%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM023+1 : TPTP v8.1.2. Released v4.0.0. % 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 18:44:18 EDT 2023 % Result : Theorem 12.68s 2.47s % Output : Proof 15.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : COM023+1 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 13:30:55 EDT 2023 % 0.12/0.33 % CPUTime : % 0.57/0.59 ________ _____ % 0.57/0.60 ___ __ \_________(_)________________________________ % 0.57/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.60 % 0.57/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.60 (2023-06-19) % 0.57/0.60 % 0.57/0.60 (c) Philipp Rümmer, 2009-2023 % 0.57/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.60 Amanda Stjerna. % 0.57/0.60 Free software under BSD-3-Clause. % 0.57/0.60 % 0.57/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.60 % 0.57/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.62/0.61 Running up to 7 provers in parallel. % 0.62/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.62/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.57/1.09 Prover 1: Preprocessing ... % 2.98/1.10 Prover 4: Preprocessing ... % 2.98/1.13 Prover 5: Preprocessing ... % 2.98/1.13 Prover 6: Preprocessing ... % 2.98/1.13 Prover 0: Preprocessing ... % 2.98/1.13 Prover 3: Preprocessing ... % 2.98/1.13 Prover 2: Preprocessing ... % 5.65/1.47 Prover 5: Constructing countermodel ... % 5.65/1.48 Prover 2: Constructing countermodel ... % 6.09/1.55 Prover 1: Constructing countermodel ... % 6.09/1.56 Prover 3: Constructing countermodel ... % 6.09/1.58 Prover 6: Proving ... % 8.86/1.95 Prover 4: Constructing countermodel ... % 10.46/2.13 Prover 0: Proving ... % 12.68/2.46 Prover 3: proved (1847ms) % 12.68/2.47 % 12.68/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.68/2.47 % 12.68/2.47 Prover 2: stopped % 12.68/2.47 Prover 5: stopped % 12.68/2.48 Prover 0: stopped % 12.68/2.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.68/2.48 Prover 6: stopped % 12.68/2.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.68/2.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.68/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.68/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.68/2.50 Prover 7: Preprocessing ... % 13.42/2.53 Prover 7: Constructing countermodel ... % 13.42/2.54 Prover 13: Preprocessing ... % 13.42/2.54 Prover 10: Preprocessing ... % 13.42/2.54 Prover 11: Preprocessing ... % 13.42/2.57 Prover 8: Preprocessing ... % 13.42/2.58 Prover 10: Constructing countermodel ... % 14.07/2.60 Prover 13: Constructing countermodel ... % 14.88/2.70 Prover 8: Warning: ignoring some quantifiers % 14.88/2.72 Prover 8: Constructing countermodel ... % 15.03/2.75 Prover 13: Found proof (size 12) % 15.03/2.75 Prover 13: proved (259ms) % 15.03/2.75 Prover 7: stopped % 15.03/2.75 Prover 4: stopped % 15.03/2.75 Prover 8: stopped % 15.03/2.75 Prover 1: stopped % 15.03/2.76 Prover 10: stopped % 15.59/2.84 Prover 11: Constructing countermodel ... % 15.59/2.85 Prover 11: stopped % 15.59/2.85 % 15.59/2.