 | | CLOSE: (9) is inconsistent. % 10.75/2.15 | | % 10.75/2.15 | Case 2: % 10.75/2.15 | | % 10.75/2.15 | | (10) ~ ($lesseq(1, all_25_2)) | ? [v0: int] : ? [v1: int] : ? [v2: % 10.75/2.15 | | general] : ? [v3: general] : (div(all_25_1, all_25_0, v2, v3) = 0 % 10.75/2.15 | | & f__integer__(v1) = v3 & f__integer__(v0) = v2 & general(v3) & % 10.75/2.15 | | general(v2)) % 10.75/2.15 | | % 10.75/2.15 | | BETA: splitting (10) gives: % 10.75/2.15 | | % 10.75/2.15 | | Case 1: % 10.75/2.15 | | | % 10.75/2.15 | | | (11) $lesseq(all_25_2, 0) % 10.75/2.15 | | | % 10.75/2.15 | | | COMBINE_INEQS: (3), (11) imply: % 10.75/2.15 | | | (12) $false % 10.75/2.15 | | | % 10.75/2.15 | | | CLOSE: (12) is inconsistent. % 10.75/2.15 | | | % 10.75/2.15 | | Case 2: % 10.75/2.15 | | | % 10.75/2.15 | | | (13) ? [v0: int] : ? [v1: int] : ? [v2: general] : ? [v3: general] % 10.75/2.15 | | | : (div(all_25_1, all_25_0, v2, v3) = 0 & f__integer__(v1) = v3 & % 10.75/2.15 | | | f__integer__(v0) = v2 & general(v3) & general(v2)) % 10.75/2.15 | | | % 10.75/2.15 | | | DELTA: instantiating (13) with fresh symbols all_70_0, all_70_1, all_70_2, % 10.75/2.15 | | | all_70_3 gives: % 10.75/2.15 | | | (14) div(all_25_1, all_25_0, all_70_1, all_70_0) = 0 & % 10.75/2.15 | | | f__integer__(all_70_2) = all_70_0 & f__integer__(all_70_3) = % 10.75/2.15 | | | all_70_1 & general(all_70_0) & general(all_70_1) % 10.75/2.15 | | | % 10.75/2.15 | | | ALPHA: (14) implies: % 10.75/2.15 | | | (15) f__integer__(all_70_3) = all_70_1 % 10.75/2.15 | | | (16) f__integer__(all_70_2) = all_70_0 % 10.75/2.15 | | | (17) div(all_25_1, all_25_0, all_70_1, all_70_0) = 0 % 10.75/2.15 | | | % 10.75/2.15 | | | GROUND_INST: instantiating (6) with all_70_3, all_70_2, all_70_1, % 10.75/2.15 | | | all_70_0, simplifying with (15), (16), (17) gives: % 10.75/2.15 | | | (18) $false % 10.75/2.15 | | | % 10.75/2.15 | | | CLOSE: (18) is inconsistent. % 10.75/2.15 | | | % 10.75/2.15 | | End of split % 10.75/2.15 | | % 10.75/2.15 | End of split % 10.75/2.15 | % 10.75/2.15 End of proof % 10.75/2.15 % SZS output end Proof for theBenchmark % 10.75/2.15 % 10.75/2.15 1534ms %------------------------------------------------------------------------------