%------------------------------------------------------------------------------ % 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 : n014.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 10.19s 2.11s % Output : Proof 13.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n014.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 02:58:34 EDT 2025 % 0.19/0.34 % CPUTime : % 0.60/0.60 ________ _____ % 0.60/0.60 ___ __ \_________(_)________________________________ % 0.60/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.60/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.60/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.60/0.60 % 0.60/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.60/0.60 (2023-06-19) % 0.60/0.60 % 0.60/0.60 (c) Philipp Rümmer, 2009-2023 % 0.60/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.60/0.60 Amanda Stjerna. % 0.60/0.60 Free software under BSD-3-Clause. % 0.60/0.60 % 0.60/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.60/0.60 % 0.60/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.60/0.62 Running up to 7 provers in parallel. % 0.74/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.74/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.39/1.18 Prover 1: Preprocessing ... % 3.39/1.18 Prover 4: Preprocessing ... % 3.61/1.22 Prover 0: Preprocessing ... % 3.61/1.22 Prover 3: Preprocessing ... % 3.61/1.22 Prover 2: Preprocessing ... % 3.61/1.22 Prover 5: Preprocessing ... % 3.61/1.22 Prover 6: Preprocessing ... % 6.83/1.65 Prover 5: Proving ... % 6.83/1.67 Prover 6: Proving ... % 6.83/1.67 Prover 2: Proving ... % 6.83/1.67 Prover 0: Proving ... % 6.83/1.68 Prover 3: Constructing countermodel ... % 6.83/1.69 Prover 4: Constructing countermodel ... % 6.83/1.70 Prover 1: Constructing countermodel ... % 8.12/1.91 Prover 3: gave up % 8.82/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.82/1.94 Prover 1: gave up % 8.82/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.36/2.03 Prover 7: Preprocessing ... % 9.36/2.07 Prover 8: Preprocessing ... % 9.99/2.09 Prover 4: gave up % 10.19/2.11 Prover 5: proved (1465ms) % 10.19/2.11 % 10.19/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.19/2.11 % 10.19/2.11 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 10.19/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.19/2.11 Prover 0: stopped % 10.19/2.11 Prover 6: stopped % 10.19/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.19/2.11 Prover 2: stopped % 10.36/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.36/2.13 Prover 7: Warning: ignoring some quantifiers % 10.36/2.13 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.36/2.14 Prover 7: Constructing countermodel ... % 10.36/2.18 Prover 13: Preprocessing ... % 10.36/2.18 Prover 9: Preprocessing ... % 10.36/2.18 Prover 10: Preprocessing ... % 10.36/2.20 Prover 11: Preprocessing ... % 10.36/2.22 Prover 16: Preprocessing ... % 11.15/2.25 Prover 8: Warning: ignoring some quantifiers % 11.15/2.26 Prover 8: Constructing countermodel ... % 11.15/2.26 Prover 10: Warning: ignoring some quantifiers % 11.15/2.27 Prover 10: Constructing countermodel ... % 11.15/2.27 Prover 16: Warning: ignoring some quantifiers % 