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.59/2.85 % 15.59/2.85 % SZS output start Proof for theBenchmark % 15.59/2.85 Assumptions after simplification: % 15.59/2.85 --------------------------------- % 15.59/2.85 % 15.59/2.85 (mCRDef) % 15.59/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 15.59/2.86 | ~ $i(v1) | ~ $i(v0) | ~ isConfluent0(v0) | ~ sdtmndtasgtdt0(v1, v0, % 15.59/2.86 v3) | ~ sdtmndtasgtdt0(v1, v0, v2) | ~ aRewritingSystem0(v0) | ~ % 15.59/2.86 aElement0(v3) | ~ aElement0(v2) | ~ aElement0(v1) | ? [v4: $i] : ($i(v4) % 15.59/2.86 & sdtmndtasgtdt0(v3, v0, v4) & sdtmndtasgtdt0(v2, v0, v4) & % 15.59/2.86 aElement0(v4))) & ! [v0: $i] : ( ~ $i(v0) | ~ aRewritingSystem0(v0) | % 15.59/2.86 isConfluent0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 15.59/2.86 $i(v2) & $i(v1) & sdtmndtasgtdt0(v1, v0, v3) & sdtmndtasgtdt0(v1, v0, v2) % 15.59/2.86 & aElement0(v3) & aElement0(v2) & aElement0(v1) & ! [v4: $i] : ( ~ $i(v4) % 15.59/2.86 | ~ sdtmndtasgtdt0(v3, v0, v4) | ~ sdtmndtasgtdt0(v2, v0, v4) | ~ % 15.59/2.86 aElement0(v4)))) % 15.59/2.86 % 15.59/2.86 (m__) % 15.59/2.86 $i(xR) & ~ isConfluent0(xR) % 15.59/2.86 % 15.59/2.86 (m__656) % 15.59/2.86 $i(xR) & aRewritingSystem0(xR) % 15.59/2.86 % 15.59/2.86 (m__715) % 15.59/2.86 $i(xR) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 15.59/2.86 $i(v0) | ~ sdtmndtasgtdt0(v0, xR, v2) | ~ sdtmndtasgtdt0(v0, xR, v1) | ~ % 15.59/2.86 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v3: $i] : ($i(v3) % 15.59/2.86 & sdtmndtasgtdt0(v2, xR, v3) & sdtmndtasgtdt0(v1, xR, v3) & % 15.59/2.86 aElement0(v3))) % 15.59/2.86 % 15.59/2.86 Further assumptions not needed in the proof: % 15.59/2.86 -------------------------------------------- % 15.59/2.86 mElmSort, mNFRDef, mReduct, mRelSort, mTCDef, mTCRDef, mTCRTrans, mTCTrans, % 15.59/2.86 mTCbr, mTermNF, mTermin, mWCRDef, mWFOrd, m__656_01 % 15.59/2.86 % 15.59/2.86 Those formulas are unsatisfiable: % 15.59/2.86 --------------------------------- % 15.59/2.86 % 15.59/2.86 Begin of proof % 15.59/2.86 | % 15.59/2.86 | ALPHA: (m__) implies: % 15.59/2.87 | (1) ~ isConfluent0(xR) % 15.59/2.87 | % 15.59/2.87 | ALPHA: (m__715) implies: % 15.59/2.87 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 15.59/2.87 | $i(v0) | ~ sdtmndtasgtdt0(v0, xR, v2) | ~ sdtmndtasgtdt0(v0, xR, % 15.59/2.87 | v1) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 15.59/2.87 | [v3: $i] : ($i(v3) & sdtmndtasgtdt0(v2, xR, v3) & sdtmndtasgtdt0(v1, % 15.59/2.87 | xR, v3) & aElement0(v3))) % 15.59/2.87 | % 15.59/2.87 | ALPHA: (m__656) implies: % 15.59/2.87 | (3) aRewritingSystem0(xR) % 15.59/2.87 | (4) $i(xR) % 15.59/2.87 | % 15.59/2.87 | ALPHA: (mCRDef) implies: % 15.59/2.87 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aRewritingSystem0(v0) | isConfluent0(v0) % 15.59/2.87 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & $i(v1) % 15.59/2.87 | & sdtmndtasgtdt0(v1, v0, v3) & sdtmndtasgtdt0(v1, v0, v2) & % 