%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM013+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 : n029.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 18:44:15 EDT 2023 % Result : Theorem 9.81s 2.10s % Output : Proof 13.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COM013+4 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 13:05:11 EDT 2023 % 0.12/0.34 % CPUTime : % 0.48/0.61 ________ _____ % 0.48/0.61 ___ __ \_________(_)________________________________ % 0.48/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.48/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.48/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.48/0.61 % 0.48/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.48/0.61 (2023-06-19) % 0.48/0.61 % 0.48/0.61 (c) Philipp Rümmer, 2009-2023 % 0.48/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.48/0.61 Amanda Stjerna. % 0.48/0.61 Free software under BSD-3-Clause. % 0.48/0.61 % 0.48/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.48/0.61 % 0.48/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.48/0.62 Running up to 7 provers in parallel. % 0.74/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.74/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.02/1.12 Prover 4: Preprocessing ... % 3.02/1.12 Prover 1: Preprocessing ... % 3.24/1.17 Prover 5: Preprocessing ... % 3.24/1.17 Prover 6: Preprocessing ... % 3.24/1.17 Prover 0: Preprocessing ... % 3.24/1.17 Prover 3: Preprocessing ... % 3.24/1.17 Prover 2: Preprocessing ... % 5.42/1.45 Prover 5: Constructing countermodel ... % 5.42/1.51 Prover 2: Constructing countermodel ... % 6.46/1.63 Prover 1: Constructing countermodel ... % 7.01/1.66 Prover 3: Constructing countermodel ... % 7.13/1.72 Prover 6: Proving ... % 9.81/2.06 Prover 4: Constructing countermodel ... % 9.81/2.10 Prover 5: proved (1448ms) % 9.81/2.10 % 9.81/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.81/2.10 % 9.81/2.10 Prover 2: stopped % 9.81/2.10 Prover 3: stopped % 9.81/2.11 Prover 6: stopped % 9.81/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.81/2.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.81/2.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.81/2.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.40/2.16 Prover 7: Preprocessing ... % 10.40/2.16 Prover 0: Proving ... % 10.40/2.16 Prover 0: stopped % 10.40/2.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.40/2.18 Prover 8: Preprocessing ... % 10.85/2.18 Prover 11: Preprocessing ... % 10.85/2.22 Prover 10: Preprocessing ... % 10.85/2.22 Prover 13: Preprocessing ... % 10.85/2.23 Prover 7: Constructing countermodel ... % 11.41/2.26 Prover 13: Constructing countermodel ... % 11.58/2.31 Prover 10: Constructing countermodel ... % 11.99/2.34 Prover 8: Warning: ignoring some quantifiers % 11.99/2.35 Prover 8: Constructing countermodel ... % 13.02/2.50 Prover 13: Found proof (size 21) % 13.02/2.51 Prover 13: proved (334ms) % 13.02/2.51 Prover 10: stopped % 13.02/2.51 Prover 1: stopped % 13.02/2.51 Prover 7: stopped % 13.02/2.51 Prover 4: stopped % 13.02/2.51 Prover 8: stopped % 13.02/2.54 Prover 11: Constructing countermodel ... % 13.02/2.54 Prover 11: stopped % 13.02/2.54 % 13.02/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.02/2.54 % 13.02/2.55 % SZS output start Proof