%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT025_1 : TPTP v8.1.2. Released v5.0.0. % 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 22:18:55 EDT 2023 % Result : Theorem 5.06s 1.50s % Output : Proof 6.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : DAT025_1 : TPTP v8.1.2. Released v5.0.0. % 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 14:27:41 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.96/1.04 Prover 1: Preprocessing ... % 2.51/1.04 Prover 4: Preprocessing ... % 2.51/1.08 Prover 0: Preprocessing ... % 2.51/1.08 Prover 5: Preprocessing ... % 2.51/1.08 Prover 6: Preprocessing ... % 2.51/1.08 Prover 2: Preprocessing ... % 2.51/1.08 Prover 3: Preprocessing ... % 4.05/1.27 Prover 6: Proving ... % 4.05/1.27 Prover 5: Proving ... % 4.05/1.28 Prover 3: Constructing countermodel ... % 4.05/1.29 Prover 2: Proving ... % 4.05/1.29 Prover 4: Constructing countermodel ... % 4.05/1.31 Prover 1: Constructing countermodel ... % 4.05/1.32 Prover 0: Proving ... % 4.67/1.39 Prover 1: gave up % 4.67/1.40 Prover 3: gave up % 4.67/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.67/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.67/1.42 Prover 7: Preprocessing ... % 4.67/1.45 Prover 8: Preprocessing ... % 4.67/1.47 Prover 7: Constructing countermodel ... % 5.06/1.50 Prover 5: proved (828ms) % 5.06/1.50 Prover 0: proved (845ms) % 5.06/1.50 % 5.06/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.06/1.50 % 5.06/1.50 % 5.06/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.06/1.50 % 5.06/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.06/1.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.06/1.50 Prover 6: stopped % 5.06/1.50 Prover 2: stopped % 5.06/1.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.06/1.50 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 5.06/1.52 Prover 4: Found proof (size 22) % 5.06/1.52 Prover 4: proved (863ms) % 5.06/1.52 Prover 7: stopped % 5.06/1.52 Prover 11: Preprocessing ... % 5.06/1.52 Prover 8: Warning: ignoring some quantifiers % 5.06/1.53 Prover 16: Preprocessing ... % 5.06/1.53 Prover 8: Constructing countermodel ... % 5.06/1.53 Prover 10: Preprocessing ... % 5.06/1.53 Prover 13: Preprocessing ... % 5.06/1.54 Prover 8: stopped % 5.06/1.55 Prover 11: stopped % 5.06/1.55 Prover 16: stopped % 6.07/1.55 Prover 10: stopped % 6.07/1.55 Prover 13: stopped % 6.07/1.55 % 6.07/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.07/1.55 % 6.07/1.56 % SZS output start Proof for theBenchmark % 6.07/1.56 Assumptions after simplification: % 6.07/1.56 --------------------------------- % 6.07/1.56 % 6.07/1.56 (ax3) % 6.17/1.58 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 6.17/1.58 = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v2) = % 6.17/1.58 v3)) % 6.17/1.58 % 6.17/1.58 (ax5) % 6.17/1.59 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 6.17/1.59 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = % 6.17/1.59 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 6.17/1.59 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ( % 