%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET639+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 : 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 : Thu Aug 31 15:25:48 EDT 2023 % Result : Theorem 5.11s 1.50s % Output : Proof 6.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET639+3 : TPTP v8.1.2. Released v2.2.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 09:13:24 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.30/1.06 Prover 4: Preprocessing ... % 2.30/1.06 Prover 1: Preprocessing ... % 2.55/1.10 Prover 3: Preprocessing ... % 2.55/1.10 Prover 0: Preprocessing ... % 2.55/1.10 Prover 5: Preprocessing ... % 2.55/1.10 Prover 2: Preprocessing ... % 2.55/1.10 Prover 6: Preprocessing ... % 4.21/1.38 Prover 1: Warning: ignoring some quantifiers % 4.21/1.39 Prover 2: Proving ... % 4.21/1.39 Prover 3: Warning: ignoring some quantifiers % 4.21/1.39 Prover 3: Constructing countermodel ... % 4.21/1.39 Prover 6: Proving ... % 4.21/1.40 Prover 5: Proving ... % 4.21/1.40 Prover 1: Constructing countermodel ... % 4.21/1.40 Prover 4: Warning: ignoring some quantifiers % 4.21/1.41 Prover 0: Proving ... % 4.74/1.42 Prover 4: Constructing countermodel ... % 5.11/1.49 Prover 2: proved (853ms) % 5.11/1.50 % 5.11/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.11/1.50 % 5.11/1.51 Prover 3: stopped % 5.11/1.51 Prover 5: stopped % 5.11/1.51 Prover 6: stopped % 5.11/1.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.11/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.11/1.51 Prover 0: stopped % 5.11/1.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.11/1.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.11/1.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.11/1.53 Prover 4: Found proof (size 12) % 5.11/1.53 Prover 4: proved (883ms) % 5.11/1.53 Prover 7: Preprocessing ... % 5.11/1.53 Prover 8: Preprocessing ... % 5.11/1.54 Prover 11: Preprocessing ... % 5.11/1.54 Prover 1: stopped % 5.11/1.54 Prover 10: Preprocessing ... % 5.11/1.55 Prover 13: Preprocessing ... % 5.64/1.56 Prover 7: stopped % 5.64/1.56 Prover 10: stopped % 5.64/1.57 Prover 13: stopped % 5.64/1.58 Prover 11: stopped % 5.85/1.62 Prover 8: Warning: ignoring some quantifiers % 5.85/1.62 Prover 8: Constructing countermodel ... % 6.08/1.63 Prover 8: stopped % 6.08/1.63 % 6.08/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.08/1.63 % 6.08/1.63 % SZS output start Proof for theBenchmark % 6.08/1.64 Assumptions after simplification: % 6.08/1.64 --------------------------------- % 6.08/1.64 % 6.08/1.64 (commutativity_of_intersection) % 6.18/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~ % 6.18/1.66 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : % 6.18/1.66 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~ % 6.18/1.66 $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 6.18/1.66 % 6.18/1.66 (prove_th121) % 6.18/1.66 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = empty_set) & % 6.18/1.66 intersection(v1, v0) = empty_set & subset(v0, v1) = 0 & $i(v1) & $i(v0)) % 6.18/1.66 % 6.18/1.66 (subset_intersection) % 6.18/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (intersection(v0, v1) % 6.18/1.67 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0, % 6.18/1.67 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 6.18/1.67 $i(v1) | ~ $i(v0) | intersection(v0, v1) = v0) % 6.18/1.67 % 6.18/1.67 (function-axioms) % 6.18/1.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.18/1.67 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & % 6.18/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.18/1.67 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: % 6.18/1.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 6.18/1.67 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 6.18/1.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 6.18/1.67 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 6.18/1.67 % 6.18/1.67 Further assumptions not needed in the proof: % 6.18/1.67 -------------------------------------------- % 6.18/1.67 empty_defn, empty_set_defn, equal_defn, equal_member_defn, intersection_defn, % 6.18/1.67 reflexivity_of_subset, subset_defn % 6.18/1.67 % 6.18/1.67 Those formulas are unsatisfiable: % 6.18/1.67 --------------------------------- % 6.18/1.67 % 6.18/1.67 Begin of proof % 6.18/1.67 | % 6.18/1.67 | ALPHA: (subset_intersection) implies: % 6.18/1.67 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 6.18/1.67 | $i(v0) | intersection(v0, v1) = v0) % 6.18/1.67 | % 6.18/1.67 | ALPHA: (commutativity_of_intersection) implies: % 6.18/1.67 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = % 6.18/1.67 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) % 6.18/1.67 | % 6.18/1.67 | ALPHA: (prove_th121) implies: % 6.18/1.67 | (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = empty_set) & intersection(v1, v0) % 6.18/1.67 | = empty_set & subset(v0, v1) = 0 & $i(v1) & $i(v0)) % 6.18/1.68 | % 6.18/1.68 | ALPHA: (function-axioms) implies: % 6.18/1.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.18/1.68 | (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 6.18/1.68 | % 6.18/1.68 | DELTA: instantiating (3) with fresh symbols all_12_0, all_12_1 gives: % 6.18/1.68 | (5) ~ (all_12_1 = empty_set) & intersection(all_12_0, all_12_1) = % 6.18/1.68 | empty_set & subset(all_12_1, all_12_0) = 0 & $i(all_12_0) & % 6.18/1.68 | $i(all_12_1) % 6.18/1.68 | % 6.18/1.68 | ALPHA: (5) implies: % 6.18/1.68 | (6) ~ (all_12_1 = empty_set) % 6.18/1.68 | (7) $i(all_12_1) % 6.18/1.68 | (8) $i(all_12_0) % 6.18/1.68 | (9) subset(all_12_1, all_12_0) = 0 % 6.18/1.68 | (10) intersection(all_12_0, all_12_1) = empty_set % 6.18/1.68 | % 6.18/1.68 | GROUND_INST: instantiating (1) with all_12_1, all_12_0, simplifying with (7), % 6.18/1.68 | (8), (9) gives: % 6.18/1.68 | (11) intersection(all_12_1, all_12_0) = all_12_1 % 6.18/1.68 | % 6.18/1.68 | GROUND_INST: instantiating (2) with all_12_1, all_12_0, empty_set, simplifying % 6.18/1.68 | with (7), (8), (10) gives: % 6.18/1.68 | (12) intersection(all_12_1, all_12_0) = empty_set & $i(empty_set) % 6.18/1.68 | % 6.18/1.68 | ALPHA: (12) implies: % 6.18/1.68 | (13) intersection(all_12_1, all_12_0) = empty_set % 6.18/1.68 | % 6.18/1.68 | GROUND_INST: instantiating (4) with empty_set, all_12_1, all_12_0, all_12_1, % 6.18/1.68 | simplifying with (11), (13) gives: % 6.18/1.68 | (14) all_12_1 = empty_set % 6.18/1.68 | % 6.18/1.68 | REDUCE: (6), (14) imply: % 6.18/1.68 | (15) $false % 6.18/1.68 | % 6.18/1.68 | CLOSE: (15) is inconsistent. % 6.18/1.68 | % 6.18/1.68 End of proof % 6.18/1.68 % SZS output end Proof for theBenchmark % 6.18/1.69 % 6.18/1.69 1073ms %------------------------------------------------------------------------------