for theBenchmark % 13.02/2.55 Assumptions after simplification: % 13.02/2.55 --------------------------------- % 13.02/2.55 % 13.02/2.55 (mReduct) % 13.50/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.50/2.56 ~ aReductOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) | % 13.50/2.56 aElement0(v2)) % 13.50/2.56 % 13.50/2.56 (mTCDef) % 13.50/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 13.50/2.56 | ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v3, v1, v2) | ~ % 13.50/2.56 aReductOfIn0(v3, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) | ~ % 13.50/2.56 aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) & ! [v0: $i] % 13.50/2.56 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 13.50/2.56 sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | % 13.50/2.56 ~ aElement0(v0) | aReductOfIn0(v2, v0, v1) | ? [v3: $i] : ($i(v3) & % 13.50/2.56 sdtmndtplgtdt0(v3, v1, v2) & aReductOfIn0(v3, v0, v1) & aElement0(v3))) & % 13.50/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.50/2.56 ~ aReductOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | % 13.50/2.56 ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) % 13.50/2.56 % 13.50/2.56 (mTCRDef) % 13.50/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ $i(v2) | ~ $i(v1) | % 13.50/2.57 ~ $i(v0) | ~ sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ % 13.50/2.57 aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) & ! [v0: $i] % 13.50/2.57 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 13.50/2.57 sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | % 13.50/2.57 ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : % 13.50/2.57 ( ~ $i(v1) | ~ $i(v0) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) | % 13.50/2.57 sdtmndtasgtdt0(v0, v1, v0)) % 13.50/2.57 % 13.50/2.57 (mTCRTrans) % 13.50/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 13.50/2.57 | ~ $i(v1) | ~ $i(v0) | ~ sdtmndtasgtdt0(v2, v1, v3) | ~ % 13.50/2.57 sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) | % 13.50/2.57 ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v3)) % 13.50/2.57 % 13.50/2.57 (m__) % 13.50/2.57 $i(xR) & ? [v0: $i] : ($i(v0) & aElement0(v0) & ! [v1: $i] : ! [v2: $i] : ( % 13.50/2.57 ~ $i(v2) | ~ $i(v1) | ~ sdtmndtplgtdt0(v2, xR, v1) | ~ aReductOfIn0(v2, % 13.50/2.57 v0, xR) | ~ aElement0(v2) | ~ aElement0(v1) | ? [v3: $i] : ($i(v3) & % 13.50/2.57 aReductOfIn0(v3, v1, xR))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 13.50/2.57 aNormalFormOfIn0(v1, v0, xR)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 13.50/2.57 sdtmndtasgtdt0(v0, xR, v1) | ~ aElement0(v1) | ? [v2: $i] : ($i(v2) & % 13.50/2.57 aReductOfIn0(v2, v1, xR))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 13.50/2.57 sdtmndtplgtdt0(v0, xR, v1) | ~ aElement0(v1) | ? [v2: $i] : ($i(v2) & % 13.50/2.57 aReductOfIn0(v2, v1, xR))) & ! [v1: $i] : ( ~ $i(v1) | ~ iLess0(v1, % 13.50/2.57 v0) | ~ aElement0(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & % 13.50/2.57 aNormalFormOfIn0(v2, v1, xR) & sdtmndtasgtdt0(v1, xR, v2) & % 13.50/2.57 aElement0(v2) & ! [v4: $i] : ( ~ $i(v4) | ~ aReductOfIn0(v4, v2, xR)) % 13.50/2.57 & (v2 = v1 | (sdtmndtplgtdt0(v1, xR, v2) & (aReductOfIn0(v2, v1, xR) | % 13.50/2.57 (sdtmndtplgtdt0(v3, xR, v2) & aReductOfIn0(v3, v1, xR) & % 13.50/2.57 