%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.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 18:44:17 EDT 2023 % Result : Theorem 51.80s 7.51s % Output : Proof 58.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.10 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0. % 0.09/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n032.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Tue Aug 29 13:00:31 EDT 2023 % 0.10/0.31 % CPUTime : % 0.16/0.53 ________ _____ % 0.16/0.53 ___ __ \_________(_)________________________________ % 0.16/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.53 % 0.16/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.53 (2023-06-19) % 0.16/0.53 % 0.16/0.53 (c) Philipp Rümmer, 2009-2023 % 0.16/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.53 Amanda Stjerna. % 0.16/0.53 Free software under BSD-3-Clause. % 0.16/0.53 % 0.16/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.53 % 0.16/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.55 Running up to 7 provers in parallel. % 0.16/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.09/1.08 Prover 4: Preprocessing ... % 3.09/1.08 Prover 1: Preprocessing ... % 3.46/1.12 Prover 3: Preprocessing ... % 3.46/1.12 Prover 0: Preprocessing ... % 3.46/1.12 Prover 6: Preprocessing ... % 3.46/1.12 Prover 5: Preprocessing ... % 3.46/1.12 Prover 2: Preprocessing ... % 5.97/1.51 Prover 5: Constructing countermodel ... % 8.16/1.78 Prover 1: Constructing countermodel ... % 8.69/1.82 Prover 3: Constructing countermodel ... % 8.69/1.87 Prover 6: Proving ... % 8.69/1.92 Prover 2: Constructing countermodel ... % 14.75/2.66 Prover 4: Constructing countermodel ... % 15.36/2.73 Prover 0: Proving ... % 51.80/7.51 Prover 3: proved (6954ms) % 51.80/7.51 % 51.80/7.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 51.80/7.51 % 51.80/7.51 Prover 5: stopped % 51.80/7.51 Prover 2: stopped % 51.80/7.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 51.80/7.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 51.80/7.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 52.40/7.52 Prover 6: stopped % 52.40/7.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 52.88/7.63 Prover 0: stopped % 52.88/7.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 52.88/7.64 Prover 8: Preprocessing ... % 53.50/7.70 Prover 10: Preprocessing ... % 53.50/7.70 Prover 7: Preprocessing ... % 53.50/7.70 Prover 11: Preprocessing ... % 53.50/7.73 Prover 8: Warning: ignoring some quantifiers % 53.50/7.75 Prover 8: Constructing countermodel ... % 53.50/7.75 Prover 13: Preprocessing ... % 54.58/7.82 Prover 10: Constructing countermodel ... % 54.73/7.85 Prover 7: Constructing countermodel ... % 54.73/7.90 Prover 13: Constructing countermodel ... % 58.37/8.29 Prover 11: Constructing countermodel ... % 58.37/8.35 Prover 13: Found proof (size 12) % 58.37/8.35 Prover 13: proved (713ms) % 58.37/8.35 Prover 10: stopped % 58.37/8.35 Prover 11: stopped % 58.37/8.35 Prover 1: stopped % 58.37/8.35 Prover 7: stopped % 58.37/8.35 Prover 4: stopped % 58.37/8.37 Prover 8: stopped % 58.37/8.37 % 58.37/8.