%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET590+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 : n008.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 15:25:27 EDT 2023 % Result : Theorem 3.69s 1.25s % Output : Proof 4.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET590+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 : n008.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 09:39:47 EDT 2023 % 0.12/0.34 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.65/0.96 Prover 4: Preprocessing ... % 1.65/0.96 Prover 1: Preprocessing ... % 2.05/1.00 Prover 2: Preprocessing ... % 2.05/1.00 Prover 5: Preprocessing ... % 2.05/1.00 Prover 6: Preprocessing ... % 2.05/1.00 Prover 3: Preprocessing ... % 2.05/1.00 Prover 0: Preprocessing ... % 3.23/1.14 Prover 5: Proving ... % 3.23/1.14 Prover 6: Proving ... % 3.23/1.14 Prover 2: Proving ... % 3.23/1.15 Prover 1: Constructing countermodel ... % 3.23/1.15 Prover 4: Constructing countermodel ... % 3.23/1.15 Prover 3: Constructing countermodel ... % 3.23/1.15 Prover 0: Proving ... % 3.69/1.24 Prover 3: proved (608ms) % 3.69/1.25 % 3.69/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.69/1.25 % 3.69/1.25 Prover 5: stopped % 3.69/1.25 Prover 2: stopped % 3.69/1.25 Prover 6: stopped % 3.69/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.69/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.69/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.69/1.25 Prover 0: stopped % 3.69/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.69/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.08/1.27 Prover 10: Preprocessing ... % 4.08/1.27 Prover 11: Preprocessing ... % 4.08/1.27 Prover 13: Preprocessing ... % 4.08/1.27 Prover 7: Preprocessing ... % 4.08/1.28 Prover 8: Preprocessing ... % 4.08/1.29 Prover 10: Warning: ignoring some quantifiers % 4.08/1.30 Prover 10: Constructing countermodel ... % 4.08/1.30 Prover 4: Found proof (size 17) % 4.08/1.30 Prover 4: proved (651ms) % 4.08/1.30 Prover 7: Warning: ignoring some quantifiers % 4.08/1.30 Prover 1: stopped % 4.08/1.31 Prover 7: Constructing countermodel ... % 4.08/1.31 Prover 10: stopped % 4.08/1.31 Prover 7: stopped % 4.08/1.32 Prover 13: Warning: ignoring some quantifiers % 4.08/1.32 Prover 13: Constructing countermodel ... % 4.08/1.33 Prover 13: stopped % 4.08/1.33 Prover 8: Warning: ignoring some quantifiers % 4.08/1.34 Prover 11: Constructing countermodel ... % 4.08/1.34 Prover 8: Constructing countermodel ... % 4.08/1.34 Prover 11: stopped % 4.08/1.34 Prover 8: stopped % 4.08/1.34 % 4.08/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.08/1.34 % 4.08/1.35 % SZS output start Proof for theBenchmark % 4.08/1.35 Assumptions after simplification: % 4.08/1.35 --------------------------------- % 4.08/1.35 % 4.08/1.35 (difference_defn) % 4.71/1.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 4.71/1.38 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 4.71/1.38 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 4.71/1.38 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 4.71/1.38 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, % 4.71/1.38 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 4.71/1.39 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 4.71/1.39 % 4.71/1.39 (prove_th49) % 4.71/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 4.71/1.39 subset(v2, v0) = v3 & difference(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 4.71/1.39 % 4.71/1.39 (subset_defn) % 4.71/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.71/1.39 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 4.71/1.39 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 4.71/1.39 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 4.71/1.39 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 4.71/1.39 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 4.71/1.39 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 4.71/1.39 ~ $i(v0) | member(v2, v1) = 0) % 4.71/1.39 % 4.71/1.39 (function-axioms) % 4.71/1.40 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.71/1.40 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 4.71/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.71/1.40 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: % 4.71/1.