%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT103_1 : TPTP v8.1.2. Released v6.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 : Wed Aug 30 22:19:11 EDT 2023 % Result : Theorem 4.83s 1.34s % Output : Proof 5.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : DAT103_1 : TPTP v8.1.2. Released v6.1.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n023.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 : Thu Aug 24 14:15:42 EDT 2023 % 0.13/0.34 % CPUTime : % 0.61/0.60 ________ _____ % 0.61/0.60 ___ __ \_________(_)________________________________ % 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.60 (2023-06-19) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2023 % 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.60 Amanda Stjerna. % 0.61/0.60 Free software under BSD-3-Clause. % 0.61/0.60 % 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.61 Running up to 7 provers in parallel. % 0.61/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.05/0.98 Prover 1: Preprocessing ... % 2.05/0.98 Prover 4: Preprocessing ... % 2.48/1.03 Prover 0: Preprocessing ... % 2.48/1.03 Prover 3: Preprocessing ... % 2.48/1.03 Prover 5: Preprocessing ... % 2.48/1.03 Prover 6: Preprocessing ... % 2.48/1.03 Prover 2: Preprocessing ... % 3.66/1.20 Prover 6: Proving ... % 3.91/1.21 Prover 3: Constructing countermodel ... % 3.91/1.21 Prover 5: Proving ... % 3.91/1.21 Prover 2: Proving ... % 3.91/1.21 Prover 0: Proving ... % 3.91/1.21 Prover 1: Constructing countermodel ... % 3.91/1.22 Prover 4: Constructing countermodel ... % 4.83/1.33 Prover 3: proved (714ms) % 4.83/1.34 % 4.83/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.83/1.34 % 4.83/1.34 Prover 0: stopped % 4.83/1.34 Prover 6: stopped % 4.83/1.34 Prover 5: stopped % 4.83/1.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.83/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.83/1.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.83/1.34 Prover 2: stopped % 4.83/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.83/1.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.83/1.38 Prover 10: Preprocessing ... % 4.83/1.38 Prover 11: Preprocessing ... % 4.83/1.39 Prover 7: Preprocessing ... % 4.83/1.39 Prover 13: Preprocessing ... % 5.27/1.40 Prover 8: Preprocessing ... % 5.27/1.42 Prover 1: Found proof (size 16) % 5.27/1.42 Prover 1: proved (801ms) % 5.27/1.42 Prover 10: stopped % 5.27/1.42 Prover 4: Found proof (size 17) % 5.27/1.42 Prover 4: proved (802ms) % 5.27/1.43 Prover 7: Warning: ignoring some quantifiers % 5.27/1.43 Prover 7: Constructing countermodel ... % 5.27/1.44 Prover 7: stopped % 5.27/1.44 Prover 11: Constructing countermodel ... % 5.27/1.44 Prover 11: stopped % 5.27/1.45 Prover 8: Warning: ignoring some quantifiers % 5.27/1.45 Prover 13: Warning: ignoring some quantifiers % 5.27/1.45 Prover 8: Constructing countermodel ... % 5.77/1.46 Prover 13: Constructing countermodel ... % 5.77/1.46 Prover 8: stopped % 5.77/1.46 Prover 13: stopped % 5.77/1.46 % 5.77/1.