%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET598+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 : Thu Aug 31 15:25:30 EDT 2023 % Result : Theorem 5.12s 1.55s % Output : Proof 8.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET598+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n028.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 : Sat Aug 26 16:28:22 EDT 2023 % 0.13/0.34 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 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 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 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 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 % 2.06/0.99 Prover 4: Preprocessing ... % 2.06/0.99 Prover 1: Preprocessing ... % 2.06/1.03 Prover 2: Preprocessing ... % 2.06/1.03 Prover 0: Preprocessing ... % 2.06/1.03 Prover 6: Preprocessing ... % 2.06/1.03 Prover 5: Preprocessing ... % 2.06/1.04 Prover 3: Preprocessing ... % 4.18/1.27 Prover 1: Warning: ignoring some quantifiers % 4.18/1.27 Prover 3: Warning: ignoring some quantifiers % 4.18/1.28 Prover 4: Warning: ignoring some quantifiers % 4.18/1.28 Prover 3: Constructing countermodel ... % 4.18/1.28 Prover 5: Proving ... % 4.18/1.28 Prover 0: Proving ... % 4.18/1.28 Prover 2: Proving ... % 4.18/1.28 Prover 6: Proving ... % 4.18/1.28 Prover 1: Constructing countermodel ... % 4.18/1.29 Prover 4: Constructing countermodel ... % 5.12/1.54 Prover 0: proved (922ms) % 5.12/1.55 % 5.12/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.12/1.55 % 5.12/1.55 Prover 3: stopped % 5.12/1.55 Prover 5: stopped % 5.12/1.55 Prover 2: stopped % 5.12/1.56 Prover 6: stopped % 5.12/1.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.12/1.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.12/1.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.12/1.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.12/1.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.12/1.58 Prover 10: Preprocessing ... % 6.35/1.58 Prover 8: Preprocessing ... % 6.35/1.58 Prover 7: Preprocessing ... % 6.35/1.59 Prover 13: Preprocessing ... % 6.35/1.61 Prover 11: Preprocessing ... % 6.35/1.63 Prover 10: Warning: ignoring some quantifiers % 6.35/1.63 Prover 7: Warning: ignoring some quantifiers % 6.35/1.63 Prover 10: Constructing countermodel ... % 6.35/1.63 Prover 7: Constructing countermodel ... % 6.81/1.65 Prover 13: Warning: ignoring some quantifiers % 6.91/1.66 Prover 13: Constructing countermodel ... % 6.91/1.68 Prover 8: Warning: ignoring some quantifiers % 6.91/1.69 Prover 8: Constructing countermodel ... % 7.33/1.71 Prover 11: Warning: ignoring some quantifiers % 7.33/1.72 Prover 11: Constructing countermodel ... % 7.33/1.72 Prover 1: gave up % 7.33/1.73 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.65/1.75 Prover 10: Found proof (size 28) % 7.65/1.75 Prover 10: proved (197ms) % 7.65/1.75 Prover 7: stopped % 7.65/1.75 Prover 11: