%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT022_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 : 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 22:18:54 EDT 2023 % Result : Theorem 5.03s 1.41s % Output : Proof 6.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : DAT022_1 : TPTP v8.1.2. Released v5.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n023.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 14:56:57 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.56 ________ _____ % 0.20/0.56 ___ __ \_________(_)________________________________ % 0.20/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.56 % 0.20/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.56 (2023-06-19) % 0.20/0.56 % 0.20/0.56 (c) Philipp Rümmer, 2009-2023 % 0.20/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.56 Amanda Stjerna. % 0.20/0.56 Free software under BSD-3-Clause. % 0.20/0.56 % 0.20/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.56 % 0.20/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.57 Running up to 7 provers in parallel. % 0.20/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.33/1.01 Prover 1: Preprocessing ... % 2.33/1.01 Prover 4: Preprocessing ... % 2.33/1.05 Prover 0: Preprocessing ... % 2.33/1.05 Prover 2: Preprocessing ... % 2.33/1.05 Prover 6: Preprocessing ... % 2.77/1.07 Prover 5: Preprocessing ... % 2.77/1.07 Prover 3: Preprocessing ... % 4.05/1.25 Prover 5: Proving ... % 4.05/1.25 Prover 6: Proving ... % 4.05/1.25 Prover 0: Proving ... % 4.05/1.25 Prover 1: Constructing countermodel ... % 4.05/1.26 Prover 4: Constructing countermodel ... % 4.05/1.26 Prover 3: Constructing countermodel ... % 4.05/1.27 Prover 2: Proving ... % 5.03/1.40 Prover 3: proved (828ms) % 5.03/1.41 % 5.03/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.03/1.41 % 5.03/1.41 Prover 6: stopped % 5.03/1.41 Prover 0: stopped % 5.03/1.41 Prover 2: stopped % 5.03/1.41 Prover 5: stopped % 5.03/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.03/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.03/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.03/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.03/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.03/1.44 Prover 1: Found proof (size 15) % 5.03/1.44 Prover 1: proved (863ms) % 5.03/1.44 Prover 4: stopped % 5.49/1.45 Prover 7: Preprocessing ... % 5.49/1.46 Prover 8: Preprocessing ... % 5.49/1.46 Prover 11: Preprocessing ... % 5.55/1.46 Prover 13: Preprocessing ... % 5.55/1.46 Prover 10: Preprocessing ... % 5.55/1.48 Prover 7: stopped % 5.55/1.50 Prover 13: stopped % 5.55/1.50 Prover 11: stopped % 5.55/1.50 Prover 10: stopped % 6.00/1.54 Prover 8: Warning: ignoring some quantifiers % 6.00/1.55 Prover 8: Constructing countermodel ... % 6.00/1.56 Prover 8: stopped % 6.00/1.56 % 6.00/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.00/1.56 % 6.00/1.56 % SZS output start Proof for theBenchmark % 6.00/1.56 Assumptions after simplification: % 6.00/1.56 --------------------------------- % 6.00/1.56 % 6.00/1.56 (ax4) % 6.00/1.60 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 6.00/1.60 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ % 6.00/1.60 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = % 6.00/1.60 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: % 6.00/1.60 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 6.00/1.60 collection(v1) | in(v0, v1) = 0) % 6.00/1.60 % 6.00/1.60 (ax5) % 6.00/1.61 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 6.00/1.61 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = % 6.00/1.61 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 6.00/1.61 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ( % 6.00/1.61 