%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM524+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 : n006.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 : Thu Aug 31 11:48:22 EDT 2023 % Result : Theorem 14.12s 2.62s % Output : Proof 28.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM524+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.35 % Computer : n006.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.36 % CPULimit : 300 % 0.17/0.36 % WCLimit : 300 % 0.17/0.36 % DateTime : Fri Aug 25 07:45:07 EDT 2023 % 0.17/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.32/1.19 Prover 4: Preprocessing ... % 3.32/1.19 Prover 1: Preprocessing ... % 3.70/1.23 Prover 5: Preprocessing ... % 3.70/1.23 Prover 3: Preprocessing ... % 3.70/1.23 Prover 0: Preprocessing ... % 3.70/1.23 Prover 6: Preprocessing ... % 3.70/1.23 Prover 2: Preprocessing ... % 8.96/1.98 Prover 1: Constructing countermodel ... % 8.96/2.00 Prover 3: Constructing countermodel ... % 8.96/2.06 Prover 6: Proving ... % 10.30/2.13 Prover 5: Constructing countermodel ... % 11.45/2.30 Prover 2: Proving ... % 11.99/2.39 Prover 0: Proving ... % 12.67/2.43 Prover 4: Constructing countermodel ... % 14.12/2.62 Prover 3: proved (1966ms) % 14.12/2.62 % 14.12/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.12/2.62 % 14.12/2.62 Prover 0: stopped % 14.12/2.63 Prover 2: stopped % 14.12/2.64 Prover 5: stopped % 14.12/2.64 Prover 6: stopped % 14.12/2.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.12/2.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.12/2.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.12/2.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.12/2.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.18/2.79 Prover 8: Preprocessing ... % 15.18/2.79 Prover 11: Preprocessing ... % 15.18/2.80 Prover 10: Preprocessing ... % 15.18/2.81 Prover 13: Preprocessing ... % 15.18/2.81 Prover 7: Preprocessing ... % 16.73/2.97 Prover 13: Constructing countermodel ... % 16.73/2.98 Prover 10: Constructing countermodel ... % 16.73/3.02 Prover 8: Warning: ignoring some quantifiers % 16.73/3.03 Prover 8: Constructing countermodel ... % 17.45/3.05 Prover 7: Constructing countermodel ... % 19.71/3.40 Prover 11: Constructing countermodel ... % 28.17/4.46 Prover 10: Found proof (size 93) % 28.17/4.46 Prover 10: proved (1808ms) % 28.17/4.46 Prover 11: stopped % 28.17/4.46 Prover 7: stopped % 28.17/4.46 Prover 13: stopped % 28.17/4.46 Prover 8: stopped % 28.17/4.46 Prover 1: stopped % 28.17/4.46 Prover 4: stopped % 28.17/4.46 % 28.17/4.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 28.17/4.46 % 28.17/4.48 % SZS output start Proof for theBenchmark % 28.17/4.48 Assumptions after simplification: % 28.17/4.48 --------------------------------- % 28.17/4.48 % 28.17/4.48 (mAddAsso) % 28.17/4.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 28.17/4.52 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 28.17/4.52 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 28.17/4.52 aNaturalNumber0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, % 28.17/4.52 v5) = v4 & $i(v5) & $i(v4))) % 28.17/4.52 % 28.17/4.52 (mAddComm) % 28.17/4.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 28.17/4.52 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 28.17/4.52 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 28.17/4.52 % 28.17/4.52 (mDefDiv) % 28.17/4.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 28.17/4.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 28.17/4.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0: % 28.17/4.53 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 28.17/4.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0, % 28.17/4.53 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 28.17/4.53 % 28.17/4.53 (mDefLE) % 28.17/4.