6.17/1.59 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0, % 6.17/1.59 v1) = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 6.17/1.59 (remove(v0, v1) = v2) | ~ (in(v0, v2) = 0) | ~ collection(v1)) % 6.17/1.59 % 6.17/1.59 (co1) % 6.17/1.60 ? [v0: collection] : ? [v1: collection] : ? [v2: collection] : ? [v3: int] % 6.17/1.60 : ($lesseq(v3, 1) & remove(1, v0) = v1 & remove(0, v1) = v2 & in(v3, v0) = 0 & % 6.17/1.60 collection(v2) & collection(v1) & collection(v0) & ! [v4: int] : ! [v5: % 6.17/1.60 int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6: int] : ( ~ (v6 = 0) & % 6.17/1.60 in(v4, v0) = v6)) & ! [v4: int] : ! [v5: int] : (v5 = 0 | ~ (in(v4, % 6.17/1.60 v0) = v5) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v2) = v6)) & ! [v4: % 6.17/1.60 int] : ( ~ ($lesseq(v4, -1)) | ~ (in(v4, v0) = 0)) & ! [v4: int] : ( ~ % 6.17/1.60 (in(v4, v2) = 0) | in(v4, v0) = 0) & ! [v4: int] : ( ~ (in(v4, v0) = 0) | % 6.17/1.60 in(v4, v2) = 0)) % 6.17/1.60 % 6.17/1.60 (function-axioms) % 6.17/1.60 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] % 6.17/1.60 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0: % 6.17/1.60 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1 % 6.17/1.60 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0: % 6.17/1.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : ! % 6.17/1.60 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.17/1.60 % 6.17/1.60 Further assumptions not needed in the proof: % 6.17/1.60 -------------------------------------------- % 6.17/1.60 ax1, ax2, ax4 % 6.17/1.60 % 6.17/1.60 Those formulas are unsatisfiable: % 6.17/1.60 --------------------------------- % 6.17/1.60 % 6.17/1.60 Begin of proof % 6.17/1.60 | % 6.17/1.60 | ALPHA: (ax5) implies: % 6.17/1.61 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 6.17/1.61 | (remove(v0, v1) = v2) | ~ (in(v0, v2) = 0) | ~ collection(v1)) % 6.17/1.61 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] % 6.17/1.61 | : ( ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | % 6.17/1.61 | in(v0, v1) = 0) % 6.17/1.61 | % 6.17/1.61 | ALPHA: (function-axioms) implies: % 6.17/1.61 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 6.17/1.61 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ % 6.17/1.61 | (in(v3, v2) = v0)) % 6.17/1.61 | % 6.17/1.61 | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2, % 6.17/1.61 | all_11_3 gives: % 6.17/1.61 | (4) $lesseq(all_11_0, 1) & remove(1, all_11_3) = all_11_2 & remove(0, % 6.17/1.61 | all_11_2) = all_11_1 & in(all_11_0, all_11_3) = 0 & % 6.17/1.61 | collection(all_11_1) & collection(all_11_2) & collection(all_11_3) & ! % 6.17/1.61 | [v0: int] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_11_1) = v1) | ? % 6.17/1.61 | [v2: int] : ( ~ (v2 = 0) & in(v0, all_11_3) = v2)) & ! [v0: int] : % 6.17/1.61 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_11_3) = v1) | ? [v2: int] : ( ~ % 6.17/1.61 | (v2 = 0) & in(v0, all_11_1) = v2)) & ! [v0: int] : ( ~ % 6.17/1.61 | ($lesseq(v0, -1)) | ~ (in(v0, all_11_3) = 0)) & ! [v0: int] : ( ~ % 6.17/1.61 | (in(v0, all_11_1) = 