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | ( ~ (v2 % 6.00/1.61 = v0) & in(v0, v1) = 0)) % 6.00/1.61 % 6.00/1.61 (co1) % 6.00/1.61 ? [v0: collection] : ? [v1: collection] : ? [v2: collection] : (remove(7, % 6.00/1.61 v1) = v2 & add(2, v2) = v0 & collection(v2) & collection(v1) & % 6.00/1.61 collection(v0) & ! [v3: int] : ( ~ ($lesseq(v3, 0) | ~ (in(v3, v1) = 0)) & % 6.00/1.61 ? [v3: int] : ($lesseq(v3, 0)in(v3, v0) = 0)) % 6.00/1.61 % 6.00/1.61 Further assumptions not needed in the proof: % 6.00/1.61 -------------------------------------------- % 6.00/1.61 ax1, ax2, ax3 % 6.00/1.61 % 6.00/1.61 Those formulas are unsatisfiable: % 6.00/1.61 --------------------------------- % 6.00/1.61 % 6.00/1.61 Begin of proof % 6.00/1.61 | % 6.00/1.61 | ALPHA: (ax4) implies: % 6.00/1.62 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] % 6.00/1.62 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 6.00/1.62 | collection(v1) | in(v0, v1) = 0) % 6.00/1.62 | % 6.00/1.62 | ALPHA: (ax5) implies: % 6.00/1.62 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] % 6.00/1.62 | : ( ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | % 6.00/1.62 | ( ~ (v2 = v0) & in(v0, v1) = 0)) % 6.00/1.62 | % 6.00/1.62 | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2 % 6.00/1.62 | gives: % 6.00/1.62 | (3) remove(7, all_11_1) = all_11_0 & add(2, all_11_0) = all_11_2 & % 6.00/1.62 | collection(all_11_0) & collection(all_11_1) & collection(all_11_2) & ! % 6.00/1.62 | [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0, all_11_1) = 0)) & ? [v0: % 6.00/1.62 | int] : ($lesseq(v0, 0)in(v0, all_11_2) = 0) % 6.00/1.62 | % 6.00/1.62 | ALPHA: (3) implies: % 6.00/1.63 | (4) collection(all_11_1) % 6.00/1.63 | (5) collection(all_11_0) % 6.00/1.63 | (6) add(2, all_11_0) = all_11_2 % 6.00/1.63 | (7) remove(7, all_11_1) = all_11_0 % 6.00/1.63 | (8) ! [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0, all_11_1) = 0)) % 6.00/1.63 | (9) ? [v0: int] : ($lesseq(v0, 0)in(v0, all_11_2) = 0) % 6.00/1.63 | % 6.00/1.63 | DELTA: instantiating (9) with fresh symbol all_14_0 gives: % 6.00/1.63 | (10) $lesseq(all_14_0, 0)in(all_14_0, all_11_2) = 0 % 6.00/1.63 | % 6.00/1.63 | ALPHA: (10) implies: % 6.00/1.63 | (11) $lesseq(all_14_0, 0) % 6.00/1.63 | (12) in(all_14_0, all_11_2) = 0 % 6.00/1.63 | % 6.38/1.63 | GROUND_INST: instantiating (1) with all_14_0, all_11_0, 2, all_11_2, % 6.38/1.63 | simplifying with (5), (6), (12) gives: % 6.38/1.63 | (13) all_14_0 = 2 | in(all_14_0, all_11_0) = 0 % 6.38/1.63 | % 6.38/1.63 | BETA: splitting (13) gives: % 6.38/1.63 | % 6.38/1.63 | Case 1: % 6.38/1.63 | | % 6.38/1.63 | | (14) in(all_14_0, all_11_0) = 0 % 6.38/1.63 | | % 6.38/1.64 | | GROUND_INST: instantiating (2) with all_14_0, all_11_1, 7, all_11_0, % 6.38/1.64 | | simplifying with (4), (7), (14) gives: % 6.38/1.64 | | (15) ~ (all_14_0 = 7) & in(all_14_0, all_11_1) = 0 % 6.38/1.64 | | % 6.38/1.64 | | ALPHA: (15) implies: % 6.38/1.64 | | (16) in(all_14_0, all_11_1) = 0 % 6.38/1.64 | | % 6.38/1.64 | | GROUND_INST: instantiating (8) with all_14_0, simplifying with (16) gives: % 6.38/1.64 | | (17) $lesseq(1, all_14_0) % 6.38/1.64 | | % 6.38/1.64 | | COMBINE_INEQS: (11), (17) imply: % 6.38/1.64 | | (18) $false % 6.38/1.64 | | % 6.38/1.64 | | CLOSE: (18) is inconsistent. % 6.38/1.64 | | % 6.38/1.64 | Case 2: % 6.38/1.64 | | % 6.38/1.64 | | (19) all_14_0 = 2 % 6.38/1.64 | | % 6.38/1.64 | | REDUCE: (11), (19) imply: % 6.38/1.64 | | (20) $false % 6.38/1.64 | | % 6.38/1.64 | | CLOSE: (20) is inconsistent. % 6.38/1.64 | | % 6.38/1.64 | End of split % 6.38/1.64 | % 6.38/1.64 End of proof % 6.38/1.64 % SZS output end Proof for theBenchmark % 6.38/1.64 % 6.38/1.64 1083ms %------------------------------------------------------------------------------