%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET602+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 : n011.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 15:25:32 EDT 2023 % Result : Theorem 4.37s 1.40s % Output : Proof 5.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET602+3 : TPTP v8.1.2. Released v2.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 09:43:09 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.79/1.03 Prover 1: Preprocessing ... % 1.79/1.03 Prover 4: Preprocessing ... % 2.37/1.07 Prover 3: Preprocessing ... % 2.37/1.07 Prover 5: Preprocessing ... % 2.37/1.07 Prover 6: Preprocessing ... % 2.37/1.08 Prover 2: Preprocessing ... % 2.37/1.08 Prover 0: Preprocessing ... % 3.04/1.28 Prover 1: Constructing countermodel ... % 3.85/1.29 Prover 5: Proving ... % 3.85/1.30 Prover 2: Proving ... % 3.85/1.30 Prover 6: Proving ... % 3.85/1.31 Prover 3: Constructing countermodel ... % 3.85/1.32 Prover 4: Constructing countermodel ... % 3.85/1.33 Prover 0: Proving ... % 4.37/1.40 Prover 6: proved (719ms) % 4.37/1.40 % 4.37/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.37/1.40 % 4.37/1.40 Prover 5: stopped % 4.37/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.37/1.40 Prover 0: proved (731ms) % 4.37/1.40 % 4.37/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.37/1.40 % 4.37/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.37/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.37/1.41 Prover 2: stopped % 4.37/1.42 Prover 3: proved (744ms) % 4.37/1.42 % 4.95/1.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.95/1.42 % 4.95/1.43 Prover 8: Preprocessing ... % 4.95/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.95/1.43 Prover 1: Found proof (size 14) % 4.95/1.43 Prover 1: proved (751ms) % 4.95/1.43 Prover 7: Preprocessing ... % 4.95/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.95/1.43 Prover 10: Preprocessing ... % 4.95/1.43 Prover 11: Preprocessing ... % 4.95/1.43 Prover 4: stopped % 4.95/1.44 Prover 7: stopped % 4.95/1.45 Prover 13: Preprocessing ... % 4.95/1.45 Prover 10: stopped % 4.95/1.46 Prover 11: stopped % 4.95/1.46 Prover 13: stopped % 5.33/1.49 Prover 8: Warning: ignoring some quantifiers % 5.33/1.49 Prover 8: Constructing countermodel ... % 5.33/1.50 Prover 8: stopped % 5.33/1.50 % 5.33/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.33/1.50 % 5.33/1.50 % SZS output start Proof for theBenchmark % 5.33/1.50 Assumptions after simplification: % 5.33/1.50 --------------------------------- % 5.33/1.50 % 5.33/1.50 (difference_empty_set) % 5.33/1.53 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 5.33/1.53 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = % 5.33/1.53 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 5.33/1.53 (difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = % 5.33/1.53 0) % 5.33/1.53 % 5.33/1.53 (equal_defn) % 5.33/1.53 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | % 5.33/1.53 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] % 5.33/1.53 : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 5.33/1.53 % 5.33/1.53 (prove_self_difference_is_empty_set) % 5.33/1.53 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & % 5.33/1.54 difference(v0, v0) = v1 & $i(v1) & $i(v0)) % 5.33/1.54 % 5.33/1.54 Further assumptions not needed in the proof: % 5.33/1.54 -------------------------------------------- % 5.33/1.54 difference_defn, empty_defn, empty_set_defn, reflexivity_of_subset, subset_defn % 5.33/1.54 % 5.33/1.54 Those formulas are unsatisfiable: % 5.33/1.54 --------------------------------- % 5.33/1.54 % 5.33/1.54 Begin of proof % 5.33/1.54 | % 5.33/1.54 | ALPHA: (difference_empty_set) implies: % 5.33/1.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 5.33/1.54 | (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( % 5.33/1.54 | ~ (v3 = 0) & subset(v0, v1) = v3)) % 5.33/1.54 | % 5.33/1.54 | ALPHA: (equal_defn) implies: % 5.33/1.54 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ % 5.33/1.54 | $i(v0)) % 5.33/1.54 | % 5.33/1.54 | ALPHA: (prove_self_difference_is_empty_set) implies: % 5.33/1.54 | (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & difference(v0, v0) = % 5.33/1.54 | v1 & $i(v1) & $i(v0)) % 5.33/1.54 | % 5.33/1.54 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1 gives: % 5.33/1.54 | (4) ~ (all_11_0 = empty_set) & difference(all_11_1, all_11_1) = all_11_0 & % 5.33/1.54 | $i(all_11_0) & $i(all_11_1) % 5.33/1.54 | % 5.33/1.54 | ALPHA: (4) implies: % 5.33/1.54 | (5) ~ (all_11_0 = empty_set) % 5.33/1.54 | (6) $i(all_11_1) % 5.33/1.54 | (7) difference(all_11_1, all_11_1) = all_11_0 % 5.33/1.54 | % 5.33/1.55 | GROUND_INST: instantiating (1) with all_11_1, all_11_1, all_11_0, simplifying % 5.33/1.55 | with (6), (7) gives: % 5.33/1.55 | (8) all_11_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_11_1, % 5.33/1.55 | all_11_1) = v0) % 5.33/1.55 | % 5.33/1.55 | BETA: splitting (8) gives: % 5.33/1.55 | % 5.33/1.55 | Case 1: % 5.33/1.55 | | % 5.33/1.55 | | (9) all_11_0 = empty_set % 5.33/1.55 | | % 5.33/1.55 | | REDUCE: (5), (9) imply: % 5.33/1.55 | | (10) $false % 5.33/1.55 | | % 5.33/1.55 | | CLOSE: (10) is inconsistent. % 5.33/1.55 | | % 5.33/1.55 | Case 2: % 5.33/1.55 | | % 5.33/1.55 | | (11) ? [v0: int] : ( ~ (v0 = 0) & subset(all_11_1, all_11_1) = v0) % 5.33/1.55 | | % 5.33/1.55 | | DELTA: instantiating (11) with fresh symbol all_20_0 gives: % 5.33/1.55 | | (12) ~ (all_20_0 = 0) & subset(all_11_1, all_11_1) = all_20_0 % 5.33/1.55 | | % 5.33/1.55 | | ALPHA: (12) implies: % 5.33/1.55 | | (13) ~ (all_20_0 = 0) % 5.33/1.55 | | (14) subset(all_11_1, all_11_1) = all_20_0 % 5.33/1.55 | | % 5.33/1.55 | | GROUND_INST: instantiating (2) with all_11_1, all_20_0, simplifying with % 5.33/1.55 | | (6), (14) gives: % 5.33/1.55 | | (15) all_20_0 = 0 % 5.33/1.55 | | % 5.33/1.55 | | REDUCE: (13), (15) imply: % 5.33/1.55 | | (16) $false % 5.33/1.55 | | % 5.33/1.55 | | CLOSE: (16) is inconsistent. % 5.33/1.55 | | % 5.33/1.55 | End of split % 5.33/1.55 | % 5.33/1.55 End of proof % 5.33/1.55 % SZS output end Proof for theBenchmark % 5.33/1.55 % 5.33/1.55 898ms %------------------------------------------------------------------------------