%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT100_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 : n012.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 4.52s 1.41s % Output : Proof 6.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : DAT100_1 : TPTP v8.1.2. Released v6.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n012.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 : Thu Aug 24 14:09:27 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.89/0.98 Prover 1: Preprocessing ... % 1.89/0.99 Prover 4: Preprocessing ... % 2.49/1.03 Prover 0: Preprocessing ... % 2.49/1.03 Prover 3: Preprocessing ... % 2.49/1.03 Prover 2: Preprocessing ... % 2.49/1.03 Prover 5: Preprocessing ... % 2.49/1.03 Prover 6: Preprocessing ... % 3.68/1.18 Prover 5: Proving ... % 3.75/1.19 Prover 0: Proving ... % 3.75/1.19 Prover 6: Proving ... % 3.75/1.19 Prover 3: Constructing countermodel ... % 3.75/1.19 Prover 1: Constructing countermodel ... % 3.75/1.20 Prover 4: Constructing countermodel ... % 3.90/1.21 Prover 2: Proving ... % 4.52/1.41 Prover 6: proved (766ms) % 4.52/1.41 % 4.52/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.52/1.41 % 4.52/1.41 Prover 3: stopped % 4.52/1.41 Prover 2: stopped % 4.52/1.41 Prover 0: stopped % 4.52/1.41 Prover 5: stopped % 4.52/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.52/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.52/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.52/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.52/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.52/1.44 Prover 11: Preprocessing ... % 4.52/1.44 Prover 10: Preprocessing ... % 5.51/1.44 Prover 13: Preprocessing ... % 5.51/1.45 Prover 7: Preprocessing ... % 5.51/1.46 Prover 8: Preprocessing ... % 5.51/1.48 Prover 1: Found proof (size 30) % 5.51/1.48 Prover 1: proved (846ms) % 5.51/1.48 Prover 4: stopped % 5.51/1.48 Prover 10: Warning: ignoring some quantifiers % 5.51/1.49 Prover 10: Constructing countermodel ... % 5.51/1.49 Prover 10: stopped % 5.51/1.49 Prover 8: Warning: ignoring some quantifiers % 5.51/1.50 Prover 8: Constructing countermodel ... % 5.51/1.50 Prover 13: Warning: ignoring some quantifiers % 5.51/1.50 Prover 7: Warning: ignoring some quantifiers % 5.51/1.50 Prover 8: stopped % 5.51/1.50 Prover 7: Constructing countermodel ... % 5.51/1.50 Prover 13: Constructing countermodel ... % 5.51/1.51 Prover 7: stopped % 5.51/1.51 Prover 11: Constructing countermodel ... % 5.51/1.51 Prover 13: stopped % 5.51/1.51 Prover 11: stopped % 5.51/1.51 % 5.51/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.51/1.51 % 5.51/1.52 % SZS output start Proof for theBenchmark % 5.51/1.52 Assumptions after simplification: % 5.51/1.52 --------------------------------- % 5.51/1.52 % 5.51/1.52 (c) % 6.07/1.54 list(nil) & ? [v0: list] : ? [v1: list] : ? [v2: list] : (inRange(4, v2) = % 6.07/1.54 0 & cons(5, v0) = v1 & cons(2, nil) = v0 & cons(1, v1) = v2 & list(v2) & % 6.07/1.54 list(v1) & list(v0)) % 6.07/1.54 % 6.07/1.54 (inRange) % 6.07/1.55 list(nil) & ! [v0: int] : ! [v1: list] : ! [v2: int] : (v2 = 0 | ~ % 6.07/1.55 (inRange(v0, v1) = v2) | ~ list(v1) | ( ~ (v1 = nil) & ! [v3: int] : ! % 6.07/1.55 [v4: list] : ( ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0, v3)) | % 6.07/1.55 ~ (cons(v3, v4) = v1) | ~ list(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 6.07/1.55 inRange(v0, v4) = v5)))) & ! [v0: int] : ! [v1: list] : (v1 = nil | % 6.07/1.55 ~ (inRange(v0, v1) = 0) | ~ list(v1) | ? [v2: int] : ? [v3: list] : % 6.07/1.55 ($lesseq(1, $difference(v0, v2)) & $lesseq(0, v2) & inRange(v0, v3) = 0 & % 6.07/1.55 cons(v2, v3) = v1 & list(v3))) % 6.07/1.55 % 6.07/1.55 (l1) % 6.07/1.55 ! [v0: int] : ! [v1: list] : ! [v2: list] : ( ~ (cons(v0, v1) = v2) | ~ % 6.07/1.55 list(v1) | head(v2) = v0) % 6.07/1.55 % 6.07/1.55 (l2) % 6.07/1.55 ! [v0: int] : ! [v1: list] : ! [v2: list] : ( ~ (cons(v0, v1) = v2) | ~ % 6.07/1.55 list(v1) | tail(v2) = v1) % 6.07/1.55 % 6.07/1.55 (l4) % 6.07/1.55 list(nil) & ! [v0: int] : ! [v1: list] : ( ~ (cons(v0, v1) = nil) | ~ % 6.07/1.55 list(v1)) % 6.07/1.55 % 6.07/1.55 (function-axioms) % 6.07/1.55 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: list] : ! % 6.07/1.55 [v3: int] : (v1 = v0 | ~ (inRange(v3, v2) = v1) | ~ (inRange(v3, v2) = v0)) % 6.07/1.55 & ! [v0: list] : ! [v1: list] : ! [v2: list] : ! [v3: int] : (v1 = v0 | ~ % 6.07/1.55 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: list] : ! [v1: % 6.07/1.55 list] : ! [v2: list] : (v1 = v0 | ~ (tail(v2) = v1) | ~ (tail(v2) = v0)) % 6.07/1.55 & ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 | ~ (head(v2) = v1) % 6.07/1.55 | ~ (head(v2) = v0)) % 6.07/1.55 % 6.07/1.55 Further assumptions not needed in the proof: % 6.07/1.55 -------------------------------------------- % 6.07/1.55 l3 % 6.07/1.55 % 6.07/1.55 Those formulas are unsatisfiable: % 6.07/1.55 --------------------------------- % 6.07/1.55 % 6.07/1.55 Begin of proof % 6.07/1.56 | % 6.07/1.56 | ALPHA: (l4) implies: % 6.07/1.56 | (1) ! [v0: int] : ! [v1: list] : ( ~ (cons(v0, v1) = nil) | ~ list(v1)) % 6.07/1.56 | % 6.07/1.56 | ALPHA: (inRange) implies: % 6.07/1.56 | (2) ! [v0: int] : ! [v1: list] : (v1 = nil | ~ (inRange(v0, v1) = 0) | % 6.07/1.56 | ~ list(v1) | ? [v2: int] : ? [v3: list] : ($lesseq(1, % 6.07/1.56 | $difference(v0, v2)) & $lesseq(0, v2) & inRange(v0, v3) = 0 & % 6.07/1.56 | cons(v2, v3) = v1 & list(v3))) % 6.07/1.56 | % 6.07/1.56 | ALPHA: (c) implies: % 6.07/1.56 | (3) ? [v0: list] : ? [v1: list] : ? [v2: list] : (inRange(4, v2) = 0 & % 6.07/1.56 | cons(5, v0) = v1 & cons(2, nil) = v0 & cons(1, v1) = v2 & list(v2) & % 6.07/1.56 | list(v1) & list(v0)) % 