0) | in(v0, all_11_3) = 0) & ! [v0: int] : ( ~ % 6.17/1.61 | (in(v0, all_11_3) = 0) | in(v0, all_11_1) = 0) % 6.17/1.61 | % 6.41/1.61 | ALPHA: (4) implies: % 6.41/1.62 | (5) $lesseq(all_11_0, 1) % 6.41/1.62 | (6) collection(all_11_3) % 6.41/1.62 | (7) collection(all_11_2) % 6.41/1.62 | (8) in(all_11_0, all_11_3) = 0 % 6.41/1.62 | (9) remove(0, all_11_2) = all_11_1 % 6.41/1.62 | (10) remove(1, all_11_3) = all_11_2 % 6.41/1.62 | (11) ! [v0: int] : ( ~ (in(v0, all_11_3) = 0) | in(v0, all_11_1) = 0) % 6.41/1.62 | (12) ! [v0: int] : ( ~ ($lesseq(v0, -1)) | ~ (in(v0, all_11_3) = 0)) % 6.41/1.62 | % 6.41/1.62 | GROUND_INST: instantiating (12) with all_11_0, simplifying with (8) gives: % 6.41/1.62 | (13) $lesseq(0, all_11_0) % 6.41/1.62 | % 6.41/1.62 | GROUND_INST: instantiating (11) with all_11_0, simplifying with (8) gives: % 6.41/1.62 | (14) in(all_11_0, all_11_1) = 0 % 6.41/1.62 | % 6.41/1.62 | GROUND_INST: instantiating (ax3) with 1, all_11_3, all_11_2, simplifying with % 6.41/1.62 | (6), (10) gives: % 6.41/1.62 | (15) ? [v0: int] : ( ~ (v0 = 0) & in(1, all_11_2) = v0) % 6.41/1.62 | % 6.41/1.62 | DELTA: instantiating (15) with fresh symbol all_25_0 gives: % 6.41/1.62 | (16) ~ (all_25_0 = 0) & in(1, all_11_2) = all_25_0 % 6.41/1.62 | % 6.41/1.62 | ALPHA: (16) implies: % 6.41/1.62 | (17) ~ (all_25_0 = 0) % 6.41/1.62 | (18) in(1, all_11_2) = all_25_0 % 6.41/1.62 | % 6.41/1.62 | GROUND_INST: instantiating (1) with 0, all_11_2, all_11_1, simplifying with % 6.41/1.62 | (7), (9) gives: % 6.41/1.62 | (19) ~ (in(0, all_11_1) = 0) % 6.41/1.62 | % 6.41/1.62 | GROUND_INST: instantiating (2) with all_11_0, all_11_2, 0, all_11_1, % 6.41/1.62 | simplifying with (7), (9), (14) gives: % 6.41/1.63 | (20) in(all_11_0, all_11_2) = 0 % 6.41/1.63 | % 6.41/1.63 | GROUND_INST: instantiating (3) with all_25_0, 0, all_11_2, 1, simplifying with % 6.41/1.63 | (18) gives: % 6.41/1.63 | (21) all_25_0 = 0 | ~ (in(1, all_11_2) = 0) % 6.41/1.63 | % 6.41/1.63 | PRED_UNIFY: (14), (19) imply: % 6.41/1.63 | (22) ~ (all_11_0 = 0) % 6.41/1.63 | % 6.41/1.63 | STRENGTHEN: (13), (22) imply: % 6.41/1.63 | (23) $lesseq(1, all_11_0) % 6.41/1.63 | % 6.41/1.63 | ANTI_SYMM: (5), (23) imply: % 6.41/1.63 | (24) all_11_0 = 1 % 6.41/1.63 | % 6.41/1.63 | REDUCE: (20), (24) imply: % 6.41/1.63 | (25) in(1, all_11_2) = 0 % 6.41/1.63 | % 6.41/1.63 | BETA: splitting (21) gives: % 6.41/1.63 | % 6.41/1.63 | Case 1: % 6.41/1.63 | | % 6.41/1.63 | | (26) ~ (in(1, all_11_2) = 0) % 6.41/1.63 | | % 6.41/1.63 | | PRED_UNIFY: (25), (26) imply: % 6.41/1.63 | | (27) $false % 6.41/1.63 | | % 6.41/1.63 | | CLOSE: (27) is inconsistent. % 6.41/1.63 | | % 6.41/1.63 | Case 2: % 6.41/1.63 | | % 6.41/1.63 | | (28) all_25_0 = 0 % 6.41/1.63 | | % 6.41/1.63 | | REDUCE: (17), (28) imply: % 6.41/1.63 | | (29) $false % 6.41/1.63 | | % 6.41/1.63 | | CLOSE: (29) is inconsistent. % 6.41/1.63 | | % 6.41/1.63 | End of split % 6.41/1.63 | % 6.41/1.63 End of proof % 6.41/1.63 % SZS output end Proof for theBenchmark % 6.41/1.63 % 6.41/1.63 999ms %------------------------------------------------------------------------------