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 58.37/8.37 % 58.37/8.37 % SZS output start Proof for theBenchmark % 58.37/8.38 Assumptions after simplification: % 58.37/8.38 --------------------------------- % 58.37/8.38 % 58.37/8.38 (mTermNF) % 58.37/8.38 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ isTerminating0(v0) | % 58.37/8.38 ~ aRewritingSystem0(v0) | ~ aElement0(v1) | ? [v2: $i] : ($i(v2) & % 58.37/8.38 aNormalFormOfIn0(v2, v1, v0))) % 58.37/8.38 % 58.37/8.38 (m__) % 58.37/8.39 $i(xw) & $i(xR) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 58.37/8.39 sdtmndtplgtdt0(v1, xR, v0) | ~ aReductOfIn0(v1, xw, xR) | ~ aElement0(v1) % 58.37/8.39 | ~ aElement0(v0) | ? [v2: $i] : ($i(v2) & aReductOfIn0(v2, v0, xR))) & ! % 58.37/8.39 [v0: $i] : ( ~ $i(v0) | ~ aNormalFormOfIn0(v0, xw, xR)) & ! [v0: $i] : ( ~ % 58.37/8.39 $i(v0) | ~ sdtmndtasgtdt0(xw, xR, v0) | ~ aElement0(v0) | ? [v1: $i] : % 58.37/8.39 ($i(v1) & aReductOfIn0(v1, v0, xR))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 58.37/8.39 sdtmndtplgtdt0(xw, xR, v0) | ~ aElement0(v0) | ? [v1: $i] : ($i(v1) & % 58.37/8.39 aReductOfIn0(v1, v0, xR))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 58.37/8.39 aReductOfIn0(v0, xw, xR) | ~ aElement0(v0) | ? [v1: $i] : ($i(v1) & % 58.37/8.39 aReductOfIn0(v1, v0, xR))) & ( ~ aElement0(xw) | ? [v0: $i] : ($i(v0) & % 58.37/8.39 aReductOfIn0(v0, xw, xR))) % 58.37/8.39 % 58.37/8.39 (m__656) % 58.37/8.39 $i(xR) & aRewritingSystem0(xR) % 58.37/8.39 % 58.37/8.39 (m__656_01) % 58.37/8.39 $i(xR) & isTerminating0(xR) & isLocallyConfluent0(xR) & ! [v0: $i] : ! [v1: % 58.37/8.39 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 58.37/8.39 sdtmndtplgtdt0(v2, xR, v1) | ~ aReductOfIn0(v2, v0, xR) | ~ aElement0(v2) % 58.37/8.39 | ~ aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : ! % 58.37/8.39 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 58.37/8.39 aReductOfIn0(v2, v0, xR) | ~ aReductOfIn0(v1, v0, xR) | ~ aElement0(v2) | % 58.37/8.39 ~ aElement0(v1) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 58.37/8.39 : ($i(v5) & $i(v4) & $i(v3) & sdtmndtasgtdt0(v2, xR, v3) & % 58.37/8.39 sdtmndtasgtdt0(v1, xR, v3) & aElement0(v3) & (v3 = v2 | % 58.37/8.39 (sdtmndtplgtdt0(v2, xR, v3) & (aReductOfIn0(v3, v2, xR) | % 58.37/8.39 (sdtmndtplgtdt0(v4, xR, v3) & aReductOfIn0(v4, v2, xR) & % 58.37/8.39 aElement0(v4))))) & (v3 = v1 | (sdtmndtplgtdt0(v1, xR, v3) & % 58.37/8.39 (aReductOfIn0(v3, v1, xR) | (sdtmndtplgtdt0(v5, xR, v3) & % 58.37/8.39 aReductOfIn0(v5, v1, xR) & aElement0(v5))))))) & ! [v0: $i] : ! % 58.37/8.39 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v0, xR, v1) | ~ % 58.37/8.39 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : ! [v1: % 58.37/8.39 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aReductOfIn0(v1, v0, xR) | ~ % 58.37/8.39 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) % 58.37/8.39 % 58.37/8.39 (m__799) % 58.37/8.39 $i(xw) & $i(xv) & $i(xu) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ($i(v1) & % 58.37/8.39 $i(v0) & sdtmndtasgtdt0(xv, xR, xw) & sdtmndtasgtdt0(xu, xR, xw) & % 58.37/8.39 aElement0(xw) & (xw = xv | (sdtmndtplgtdt0(xv, xR, xw) & (aReductOfIn0(xw, % 58.37/8.39 xv, xR) | (sdtmndtplgtdt0(v0, xR, xw) & aReductOfIn0(v0, xv, xR) & % 58.37/8.39 aElement0(v0))))) & (xw = xu | (sdtmndtplgtdt0(xu, xR, xw) & % 58.37/8.39 (aReductOfIn0(xw, xu, xR) | (sdtmndtplgtdt0(v1, xR, xw) & % 58.37/8.39 aReductOfIn0(v1, xu, xR) & aElement0(v1)))))) % 58.37/8.39 % 58.37/8.39 Further assumptions not needed in the proof: % 58.37/8.39 -------------------------------------------- % 58.37/8.39 mCRDef, mElmSort, mNFRDef, mReduct, mRelSort, mTCDef, mTCRDef, mTCRTrans, % 58.37/8.39 mTCTrans, mTCbr, mTermin, mWCRDef, mWFOrd, m__715, m__731, m__731_02, m__755, % 58.37/8.39 m__779 % 58.37/8.39 % 58.37/8.39 Those formulas are unsatisfiable: % 58.37/8.39 --------------------------------- % 58.37/8.39 % 58.37/8.39 Begin of proof % 58.37/8.40 | % 58.37/8.40 | ALPHA: (m__) implies: % 58.37/8.40 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ aNormalFormOfIn0(v0, xw, xR)) % 58.37/8.40 | % 58.37/8.40 | ALPHA: (m__799) implies: % 58.37/8.40 | (2) $i(xw) % 58.37/8.40 | (3) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & sdtmndtasgtdt0(xv, xR, % 58.37/8.40 | xw) & sdtmndtasgtdt0(xu, xR, xw) & aElement0(xw) & (xw = xv | % 58.37/8.40 | (sdtmndtplgtdt0(xv, xR, xw) & (aReductOfIn0(xw, xv, xR) | % 58.37/8.40 | (sdtmndtplgtdt0(v0, xR, xw) & aReductOfIn0(v0, xv, xR) & % 58.37/8.40 | aElement0(v0))))) & (xw = xu | (sdtmndtplgtdt0(xu, xR, xw) & % 58.37/8.40 | (aReductOfIn0(xw, xu, xR) | (sdtmndtplgtdt0(v1, xR, xw) & % 58.37/8.40 | aReductOfIn0(v1, xu, xR) & aElement0(v1)))))) % 58.37/8.40 | % 58.37/8.40 | ALPHA: (m__656_01) implies: % 58.37/8.40 | (4) isTerminating0(xR) % 58.37/8.40 | % 58.37/8.40 | ALPHA: (m__656) implies: % 58.37/8.40 | (5) aRewritingSystem0(xR) % 58.37/8.40 | (6) $i(xR) % 58.37/8.40 | % 58.37/8.40 | DELTA: instantiating (3) with fresh symbols all_22_0, all_22_1 gives: % 58.37/8.40 | (7) $i(all_22_0) & $i(all_22_1) & sdtmndtasgtdt0(xv, xR, xw) & % 58.37/8.40 | sdtmndtasgtdt0(xu, xR, xw) & aElement0(xw) & (xw = xv | % 58.37/8.40 | (sdtmndtplgtdt0(xv, xR, xw) & (aReductOfIn0(xw, xv, xR) | % 58.37/8.40 | (sdtmndtplgtdt0(all_22_1, xR, xw) & aReductOfIn0(all_22_1, xv, % 58.37/8.40 | xR) & aElement0(all_22_1))))) & (xw = xu | % 58.37/8.40 | (sdtmndtplgtdt0(xu, xR, xw) & (aReductOfIn0(xw, xu, xR) | % 58.37/8.40 | (sdtmndtplgtdt0(all_22_0, xR, xw) & aReductOfIn0(all_22_0, xu, % 58.37/8.40 | xR) & aElement0(all_22_0))))) % 58.37/8.40 | % 58.37/8.40 | ALPHA: (7) implies: % 58.37/8.40 | (8) aElement0(xw) % 58.37/8.40 | % 58.37/8.40 | GROUND_INST: instantiating (mTermNF) with xR, xw, simplifying with (2), (4), % 58.37/8.40 | (5), (6), (8) gives: % 58.37/8.40 | (9) ? [v0: $i] : ($i(v0) & aNormalFormOfIn0(v0, xw, xR)) % 58.37/8.40 | % 58.37/8.40 | DELTA: instantiating (9) with fresh symbol all_42_0 gives: % 58.37/8.40 | (10) $i(all_42_0) & aNormalFormOfIn0(all_42_0, xw, xR) % 58.37/8.40 | % 58.37/8.40 | ALPHA: (10) implies: % 58.37/8.40 | (11) aNormalFormOfIn0(all_42_0, xw, xR) % 58.37/8.40 | (12) $i(all_42_0) % 58.37/8.40 | % 58.37/8.40 | GROUND_INST: instantiating (1) with all_42_0, simplifying with (11), (12) % 58.37/8.40 | gives: % 58.37/8.40 | (13) $false % 58.37/8.41 | % 58.37/8.41 | CLOSE: (13) is inconsistent. % 58.37/8.41 | % 58.37/8.41 End of proof % 58.37/8.41 % SZS output end Proof for theBenchmark % 58.37/8.41 % 58.37/8.41 7871ms %------------------------------------------------------------------------------