%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET002+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 : n001.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 15:23:01 EDT 2023 % Result : Theorem 4.42s 1.34s % Output : Proof 5.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET002+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.18/0.34 % Computer : n001.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Sat Aug 26 09:30:15 EDT 2023 % 0.18/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.83/0.97 Prover 4: Preprocessing ... % 1.83/0.97 Prover 1: Preprocessing ... % 2.32/1.02 Prover 2: Preprocessing ... % 2.32/1.02 Prover 3: Preprocessing ... % 2.32/1.02 Prover 6: Preprocessing ... % 2.32/1.02 Prover 5: Preprocessing ... % 2.32/1.02 Prover 0: Preprocessing ... % 3.95/1.22 Prover 3: Warning: ignoring some quantifiers % 3.95/1.22 Prover 5: Proving ... % 3.95/1.22 Prover 6: Proving ... % 3.95/1.23 Prover 1: Warning: ignoring some quantifiers % 3.95/1.23 Prover 2: Proving ... % 3.95/1.23 Prover 1: Constructing countermodel ... % 3.95/1.24 Prover 4: Warning: ignoring some quantifiers % 3.95/1.24 Prover 3: Constructing countermodel ... % 3.95/1.25 Prover 4: Constructing countermodel ... % 3.95/1.25 Prover 0: Proving ... % 4.42/1.34 Prover 3: proved (705ms) % 4.42/1.34 % 4.42/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.42/1.34 % 4.42/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.42/1.34 Prover 2: stopped % 4.42/1.34 Prover 0: stopped % 4.42/1.35 Prover 5: stopped % 4.42/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.42/1.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.42/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.42/1.35 Prover 6: proved (719ms) % 4.42/1.35 % 4.42/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.42/1.35 % 4.42/1.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.92/1.37 Prover 11: Preprocessing ... % 4.92/1.37 Prover 4: Found proof (size 14) % 4.92/1.37 Prover 4: proved (740ms) % 4.92/1.37 Prover 1: stopped % 4.92/1.37 Prover 7: Preprocessing ... % 4.92/1.38 Prover 10: Preprocessing ... % 4.92/1.38 Prover 8: Preprocessing ... % 4.92/1.39 Prover 13: Preprocessing ... % 4.92/1.39 Prover 10: stopped % 4.92/1.39 Prover 7: stopped % 4.92/1.40 Prover 13: stopped % 4.92/1.41 Prover 11: stopped % 4.92/1.43 Prover 8: Warning: ignoring some quantifiers % 4.92/1.44 Prover 8: Constructing countermodel ... % 4.92/1.44 Prover 8: stopped % 4.92/1.44 % 4.92/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.92/1.44 % 4.92/1.45 % SZS output start Proof for theBenchmark % 4.92/1.45 Assumptions after simplification: % 4.92/1.45 --------------------------------- % 4.92/1.45 % 4.92/1.45 (equal_defn) % 4.92/1.48 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ $i(v1) | % 4.92/1.48 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0: $i] % 4.92/1.48 : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 4.92/1.48 ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] : ! [v1: % 4.92/1.48 int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 4.92/1.48 % 4.92/1.48 (prove_idempotency_of_union) % 5.51/1.48 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & union(v0, v0) = v1 & $i(v1) & % 5.51/1.48 $i(v0)) % 5.51/1.48 % 5.51/1.48 (subset_union) % 5.51/1.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0, v1) = v2) | % 5.51/1.48 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 5.51/1.48 & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) % 5.51/1.48 | union(v0, v1) = v1) % 5.51/1.48 % 5.51/1.48 Further assumptions not needed in the proof: % 5.51/1.48 -------------------------------------------- % 5.51/1.48 commutativity_of_union, equal_member_defn, reflexivity_of_subset, subset_defn, % 5.51/1.48 union_defn % 5.51/1.48 % 5.51/1.48 Those formulas are unsatisfiable: % 5.51/1.48 --------------------------------- % 5.51/1.48 % 5.51/1.48 Begin of proof % 5.51/1.49 | % 5.51/1.49 | ALPHA: (subset_union) implies: % 5.51/1.49 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0, v1) % 5.51/1.49 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 5.51/1.49 | subset(v0, v1) = v3)) % 5.51/1.49 | % 5.51/1.49 | ALPHA: (equal_defn) implies: % 5.51/1.49 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ % 5.51/1.49 | $i(v0)) % 5.51/1.49 | % 5.51/1.49 | DELTA: instantiating (prove_idempotency_of_union) with fresh symbols all_9_0, % 5.51/1.49 | all_9_1 gives: % 5.51/1.49 | (3) ~ (all_9_0 = all_9_1) & union(all_9_1, all_9_1) = all_9_0 & % 5.51/1.49 | $i(all_9_0) & $i(all_9_1) % 5.51/1.49 | % 5.51/1.49 | ALPHA: (3) implies: % 5.51/1.49 | (4) ~ (all_9_0 = all_9_1) % 5.51/1.49 | (5) $i(all_9_1) % 5.51/1.49 | (6) union(all_9_1, all_9_1) = all_9_0 % 5.51/1.49 | % 5.51/1.49 | GROUND_INST: instantiating (1) with all_9_1, all_9_1, all_9_0, simplifying % 5.51/1.49 | with (5), (6) gives: % 5.51/1.49 | (7) all_9_0 = all_9_1 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1, % 5.51/1.49 | all_9_1) = v0) % 5.51/1.49 | % 5.51/1.49 | BETA: splitting (7) gives: % 5.51/1.49 | % 5.51/1.49 | Case 1: % 5.51/1.49 | | % 5.51/1.49 | | (8) all_9_0 = all_9_1 % 5.51/1.49 | | % 5.51/1.50 | | REDUCE: (4), (8) imply: % 5.51/1.50 | | (9) $false % 5.51/1.50 | | % 5.51/1.50 | | CLOSE: (9) is inconsistent. % 5.51/1.50 | | % 5.51/1.50 | Case 2: % 5.51/1.50 | | % 5.51/1.50 | | (10) ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1, all_9_1) = v0) % 5.51/1.50 | | % 5.51/1.50 | | DELTA: instantiating (10) with fresh symbol all_23_0 gives: % 5.51/1.50 | | (11) ~ (all_23_0 = 0) & subset(all_9_1, all_9_1) = all_23_0 % 5.51/1.50 | | % 5.51/1.50 | | ALPHA: (11) implies: % 5.51/1.50 | | (12) ~ (all_23_0 = 0) % 5.51/1.50 | | (13) subset(all_9_1, all_9_1) = all_23_0 % 5.51/1.50 | | % 5.51/1.50 | | GROUND_INST: instantiating (2) with all_9_1, all_23_0, simplifying with (5), % 5.51/1.50 | | (13) gives: % 5.51/1.50 | | (14) all_23_0 = 0 % 5.51/1.50 | | % 5.51/1.50 | | REDUCE: (12), (14) imply: % 5.51/1.50 | | (15) $false % 5.51/1.50 | | % 5.51/1.50 | | CLOSE: (15) is inconsistent. % 5.51/1.50 | | % 5.51/1.50 | End of split % 5.51/1.50 | % 5.51/1.50 End of proof % 5.51/1.50 % SZS output end Proof for theBenchmark % 5.51/1.50 % 5.51/1.50 890ms %------------------------------------------------------------------------------