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.77/1.46 % 5.81/1.47 % SZS output start Proof for theBenchmark % 5.81/1.47 Assumptions after simplification: % 5.81/1.47 --------------------------------- % 5.81/1.47 % 5.81/1.47 (c) % 5.81/1.49 list(nil) & ? [v0: list] : ? [v1: int] : ? [v2: int] : ( ~ (v0 = nil) & % 5.81/1.49 $lesseq(v1, v2) & inRange(v1, v0) = 0 & head(v0) = v2 & list(v0)) % 5.81/1.49 % 5.81/1.49 (inRange) % 5.81/1.50 list(nil) & ! [v0: int] : ! [v1: list] : ! [v2: int] : (v2 = 0 | ~ % 5.81/1.50 (inRange(v0, v1) = v2) | ~ list(v1) | ( ~ (v1 = nil) & ! [v3: int] : ! % 5.81/1.50 [v4: list] : ( ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0, v3)) | % 5.81/1.50 ~ (cons(v3, v4) = v1) | ~ list(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 5.81/1.50 inRange(v0, v4) = v5)))) & ! [v0: int] : ! [v1: list] : (v1 = nil | % 5.81/1.50 ~ (inRange(v0, v1) = 0) | ~ list(v1) | ? [v2: int] : ? [v3: list] : % 5.81/1.50 ($lesseq(1, $difference(v0, v2)) & $lesseq(0, v2) & inRange(v0, v3) = 0 & % 5.81/1.50 cons(v2, v3) = v1 & list(v3))) % 5.81/1.50 % 5.81/1.50 (l1) % 5.81/1.50 ! [v0: int] : ! [v1: list] : ! [v2: list] : ( ~ (cons(v0, v1) = v2) | ~ % 5.81/1.50 list(v1) | head(v2) = v0) % 5.81/1.50 % 5.81/1.50 (function-axioms) % 5.81/1.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: list] : ! % 5.81/1.50 [v3: int] : (v1 = v0 | ~ (inRange(v3, v2) = v1) | ~ (inRange(v3, v2) = v0)) % 5.81/1.50 & ! [v0: list] : ! [v1: list] : ! [v2: list] : ! [v3: int] : (v1 = v0 | ~ % 5.81/1.50 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: list] : ! [v1: % 5.81/1.50 list] : ! [v2: list] : (v1 = v0 | ~ (tail(v2) = v1) | ~ (tail(v2) = v0)) % 5.99/1.50 & ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 | ~ (head(v2) = v1) % 5.99/1.50 | ~ (head(v2) = v0)) % 5.99/1.50 % 5.99/1.50 Further assumptions not needed in the proof: % 5.99/1.50 -------------------------------------------- % 5.99/1.50 l2, l3, l4 % 5.99/1.50 % 5.99/1.50 Those formulas are unsatisfiable: % 5.99/1.50 --------------------------------- % 5.99/1.50 % 5.99/1.50 Begin of proof % 5.99/1.51 | % 5.99/1.51 | ALPHA: (inRange) implies: % 5.99/1.51 | (1) ! [v0: int] : ! [v1: list] : (v1 = nil | ~ (inRange(v0, v1) = 0) | % 5.99/1.51 | ~ list(v1) | ? [v2: int] : ? [v3: list] : ($lesseq(1, % 5.99/1.51 | $difference(v0, v2)) & $lesseq(0, v2) & inRange(v0, v3) = 0 & % 5.99/1.51 | cons(v2, v3) = v1 & list(v3))) % 5.99/1.51 | % 5.99/1.51 | ALPHA: (c) implies: % 5.99/1.51 | (2) ? [v0: list] : ? [v1: int] : ? [v2: int] : ( ~ (v0 = nil) & % 5.99/1.51 | $lesseq(v1, v2) & inRange(v1, v0) = 0 & head(v0) = v2 & list(v0)) % 5.99/1.51 | % 5.99/1.51 | ALPHA: (function-axioms) implies: % 5.99/1.51 | (3) ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 | ~ (head(v2) = % 