15.59/2.87 | aElement0(v3) & aElement0(v2) & aElement0(v1) & ! [v4: $i] : ( ~ % 15.59/2.87 | $i(v4) | ~ sdtmndtasgtdt0(v3, v0, v4) | ~ sdtmndtasgtdt0(v2, % 15.59/2.87 | v0, v4) | ~ aElement0(v4)))) % 15.59/2.87 | % 15.59/2.87 | GROUND_INST: instantiating (5) with xR, simplifying with (1), (3), (4) gives: % 15.59/2.87 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) & % 15.59/2.87 | sdtmndtasgtdt0(v0, xR, v2) & sdtmndtasgtdt0(v0, xR, v1) & % 15.59/2.87 | aElement0(v2) & aElement0(v1) & aElement0(v0) & ! [v3: $i] : ( ~ % 15.59/2.87 | $i(v3) | ~ sdtmndtasgtdt0(v2, xR, v3) | ~ sdtmndtasgtdt0(v1, xR, % 15.59/2.87 | v3) | ~ aElement0(v3))) % 15.59/2.87 | % 15.59/2.87 | DELTA: instantiating (6) with fresh symbols all_19_0, all_19_1, all_19_2 % 15.59/2.87 | gives: % 15.59/2.87 | (7) $i(all_19_0) & $i(all_19_1) & $i(all_19_2) & sdtmndtasgtdt0(all_19_2, % 15.59/2.87 | xR, all_19_0) & sdtmndtasgtdt0(all_19_2, xR, all_19_1) & % 15.59/2.87 | aElement0(all_19_0) & aElement0(all_19_1) & aElement0(all_19_2) & ! % 15.59/2.87 | [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(all_19_0, xR, v0) | ~ % 15.59/2.87 | sdtmndtasgtdt0(all_19_1, xR, v0) | ~ aElement0(v0)) % 15.59/2.87 | % 15.59/2.87 | ALPHA: (7) implies: % 15.59/2.87 | (8) aElement0(all_19_2) % 15.59/2.87 | (9) aElement0(all_19_1) % 15.59/2.87 | (10) aElement0(all_19_0) % 15.59/2.87 | (11) sdtmndtasgtdt0(all_19_2, xR, all_19_1) % 15.59/2.87 | (12) sdtmndtasgtdt0(all_19_2, xR, all_19_0) % 15.59/2.87 | (13) $i(all_19_2) % 15.59/2.87 | (14) $i(all_19_1) % 15.59/2.87 | (15) $i(all_19_0) % 15.59/2.87 | (16) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(all_19_0, xR, v0) | ~ % 15.59/2.87 | sdtmndtasgtdt0(all_19_1, xR, v0) | ~ aElement0(v0)) % 15.59/2.87 | % 15.59/2.88 | GROUND_INST: instantiating (2) with all_19_2, all_19_1, all_19_0, simplifying % 15.59/2.88 | with (8), (9), (10), (11), (12), (13), (14), (15) gives: % 15.59/2.88 | (17) ? [v0: $i] : ($i(v0) & sdtmndtasgtdt0(all_19_0, xR, v0) & % 15.59/2.88 | sdtmndtasgtdt0(all_19_1, xR, v0) & aElement0(v0)) % 15.59/2.88 | % 15.59/2.88 | DELTA: instantiating (17) with fresh symbol all_38_0 gives: % 15.59/2.88 | (18) $i(all_38_0) & sdtmndtasgtdt0(all_19_0, xR, all_38_0) & % 15.59/2.88 | sdtmndtasgtdt0(all_19_1, xR, all_38_0) & aElement0(all_38_0) % 15.59/2.88 | % 15.59/2.88 | ALPHA: (18) implies: % 15.59/2.88 | (19) aElement0(all_38_0) % 15.59/2.88 | (20) sdtmndtasgtdt0(all_19_1, xR, all_38_0) % 15.59/2.88 | (21) sdtmndtasgtdt0(all_19_0, xR, all_38_0) % 15.59/2.88 | (22) $i(all_38_0) % 15.59/2.88 | % 15.59/2.88 | GROUND_INST: instantiating (16) with all_38_0, simplifying with (19), (20), % 15.59/2.88 | (21), (22) gives: % 15.59/2.88 | (23) $false % 15.59/2.88 | % 15.59/2.88 | CLOSE: (23) is inconsistent. % 15.59/2.88 | % 15.59/2.88 End of proof % 15.59/2.88 % SZS output end Proof for theBenchmark % 15.59/2.88 % 15.59/2.88 2282ms %------------------------------------------------------------------------------