%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET027+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 : n005.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 15:23:15 EDT 2023 % Result : Theorem 3.87s 1.35s % Output : Proof 5.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : SET027+3 : TPTP v8.1.2. Released v2.2.0. % 0.05/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n005.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sat Aug 26 10:42:38 EDT 2023 % 0.11/0.32 % CPUTime : % 0.16/0.60 ________ _____ % 0.16/0.60 ___ __ \_________(_)________________________________ % 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.60 % 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.60 (2023-06-19) % 0.16/0.60 % 0.16/0.60 (c) Philipp Rümmer, 2009-2023 % 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.60 Amanda Stjerna. % 0.16/0.60 Free software under BSD-3-Clause. % 0.16/0.60 % 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.60 % 0.16/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.62 Running up to 7 provers in parallel. % 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.52/1.01 Prover 1: Preprocessing ... % 1.52/1.01 Prover 4: Preprocessing ... % 2.02/1.06 Prover 3: Preprocessing ... % 2.02/1.06 Prover 2: Preprocessing ... % 2.02/1.06 Prover 0: Preprocessing ... % 2.02/1.06 Prover 6: Preprocessing ... % 2.02/1.06 Prover 5: Preprocessing ... % 2.82/1.16 Prover 5: Proving ... % 2.82/1.16 Prover 2: Proving ... % 2.89/1.17 Prover 0: Proving ... % 2.89/1.17 Prover 6: Proving ... % 2.89/1.18 Prover 1: Constructing countermodel ... % 2.89/1.18 Prover 3: Constructing countermodel ... % 2.89/1.18 Prover 4: Constructing countermodel ... % 3.87/1.35 Prover 3: proved (722ms) % 3.87/1.35 % 3.87/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.87/1.35 % 3.87/1.35 Prover 6: stopped % 3.87/1.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.87/1.36 Prover 2: stopped % 3.87/1.36 Prover 5: stopped % 3.87/1.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.87/1.36 Prover 0: proved (740ms) % 3.87/1.36 % 3.87/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.87/1.36 % 3.87/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.87/1.38 Prover 7: Preprocessing ... % 3.87/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.87/1.38 Prover 11: Preprocessing ... % 3.87/1.38 Prover 10: Preprocessing ... % 3.87/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.87/1.39 Prover 13: Preprocessing ... % 3.87/1.39 Prover 10: Warning: ignoring some quantifiers % 3.87/1.39 Prover 8: Preprocessing ... % 3.87/1.39 Prover 10: Constructing countermodel ... % 3.87/1.41 Prover 7: Warning: ignoring some quantifiers % 3.87/1.41 Prover 7: Constructing countermodel ... % 3.87/1.42 Prover 13: Warning: ignoring some quantifiers % 3.87/1.42 Prover 4: Found proof (size 20) % 3.87/1.42 Prover 4: proved (790ms) % 3.87/1.42 Prover 13: Constructing countermodel ... % 3.87/1.42 Prover 7: stopped % 3.87/1.42 Prover 10: stopped % 3.87/1.42 Prover 13: stopped % 4.55/1.43 Prover 1: Found proof (size 17) % 4.55/1.43 Prover 1: proved (800ms) % 4.55/1.44 Prover 11: Constructing countermodel ... % 4.55/1.44 Prover 11: stopped % 4.55/1.44 Prover 8: Warning: ignoring some quantifiers % 4.55/1.45 Prover 8: Constructing countermodel ... % 4.55/1.45 Prover 8: stopped % 4.55/1.45 % 4.55/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.55/1.45 % 4.55/1.46 % SZS output start Proof for theBenchmark % 4.55/1.46 Assumptions after simplification: % 4.55/1.46 --------------------------------- % 4.55/1.46 % 4.55/1.46 (prove_transitivity_of_subset) % 4.86/1.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 4.86/1.51 subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & $i(v2) & % 4.86/1.51 $i(v1) & $i(v0)) % 4.86/1.51 % 4.86/1.51 (subset_defn) % 4.86/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.86/1.52 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 4.86/1.52 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 4.86/1.52 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 4.86/1.52 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 4.86/1.52 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 4.86/1.52 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 4.86/1.52 ~ $i(v0) | member(v2, v1) = 0) % 4.86/1.52 % 4.86/1.52 (function-axioms) % 4.86/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.86/1.52 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 4.86/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 4.86/1.52 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.86/1.52 % 4.86/1.52 Further assumptions not needed in the proof: % 4.86/1.52 -------------------------------------------- % 4.86/1.53 reflexivity_of_subset % 4.86/1.53 % 4.86/1.53 