6.07/1.56 | % 6.07/1.56 | ALPHA: (function-axioms) implies: % 6.07/1.56 | (4) ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 | ~ (head(v2) = % 6.07/1.56 | v1) | ~ (head(v2) = v0)) % 6.07/1.56 | (5) ! [v0: list] : ! [v1: list] : ! [v2: list] : (v1 = v0 | ~ (tail(v2) % 6.07/1.56 | = v1) | ~ (tail(v2) = v0)) % 6.07/1.56 | % 6.07/1.56 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2 % 6.07/1.56 | gives: % 6.07/1.57 | (6) inRange(4, all_11_0) = 0 & cons(5, all_11_2) = all_11_1 & cons(2, nil) % 6.07/1.57 | = all_11_2 & cons(1, all_11_1) = all_11_0 & list(all_11_0) & % 6.07/1.57 | list(all_11_1) & list(all_11_2) % 6.07/1.57 | % 6.07/1.57 | ALPHA: (6) implies: % 6.07/1.57 | (7) list(all_11_2) % 6.07/1.57 | (8) list(all_11_1) % 6.07/1.57 | (9) list(all_11_0) % 6.07/1.57 | (10) cons(1, all_11_1) = all_11_0 % 6.07/1.57 | (11) cons(5, all_11_2) = all_11_1 % 6.07/1.57 | (12) inRange(4, all_11_0) = 0 % 6.07/1.57 | % 6.07/1.57 | GROUND_INST: instantiating (l2) with 1, all_11_1, all_11_0, simplifying with % 6.07/1.57 | (8), (10) gives: % 6.07/1.57 | (13) tail(all_11_0) = all_11_1 % 6.07/1.57 | % 6.07/1.57 | GROUND_INST: instantiating (l1) with 5, all_11_2, all_11_1, simplifying with % 6.07/1.57 | (7), (11) gives: % 6.07/1.57 | (14) head(all_11_1) = 5 % 6.07/1.57 | % 6.07/1.57 | GROUND_INST: instantiating (2) with 4, all_11_0, simplifying with (9), (12) % 6.07/1.57 | gives: % 6.07/1.57 | (15) all_11_0 = nil | ? [v0: int] : ? [v1: list] : ($lesseq(v0, 3) & % 6.07/1.57 | $lesseq(0, v0) & inRange(4, v1) = 0 & cons(v0, v1) = all_11_0 & % 6.07/1.57 | list(v1)) % 6.07/1.57 | % 6.07/1.57 | BETA: splitting (15) gives: % 6.07/1.57 | % 6.07/1.57 | Case 1: % 6.07/1.57 | | % 6.07/1.57 | | (16) all_11_0 = nil % 6.07/1.57 | | % 6.07/1.57 | | REDUCE: (10), (16) imply: % 6.07/1.57 | | (17) cons(1, all_11_1) = nil % 6.07/1.57 | | % 6.07/1.57 | | GROUND_INST: instantiating (1) with 1, all_11_1, simplifying with (8), (17) % 6.07/1.57 | | gives: % 6.07/1.58 | | (18) $false % 6.07/1.58 | | % 6.07/1.58 | | CLOSE: (18) is inconsistent. % 6.07/1.58 | | % 6.07/1.58 | Case 2: % 6.07/1.58 | | % 6.07/1.58 | | (19) ? [v0: int] : ? [v1: list] : ($lesseq(v0, 3) & $lesseq(0, v0) & % 6.07/1.58 | | inRange(4, v1) = 0 & cons(v0, v1) = all_11_0 & list(v1)) % 6.07/1.58 | | % 6.07/1.58 | | DELTA: instantiating (19) with fresh symbols all_26_0, all_26_1 gives: % 6.33/1.58 | | (20) $lesseq(all_26_1, 3) & $lesseq(0, all_26_1) & inRange(4, all_26_0) = % 6.33/1.58 | | 0 & cons(all_26_1, all_26_0) = all_11_0 & list(all_26_0) % 6.33/1.58 | | % 6.33/1.58 | | ALPHA: (20) implies: % 6.33/1.58 | | (21) list(all_26_0) % 6.33/1.58 | | (22) cons(all_26_1, all_26_0) = all_11_0 % 6.33/1.58 | | (23) inRange(4, all_26_0) = 0 % 6.33/1.58 | | % 6.33/1.58 | | GROUND_INST: instantiating (l2) with all_26_1, all_26_0, all_11_0, % 6.33/1.58 | | simplifying