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 28.61/4.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 28.61/4.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 28.61/4.53 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 28.61/4.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 28.61/4.53 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 28.61/4.53 % 28.61/4.53 (mDefQuot) % 28.61/4.54 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 28.61/4.54 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 28.61/4.54 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 28.61/4.54 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 28.61/4.54 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 28.61/4.54 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 28.61/4.54 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 28.61/4.54 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 28.61/4.54 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 28.61/4.54 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 28.61/4.54 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 28.61/4.54 % 28.61/4.54 (mDivLE) % 28.61/4.54 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 28.61/4.54 doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 28.61/4.54 sdtlseqdt0(v0, v1)) % 28.61/4.54 % 28.61/4.54 (mLETotal) % 28.61/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | % 28.61/4.54 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 28.61/4.54 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 28.61/4.54 % 28.61/4.54 (mMonMul2) % 28.61/4.54 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 28.61/4.54 (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | % 28.61/4.54 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) % 28.61/4.54 % 28.61/4.54 (mMulAsso) % 28.61/4.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 28.61/4.54 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 28.61/4.54 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 28.61/4.54 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 28.61/4.54 v5) = v4 & $i(v5) & $i(v4))) % 28.61/4.54 % 28.61/4.54 (mMulCanc) % 28.61/4.55 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 28.61/4.55 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = % 28.61/4.55 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 28.61/4.55 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( % 28.61/4.55 ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & $i(v6) & % 28.61/4.55 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = % 28.61/4.55 v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | % 28.61/4.55 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 28.61/4.55 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 28.61/4.55 % 28.61/4.55 (mMulComm) % 28.61/4.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 28.61/4.55 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 28.61/4.55 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 28.61/4.55 % 28.61/4.55 (mSortsB_02) % 28.61/4.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 28.61/4.55 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 28.61/4.55 aNaturalNumber0(v2)) % 28.61/4.55 % 28.61/4.55 (m__) % 28.61/4.55 $i(xq) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 28.61/4.55 v0) & sdtasdt0(xq, xq) = v1 & sdtasdt0(xp, v1) = v2 & sdtasdt0(xm, xm) = % 28.61/4.55 v0 & $i(v2) & $i(v1) & $i(v0)) % 28.61/4.55 % 28.61/4.55 (m__2987) % 28.61/4.55 ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & $i(xp) & $i(xm) & $i(xn) & % 28.61/4.55 $i(sz00) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) % 28.61/4.55 % 28.61/4.55 (m__3014) % 28.61/4.55 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 % 28.61/4.55 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 28.61/4.55 % 28.61/4.55 (m__3046) % 28.61/4.55 $i(xp) & $i(xn) & ? [v0: $i] : (sdtasdt0(xn, xn) = v0 & $i(v0) & % 28.61/4.55 doDivides0(xp, v0) & doDivides0(xp, xn)) % 28.61/4.55 % 28.61/4.55 (m__3059) % 28.61/4.56 sdtsldt0(xn, xp) = xq & $i(xq) & $i(xp) & $i(xn) % 28.61/4.56 % 28.61/4.56 (function-axioms) % 28.61/4.