%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET148+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 : n004.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 15:24:02 EDT 2023 % Result : Theorem 4.14s 1.28s % Output : Proof 5.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET148+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n004.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 : Sat Aug 26 09:21:52 EDT 2023 % 0.19/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 1.96/0.94 Prover 1: Preprocessing ... % 1.96/0.94 Prover 4: Preprocessing ... % 1.96/0.98 Prover 3: Preprocessing ... % 1.96/0.98 Prover 6: Preprocessing ... % 1.96/0.98 Prover 0: Preprocessing ... % 1.96/0.98 Prover 5: Preprocessing ... % 1.96/0.98 Prover 2: Preprocessing ... % 3.43/1.16 Prover 5: Proving ... % 3.43/1.18 Prover 2: Proving ... % 3.43/1.19 Prover 3: Warning: ignoring some quantifiers % 3.43/1.19 Prover 6: Proving ... % 3.43/1.19 Prover 3: Constructing countermodel ... % 3.43/1.20 Prover 1: Warning: ignoring some quantifiers % 3.43/1.20 Prover 4: Warning: ignoring some quantifiers % 3.43/1.21 Prover 1: Constructing countermodel ... % 4.14/1.22 Prover 4: Constructing countermodel ... % 4.14/1.22 Prover 0: Proving ... % 4.14/1.27 Prover 3: proved (658ms) % 4.14/1.28 % 4.14/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.14/1.28 % 4.14/1.28 Prover 0: proved (653ms) % 4.14/1.28 Prover 6: proved (657ms) % 4.14/1.28 % 4.14/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.14/1.28 % 4.14/1.28 % 4.14/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.14/1.28 % 4.14/1.28 Prover 5: stopped % 4.14/1.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.14/1.28 Prover 2: stopped % 4.14/1.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.14/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.14/1.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.14/1.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.68/1.30 Prover 10: Preprocessing ... % 4.68/1.31 Prover 7: Preprocessing ... % 4.68/1.31 Prover 13: Preprocessing ... % 4.68/1.31 Prover 8: Preprocessing ... % 4.68/1.31 Prover 11: Preprocessing ... % 4.68/1.31 Prover 1: Found proof (size 13) % 4.68/1.31 Prover 1: proved (702ms) % 4.68/1.32 Prover 4: stopped % 4.68/1.33 Prover 10: stopped % 4.68/1.33 Prover 7: stopped % 4.68/1.33 Prover 13: stopped % 4.68/1.34 Prover 11: stopped % 5.16/1.38 Prover 8: Warning: ignoring some quantifiers % 5.16/1.38 Prover 8: Constructing countermodel ... % 5.16/1.39 Prover 8: stopped % 5.16/1.39 % 5.16/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.16/1.39 % 5.16/1.39 % SZS output start Proof for theBenchmark % 5.16/1.39 Assumptions after simplification: % 5.16/1.39 --------------------------------- % 5.16/1.39 % 5.16/1.39 (equal_defn) % 5.16/1.42 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | % 5.16/1.42 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] % 5.16/1.42 : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 5.16/1.42 % 5.16/1.42 (prove_idempotency_of_intersection) % 5.16/1.43 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & intersection(v0, v0) = v1 & $i(v1) % 5.16/1.43 & $i(v0)) % 5.16/1.43 % 5.16/1.43 (subset_intersection) % 5.16/1.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (intersection(v0, v1) % 5.16/1.43 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0, % 5.16/1.43 v1) = v3)) % 5.16/1.43 % 5.16/1.43 Further assumptions not needed in the proof: % 5.16/1.43 -------------------------------------------- % 5.16/1.43 commutativity_of_intersection, equal_member_defn, intersection_defn, % 5.16/1.43 reflexivity_of_subset, subset_defn % 5.16/1.43 % 5.16/1.43 Those formulas are unsatisfiable: % 5.16/1.43 --------------------------------- % 5.16/1.43 % 5.16/1.43 Begin of proof % 5.16/1.43 | % 5.16/1.43 | ALPHA: (equal_defn) implies: % 5.16/1.43 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ % 5.16/1.43 | $i(v0)) % 5.16/1.43 | % 5.16/1.43 | DELTA: instantiating (prove_idempotency_of_intersection) with fresh symbols % 5.16/1.43 | all_9_0, all_9_1 gives: % 5.16/1.43 | (2) ~ (all_9_0 = all_9_1) & intersection(all_9_1, all_9_1) = all_9_0 & % 5.16/1.43 | $i(all_9_0) & $i(all_9_1) % 5.16/1.43 | % 5.16/1.43 | ALPHA: (2) implies: % 5.16/1.44 | (3) ~ (all_9_0 = all_9_1) % 5.16/1.44 | (4) $i(all_9_1) % 5.16/1.44 | (5) intersection(all_9_1, all_9_1) = all_9_0 % 5.16/1.44 | % 5.16/1.44 | GROUND_INST: instantiating (subset_intersection) with all_9_1, all_9_1, % 5.16/1.44 | all_9_0, simplifying with (4), (5) gives: % 5.16/1.44 | (6) all_9_0 = all_9_1 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1, % 5.16/1.44 | all_9_1) = v0) % 5.16/1.44 | % 5.16/1.44 | BETA: splitting (6) gives: % 5.16/1.44 | % 5.16/1.44 | Case 1: % 5.16/1.44 | | % 5.16/1.44 | | (7) all_9_0 = all_9_1 % 5.16/1.44 | | % 5.16/1.44 | | REDUCE: (3), (7) imply: % 5.16/1.44 | | (8) $false % 5.16/1.44 | | % 5.16/1.44 | | CLOSE: (8) is inconsistent. % 5.16/1.44 | | % 5.16/1.44 | Case 2: % 5.16/1.44 | | % 5.16/1.44 | | (9) ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1, all_9_1) = v0) % 5.16/1.44 | | % 5.16/1.44 | | DELTA: instantiating (9) with fresh symbol all_23_0 gives: % 5.16/1.44 | | (10) ~ (all_23_0 = 0) & subset(all_9_1, all_9_1) = all_23_0 % 5.16/1.44 | | % 5.16/1.44 | | ALPHA: (10) implies: % 5.16/1.44 | | (11) ~ (all_23_0 = 0) % 5.16/1.44 | | (12) subset(all_9_1, all_9_1) = all_23_0 % 5.16/1.44 | | % 5.16/1.44 | | GROUND_INST: instantiating (1) with all_9_1, all_23_0, simplifying with (4), % 5.16/1.44 | | (12) gives: % 5.16/1.44 | | (13) all_23_0 = 0 % 5.16/1.44 | | % 5.16/1.44 | | REDUCE: (11), (13) imply: % 5.16/1.44 | | (14) $false % 5.16/1.44 | | % 5.16/1.44 | | CLOSE: (14) is inconsistent. % 5.16/1.44 | | % 5.16/1.44 | End of split % 5.16/1.44 | % 5.16/1.44 End of proof % 5.16/1.45 % SZS output end Proof for theBenchmark % 5.16/1.45 % 5.16/1.45 852ms %------------------------------------------------------------------------------