%------------------------------------------------------------------------------ % 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 : n024.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 7.51s 1.72s % Output : Proof 9.52s % 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 : n024.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 02:50:51 EDT 2025 % 0.13/0.35 % CPUTime : % 0.51/0.62 ________ _____ % 0.51/0.62 ___ __ \_________(_)________________________________ % 0.51/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.62 % 0.51/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.62 (2023-06-19) % 0.51/0.62 % 0.51/0.62 (c) Philipp Rümmer, 2009-2023 % 0.51/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.62 Amanda Stjerna. % 0.51/0.62 Free software under BSD-3-Clause. % 0.51/0.62 % 0.51/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.62 % 0.51/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.64/0.64 Running up to 7 provers in parallel. % 0.64/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.51/1.16 Prover 4: Preprocessing ... % 3.51/1.16 Prover 1: Preprocessing ... % 3.73/1.20 Prover 2: Preprocessing ... % 3.73/1.20 Prover 5: Preprocessing ... % 3.73/1.20 Prover 0: Preprocessing ... % 3.73/1.20 Prover 3: Preprocessing ... % 3.73/1.20 Prover 6: Preprocessing ... % 6.52/1.60 Prover 5: Proving ... % 6.52/1.60 Prover 3: Constructing countermodel ... % 6.52/1.62 Prover 2: Proving ... % 7.12/1.63 Prover 1: Constructing countermodel ... % 7.12/1.64 Prover 6: Proving ... % 7.12/1.65 Prover 0: Proving ... % 7.12/1.66 Prover 4: Constructing countermodel ... % 7.51/1.72 Prover 5: proved (1074ms) % 7.51/1.72 % 7.51/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.51/1.72 % 7.51/1.72 Prover 3: proved (1079ms) % 7.51/1.72 % 7.51/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.51/1.72 % 7.51/1.73 Prover 2: stopped % 7.51/1.74 Prover 6: stopped % 7.51/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.51/1.74 Prover 0: stopped % 7.51/1.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.51/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.06/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.06/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.06/1.77 Prover 1: Found proof (size 11) % 8.06/1.77 Prover 1: proved (1129ms) % 8.06/1.77 Prover 4: stopped % 8.64/1.85 Prover 7: Preprocessing ... % 8.64/1.86 Prover 8: Preprocessing ... % 8.64/1.87 Prover 13: Preprocessing ... % 8.64/1.87 Prover 10: Preprocessing ... % 8.64/1.88 Prover 7: stopped % 8.64/1.88 Prover 11: Preprocessing ... % 8.64/1.89 Prover 10: stopped % 8.64/1.90 Prover 13: stopped % 8.64/1.91 Prover 11: stopped % 9.52/1.98 Prover 8: Warning: ignoring some quantifiers % 9.52/1.99 Prover 8: Constructing countermodel ... % 9.52/2.00 Prover 8: stopped % 9.52/2.00 % 9.52/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.52/2.00 % 9.52/2.01 % SZS output start Proof for theBenchmark % 9.52/2.01 Assumptions after simplification: % 9.52/2.01 --------------------------------- % 9.52/2.01 % 9.52/2.01 (formula_5_completed_definition_of_in_cover_1) % 9.52/2.03 ! [v0: general] : ( ~ (in_cover(v0) = 0) | ~ general(v0) | ? [v1: int] : % 9.52/2.03 ($lesseq(v1, n_i) & $lesseq(1, v1) & f__integer__(v1) = v0)) % 9.52/2.03 % 9.52/2.03 (formula_8_completed_definition_of_in_cover_1) % 