11.15/2.28 Prover 16: Constructing countermodel ... % 11.74/2.31 Prover 13: Warning: ignoring some quantifiers % 11.74/2.32 Prover 13: Constructing countermodel ... % 11.74/2.33 Prover 9: Constructing countermodel ... % 11.74/2.33 Prover 9: stopped % 11.74/2.33 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.74/2.36 Prover 19: Preprocessing ... % 12.34/2.41 Prover 11: Constructing countermodel ... % 12.34/2.44 Prover 8: gave up % 13.15/2.50 Prover 10: Found proof (size 31) % 13.15/2.50 Prover 10: proved (392ms) % 13.15/2.50 Prover 7: stopped % 13.15/2.50 Prover 16: stopped % 13.15/2.50 Prover 11: stopped % 13.15/2.50 Prover 13: stopped % 13.32/2.56 Prover 19: Warning: ignoring some quantifiers % 13.32/2.57 Prover 19: Constructing countermodel ... % 13.32/2.58 Prover 19: stopped % 13.32/2.58 % 13.32/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.32/2.58 % 13.32/2.59 % SZS output start Proof for theBenchmark % 13.32/2.59 Assumptions after simplification: % 13.32/2.59 --------------------------------- % 13.32/2.59 % 13.32/2.59 (formula_3_constraint_0) % 13.32/2.60 ! [v0: general] : ! [v1: general] : ! [v2: general] : ( ~ general(v2) | ~ % 13.32/2.60 general(v1) | ~ general(v0) | ~ s(v2, v1) | ~ s(v2, v0) | ~ in_cover(v1) % 13.32/2.60 | ~ in_cover(v0) | ~ p__less__(v0, v1)) % 13.32/2.60 % 13.32/2.60 (formula_5_completed_definition_of_in_cover_1) % 13.73/2.61 ! [v0: general] : ( ~ general(v0) | ~ in_cover(v0) | ? [v1: int] : % 13.73/2.61 ($lesseq(v1, n_i) & $lesseq(1, v1) & f__integer__(v1) = v0)) % 13.73/2.61 % 13.73/2.61 (formula_6_constraint_0) % 13.73/2.61 ? [v0: general] : ? [v1: general] : ? [v2: general] : ( ~ (v1 = v0) & % 13.73/2.61 general(v2) & general(v1) & general(v0) & s(v2, v1) & s(v2, v0) & % 13.73/2.61 in_cover(v1) & in_cover(v0)) % 13.73/2.61 % 13.73/2.61 (numeral_ordering_ax) % 13.73/2.61 ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 13.73/2.61 ($lesseq(1, $difference(v0, v1))) | ~ (f__integer__(v1) = v3) | ~ % 13.73/2.61 (f__integer__(v0) = v2) | ~ p__less_equal__(v2, v3)) & ! [v0: int] : ! % 13.73/2.61 [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ ($lesseq(v0, v1)) | ~ % 13.73/2.61 (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | p__less_equal__(v2, % 13.73/2.61 v3)) % 13.73/2.61 % 13.73/2.61 (p__less__def_ax) % 13.73/2.62 ! [v0: general] : ! [v1: general] : (v1 = v0 | ~ general(v1) | ~ % 13.73/2.62 general(v0) | ~ p__less_equal__(v0, v1) | p__less__(v0, v1)) & ! [v0: % 13.73/2.62 general] : ! [v1: general] : ( ~ general(v1) | ~ general(v0) | ~ % 13.73/2.62 p__less__(v0, v1) | p__less_equal__(v0, v1)) & ! [v0: general] : ( ~ % 13.73/2.62 general(v0) | ~ p__less__(v0, v0)) % 13.73/2.62 % 13.73/2.62 Further assumptions not needed in the proof: % 13.73/2.62 -------------------------------------------- % 13.73/2.62 antisymmetric_ordering_ax, f__integer__def_ax, f__symbolic__def_ax, % 13.73/2.62 formula_0_unnamed_formula, formula_1_completed_definition_of_covered_1, % 13.73/2.62 formula_2_completed_definition_of_covered_1, formula_4_constraint_1, % 13.73/2.62 general_universe_ax, maximal_element_ax, minimal_element_ax, % 13.73/2.62 numerals_less_than_symbols_ax, p__greater__def_ax, p__greater_equal__def_ax, % 