with (21), (22) gives: % 6.33/1.58 | | (24) tail(all_11_0) = all_26_0 % 6.33/1.58 | | % 6.33/1.58 | | GROUND_INST: instantiating (2) with 4, all_26_0, simplifying with (21), (23) % 6.33/1.58 | | gives: % 6.33/1.58 | | (25) all_26_0 = nil | ? [v0: int] : ? [v1: list] : ($lesseq(v0, 3) & % 6.33/1.58 | | $lesseq(0, v0) & inRange(4, v1) = 0 & cons(v0, v1) = all_26_0 & % 6.33/1.58 | | list(v1)) % 6.33/1.58 | | % 6.33/1.58 | | GROUND_INST: instantiating (5) with all_11_1, all_26_0, all_11_0, % 6.33/1.58 | | simplifying with (13), (24) gives: % 6.33/1.58 | | (26) all_26_0 = all_11_1 % 6.33/1.58 | | % 6.33/1.58 | | BETA: splitting (25) gives: % 6.33/1.58 | | % 6.33/1.58 | | Case 1: % 6.33/1.58 | | | % 6.33/1.58 | | | (27) all_26_0 = nil % 6.33/1.58 | | | % 6.33/1.58 | | | COMBINE_EQS: (26), (27) imply: % 6.33/1.58 | | | (28) all_11_1 = nil % 6.33/1.58 | | | % 6.33/1.58 | | | REDUCE: (11), (28) imply: % 6.33/1.58 | | | (29) cons(5, all_11_2) = nil % 6.33/1.58 | | | % 6.33/1.58 | | | GROUND_INST: instantiating (1) with 5, all_11_2, simplifying with (7), % 6.33/1.58 | | | (29) gives: % 6.33/1.58 | | | (30) $false % 6.33/1.58 | | | % 6.33/1.58 | | | CLOSE: (30) is inconsistent. % 6.33/1.58 | | | % 6.33/1.58 | | Case 2: % 6.33/1.58 | | | % 6.33/1.58 | | | (31) ? [v0: int] : ? [v1: list] : ($lesseq(v0, 3) & $lesseq(0, v0) & % 6.33/1.58 | | | inRange(4, v1) = 0 & cons(v0, v1) = all_26_0 & list(v1)) % 6.33/1.58 | | | % 6.33/1.58 | | | DELTA: instantiating (31) with fresh symbols all_49_0, all_49_1 gives: % 6.33/1.59 | | | (32) $lesseq(all_49_1, 3) & $lesseq(0, all_49_1) & inRange(4, all_49_0) % 6.33/1.59 | | | = 0 & cons(all_49_1, all_49_0) = all_26_0 & list(all_49_0) % 6.33/1.59 | | | % 6.33/1.59 | | | ALPHA: (32) implies: % 6.33/1.59 | | | (33) $lesseq(all_49_1, 3) % 6.33/1.59 | | | (34) list(all_49_0) % 6.33/1.59 | | | (35) cons(all_49_1, all_49_0) = all_26_0 % 6.33/1.59 | | | % 6.33/1.59 | | | REDUCE: (26), (35) imply: % 6.33/1.59 | | | (36) cons(all_49_1, all_49_0) = all_11_1 % 6.33/1.59 | | | % 6.33/1.59 | | | GROUND_INST: instantiating (l1) with all_49_1, all_49_0, all_11_1, % 6.33/1.59 | | | simplifying with (34), (36) gives: % 6.33/1.59 | | | (37) head(all_11_1) = all_49_1 % 6.33/1.59 | | | % 6.33/1.59 | | | GROUND_INST: instantiating (4) with 5, all_49_1, all_11_1, simplifying % 6.33/1.59 | | | with (14), (37) gives: % 6.33/1.59 | | | (38) all_49_1 = 5 % 6.33/1.59 | | | % 6.33/1.59 | | | REDUCE: (33), (38) imply: % 6.33/1.59 | | | (39) $false % 6.33/1.59 | | | % 6.33/1.59 | | | CLOSE: (39) is inconsistent. % 6.33/1.59 | | | % 6.33/1.59 | | End of split % 6.33/1.59 | | % 6.33/1.59 | End of split % 6.33/1.59 | % 6.33/1.59 End of proof % 6.33/1.59 % SZS output end Proof for theBenchmark % 6.33/1.59 % 6.33/1.59 973ms %------------------------------------------------------------------------------