9.52/2.03 ? [v0: general] : (in_cover(v0) = 0 & general(v0) & ! [v1: int] : ( ~ % 9.52/2.03 ($lesseq(v1, n_i)) | ~ ($lesseq(1, v1)) | ~ (f__integer__(v1) = v0))) % 9.52/2.03 % 9.52/2.03 Further assumptions not needed in the proof: % 9.52/2.03 -------------------------------------------- % 9.52/2.03 antisymmetric_ordering_ax, f__integer__def_ax, f__symbolic__def_ax, % 9.52/2.03 formula_0_unnamed_formula, formula_1_completed_definition_of_covered_1, % 9.52/2.03 formula_2_completed_definition_of_covered_1, formula_3_constraint_0, % 9.52/2.03 formula_4_constraint_1, formula_6_constraint_0, formula_7_constraint_1, % 9.52/2.03 general_universe_ax, maximal_element_ax, minimal_element_ax, % 9.52/2.03 numeral_ordering_ax, numerals_less_than_symbols_ax, p__greater__def_ax, % 9.52/2.03 p__greater_equal__def_ax, p__is_integer__def_ax, p__is_symbolic__def_ax, % 9.52/2.03 p__less__def_ax, strongly_connected_ordering_ax, transitive_ordering_ax % 9.52/2.03 % 9.52/2.03 Those formulas are unsatisfiable: % 9.52/2.03 --------------------------------- % 9.52/2.03 % 9.52/2.03 Begin of proof % 9.52/2.03 | % 9.52/2.03 | DELTA: instantiating (formula_8_completed_definition_of_in_cover_1) with fresh % 9.52/2.03 | symbol all_30_0 gives: % 9.52/2.03 | (1) in_cover(all_30_0) = 0 & general(all_30_0) & ! [v0: int] : ( ~ % 9.52/2.03 | ($lesseq(v0, n_i)) | ~ ($lesseq(1, v0)) | ~ (f__integer__(v0) = % 9.52/2.03 | all_30_0)) % 9.52/2.03 | % 9.52/2.04 | ALPHA: (1) implies: % 9.52/2.04 | (2) general(all_30_0) % 9.52/2.04 | (3) in_cover(all_30_0) = 0 % 9.52/2.04 | (4) ! [v0: int] : ( ~ ($lesseq(v0, n_i)) | ~ ($lesseq(1, v0)) | ~ % 9.52/2.04 | (f__integer__(v0) = all_30_0)) % 9.52/2.04 | % 9.52/2.04 | GROUND_INST: instantiating (formula_5_completed_definition_of_in_cover_1) with % 9.52/2.04 | all_30_0, simplifying with (2), (3) gives: % 9.52/2.04 | (5) ? [v0: int] : ($lesseq(v0, n_i) & $lesseq(1, v0) & f__integer__(v0) = % 9.52/2.04 | all_30_0) % 9.52/2.04 | % 9.52/2.04 | DELTA: instantiating (5) with fresh symbol all_38_0 gives: % 9.52/2.04 | (6) $lesseq(all_38_0, n_i) & $lesseq(1, all_38_0) & f__integer__(all_38_0) % 9.52/2.04 | = all_30_0 % 9.52/2.04 | % 9.52/2.04 | ALPHA: (6) implies: % 9.52/2.04 | (7) $lesseq(1, all_38_0) % 9.52/2.04 | (8) $lesseq(all_38_0, n_i) % 9.52/2.04 | (9) f__integer__(all_38_0) = all_30_0 % 9.52/2.04 | % 9.52/2.04 | GROUND_INST: instantiating (4) with all_38_0, simplifying with (9) gives: % 9.52/2.04 | (10) ~ ($lesseq(all_38_0, n_i)) | ~ ($lesseq(1, all_38_0)) % 9.52/2.04 | % 9.52/2.04 | BETA: splitting (10) gives: % 9.52/2.04 | % 9.52/2.04 | Case 1: % 9.52/2.04 | | % 9.52/2.04 | | (11) $lesseq(1, $difference(all_38_0, n_i)) % 9.52/2.04 | | % 9.52/2.04 | | COMBINE_INEQS: (8), (11) imply: % 9.52/2.04 | | (12) $false % 9.52/2.04 | | % 9.52/2.04 | | CLOSE: (12) is inconsistent. % 9.52/2.04 | | % 9.52/2.04 | Case 2: % 9.52/2.04 | | % 9.52/2.04 | | (13) $lesseq(all_38_0, 0) % 9.52/2.04 | | % 9.52/2.04 | | COMBINE_INEQS: (7), (13) imply: % 9.52/2.04 | | (14) $false % 9.52/2.04 | | % 9.52/2.04 | | CLOSE: (14) is inconsistent. % 9.52/2.04 | | % 9.52/2.04 | End of split % 9.52/2.04 | % 9.52/2.04 End of proof % 9.52/2.04 % SZS output end Proof for theBenchmark % 9.52/2.04 % 9.52/2.04 1420ms %------------------------------------------------------------------------------