stopped % 7.65/1.76 Prover 4: stopped % 7.65/1.76 Prover 13: stopped % 7.65/1.76 Prover 8: stopped % 7.65/1.76 Prover 16: Preprocessing ... % 7.65/1.77 Prover 16: stopped % 7.65/1.77 % 7.65/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.65/1.77 % 7.65/1.78 % SZS output start Proof for theBenchmark % 7.65/1.78 Assumptions after simplification: % 7.65/1.78 --------------------------------- % 7.65/1.78 % 7.65/1.78 (commutativity_of_intersection) % 7.65/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ % 7.65/1.81 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 7.65/1.81 % 7.65/1.81 (equal_defn) % 7.65/1.81 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v1, % 7.65/1.81 v0) | ~ subset(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | subset(v0, v0)) % 7.65/1.81 % 7.65/1.81 (intersection_is_subset) % 7.65/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ % 7.65/1.81 $i(v1) | ~ $i(v0) | subset(v2, v0)) % 7.65/1.81 % 7.65/1.81 (intersection_of_subsets) % 7.65/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, % 7.65/1.81 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v2) | ~ % 7.65/1.81 subset(v0, v1) | subset(v0, v3)) % 7.65/1.81 % 7.65/1.81 (prove_th57) % 7.65/1.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 7.65/1.81 (intersection(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v3 % 7.65/1.81 = v0 & ( ~ subset(v0, v2) | ~ subset(v0, v1) | (subset(v4, v2) & % 7.65/1.81 subset(v4, v1) & ~ subset(v4, v0)))) | ( ~ (v3 = v0) & subset(v0, % 7.65/1.81 v2) & subset(v0, v1) & ! [v5: $i] : ( ~ $i(v5) | ~ subset(v5, v2) | % 7.65/1.81 ~ subset(v5, v1) | subset(v5, v0))))) % 7.65/1.81 % 7.65/1.81 Further assumptions not needed in the proof: % 7.65/1.81 -------------------------------------------- % 7.65/1.82 equal_member_defn, intersection_defn, reflexivity_of_subset, subset_defn % 7.65/1.82 % 7.65/1.82 Those formulas are unsatisfiable: % 7.65/1.82 --------------------------------- % 7.65/1.82 % 7.65/1.82 Begin of proof % 7.65/1.82 | % 7.65/1.82 | ALPHA: (equal_defn) implies: % 7.65/1.82 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 7.65/1.82 | subset(v1, v0) | ~ subset(v0, v1)) % 7.65/1.82 | % 7.65/1.82 | DELTA: instantiating (prove_th57) with fresh symbols all_13_0, all_13_1, % 7.65/1.82 | all_13_2, all_13_3, all_13_4 gives: % 7.65/1.82 | (2) intersection(all_13_3, all_13_2) = all_13_1 & $i(all_13_0) & % 7.65/1.82 | $i(all_13_1) & $i(all_13_2) & $i(all_13_3) & $i(all_13_4) & ((all_13_1 % 7.65/1.82 | = all_13_4 & ( ~ subset(all_13_4, all_13_2) | ~ subset(all_13_4, % 7.65/1.82 | all_13_3) | (subset(all_13_0, all_13_2) & subset(all_13_0, % 7.65/1.82 | all_13_3) & ~ subset(all_13_0, all_13_4)))) | ( ~ (all_13_1 % 7.65/1.82 | = all_13_4) & subset(all_13_4, all_13_2) & subset(all_13_4, % 7.65/1.82 | all_13_3) & ! [v0: $i] : ( ~ $i(v0) | ~ subset(v0, all_13_2) | % 7.65/1.82 | ~ subset(v0, all_13_3) | subset(v0, all_13_4)))) % 7.65/1.82 | % 7.65/1.82 | ALPHA: (2) implies: % 7.65/1.82 | (3) $i(all_13_4) % 7.65/1.82 | (4) $i(all_13_3) % 7.65/1.82 | (5) $i(all_13_2) % 7.65/1.82 | (6) $i(all_13_0) % 7.65/1.82 | (7) intersection(all_13_3, all_13_2) = all_13_1 % 7.65/1.82 | (8) (all_13_1 = all_13_4 & ( ~ subset(all_13_4, all_13_2) | ~ % 7.65/1.82 | subset(all_13_4, all_13_3) | (subset(all_13_0, all_13_2) & % 7.65/1.82 | subset(all_13_0, all_13_3) & ~ subset(all_13_0, all_13_4)))) | ( % 7.65/1.83 | ~ (all_13_1 = all_13_4) & subset(all_13_4, all_13_2) & % 7.65/1.83 | subset(all_13_4, all_13_3) & ! [v0: $i] : ( ~ $i(v0) | ~ subset(v0, % 7.65/1.83 | all_13_2) | ~ subset(v0, all_13_3) | subset(v0, all_13_4))) % 7.65/1.83 | % 7.65/1.83 | GROUND_INST: instantiating (intersection_is_subset) with all_13_3, all_13_2, % 7.65/1.83 | all_13_1, simplifying with (4), (5), (7) gives: % 7.65/1.83 | (9) subset(all_13_1, all_13_3) % 7.65/1.83 | % 7.65/1.83 | GROUND_INST: instantiating (commutativity_of_intersection) with all_13_3, % 7.65/1.83 | all_13_2, all_13_1, simplifying with (4), (5), (7) gives: % 7.65/1.83 | (10) intersection(all_13_2, all_13_3) = all_13_1 & $i(all_13_1) % 7.65/1.83 | % 7.65/1.83 | ALPHA: (10) implies: % 7.65/1.83 | (11) $i(all_13_1) % 7.65/1.83 | (12) intersection(all_13_2, all_13_3) = all_13_1 % 7.65/1.83 | % 7.65/1.83 | GROUND_INST: instantiating (intersection_is_subset) with all_13_2, all_13_3, % 7.65/1.83 | all_13_1, simplifying with (4), (5), (12) gives: % 7.65/1.83 | (13) subset(all_13_1, all_13_2) % 7.65/1.83 | % 7.65/1.83 | BETA: splitting (8) gives: % 7.65/1.83 | % 7.65/1.83 | Case 1: % 7.65/1.83 | | % 7.65/1.83 | | (14) all_13_1 = all_13_4 & ( ~ subset(all_13_4, all_13_2) | ~ % 7.65/1.83 | | subset(all_13_4, all_13_3) | (subset(all_13_0, all_13_2) & % 7.65/1.83 | | subset(all_13_0, all_13_3) & ~ subset(all_13_0, all_13_4))) % 7.65/1.83 | | % 7.65/1.83 | | ALPHA: (14) implies: % 7.65/1.83 | | (15) all_13_1 = all_13_4 % 7.65/1.83 | | (16) ~ subset(all_13_4, all_13_2) | ~ subset(all_13_4, all_13_3) | % 7.65/1.83 | | (subset(all_13_0, all_13_2) & subset(all_13_0, all_13_3) & ~ % 7.65/1.83 | | subset(all_13_0, all_13_4)) % 7.65/1.83 | | % 7.65/1.83 | | REDUCE: (12), (15) imply: % 7.65/1.83 | | (17) intersection(all_13_2, all_13_3) = all_13_4 % 7.65/1.83 | | % 7.65/1.83 | | REDUCE: (13), (15) imply: % 7.65/1.83 | | (18) subset(all_13_4, all_13_2) % 7.65/1.83 | | % 7.65/1.83 | | REDUCE: (9), (15) imply: % 7.65/1.83 | | (19) subset(all_13_4, all_13_3) % 7.65/1.83 | | % 7.65/1.83 | | BETA: splitting (16) gives: % 7.65/1.83 | | % 7.65/1.83 | | Case 1: % 7.65/1.83 | | | % 7.65/1.83 | | | (20) ~ subset(all_13_4, all_13_2) % 7.65/1.83 | | | % 7.65/1.83 | | | PRED_UNIFY: (18), (20) imply: % 7.65/1.83 | | | (21) $false % 7.65/1.83 | | | % 7.65/1.83 | | | CLOSE: (21) is inconsistent. % 7.65/1.83 | | | % 7.65/1.83 | | Case 2: % 7.65/1.83 | | | % 7.65/1.83 | | | (22) ~ subset(all_13_4, all_13_3) | (subset(all_13_0, all_13_2) & % 7.65/1.83 | | | subset(all_13_0, all_13_3) & ~ subset(all_13_0, all_13_4)) % 7.65/1.83 | | | % 7.65/1.83 | | | BETA: splitting (22) gives: % 7.65/1.83 | | | % 7.65/1.83 | | | Case 1: % 7.65/1.83 | | | | % 7.65/1.83 | | | | (23) ~ subset(all_13_4, all_13_3) % 7.65/1.83 | | | | % 7.65/1.83 | | | | PRED_UNIFY: (19), (23) imply: % 7.65/1.83 | | | | (24) $false % 7.65/1.83 | | | | % 7.65/1.83 | | | | CLOSE: (24) is inconsistent. % 7.65/1.83 | | | | % 7.65/1.83 | | | Case 2: % 7.65/1.83 | | | | % 7.65/1.83 | | | | (25) subset(all_13_0, all_13_2) & subset(all_13_0, all_13_3) & ~ % 7.65/1.83 | | | | subset(all_13_0, all_13_4) % 7.65/1.83 | | | | % 7.65/1.83 | | | | ALPHA: (25) implies: % 7.65/1.83 | | | | (26) ~ subset(all_13_0, all_13_4) % 7.65/1.83 | | | | (27) subset(all_13_0, all_13_3) % 7.65/1.83 | | | | (28) subset(all_13_0, all_13_2) % 7.65/1.84 | | | | % 7.65/1.84 | | | | GROUND_INST: instantiating (intersection_of_subsets) with all_13_0, % 7.65/1.84 | | | | all_13_2, all_13_3, all_13_4, simplifying with (4), (5), % 7.65/1.84 | | | | (6), (17), (26), (27), (28) gives: % 7.65/1.84 | | | | (29) $false % 7.65/1.84 | | | | % 7.65/1.84 | | | | CLOSE: (29) is inconsistent. % 7.65/1.84 | | | | % 7.65/1.84 | | | End of split % 7.65/1.84 | | | % 7.65/1.84 | | End of split % 7.65/1.84 | | % 7.65/1.84 | Case 2: % 7.65/1.84 | | % 7.65/1.84 | | (30) ~ (all_13_1 = all_13_4) & subset(all_13_4, all_13_2) & % 7.65/1.84 | | subset(all_13_4, all_13_3) & ! [v0: $i] : ( ~ $i(v0) | ~ % 7.65/1.84 | | subset(v0, all_13_2) | ~ subset(v0, all_13_3) | subset(v0, % 7.65/1.84 | | all_13_4)) % 7.65/1.84 | | % 7.65/1.84 | | ALPHA: (30) implies: % 7.65/1.84 | | (31) ~ (all_13_1 = all_13_4) % 7.65/1.84 | | (32) subset(all_13_4, all_13_3) % 7.65/1.84 | | (33) subset(all_13_4, all_13_2) % 8.08/1.84 | | (34) ! [v0: $i] : ( ~ $i(v0) | ~ subset(v0, all_13_2) | ~ subset(v0, % 8.08/1.84 | | all_13_3) | subset(v0, all_13_4)) % 8.08/1.84 | | % 8.08/1.84 | | GROUND_INST: instantiating (34) with all_13_1, simplifying with (9), (11), % 8.08/1.84 | | (13) gives: % 8.08/1.84 | | (35) subset(all_13_1, all_13_4) % 8.08/1.84 | | % 8.08/1.84 | | GROUND_INST: instantiating (intersection_of_subsets) with all_13_4, % 8.08/1.84 | | all_13_3, all_13_2, all_13_1, simplifying with (3), (4), (5), % 8.08/1.84 | | (7), (32), (33) gives: % 8.08/1.84 | | (36) subset(all_13_4, all_13_1) % 8.08/1.84 | | % 8.08/1.84 | | GROUND_INST: instantiating (1) with all_13_1, all_13_4, simplifying with % 8.08/1.84 | | (3), (11), (35), (36) gives: % 8.08/1.84 | | (37) all_13_1 = all_13_4 % 8.08/1.84 | | % 8.08/1.84 | | REDUCE: (31), (37) imply: % 8.08/1.84 | | (38) $false % 8.08/1.84 | | % 8.08/1.84 | | CLOSE: (38) is inconsistent. % 8.08/1.84 | | % 8.08/1.84 | End of split % 8.08/1.84 | % 8.08/1.84 End of proof % 8.08/1.84 % SZS output end Proof for theBenchmark % 8.08/1.84 % 8.08/1.84 1239ms %------------------------------------------------------------------------------