5.99/1.51 | v1) | ~ (head(v2) = v0)) % 5.99/1.51 | % 5.99/1.51 | DELTA: instantiating (2) with fresh symbols all_11_0, all_11_1, all_11_2 % 5.99/1.51 | gives: % 5.99/1.51 | (4) ~ (all_11_2 = nil) & $lesseq(all_11_1, all_11_0) & inRange(all_11_1, % 5.99/1.51 | all_11_2) = 0 & head(all_11_2) = all_11_0 & list(all_11_2) % 5.99/1.51 | % 5.99/1.51 | ALPHA: (4) implies: % 5.99/1.51 | (5) ~ (all_11_2 = nil) % 5.99/1.51 | (6) $lesseq(all_11_1, all_11_0) % 5.99/1.51 | (7) list(all_11_2) % 5.99/1.51 | (8) head(all_11_2) = all_11_0 % 5.99/1.51 | (9) inRange(all_11_1, all_11_2) = 0 % 5.99/1.52 | % 5.99/1.52 | GROUND_INST: instantiating (1) with all_11_1, all_11_2, simplifying with (7), % 5.99/1.52 | (9) gives: % 5.99/1.52 | (10) all_11_2 = nil | ? [v0: int] : ? [v1: list] : ($lesseq(1, % 5.99/1.52 | $difference(all_11_1, v0)) & $lesseq(0, v0) & inRange(all_11_1, % 5.99/1.52 | v1) = 0 & cons(v0, v1) = all_11_2 & list(v1)) % 5.99/1.52 | % 5.99/1.52 | BETA: splitting (10) gives: % 5.99/1.52 | % 5.99/1.52 | Case 1: % 5.99/1.52 | | % 5.99/1.52 | | (11) all_11_2 = nil % 5.99/1.52 | | % 5.99/1.52 | | REDUCE: (5), (11) imply: % 5.99/1.52 | | (12) $false % 5.99/1.52 | | % 5.99/1.52 | | CLOSE: (12) is inconsistent. % 5.99/1.52 | | % 5.99/1.52 | Case 2: % 5.99/1.52 | | % 5.99/1.52 | | (13) ? [v0: int] : ? [v1: list] : ($lesseq(1, $difference(all_11_1, % 5.99/1.52 | | v0)) & $lesseq(0, v0) & inRange(all_11_1, v1) = 0 & cons(v0, % 5.99/1.52 | | v1) = all_11_2 & list(v1)) % 5.99/1.52 | | % 5.99/1.52 | | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1 gives: % 5.99/1.52 | | (14) $lesseq(1, $difference(all_11_1, all_24_1)) & $lesseq(0, all_24_1) & % 5.99/1.52 | | inRange(all_11_1, all_24_0) = 0 & cons(all_24_1, all_24_0) = % 5.99/1.52 | | all_11_2 & list(all_24_0) % 5.99/1.52 | | % 5.99/1.52 | | ALPHA: (14) implies: % 5.99/1.52 | | (15) $lesseq(1, $difference(all_11_1, all_24_1)) % 5.99/1.52 | | (16) list(all_24_0) % 5.99/1.52 | | (17) cons(all_24_1, all_24_0) = all_11_2 % 5.99/1.52 | | % 5.99/1.52 | | GROUND_INST: instantiating (l1) with all_24_1, all_24_0, all_11_2, % 5.99/1.52 | | simplifying with (16), (17) gives: % 5.99/1.52 | | (18) head(all_11_2) = all_24_1 % 5.99/1.52 | | % 5.99/1.52 | | GROUND_INST: instantiating (3) with all_11_0, all_24_1, all_11_2, % 5.99/1.52 | | simplifying with (8), (18) gives: % 5.99/1.52 | | (19) all_24_1 = all_11_0 % 5.99/1.52 | | % 5.99/1.52 | | REDUCE: (15), (19) imply: % 5.99/1.52 | | (20) $lesseq(1, $difference(all_11_1, all_11_0)) % 5.99/1.52 | | % 5.99/1.53 | | COMBINE_INEQS: (6), (20) imply: % 5.99/1.53 | | (21) $false % 5.99/1.53 | | % 5.99/1.53 | | CLOSE: (21) is inconsistent. % 5.99/1.53 | | % 5.99/1.53 | End of split % 5.99/1.53 | % 5.99/1.53 End of proof % 5.99/1.53 % SZS output end Proof for theBenchmark % 5.99/1.53 % 5.99/1.53 926ms %------------------------------------------------------------------------------