%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET063+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 : n006.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 15:23:31 EDT 2023 % Result : Theorem 4.06s 1.30s % Output : Proof 5.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET063+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 : n006.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 13:59:52 EDT 2023 % 0.19/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 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 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 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 % 1.89/1.01 Prover 1: Preprocessing ... % 1.89/1.01 Prover 4: Preprocessing ... % 2.43/1.05 Prover 0: Preprocessing ... % 2.43/1.05 Prover 5: Preprocessing ... % 2.43/1.05 Prover 6: Preprocessing ... % 2.43/1.05 Prover 3: Preprocessing ... % 2.43/1.05 Prover 2: Preprocessing ... % 3.09/1.18 Prover 5: Proving ... % 3.09/1.18 Prover 2: Proving ... % 3.09/1.19 Prover 6: Proving ... % 3.50/1.20 Prover 3: Constructing countermodel ... % 3.50/1.21 Prover 1: Constructing countermodel ... % 3.50/1.22 Prover 4: Constructing countermodel ... % 3.50/1.22 Prover 0: Proving ... % 4.06/1.30 Prover 0: proved (670ms) % 4.06/1.30 Prover 2: proved (670ms) % 4.06/1.30 Prover 5: proved (664ms) % 4.06/1.30 Prover 6: proved (664ms) % 4.06/1.30 % 4.06/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.06/1.30 % 4.06/1.30 % 4.06/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.06/1.30 % 4.06/1.30 % 4.06/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.06/1.30 % 4.06/1.30 % 4.06/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.06/1.30 % 4.06/1.30 Prover 3: proved (669ms) % 4.06/1.30 % 4.06/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.06/1.30 % 4.06/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.06/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.06/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.06/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.06/1.31 Prover 4: Found proof (size 14) % 4.06/1.31 Prover 1: Found proof (size 14) % 4.06/1.31 Prover 1: proved (680ms) % 4.06/1.31 Prover 4: proved (674ms) % 4.06/1.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.06/1.32 Prover 11: Preprocessing ... % 4.06/1.33 Prover 8: Preprocessing ... % 4.06/1.33 Prover 10: Preprocessing ... % 4.06/1.33 Prover 13: Preprocessing ... % 4.06/1.33 Prover 7: Preprocessing ... % 4.06/1.36 Prover 7: Warning: ignoring some quantifiers % 4.06/1.36 Prover 13: Warning: ignoring some quantifiers % 4.06/1.36 Prover 11: stopped % 4.06/1.36 Prover 7: Constructing countermodel ... % 4.06/1.36 Prover 13: Constructing countermodel ... % 4.06/1.37 Prover 13: stopped % 4.06/1.37 Prover 7: stopped % 4.06/1.37 Prover 10: Warning: ignoring some quantifiers % 4.06/1.37 Prover 10: Constructing countermodel ... % 4.06/1.38 Prover 10: stopped % 4.06/1.39 Prover 8: Warning: ignoring some quantifiers % 4.06/1.39 Prover 8: Constructing countermodel ... % 4.55/1.40 Prover 8: stopped % 4.55/1.40 % 4.55/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.55/1.40 % 4.55/1.40 % SZS output start Proof for theBenchmark % 4.55/1.40 Assumptions after simplification: % 4.55/1.40 --------------------------------- % 4.55/1.40 % 4.55/1.41 (empty_set_subset) % 5.09/1.43 $i(empty_set) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, % 5.09/1.43 v0) = v1) | ~ $i(v0)) % 5.09/1.43 % 5.09/1.43 (equal_defn) % 5.09/1.44 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | % 5.09/1.44 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] % 5.09/1.44 : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 5.09/1.44 % 5.09/1.44 (prove_subset_of_empty_set_is_empty_set) % 5.09/1.44 $i(empty_set) & ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, empty_set) = 0 % 5.09/1.44 & $i(v0)) % 5.09/1.44 % 5.09/1.44 Further assumptions not needed in the proof: % 5.09/1.44 -------------------------------------------- % 5.09/1.44 empty_defn, empty_set_defn, reflexivity_of_subset, subset_defn % 5.09/1.44 % 5.09/1.44 Those formulas are unsatisfiable: % 5.09/1.44 --------------------------------- % 5.09/1.44 % 5.09/1.44 Begin of proof % 5.09/1.44 | % 5.09/1.44 | ALPHA: (empty_set_subset) implies: % 5.09/1.44 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, v0) = v1) % 5.09/1.44 | | ~ $i(v0)) % 5.09/1.44 | % 5.09/1.44 | ALPHA: (equal_defn) implies: % 5.09/1.44 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ % 5.09/1.45 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = % 5.09/1.45 | v2)) % 5.09/1.45 | % 5.09/1.45 | ALPHA: (prove_subset_of_empty_set_is_empty_set) implies: % 5.09/1.45 | (3) $i(empty_set) % 5.09/1.45 | (4) ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, empty_set) = 0 & % 5.09/1.45 | $i(v0)) % 5.09/1.45 | % 5.09/1.45 | DELTA: instantiating (4) with fresh symbol all_10_0 gives: % 5.09/1.45 | (5) ~ (all_10_0 = empty_set) & subset(all_10_0, empty_set) = 0 & % 5.09/1.45 | $i(all_10_0) % 5.09/1.45 | % 5.09/1.45 | ALPHA: (5) implies: % 5.09/1.45 | (6) ~ (all_10_0 = empty_set) % 5.09/1.45 | (7) $i(all_10_0) % 5.09/1.45 | (8) subset(all_10_0, empty_set) = 0 % 5.09/1.45 | % 5.09/1.45 | GROUND_INST: instantiating (2) with all_10_0, empty_set, simplifying with (3), % 5.09/1.45 | (7), (8) gives: % 5.09/1.45 | (9) all_10_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, % 5.09/1.45 | all_10_0) = v0) % 5.09/1.45 | % 5.09/1.45 | BETA: splitting (9) gives: % 5.09/1.45 | % 5.09/1.45 | Case 1: % 5.09/1.45 | | % 5.09/1.45 | | (10) all_10_0 = empty_set % 5.09/1.45 | | % 5.09/1.45 | | REDUCE: (6), (10) imply: % 5.09/1.45 | | (11) $false % 5.09/1.45 | | % 5.09/1.45 | | CLOSE: (11) is inconsistent. % 5.09/1.45 | | % 5.09/1.45 | Case 2: % 5.09/1.45 | | % 5.09/1.45 | | (12) ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, all_10_0) = v0) % 5.09/1.46 | | % 5.09/1.46 | | DELTA: instantiating (12) with fresh symbol all_22_0 gives: % 5.09/1.46 | | (13) ~ (all_22_0 = 0) & subset(empty_set, all_10_0) = all_22_0 % 5.09/1.46 | | % 5.09/1.46 | | ALPHA: (13) implies: % 5.09/1.46 | | (14) ~ (all_22_0 = 0) % 5.09/1.46 | | (15) subset(empty_set, all_10_0) = all_22_0 % 5.09/1.46 | | % 5.09/1.46 | | GROUND_INST: instantiating (1) with all_10_0, all_22_0, simplifying with % 5.09/1.46 | | (7), (15) gives: % 5.09/1.46 | | (16) all_22_0 = 0 % 5.09/1.46 | | % 5.09/1.46 | | REDUCE: (14), (16) imply: % 5.09/1.46 | | (17) $false % 5.09/1.46 | | % 5.09/1.46 | | CLOSE: (17) is inconsistent. % 5.09/1.46 | | % 5.09/1.46 | End of split % 5.09/1.46 | % 5.09/1.46 End of proof % 5.09/1.46 % SZS output end Proof for theBenchmark % 5.09/1.46 % 5.09/1.46 850ms %------------------------------------------------------------------------------