13.73/2.62 p__is_integer__def_ax, p__is_symbolic__def_ax, strongly_connected_ordering_ax, % 13.73/2.62 transitive_ordering_ax % 13.73/2.62 % 13.73/2.62 Those formulas are unsatisfiable: % 13.73/2.62 --------------------------------- % 13.73/2.62 % 13.73/2.62 Begin of proof % 13.73/2.62 | % 13.73/2.62 | ALPHA: (numeral_ordering_ax) implies: % 13.73/2.62 | (1) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 13.73/2.62 | ($lesseq(v0, v1)) | ~ (f__integer__(v1) = v3) | ~ (f__integer__(v0) % 13.73/2.62 | = v2) | p__less_equal__(v2, v3)) % 13.73/2.62 | % 13.73/2.62 | ALPHA: (p__less__def_ax) implies: % 13.73/2.62 | (2) ! [v0: general] : ! [v1: general] : (v1 = v0 | ~ general(v1) | ~ % 13.73/2.62 | general(v0) | ~ p__less_equal__(v0, v1) | p__less__(v0, v1)) % 13.73/2.62 | % 13.73/2.62 | DELTA: instantiating (formula_6_constraint_0) with fresh symbols all_28_0, % 13.73/2.62 | all_28_1, all_28_2 gives: % 13.73/2.62 | (3) ~ (all_28_1 = all_28_2) & general(all_28_0) & general(all_28_1) & % 13.73/2.62 | general(all_28_2) & s(all_28_0, all_28_1) & s(all_28_0, all_28_2) & % 13.73/2.62 | in_cover(all_28_1) & in_cover(all_28_2) % 13.73/2.62 | % 13.73/2.62 | ALPHA: (3) implies: % 13.73/2.62 | (4) ~ (all_28_1 = all_28_2) % 13.73/2.62 | (5) in_cover(all_28_2) % 13.73/2.62 | (6) in_cover(all_28_1) % 13.73/2.62 | (7) s(all_28_0, all_28_2) % 13.73/2.62 | (8) s(all_28_0, all_28_1) % 13.73/2.62 | (9) general(all_28_2) % 13.73/2.62 | (10) general(all_28_1) % 13.73/2.62 | (11) general(all_28_0) % 13.73/2.62 | % 13.73/2.62 | GROUND_INST: instantiating (formula_5_completed_definition_of_in_cover_1) with % 13.73/2.62 | all_28_2, simplifying with (5), (9) gives: % 13.73/2.62 | (12) ? [v0: int] : ($lesseq(v0, n_i) & $lesseq(1, v0) & f__integer__(v0) = % 13.73/2.62 | all_28_2) % 13.73/2.62 | % 13.73/2.62 | GROUND_INST: instantiating (formula_5_completed_definition_of_in_cover_1) with % 13.73/2.62 | all_28_1, simplifying with (6), (10) gives: % 13.73/2.62 | (13) ? [v0: int] : ($lesseq(v0, n_i) & $lesseq(1, v0) & f__integer__(v0) = % 13.73/2.62 | all_28_1) % 13.73/2.62 | % 13.73/2.62 | DELTA: instantiating (13) with fresh symbol all_41_0 gives: % 13.73/2.62 | (14) $lesseq(all_41_0, n_i) & $lesseq(1, all_41_0) & f__integer__(all_41_0) % 13.73/2.62 | = all_28_1 % 13.73/2.62 | % 13.73/2.62 | ALPHA: (14) implies: % 13.73/2.63 | (15) f__integer__(all_41_0) = all_28_1 % 13.73/2.63 | % 13.73/2.63 | DELTA: instantiating (12) with fresh symbol all_44_0 gives: % 13.73/2.63 | (16) $lesseq(all_44_0, n_i) & $lesseq(1, all_44_0) & f__integer__(all_44_0) % 13.73/2.63 | = all_28_2 % 13.73/2.63 | % 13.73/2.63 | ALPHA: (16) implies: % 13.73/2.63 | (17) f__integer__(all_44_0) = all_28_2 % 13.73/2.63 | % 13.73/2.63 | GROUND_INST: instantiating (1) with all_41_0, all_44_0, all_28_1, all_28_2, % 13.73/2.63 | simplifying with (15), (17) gives: % 13.73/2.63 | (18) ~ ($lesseq(all_41_0, all_44_0)) | p__less_equal__(all_28_1, all_28_2) % 13.73/2.63 | % 13.73/2.63 | GROUND_INST: instantiating (1) with all_44_0, all_41_0, all_28_2, all_28_1, % 13.73/2.63 | simplifying with (15), (17) gives: % 13.73/2.63 | (19) ~ ($lesseq(all_44_0, all_41_0)) | p__less_equal__(all_28_2, all_28_1) % 13.73/2.63 | % 13.73/2.63 | BETA: splitting (19) gives: % 13.73/2.63 | % 13.73/2.63 | Case 1: % 13.73/2.63 | | % 13.73/2.63 | | (20) p__less_equal__(all_28_2, all_28_1) % 13.73/2.63 | | % 13.73/2.63 | | GROUND_INST: instantiating (2) with all_28_2, all_28_1, simplifying with % 13.73/2.63 | | (9), (10), (20) gives: % 13.73/2.63 | | (21) all_28_1 = all_28_2 | p__less__(all_28_2, all_28_1) % 13.73/2.63 | | % 13.73/2.63 | | BETA: splitting (21) gives: % 13.73/2.63 | | % 13.73/2.63 | | Case 1: % 13.73/2.63 | | | % 13.73/2.63 | | | (22) p__less__(all_28_2, all_28_1) % 13.73/2.63 | | | % 13.73/2.63 | | | GROUND_INST: instantiating (formula_3_constraint_0) with all_28_2, % 13.73/2.63 | | | all_28_1, all_28_0, simplifying with (5), (6), (7), (8), (9), % 13.73/2.63 | | | (10), (11), (22) gives: % 13.73/2.63 | | | (23) $false % 13.73/2.63 | | | % 13.73/2.63 | | | CLOSE: (23) is inconsistent. % 13.73/2.63 | | | % 13.73/2.63 | | Case 2: % 13.73/2.63 | | | % 13.73/2.63 | | | (24) all_28_1 = all_28_2 % 13.73/2.63 | | | % 13.73/2.63 | | | REDUCE: (4), (24) imply: % 13.73/2.63 | | | (25) $false % 13.73/2.63 | | | % 13.73/2.63 | | | CLOSE: (25) is inconsistent. % 13.73/2.63 | | | % 13.73/2.63 | | End of split % 13.73/2.63 | | % 13.73/2.63 | Case 2: % 13.73/2.63 | | % 13.73/2.63 | | (26) $lesseq(1, $difference(all_44_0, all_41_0)) % 13.73/2.63 | | % 13.73/2.63 | | BETA: splitting (18) gives: % 13.73/2.63 | | % 13.73/2.63 | | Case 1: % 13.73/2.63 | | | % 13.73/2.63 | | | (27) p__less_equal__(all_28_1, all_28_2) % 13.73/2.63 | | | % 13.73/2.63 | | | GROUND_INST: instantiating (2) with all_28_1, all_28_2, simplifying with % 13.73/2.63 | | | (9), (10), (27) gives: % 13.73/2.63 | | | (28) all_28_1 = all_28_2 | p__less__(all_28_1, all_28_2) % 13.73/2.63 | | | % 13.73/2.63 | | | BETA: splitting (28) gives: % 13.73/2.63 | | | % 13.73/2.63 | | | Case 1: % 13.73/2.63 | | | | % 13.73/2.63 | | | | (29) p__less__(all_28_1, all_28_2) % 13.73/2.63 | | | | % 13.73/2.63 | | | | GROUND_INST: instantiating (formula_3_constraint_0) with all_28_1, % 13.73/2.63 | | | | all_28_2, all_28_0, simplifying with (5), (6), (7), (8), % 13.73/2.63 | | | | (9), (10), (11), (29) gives: % 13.73/2.63 | | | | (30) $false % 13.73/2.63 | | | | % 13.73/2.63 | | | | CLOSE: (30) is inconsistent. % 13.73/2.63 | | | | % 13.73/2.63 | | | Case 2: % 13.73/2.63 | | | | % 13.73/2.63 | | | | (31) all_28_1 = all_28_2 % 13.73/2.63 | | | | % 13.73/2.63 | | | | REDUCE: (4), (31) imply: % 13.73/2.63 | | | | (32) $false % 13.73/2.63 | | | | % 13.73/2.63 | | | | CLOSE: (32) is inconsistent. % 13.73/2.63 | | | | % 13.73/2.63 | | | End of split % 13.73/2.63 | | | % 13.73/2.63 | | Case 2: % 13.73/2.63 | | | % 13.73/2.63 | | | (33) $lesseq(1, $difference(all_41_0, all_44_0)) % 13.73/2.63 | | | % 13.73/2.63 | | | COMBINE_INEQS: (26), (33) imply: % 13.73/2.63 | | | (34) $false % 13.73/2.63 | | | % 13.73/2.63 | | | CLOSE: (34) is inconsistent. % 13.73/2.63 | | | % 13.73/2.63 | | End of split % 13.73/2.63 | | % 13.73/2.63 | End of split % 13.73/2.63 | % 13.73/2.63 End of proof % 13.73/2.63 % SZS output end Proof for theBenchmark % 13.73/2.63 % 13.73/2.63 2030ms %------------------------------------------------------------------------------