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/4.56 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 28.61/4.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 28.61/4.56 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 28.61/4.56 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 28.61/4.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/4.56 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 28.61/4.56 % 28.61/4.56 Further assumptions not needed in the proof: % 28.61/4.56 -------------------------------------------- % 28.61/4.56 mAMDistr, mAddCanc, mDefDiff, mDefPrime, mDivAsso, mDivMin, mDivSum, mDivTrans, % 28.61/4.56 mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETran, mMonAdd, mMonMul, mNatSort, % 28.61/4.56 mPDP, mPrimDiv, mSortsB, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, % 28.61/4.56 m_MulUnit, m_MulZero, m__2963, m__3025 % 28.61/4.56 % 28.61/4.56 Those formulas are unsatisfiable: % 28.61/4.56 --------------------------------- % 28.61/4.56 % 28.61/4.56 Begin of proof % 28.61/4.56 | % 28.61/4.56 | ALPHA: (mMulCanc) implies: % 28.61/4.56 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = % 28.61/4.56 | sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 28.61/4.56 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 28.61/4.56 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 28.61/4.56 | % 28.61/4.56 | ALPHA: (mDefLE) implies: % 28.61/4.56 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, % 28.61/4.56 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 28.61/4.56 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 28.61/4.56 | % 28.61/4.56 | ALPHA: (mLETotal) implies: % 28.61/4.57 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 28.61/4.57 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | % 28.61/4.57 | sdtlseqdt0(v0, v1)) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (mMonMul2) implies: % 28.61/4.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtasdt0(v1, % 28.61/4.57 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 28.61/4.57 | aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (mDefDiv) implies: % 28.61/4.57 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, % 28.61/4.57 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 28.61/4.57 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (mDefQuot) implies: % 28.61/4.57 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 28.61/4.57 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 28.61/4.57 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 28.61/4.57 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 28.61/4.57 | aNaturalNumber0(v0)) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (mDivLE) implies: % 28.61/4.57 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 28.61/4.57 | doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) % 28.61/4.57 | | sdtlseqdt0(v0, v1)) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (m__2987) implies: % 28.61/4.57 | (8) ~ (xn = sz00) % 28.61/4.57 | (9) ~ (xm = sz00) % 28.61/4.57 | (10) ~ (xp = sz00) % 28.61/4.57 | (11) aNaturalNumber0(xn) % 28.61/4.57 | (12) aNaturalNumber0(xm) % 28.61/4.57 | (13) aNaturalNumber0(xp) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (m__3014) implies: % 28.61/4.57 | (14) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) % 