%------------------------------------------------------------------------------ % 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 : n012.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 10:08:50 AM UTC 2025 % Result : Theorem 7.02s 1.64s % Output : Proof 8.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n012.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Apr 6 02:51:16 EDT 2025 % 0.12/0.34 % CPUTime : % 0.65/0.61 ________ _____ % 0.65/0.61 ___ __ \_________(_)________________________________ % 0.65/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.61 % 0.65/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.61 (2023-06-19) % 0.65/0.61 % 0.65/0.61 (c) Philipp Rümmer, 2009-2023 % 0.65/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.61 Amanda Stjerna. % 0.65/0.61 Free software under BSD-3-Clause. % 0.65/0.62 % 0.65/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.62 % 0.65/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.63 Running up to 7 provers in parallel. % 0.69/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.15/1.13 Prover 4: Preprocessing ... % 3.15/1.13 Prover 1: Preprocessing ... % 3.15/1.17 Prover 5: Preprocessing ... % 3.15/1.17 Prover 2: Preprocessing ... % 3.78/1.18 Prover 6: Preprocessing ... % 3.87/1.19 Prover 3: Preprocessing ... % 3.87/1.19 Prover 0: Preprocessing ... % 6.43/1.53 Prover 1: Warning: ignoring some quantifiers % 6.43/1.54 Prover 5: Proving ... % 6.43/1.54 Prover 3: Warning: ignoring some quantifiers % 6.43/1.54 Prover 2: Proving ... % 6.43/1.55 Prover 4: Constructing countermodel ... % 6.43/1.55 Prover 1: Constructing countermodel ... % 6.43/1.56 Prover 6: Proving ... % 6.43/1.56 Prover 3: Constructing countermodel ... % 6.43/1.59 Prover 0: Proving ... % 7.02/1.64 Prover 3: proved (999ms) % 7.02/1.64 % 7.02/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.02/1.64 % 7.02/1.64 Prover 2: stopped % 7.02/1.64 Prover 0: stopped % 7.02/1.64 Prover 6: stopped % 7.02/1.64 Prover 5: proved (1005ms) % 7.02/1.64 % 7.02/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.02/1.64 % 7.02/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.02/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.02/1.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.02/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.02/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.58/1.71 Prover 4: Found proof (size 11) % 7.58/1.71 Prover 4: proved (1070ms) % 7.58/1.71 Prover 1: Found proof (size 11) % 7.58/1.71 Prover 1: proved (1077ms) % 7.58/1.72 Prover 10: Preprocessing ... % 7.58/1.73 Prover 7: Preprocessing ... % 7.58/1.73 Prover 13: Preprocessing ... % 7.58/1.73 Prover 8: Preprocessing ... % 7.58/1.74 Prover 11: Preprocessing ... % 7.58/1.75 Prover 10: stopped % 7.58/1.76 Prover 7: stopped % 7.58/1.77 Prover 13: stopped % 8.22/1.78 Prover 11: stopped % 8.43/1.84 Prover 8: Warning: ignoring some quantifiers % 8.43/1.86 Prover 8: Constructing countermodel ... % 8.43/1.87 Prover 8: stopped % 8.43/1.87 % 8.43/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.43/1.87 % 8.43/1.87 % SZS output start Proof for theBenchmark % 8.43/1.87 Assumptions after simplification: % 8.43/1.87 --------------------------------- % 8.43/1.87 % 8.43/1.87 (formula_5_completed_definition_of_in_cover_1) % 8.43/1.89 ! [v0: general] : ( ~ (in_cover(v0) = 0) | ~ general(v0) | ? [v1: int] : % 8.43/1.89 ($lesseq(v1, n_i) & $lesseq(1, v1) & f__integer__(v1) = v0)) % 8.43/1.89 % 8.43/1.89 (formula_6_unnamed_formula) % 8.43/1.89 ? [v0: general] : (in_cover(v0) = 0 & general(v0) & ! [v1: int] : ( ~ % 8.43/1.89 ($lesseq(v1, n_i)) | ~ ($lesseq(1, v1)) | ~ (f__integer__(v1) = v0))) % 8.43/1.89 % 8.43/1.89 Further assumptions not needed in the proof: % 8.43/1.89 -------------------------------------------- % 8.43/1.89 antisymmetric_ordering_ax, f__integer__def_ax, f__symbolic__def_ax, % 8.43/1.89 formula_0_unnamed_formula, formula_1_unnamed_formula, % 8.43/1.89 formula_2_completed_definition_of_covered_1, formula_3_constraint_0, % 8.43/1.90 formula_4_constraint_1, general_universe_ax, maximal_element_ax, % 8.43/1.90 minimal_element_ax, numeral_ordering_ax, numerals_less_than_symbols_ax, % 8.43/1.90 p__greater__def_ax, p__greater_equal__def_ax, p__is_integer__def_ax, % 8.43/1.90 p__is_symbolic__def_ax, p__less__def_ax, strongly_connected_ordering_ax, % 8.43/1.90 transitive_ordering_ax % 8.43/1.90 % 8.43/1.90 Those formulas are unsatisfiable: % 8.43/1.90 --------------------------------- % 8.43/1.90 % 8.43/1.90 Begin of proof % 8.43/1.90 | % 8.43/1.90 | DELTA: instantiating (formula_6_unnamed_formula) with fresh symbol all_28_0 % 8.43/1.90 | gives: % 8.43/1.90 | (1) in_cover(all_28_0) = 0 & general(all_28_0) & ! [v0: int] : ( ~ % 8.43/1.90 | ($lesseq(v0, n_i)) | ~ ($lesseq(1, v0)) | ~ (f__integer__(v0) = % 8.43/1.90 | all_28_0)) % 8.43/1.90 | % 8.43/1.90 | ALPHA: (1) implies: % 8.43/1.90 | (2) general(all_28_0) % 8.43/1.90 | (3) in_cover(all_28_0) = 0 % 8.43/1.90 | (4) ! [v0: int] : ( ~ ($lesseq(v0, n_i)) | ~ ($lesseq(1, v0)) | ~ % 8.43/1.90 | (f__integer__(v0) = all_28_0)) % 8.43/1.90 | % 8.43/1.90 | GROUND_INST: instantiating (formula_5_completed_definition_of_in_cover_1) with % 8.43/1.90 | all_28_0, simplifying with (2), (3) gives: % 8.43/1.90 | (5) ? [v0: int] : ($lesseq(v0, n_i) & $lesseq(1, v0) & f__integer__(v0) = % 8.43/1.90 | all_28_0) % 8.43/1.90 | % 8.43/1.90 | DELTA: instantiating (5) with fresh symbol all_36_0 gives: % 8.43/1.91 | (6) $lesseq(all_36_0, n_i) & $lesseq(1, all_36_0) & f__integer__(all_36_0) % 8.43/1.91 | = all_28_0 % 8.43/1.91 | % 8.43/1.91 | ALPHA: (6) implies: % 8.43/1.91 | (7) $lesseq(1, all_36_0) % 8.43/1.91 | (8) $lesseq(all_36_0, n_i) % 8.43/1.91 | (9) f__integer__(all_36_0) = all_28_0 % 8.43/1.91 | % 8.43/1.91 | GROUND_INST: instantiating (4) with all_36_0, simplifying with (9) gives: % 8.43/1.91 | (10) ~ ($lesseq(all_36_0, n_i)) | ~ ($lesseq(1, all_36_0)) % 8.43/1.91 | % 8.43/1.91 | BETA: splitting (10) gives: % 8.43/1.91 | % 8.43/1.91 | Case 1: % 8.43/1.91 | | % 8.43/1.91 | | (11) $lesseq(1, $difference(all_36_0, n_i)) % 8.43/1.91 | | % 8.43/1.91 | | COMBINE_INEQS: (8), (11) imply: % 8.43/1.91 | | (12) $false % 8.43/1.91 | | % 8.43/1.91 | | CLOSE: (12) is inconsistent. % 8.43/1.91 | | % 8.43/1.91 | Case 2: % 8.43/1.91 | | % 8.43/1.91 | | (13) $lesseq(all_36_0, 0) % 8.43/1.91 | | % 8.43/1.91 | | COMBINE_INEQS: (7), (13) imply: % 8.43/1.91 | | (14) $false % 8.43/1.91 | | % 8.43/1.91 | | CLOSE: (14) is inconsistent. % 8.43/1.91 | | % 8.43/1.91 | End of split % 8.43/1.91 | % 8.43/1.91 End of proof % 8.43/1.91 % SZS output end Proof for theBenchmark % 8.43/1.91 % 8.43/1.91 1294ms %------------------------------------------------------------------------------