aElement0(v3))))))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 13.50/2.57 aReductOfIn0(v1, v0, xR) | ~ aElement0(v1) | ? [v2: $i] : ($i(v2) & % 13.50/2.57 aReductOfIn0(v2, v1, xR))) & ? [v1: $i] : ($i(v1) & aReductOfIn0(v1, % 13.50/2.57 v0, xR))) % 13.50/2.57 % 13.50/2.57 (m__587) % 13.50/2.57 $i(xR) & isTerminating0(xR) & aRewritingSystem0(xR) & ! [v0: $i] : ! [v1: % 13.50/2.57 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 13.50/2.57 sdtmndtplgtdt0(v2, xR, v1) | ~ aReductOfIn0(v2, v0, xR) | ~ aElement0(v2) % 13.50/2.57 | ~ aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : ! % 13.50/2.57 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v0, xR, v1) | ~ % 13.50/2.57 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : ! [v1: % 13.50/2.57 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aReductOfIn0(v1, v0, xR) | ~ % 13.50/2.57 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) % 13.50/2.57 % 13.50/2.57 Further assumptions not needed in the proof: % 13.50/2.57 -------------------------------------------- % 13.50/2.57 mCRDef, mElmSort, mNFRDef, mRelSort, mTCTrans, mTCbr, mTermin, mWCRDef, mWFOrd % 13.50/2.57 % 13.50/2.57 Those formulas are unsatisfiable: % 13.50/2.57 --------------------------------- % 13.50/2.57 % 13.50/2.57 Begin of proof % 13.50/2.57 | % 13.50/2.58 | ALPHA: (m__) implies: % 13.50/2.58 | (1) ? [v0: $i] : ($i(v0) & aElement0(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 13.50/2.58 | $i(v2) | ~ $i(v1) | ~ sdtmndtplgtdt0(v2, xR, v1) | ~ % 13.50/2.58 | aReductOfIn0(v2, v0, xR) | ~ aElement0(v2) | ~ aElement0(v1) | ? % 13.50/2.58 | [v3: $i] : ($i(v3) & aReductOfIn0(v3, v1, xR))) & ! [v1: $i] : ( ~ % 13.50/2.58 | $i(v1) | ~ aNormalFormOfIn0(v1, v0, xR)) & ! [v1: $i] : ( ~ % 13.50/2.58 | $i(v1) | ~ sdtmndtasgtdt0(v0, xR, v1) | ~ aElement0(v1) | ? [v2: % 13.50/2.58 | $i] : ($i(v2) & aReductOfIn0(v2, v1, xR))) & ! [v1: $i] : ( ~ % 13.50/2.58 | $i(v1) | ~ sdtmndtplgtdt0(v0, xR, v1) | ~ aElement0(v1) | ? [v2: % 13.50/2.58 | $i] : ($i(v2) & aReductOfIn0(v2, v1, xR))) & ! [v1: $i] : ( ~ % 13.50/2.58 | $i(v1) | ~ iLess0(v1, v0) | ~ aElement0(v1) | ? [v2: $i] : ? % 13.50/2.58 | [v3: $i] : ($i(v3) & $i(v2) & aNormalFormOfIn0(v2, v1, xR) & % 13.50/2.58 | sdtmndtasgtdt0(v1, xR, v2) & aElement0(v2) & ! [v4: $i] : ( ~ % 13.50/2.58 | $i(v4) | ~ aReductOfIn0(v4, v2, xR)) & (v2 = v1 | % 13.50/2.58 | (sdtmndtplgtdt0(v1, xR, v2) & (aReductOfIn0(v2, v1, xR) | % 13.50/2.58 | (sdtmndtplgtdt0(v3, xR, v2) & aReductOfIn0(v3, v1, xR) & % 13.50/2.58 | aElement0(v3))))))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 13.50/2.58 | aReductOfIn0(v1, v0, xR) | ~ aElement0(v1) | ? [v2: $i] : ($i(v2) % 13.50/2.58 | & aReductOfIn0(v2, v1, xR))) & ? [v1: $i] : ($i(v1) & % 13.50/2.58 | aReductOfIn0(v1, v0, xR))) % 13.50/2.58 | % 13.50/2.58 | ALPHA: (m__587) implies: % 13.50/2.58 | (2) aRewritingSystem0(xR) % 13.50/2.58 | (3) $i(xR) % 13.50/2.58 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.50/2.58 | aReductOfIn0(v1, v0, xR) | ~ aElement0(v1) | ~ aElement0(v0) | % 13.50/2.58 | iLess0(v1, v0)) % 13.50/2.58 | % 13.50/2.58 | ALPHA: (mTCRDef) implies: % 13.62/2.58 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 13.62/2.58 | $i(v0) | ~ sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | % 13.62/2.58 | ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2)) % 13.62/2.58 | % 13.62/2.58 | ALPHA: (mTCDef) implies: % 13.62/2.58 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 13.62/2.58 | $i(v0) | ~ aReductOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ % 13.62/2.58 | aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) % 13.62/2.58 | % 13.62/2.58 | DELTA: instantiating (1) with fresh symbol all_13_0 gives: % 13.62/2.59 | (7) $i(all_13_0) & aElement0(all_13_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.62/2.59 | $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v1, xR, v0) | ~ % 13.62/2.59 | aReductOfIn0(v1, all_13_0, xR) | ~ aElement0(v1) | ~ aElement0(v0) % 13.62/2.59 | | ? [v2: $i] : ($i(v2) & aReductOfIn0(v2, v0, xR))) & ! [v0: $i] : % 13.62/2.59 | ( ~ $i(v0) | ~ aNormalFormOfIn0(v0, all_13_0, xR)) & ! [v0: $i] : ( ~ % 13.62/2.59 | $i(v0) | ~ sdtmndtasgtdt0(all_13_0, xR, v0) | ~ aElement0(v0) | ? % 13.62/2.59 | [v1: $i] : ($i(v1) & aReductOfIn0(v1, v0, xR))) & ! [v0: $i] : ( ~ % 13.62/2.59 | $i(v0) | ~ sdtmndtplgtdt0(all_13_0, xR, v0) | ~ aElement0(v0) | ? % 13.62/2.59 | [v1: $i] : ($i(v1) & aReductOfIn0(v1, v0, xR))) & ! [v0: $i] : ( ~ % 13.62/2.59 | $i(v0) | ~ iLess0(v0, all_13_0) | ~ aElement0(v0) | ? [v1: $i] : % 13.62/2.59 | ? [v2: $i] : ($i(v2) & $i(v1) & aNormalFormOfIn0(v1, v0, xR) & % 13.62/2.59 | sdtmndtasgtdt0(v0, xR, v1) & aElement0(v1) & ! [v3: $i] : ( ~ % 13.62/2.59 | $i(v3) | ~ aReductOfIn0(v3, v1, xR)) & (v1 = v0 | % 13.62/2.59 | (sdtmndtplgtdt0(v0, xR, v1) & (aReductOfIn0(v1, v0, xR) | % 13.62/2.59 | (sdtmndtplgtdt0(v2, xR, v1) & aReductOfIn0(v2, v0, xR) & % 13.62/2.59 | aElement0(v2))))))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 13.62/2.59 | aReductOfIn0(v0, all_13_0, xR) | ~ aElement0(v0) | ? [v1: $i] : % 13.62/2.59 | ($i(v1) & aReductOfIn0(v1, v0, xR))) & ? [v0: $i] : ($i(v0) & % 13.62/2.59 | aReductOfIn0(v0, all_13_0, xR)) % 13.62/2.59 | % 13.62/2.59 | ALPHA: (7) implies: % 13.62/2.59 | (8) aElement0(all_13_0) % 13.62/2.59 | (9) $i(all_13_0) % 13.62/2.59 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ iLess0(v0, all_13_0) | ~ aElement0(v0) % 13.62/2.59 | | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & % 13.62/2.59 | aNormalFormOfIn0(v1, v0, xR) & sdtmndtasgtdt0(v0, xR, v1) & % 13.62/2.59 | aElement0(v1) & ! [v3: $i] : ( ~ $i(v3) | ~ aReductOfIn0(v3, v1, % 13.62/2.59 | xR)) & (v1 = v0 | (sdtmndtplgtdt0(v0, xR, v1) & % 13.62/2.59 | (aReductOfIn0(v1, v0, xR) | (sdtmndtplgtdt0(v2, xR, v1) & % 13.62/2.59 | aReductOfIn0(v2, v0, xR) & aElement0(v2))))))) % 13.62/2.59 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(all_13_0, xR, v0) | ~ % 13.62/2.59 | aElement0(v0) | ? [v1: $i] : ($i(v1) & aReductOfIn0(v1, v0, xR))) % 13.62/2.59 | (12) ? [v0: $i] : ($i(v0) & aReductOfIn0(v0, all_13_0, xR)) % 13.62/2.59 | % 13.62/2.59 | DELTA: instantiating (12) with fresh symbol all_16_0 gives: % 13.62/2.59 | (13) $i(all_16_0) & aReductOfIn0(all_16_0, all_13_0, xR) % 13.62/2.59 | % 13.62/2.59 | ALPHA: (13) implies: % 13.62/2.59 | (14) aReductOfIn0(all_16_0, all_13_0, xR) % 13.62/2.59 | (15) $i(all_16_0) % 13.62/2.59 | % 13.62/2.59 | GROUND_INST: instantiating (mReduct) with all_13_0, xR, all_16_0, simplifying % 13.62/2.59 | with (2), (3), (8), (9), (14), (15) gives: % 13.62/2.59 | (16) aElement0(all_16_0) % 13.62/2.59 | % 