28.61/4.57 | = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (m__3046) implies: % 28.61/4.57 | (15) ? [v0: $i] : (sdtasdt0(xn, xn) = v0 & $i(v0) & doDivides0(xp, v0) & % 28.61/4.57 | doDivides0(xp, xn)) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (m__3059) implies: % 28.61/4.57 | (16) $i(xn) % 28.61/4.57 | (17) sdtsldt0(xn, xp) = xq % 28.61/4.57 | % 28.61/4.57 | ALPHA: (m__) implies: % 28.61/4.57 | (18) $i(xm) % 28.61/4.57 | (19) $i(xp) % 28.61/4.57 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & sdtasdt0(xq, % 28.61/4.57 | xq) = v1 & sdtasdt0(xp, v1) = v2 & sdtasdt0(xm, xm) = v0 & $i(v2) % 28.61/4.57 | & $i(v1) & $i(v0)) % 28.61/4.57 | % 28.61/4.57 | ALPHA: (function-axioms) implies: % 28.61/4.58 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/4.58 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 28.61/4.58 | % 28.61/4.58 | DELTA: instantiating (15) with fresh symbol all_40_0 gives: % 28.61/4.58 | (22) sdtasdt0(xn, xn) = all_40_0 & $i(all_40_0) & doDivides0(xp, all_40_0) % 28.61/4.58 | & doDivides0(xp, xn) % 28.61/4.58 | % 28.61/4.58 | ALPHA: (22) implies: % 28.61/4.58 | (23) doDivides0(xp, xn) % 28.61/4.58 | (24) sdtasdt0(xn, xn) = all_40_0 % 28.61/4.58 | % 28.61/4.58 | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1 gives: % 28.61/4.58 | (25) sdtasdt0(xp, all_42_1) = all_42_0 & sdtasdt0(xm, xm) = all_42_1 & % 28.61/4.58 | sdtasdt0(xn, xn) = all_42_0 & $i(all_42_0) & $i(all_42_1) % 28.61/4.58 | % 28.61/4.58 | ALPHA: (25) implies: % 28.61/4.58 | (26) sdtasdt0(xn, xn) = all_42_0 % 28.61/4.58 | (27) sdtasdt0(xm, xm) = all_42_1 % 28.61/4.58 | (28) sdtasdt0(xp, all_42_1) = all_42_0 % 28.61/4.58 | % 28.61/4.58 | DELTA: instantiating (20) with fresh symbols all_44_0, all_44_1, all_44_2 % 28.61/4.58 | gives: % 28.61/4.58 | (29) ~ (all_44_0 = all_44_2) & sdtasdt0(xq, xq) = all_44_1 & sdtasdt0(xp, % 28.61/4.58 | all_44_1) = all_44_0 & sdtasdt0(xm, xm) = all_44_2 & $i(all_44_0) & % 28.61/4.58 | $i(all_44_1) & $i(all_44_2) % 28.61/4.58 | % 28.61/4.58 | ALPHA: (29) implies: % 28.61/4.58 | (30) ~ (all_44_0 = all_44_2) % 28.61/4.58 | (31) $i(all_44_2) % 28.61/4.58 | (32) sdtasdt0(xm, xm) = all_44_2 % 28.61/4.58 | (33) sdtasdt0(xp, all_44_1) = all_44_0 % 28.61/4.58 | (34) sdtasdt0(xq, xq) = all_44_1 % 28.61/4.58 | % 28.61/4.58 | GROUND_INST: instantiating (21) with all_40_0, all_42_0, xn, xn, simplifying % 28.61/4.58 | with (24), (26) gives: % 28.61/4.58 | (35) all_42_0 = all_40_0 % 28.61/4.58 | % 28.61/4.58 | GROUND_INST: instantiating (21) with all_42_1, all_44_2, xm, xm, simplifying % 28.61/4.58 | with (27), (32) gives: % 28.61/4.58 | (36) all_44_2 = all_42_1 % 28.61/4.58 | % 28.61/4.58 | REDUCE: (30), (36) imply: % 28.61/4.58 | (37) ~ (all_44_0 = all_42_1) % 28.61/4.58 | % 28.61/4.58 | REDUCE: (28), (35) imply: % 28.61/4.58 | (38) sdtasdt0(xp, all_42_1) = all_40_0 % 28.61/4.58 | % 28.61/4.58 | REDUCE: (31), (36) imply: % 28.61/4.58 | (39) $i(all_42_1) % 28.61/4.58 | % 28.61/4.58 | GROUND_INST: instantiating (3) with xm, xm, simplifying with (12), (18) gives: % 28.61/4.58 | (40) sdtlseqdt0(xm, xm) % 28.61/4.58 | % 28.61/4.58 | GROUND_INST: instantiating (7) with xp, xn, simplifying with (11), (13), (16), % 28.61/4.58 | (19), (23) gives: % 28.61/4.58 | (41) xn = sz00 | sdtlseqdt0(xp, xn) % 28.61/4.58 | % 28.61/4.58 | GROUND_INST: instantiating (5) with xp, xn, simplifying with (11), (13), (16), % 28.61/4.58 | (19), (23) gives: % 28.61/4.58 | (42) ? [v0: $i] : (sdtasdt0(xp, v0) = xn & $i(v0) & aNaturalNumber0(v0)) % 28.61/4.58 | % 28.61/4.58 | GROUND_INST: instantiating (mSortsB_02) with xm, xm, all_42_1, simplifying % 28.61/4.58 | with (12), (18), (27) gives: % 28.61/4.58 | (43) aNaturalNumber0(all_42_1) % 28.61/4.58 | % 28.61/4.58 | GROUND_INST: instantiating (4) with