Those formulas are unsatisfiable: % 4.86/1.53 --------------------------------- % 4.86/1.53 % 4.86/1.53 Begin of proof % 4.86/1.53 | % 4.86/1.53 | ALPHA: (subset_defn) implies: % 4.86/1.53 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 4.86/1.53 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 4.86/1.53 | v1) = 0) % 4.86/1.53 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 4.86/1.53 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 4.86/1.53 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 4.86/1.54 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.86/1.54 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ % 4.86/1.54 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = % 4.86/1.54 | v4)) % 4.86/1.54 | % 4.86/1.54 | ALPHA: (function-axioms) implies: % 4.86/1.54 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.86/1.54 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.86/1.54 | = v0)) % 4.86/1.54 | % 4.86/1.54 | DELTA: instantiating (prove_transitivity_of_subset) with fresh symbols % 4.86/1.54 | all_5_0, all_5_1, all_5_2, all_5_3 gives: % 4.86/1.54 | (5) ~ (all_5_0 = 0) & subset(all_5_2, all_5_1) = 0 & subset(all_5_3, % 4.86/1.54 | all_5_1) = all_5_0 & subset(all_5_3, all_5_2) = 0 & $i(all_5_1) & % 4.86/1.54 | $i(all_5_2) & $i(all_5_3) % 4.86/1.54 | % 4.86/1.54 | ALPHA: (5) implies: % 4.86/1.54 | (6) ~ (all_5_0 = 0) % 4.86/1.54 | (7) $i(all_5_3) % 4.86/1.54 | (8) $i(all_5_2) % 4.86/1.54 | (9) $i(all_5_1) % 4.86/1.54 | (10) subset(all_5_3, all_5_2) = 0 % 4.86/1.54 | (11) subset(all_5_3, all_5_1) = all_5_0 % 4.86/1.54 | (12) subset(all_5_2, all_5_1) = 0 % 4.86/1.54 | % 4.86/1.55 | GROUND_INST: instantiating (2) with all_5_3, all_5_1, all_5_0, simplifying % 4.86/1.55 | with (7), (9), (11) gives: % 4.86/1.55 | (13) all_5_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 4.86/1.55 | all_5_1) = v1 & member(v0, all_5_3) = 0 & $i(v0)) % 4.86/1.55 | % 4.86/1.55 | BETA: splitting (13) gives: % 4.86/1.55 | % 4.86/1.55 | Case 1: % 4.86/1.55 | | % 4.86/1.55 | | (14) all_5_0 = 0 % 4.86/1.55 | | % 4.86/1.55 | | REDUCE: (6), (14) imply: % 4.86/1.55 | | (15) $false % 4.86/1.55 | | % 4.86/1.55 | | CLOSE: (15) is inconsistent. % 4.86/1.55 | | % 4.86/1.55 | Case 2: % 4.86/1.55 | | % 4.86/1.55 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_5_1) = v1 % 4.86/1.55 | | & member(v0, all_5_3) = 0 & $i(v0)) % 4.86/1.55 | | % 4.86/1.55 | | DELTA: instantiating (16) with fresh symbols all_14_0, all_14_1 gives: % 4.86/1.55 | | (17) ~ (all_14_0 = 0) & member(all_14_1, all_5_1) = all_14_0 & % 4.86/1.55 | | member(all_14_1, all_5_3) = 0 & $i(all_14_1) % 4.86/1.55 | | % 4.86/1.55 | | ALPHA: (17) implies: % 4.86/1.56 | | (18) ~ (all_14_0 = 0) % 4.86/1.56 | | (19) $i(all_14_1) % 4.86/1.56 | | (20) member(all_14_1, all_5_3) = 0 % 4.86/1.56 | | (21) member(all_14_1, all_5_1) = all_14_0 % 4.86/1.56 | | % 4.86/1.56 | | GROUND_INST: instantiating (1) with all_5_3, all_5_2, all_14_1, simplifying % 4.86/1.56 | | with (7), (8), (10), (19), (20) gives: % 4.86/1.56 | | (22) member(all_14_1, all_5_2) = 0 % 4.86/1.56 | | % 5.19/1.56 | | GROUND_INST: instantiating (3) with all_5_2, all_5_1, all_14_1, all_14_0, % 5.19/1.56 | | simplifying with (8), (9), (12), (19), (21) gives: % 5.19/1.56 | | (23) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_14_1, % 5.19/1.56 | | all_5_2) = v0) % 5.19/1.56 | | % 5.19/1.56 | | BETA: splitting (23) gives: % 5.19/1.56 | | % 5.19/1.56 | | Case 1: % 5.19/1.56 | | | % 5.19/1.56 | | | (24) all_14_0 = 0 % 5.19/1.56 | | | % 5.19/1.56 | | | REDUCE: (18), (24) imply: % 5.19/1.56 | | | (25) $false % 5.19/1.56 | | | % 5.19/1.56 | | | CLOSE: (25) is inconsistent. % 5.19/1.56 | | | % 5.19/1.56 | | Case 2: % 5.19/1.56 | | | % 5.19/1.56 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_1, all_5_2) = v0) % 5.19/1.56 | | | % 5.19/1.56 | | | DELTA: instantiating (26) with fresh symbol all_26_0 gives: % 5.19/1.56 | | | (27) ~ (all_26_0 = 0) & member(all_14_1, all_5_2) = all_26_0 % 5.19/1.56 | | | % 5.19/1.56 | | | ALPHA: (27) implies: % 5.19/1.56 | | | (28) ~ (all_26_0 = 0) % 5.19/1.57 | | | (29) member(all_14_1, all_5_2) = all_26_0 % 5.19/1.57 | | | % 5.19/1.57 | | | GROUND_INST: instantiating (4) with 0, all_26_0, all_5_2, all_14_1, % 5.19/1.57 | | | simplifying with (22), (29) gives: % 5.19/1.57 | | | (30) all_26_0 = 0 % 5.19/1.57 | | | % 5.19/1.57 | | | REDUCE: (28), (30) imply: % 5.19/1.57 | | | (31) $false % 5.19/1.57 | | | % 5.19/1.57 | | | CLOSE: (31) is inconsistent. % 5.19/1.57 | | | % 5.19/1.57 | | End of split % 5.19/1.57 | | % 5.19/1.57 | End of split % 5.19/1.57 | % 5.19/1.57 End of proof % 5.19/1.57 % SZS output end Proof for theBenchmark % 5.19/1.57 % 5.19/1.57 966ms %------------------------------------------------------------------------------