13.62/2.59 | GROUND_INST: instantiating (6) with all_13_0, xR, all_16_0, simplifying with % 13.62/2.59 | (2), (3), (8), (9), (14), (15), (16) gives: % 13.62/2.59 | (17) sdtmndtplgtdt0(all_13_0, xR, all_16_0) % 13.62/2.59 | % 13.62/2.59 | GROUND_INST: instantiating (4) with all_13_0, all_16_0, simplifying with (8), % 13.62/2.59 | (9), (14), (15), (16) gives: % 13.62/2.59 | (18) iLess0(all_16_0, all_13_0) % 13.62/2.59 | % 13.62/2.59 | GROUND_INST: instantiating (10) with all_16_0, simplifying with (15), (16), % 13.62/2.59 | (18) gives: % 13.62/2.59 | (19) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & aNormalFormOfIn0(v0, % 13.62/2.59 | all_16_0, xR) & sdtmndtasgtdt0(all_16_0, xR, v0) & aElement0(v0) & % 13.62/2.59 | ! [v2: $i] : ( ~ $i(v2) | ~ aReductOfIn0(v2, v0, xR)) & (v0 = % 13.62/2.59 | all_16_0 | (sdtmndtplgtdt0(all_16_0, xR, v0) & (aReductOfIn0(v0, % 13.62/2.59 | all_16_0, xR) | (sdtmndtplgtdt0(v1, xR, v0) & % 13.62/2.59 | aReductOfIn0(v1, all_16_0, xR) & aElement0(v1)))))) % 13.62/2.59 | % 13.62/2.59 | GROUND_INST: instantiating (5) with all_13_0, xR, all_16_0, simplifying with % 13.62/2.59 | (2), (3), (8), (9), (15), (16), (17) gives: % 13.62/2.59 | (20) sdtmndtasgtdt0(all_13_0, xR, all_16_0) % 13.62/2.59 | % 13.62/2.59 | DELTA: instantiating (19) with fresh symbols all_42_0, all_42_1 gives: % 13.62/2.60 | (21) $i(all_42_0) & $i(all_42_1) & aNormalFormOfIn0(all_42_1, all_16_0, xR) % 13.62/2.60 | & sdtmndtasgtdt0(all_16_0, xR, all_42_1) & aElement0(all_42_1) & ! % 13.62/2.60 | [v0: $i] : ( ~ $i(v0) | ~ aReductOfIn0(v0, all_42_1, xR)) & (all_42_1 % 13.62/2.60 | = all_16_0 | (sdtmndtplgtdt0(all_16_0, xR, all_42_1) & % 13.62/2.60 | (aReductOfIn0(all_42_1, all_16_0, xR) | (sdtmndtplgtdt0(all_42_0, % 13.62/2.60 | xR, all_42_1) & aReductOfIn0(all_42_0, all_16_0, xR) & % 13.62/2.60 | aElement0(all_42_0))))) % 13.62/2.60 | % 13.62/2.60 | ALPHA: (21) implies: % 13.62/2.60 | (22) aElement0(all_42_1) % 13.62/2.60 | (23) sdtmndtasgtdt0(all_16_0, xR, all_42_1) % 13.62/2.60 | (24) $i(all_42_1) % 13.62/2.60 | (25) ! [v0: $i] : ( ~ $i(v0) | ~ aReductOfIn0(v0, all_42_1, xR)) % 13.62/2.60 | % 13.62/2.60 | GROUND_INST: instantiating (mTCRTrans) with all_13_0, xR, all_16_0, all_42_1, % 13.62/2.60 | simplifying with (2), (3), (8), (9), (15), (16), (20), (22), % 13.62/2.60 | (23), (24) gives: % 13.62/2.60 | (26) sdtmndtasgtdt0(all_13_0, xR, all_42_1) % 13.62/2.60 | % 13.62/2.60 | GROUND_INST: instantiating (11) with all_42_1, simplifying with (22), (24), % 13.62/2.60 | (26) gives: % 13.62/2.60 | (27) ? [v0: $i] : ($i(v0) & aReductOfIn0(v0, all_42_1, xR)) % 13.62/2.60 | % 13.62/2.60 | DELTA: instantiating (27) with fresh symbol all_61_0 gives: % 13.62/2.60 | (28) $i(all_61_0) & aReductOfIn0(all_61_0, all_42_1, xR) % 13.62/2.60 | % 13.62/2.60 | ALPHA: (28) implies: % 13.62/2.60 | (29) aReductOfIn0(all_61_0, all_42_1, xR) % 13.62/2.60 | (30) $i(all_61_0) % 13.62/2.60 | % 13.62/2.60 | GROUND_INST: instantiating (25) with all_61_0, simplifying with (29), (30) % 13.62/2.60 | gives: % 13.62/2.60 | (31) $false % 13.62/2.60 | % 13.62/2.60 | CLOSE: (31) is inconsistent. % 13.62/2.60 | % 13.62/2.60 End of proof % 13.62/2.60 % SZS output end Proof for theBenchmark % 13.62/2.60 % 13.62/2.60 1994ms %------------------------------------------------------------------------------