xm, xm, all_42_1, simplifying with (12), % 28.61/4.58 | (18), (27) gives: % 28.61/4.58 | (44) xm = sz00 | sdtlseqdt0(xm, all_42_1) % 28.61/4.58 | % 28.61/4.58 | DELTA: instantiating (42) with fresh symbol all_64_0 gives: % 28.89/4.58 | (45) sdtasdt0(xp, all_64_0) = xn & $i(all_64_0) & aNaturalNumber0(all_64_0) % 28.89/4.58 | % 28.89/4.59 | ALPHA: (45) implies: % 28.89/4.59 | (46) aNaturalNumber0(all_64_0) % 28.89/4.59 | (47) $i(all_64_0) % 28.89/4.59 | (48) sdtasdt0(xp, all_64_0) = xn % 28.89/4.59 | % 28.89/4.59 | BETA: splitting (41) gives: % 28.89/4.59 | % 28.89/4.59 | Case 1: % 28.89/4.59 | | % 28.89/4.59 | | (49) sdtlseqdt0(xp, xn) % 28.89/4.59 | | % 28.89/4.59 | | BETA: splitting (44) gives: % 28.89/4.59 | | % 28.89/4.59 | | Case 1: % 28.89/4.59 | | | % 28.89/4.59 | | | (50) sdtlseqdt0(xm, all_42_1) % 28.89/4.59 | | | % 28.89/4.59 | | | GROUND_INST: instantiating (mMulComm) with xp, all_42_1, all_40_0, % 28.89/4.59 | | | simplifying with (13), (19), (38), (39), (43) gives: % 28.89/4.59 | | | (51) sdtasdt0(all_42_1, xp) = all_40_0 & $i(all_40_0) % 28.89/4.59 | | | % 28.89/4.59 | | | ALPHA: (51) implies: % 28.89/4.59 | | | (52) sdtasdt0(all_42_1, xp) = all_40_0 % 28.89/4.59 | | | % 28.89/4.59 | | | GROUND_INST: instantiating (2) with xm, xm, simplifying with (12), (18), % 28.89/4.59 | | | (40) gives: % 28.89/4.59 | | | (53) ? [v0: $i] : (sdtpldt0(xm, v0) = xm & $i(v0) & % 28.89/4.59 | | | aNaturalNumber0(v0)) % 28.89/4.59 | | | % 28.89/4.59 | | | GROUND_INST: instantiating (2) with xm, all_42_1, simplifying with (12), % 28.89/4.59 | | | (18), (39), (43), (50) gives: % 28.89/4.59 | | | (54) ? [v0: $i] : (sdtpldt0(xm, v0) = all_42_1 & $i(v0) & % 28.89/4.59 | | | aNaturalNumber0(v0)) % 28.89/4.59 | | | % 28.89/4.59 | | | GROUND_INST: instantiating (2) with xp, xn, simplifying with (11), (13), % 28.89/4.59 | | | (16), (19), (49) gives: % 28.89/4.59 | | | (55) ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) & % 28.89/4.59 | | | aNaturalNumber0(v0)) % 28.89/4.59 | | | % 28.89/4.59 | | | GROUND_INST: instantiating (6) with xp, xn, xq, all_64_0, simplifying with % 28.89/4.59 | | | (11), (13), (16), (17), (19), (23), (46), (47), (48) gives: % 28.89/4.59 | | | (56) all_64_0 = xq | xp = sz00 % 28.89/4.59 | | | % 28.89/4.59 | | | GROUND_INST: instantiating (mMulAsso) with xp, all_64_0, xn, xn, all_40_0, % 28.89/4.59 | | | simplifying with (11), (13), (16), (19), (24), (46), (47), % 28.89/4.59 | | | (48) gives: % 28.89/4.59 | | | (57) ? [v0: $i] : (sdtasdt0(all_64_0, xn) = v0 & sdtasdt0(xp, v0) = % 28.89/4.59 | | | all_40_0 & $i(v0) & $i(all_40_0)) % 28.89/4.59 | | | % 28.89/4.59 | | | DELTA: instantiating (55) with fresh symbol all_88_0 gives: % 28.89/4.59 | | | (58) sdtpldt0(xp, all_88_0) = xn & $i(all_88_0) & % 28.89/4.59 | | | aNaturalNumber0(all_88_0) % 28.89/4.59 | | | % 28.89/4.59 | | | ALPHA: (58) implies: % 28.89/4.59 | | | (59) aNaturalNumber0(all_88_0) % 28.89/4.59 | | | (60) $i(all_88_0) % 28.89/4.59 | | | (61) sdtpldt0(xp, all_88_0) = xn % 28.89/4.59 | | | % 28.89/4.59 | | | DELTA: instantiating (54) with fresh symbol all_90_0 gives: % 28.89/4.59 | | | (62) sdtpldt0(xm, all_90_0) = all_42_1 & $i(all_90_0) & % 28.89/4.59 | | | aNaturalNumber0(all_90_0) % 28.89/4.59 | | | % 28.89/4.59 | | | ALPHA: (62) implies: % 28.89/4.59 | | | (63) aNaturalNumber0(all_90_0) % 28.89/4.59 | | | (64) $i(all_90_0) % 28.89/4.59 | | | (65) sdtpldt0(xm, all_90_0) = all_42_1 % 28.89/4.59 | | | % 28.89/4.59 | | | DELTA: instantiating (53) with fresh symbol all_92_0 gives: % 28.89/4.59 | | | (66) sdtpldt0(xm, all_92_0) = xm & $i(all_92_0) & % 28.89/4.59 | | | aNaturalNumber0(all_92_0) % 28.89/4.59 | | | % 28.89/4.59 | | | ALPHA: (66) implies: % 28.89/4.59 | | | (67) aNaturalNumber0(all_92_0) % 28.89/4.59 | | | (68) $i(all_92_0) % 28.89/4.59 | | | (69) sdtpldt0(xm, all_92_0) = xm % 28.89/4.59 | | | % 28.89/4.59 | | | DELTA: instantiating (57) with fresh symbol all_102_0 gives: % 28.89/4.59 | | | (70) sdtasdt0(all_64_0, xn) = all_102_0 & sdtasdt0(xp, all_102_0) = % 28.89/4.59 | | | all_40_0 & $i(all_102_0) & $i(all_40_0) % 28.89/4.59 | | | % 28.89/4.59 | | | ALPHA: (70) implies: % 28.89/4.59 | | | (71) sdtasdt0(xp, all_102_0) = all_40_0 % 28.89/4.59 | | | (72) sdtasdt0(all_64_0, xn) = all_102_0 % 28.89/4.59 | | | % 28.89/4.59 | | | BETA: splitting (56) gives: % 28.89/4.59 | | | % 28.89/4.59 | | | Case 1: % 28.89/4.59 | | | | % 28.89/4.59 | | | | (73) xp = sz00 % 28.89/4.59 | | | | % 28.89/4.59 | | | | REDUCE: (10), (73) imply: % 28.89/4.59 | | | | (74) $false % 28.89/4.60 | | | | % 28.89/4.60 | | | | CLOSE: (74) is inconsistent. % 28.89/4.60 | | | | % 28.89/4.60 | | | Case 2: % 28.89/4.60 | | | | % 28.89/4.60 | | | | (75) all_64_0 = xq % 28.89/4.60 | | | | % 28.89/4.60 | | | | REDUCE: (72), (75) imply: % 28.89/4.60 | | | | (76) sdtasdt0(xq, xn) = all_102_0 % 28.89/4.60 | | | | % 28.89/4.60 | | | | REDUCE: (48), (75) imply: % 28.89/4.60 | | | | (77) sdtasdt0(xp, xq) = xn % 28.89/4.60 | | | | % 28.89/4.60 | | | | REDUCE: (47), (75) imply: % 28.89/4.60 | | | | (78) $i(xq) % 28.89/4.60 | | | | % 28.89/4.60 | | | | REDUCE: (46), (75) imply: % 28.89/4.60 | | | | (79) aNaturalNumber0(xq) % 28.89/4.60 | | | | % 28.89/4.60 | | | | GROUND_INST: instantiating (mAddComm) with xm, all_90_0, all_42_1, % 28.89/4.60 | | | | simplifying with (12), (18), (63), (64), (65) gives: % 28.89/4.60 | | | | (80) sdtpldt0(all_90_0, xm) = all_42_1 & $i(all_42_1) % 28.89/4.60 | | | | % 28.89/4.60 | | | | GROUND_INST: instantiating (mAddAsso) with xm, all_92_0, all_90_0, xm, % 28.89/4.60 | | | | all_42_1, simplifying with (12), (18), (63), (64), (65), % 28.89/4.60 | | | | (67), (68), (69) gives: % 28.89/4.60 | | | | (81) ? [v0: $i] : (sdtpldt0(all_92_0, all_90_0) = v0 & sdtpldt0(xm, % 28.89/4.60 | | | | v0) = all_42_1 & $i(v0) & $i(all_42_1)) % 28.89/4.60 | | | | % 28.89/4.60 | | | | GROUND_INST: instantiating (mAddComm) with xp, all_88_0, xn, simplifying % 28.89/4.60 | | | | with (13), (19), (59), (60), (61) gives: % 28.89/4.60 | | | | (82) sdtpldt0(all_88_0, xp) = xn & $i(xn) % 28.89/4.60 | | | | % 28.89/4.60 | | | | GROUND_INST: instantiating (mSortsB_02) with xq, xn, all_102_0, % 28.89/4.60 | | | | simplifying with (11), (16), (76), (78), (79) gives: % 28.89/4.60 | | | | (83) aNaturalNumber0(all_102_0) % 28.89/4.60 | | | | % 28.89/4.60 | | | | GROUND_INST: instantiating (mMulComm) with xq, xn, all_102_0, % 28.89/4.60 | | | | simplifying with (11), (16), (76), (78), (79) gives: % 28.89/4.60 | | | | (84) sdtasdt0(xn, xq) = all_102_0 & $i(all_102_0) % 28.89/4.60 | | | | % 28.89/4.60 | | | | ALPHA: (84) implies: % 28.89/4.60 | | | | (85) $i(all_102_0) % 28.89/4.60 | | | | (86) sdtasdt0(xn, xq) = all_102_0 % 28.89/4.60 | | | | % 28.89/4.60 | | | | GROUND_INST: instantiating (4) with xp, all_42_1, all_40_0, simplifying % 28.89/4.60 | | | | with (13), (19), (39), (43), (52) gives: % 28.89/4.60 | | | | (87) xp = sz00 | sdtlseqdt0(all_42_1, all_40_0) % 28.89/4.60 | | | | % 28.89/4.60 | | | | DELTA: instantiating (81) with fresh symbol all_138_0 gives: % 28.89/4.60 | | | | (88) sdtpldt0(all_92_0, all_90_0) = all_138_0 & sdtpldt0(xm, % 28.89/4.60 | | | | all_138_0) = all_42_1 & $i(all_138_0) & $i(all_42_1) % 28.89/4.60 | | | | % 28.89/4.60 | | | | BETA: splitting (87) gives: % 28.89/4.60 | | | | % 28.89/4.60 | | | | Case 1: % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | GROUND_INST: instantiating (1) with xp, all_42_1, all_102_0, all_40_0, % 28.89/4.60 | | | | | simplifying with (13), (19), (38), (39), (43), (71), % 28.89/4.60 | | | | | (83), (85) gives: % 28.89/4.60 | | | | | (89) all_102_0 = all_42_1 | xp = sz00 % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | GROUND_INST: instantiating (mMulAsso) with xp, xq, xq, xn, all_102_0, % 28.89/4.60 | | | | | simplifying with (13), (19), (77), (78), (79), (86) % 28.89/4.60 | | | | | gives: % 28.89/4.60 | | | | | (90) ? [v0: $i] : (sdtasdt0(xq, xq) = v0 & sdtasdt0(xp, v0) = % 28.89/4.60 | | | | | all_102_0 & $i(v0) & $i(all_102_0)) % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | DELTA: instantiating (90) with fresh symbol all_230_0 gives: % 28.89/4.60 | | | | | (91) sdtasdt0(xq, xq) = all_230_0 & sdtasdt0(xp, all_230_0) = % 28.89/4.60 | | | | | all_102_0 & $i(all_230_0) & $i(all_102_0) % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | ALPHA: (91) implies: % 28.89/4.60 | | | | | (92) sdtasdt0(xp, all_230_0) = all_102_0 % 28.89/4.60 | | | | | (93) sdtasdt0(xq, xq) = all_230_0 % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | BETA: splitting (89) gives: % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | Case 1: % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | (94) xp = sz00 % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | REDUCE: (10), (94) imply: % 28.89/4.60 | | | | | | (95) $false % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | CLOSE: (95) is inconsistent. % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | Case 2: % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | (96) all_102_0 = all_42_1 % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | REDUCE: (92), (96) imply: % 28.89/4.60 | | | | | | (97) sdtasdt0(xp, all_230_0) = all_42_1 % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | GROUND_INST: instantiating (21) with all_44_1, all_230_0, xq, xq, % 28.89/4.60 | | | | | | simplifying with (34), (93) gives: % 28.89/4.60 | | | | | | (98) all_230_0 = all_44_1 % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | REDUCE: (97), (98) imply: % 28.89/4.60 | | | | | | (99) sdtasdt0(xp, all_44_1) = all_42_1 % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | GROUND_INST: instantiating (21) with all_44_0, all_42_1, all_44_1, % 28.89/4.60 | | | | | | xp, simplifying with (33), (99) gives: % 28.89/4.60 | | | | | | (100) all_44_0 = all_42_1 % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | REDUCE: (37), (100) imply: % 28.89/4.60 | | | | | | (101) $false % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | | CLOSE: (101) is inconsistent. % 28.89/4.60 | | | | | | % 28.89/4.60 | | | | | End of split % 28.89/4.60 | | | | | % 28.89/4.60 | | | | Case 2: % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | (102) xp = sz00 % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | REDUCE: (10), (102) imply: % 28.89/4.60 | | | | | (103) $false % 28.89/4.60 | | | | | % 28.89/4.60 | | | | | CLOSE: (103) is inconsistent. % 28.89/4.60 | | | | | % 28.89/4.60 | | | | End of split % 28.89/4.60 | | | | % 28.89/4.60 | | | End of split % 28.89/4.60 | | | % 28.89/4.60 | | Case 2: % 28.89/4.60 | | | % 28.89/4.60 | | | (104) xm = sz00 % 28.89/4.60 | | | % 28.89/4.60 | | | REDUCE: (9), (104) imply: % 28.89/4.60 | | | (105) $false % 28.89/4.61 | | | % 28.89/4.61 | | | CLOSE: (105) is inconsistent. % 28.89/4.61 | | | % 28.89/4.61 | | End of split % 28.89/4.61 | | % 28.89/4.61 | Case 2: % 28.89/4.61 | | % 28.89/4.61 | | (106) xn = sz00 % 28.89/4.61 | | % 28.89/4.61 | | REDUCE: (8), (106) imply: % 28.89/4.61 | | (107) $false % 28.89/4.61 | | % 28.89/4.61 | | CLOSE: (107) is inconsistent. % 28.89/4.61 | | % 28.89/4.61 | End of split % 28.89/4.61 | % 28.89/4.61 End of proof % 28.89/4.61 % SZS output end Proof for theBenchmark % 28.89/4.61 % 28.89/4.61 3976ms %------------------------------------------------------------------------------