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.71/1.40 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.71/1.40 % 4.71/1.40 Further assumptions not needed in the proof: % 4.71/1.40 -------------------------------------------- % 4.71/1.40 reflexivity_of_subset % 4.71/1.40 % 4.71/1.40 Those formulas are unsatisfiable: % 4.71/1.40 --------------------------------- % 4.71/1.40 % 4.71/1.40 Begin of proof % 4.71/1.40 | % 4.71/1.40 | ALPHA: (difference_defn) implies: % 4.71/1.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 4.71/1.40 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ % 4.71/1.40 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = % 4.71/1.40 | v4 & member(v2, v0) = 0)) % 4.71/1.40 | % 4.71/1.40 | ALPHA: (subset_defn) implies: % 4.71/1.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 4.71/1.40 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 4.71/1.40 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 4.71/1.40 | % 4.71/1.40 | ALPHA: (function-axioms) implies: % 4.71/1.40 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.71/1.40 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.71/1.40 | = v0)) % 4.71/1.40 | % 4.71/1.40 | DELTA: instantiating (prove_th49) with fresh symbols all_6_0, all_6_1, % 4.71/1.40 | all_6_2, all_6_3 gives: % 4.71/1.40 | (4) ~ (all_6_0 = 0) & subset(all_6_1, all_6_3) = all_6_0 & % 4.71/1.40 | difference(all_6_3, all_6_2) = all_6_1 & $i(all_6_1) & $i(all_6_2) & % 4.71/1.40 | $i(all_6_3) % 4.71/1.40 | % 4.71/1.40 | ALPHA: (4) implies: % 4.71/1.41 | (5) ~ (all_6_0 = 0) % 4.71/1.41 | (6) $i(all_6_3) % 4.71/1.41 | (7) $i(all_6_2) % 4.71/1.41 | (8) $i(all_6_1) % 4.71/1.41 | (9) difference(all_6_3, all_6_2) = all_6_1 % 4.71/1.41 | (10) subset(all_6_1, all_6_3) = all_6_0 % 4.71/1.41 | % 4.71/1.41 | GROUND_INST: instantiating (2) with all_6_1, all_6_3, all_6_0, simplifying % 4.71/1.41 | with (6), (8), (10) gives: % 4.71/1.41 | (11) all_6_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 4.71/1.41 | all_6_1) = 0 & member(v0, all_6_3) = v1 & $i(v0)) % 4.71/1.41 | % 4.71/1.41 | BETA: splitting (11) gives: % 4.71/1.41 | % 4.71/1.41 | Case 1: % 4.71/1.41 | | % 4.71/1.41 | | (12) all_6_0 = 0 % 4.71/1.41 | | % 4.71/1.41 | | REDUCE: (5), (12) imply: % 4.71/1.41 | | (13) $false % 4.71/1.41 | | % 4.71/1.41 | | CLOSE: (13) is inconsistent. % 4.71/1.41 | | % 4.71/1.41 | Case 2: % 4.71/1.41 | | % 4.71/1.41 | | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_6_1) = 0 % 4.71/1.41 | | & member(v0, all_6_3) = v1 & $i(v0)) % 4.71/1.41 | | % 4.71/1.41 | | DELTA: instantiating (14) with fresh symbols all_15_0, all_15_1 gives: % 4.71/1.41 | | (15) ~ (all_15_0 = 0) & member(all_15_1, all_6_1) = 0 & member(all_15_1, % 4.71/1.41 | | all_6_3) = all_15_0 & $i(all_15_1) % 4.71/1.41 | | % 4.71/1.41 | | ALPHA: (15) implies: % 4.71/1.41 | | (16) ~ (all_15_0 = 0) % 4.71/1.41 | | (17) $i(all_15_1) % 4.71/1.41 | | (18) member(all_15_1, all_6_3) = all_15_0 % 4.71/1.41 | | (19) member(all_15_1, all_6_1) = 0 % 4.71/1.41 | | % 4.71/1.42 | | GROUND_INST: instantiating (1) with all_6_3, all_6_2, all_15_1, all_6_1, % 4.71/1.42 | | simplifying with (6), (7), (9), (17), (19) gives: % 4.71/1.42 | | (20) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_1, all_6_2) = v0 & % 4.71/1.42 | | member(all_15_1, all_6_3) = 0) % 4.71/1.42 | | % 4.71/1.42 | | DELTA: instantiating (20) with fresh symbol all_22_0 gives: % 4.71/1.42 | | (21) ~ (all_22_0 = 0) & member(all_15_1, all_6_2) = all_22_0 & % 4.71/1.42 | | member(all_15_1, all_6_3) = 0 % 4.71/1.42 | | % 4.71/1.42 | | ALPHA: (21) implies: % 4.71/1.42 | | (22) member(all_15_1, all_6_3) = 0 % 4.71/1.42 | | % 4.71/1.42 | | GROUND_INST: instantiating (3) with all_15_0, 0, all_6_3, all_15_1, % 4.71/1.42 | | simplifying with (18), (22) gives: % 4.71/1.42 | | (23) all_15_0 = 0 % 4.71/1.42 | | % 4.71/1.42 | | REDUCE: (16), (23) imply: % 4.71/1.42 | | (24) $false % 4.71/1.42 | | % 4.71/1.42 | | CLOSE: (24) is inconsistent. % 4.71/1.42 | | % 4.71/1.42 | End of split % 4.71/1.42 | % 4.71/1.42 End of proof % 4.71/1.42 % SZS output end Proof for theBenchmark % 4.71/1.42 % 4.71/1.42 809ms %------------------------------------------------------------------------------