%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG118+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 : n005.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 13:57:59 EDT 2023 % Result : Theorem 49.72s 7.34s % Output : Proof 51.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : RNG118+1 : TPTP v8.1.2. Released v4.0.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n005.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 : Sun Aug 27 02:33:08 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.10/1.17 Prover 4: Preprocessing ... % 3.10/1.17 Prover 1: Preprocessing ... % 3.63/1.21 Prover 3: Preprocessing ... % 3.63/1.21 Prover 5: Preprocessing ... % 3.63/1.21 Prover 2: Preprocessing ... % 3.63/1.21 Prover 0: Preprocessing ... % 3.63/1.21 Prover 6: Preprocessing ... % 8.42/1.98 Prover 1: Constructing countermodel ... % 8.42/1.98 Prover 3: Constructing countermodel ... % 9.20/2.03 Prover 5: Proving ... % 9.76/2.06 Prover 6: Proving ... % 10.19/2.16 Prover 2: Proving ... % 11.15/2.25 Prover 4: Constructing countermodel ... % 11.46/2.28 Prover 0: Proving ... % 49.72/7.33 Prover 1: Found proof (size 203) % 49.72/7.33 Prover 1: proved (6679ms) % 49.72/7.34 Prover 3: stopped % 49.72/7.34 Prover 5: stopped % 49.72/7.34 Prover 2: stopped % 49.72/7.34 Prover 6: stopped % 49.72/7.34 Prover 0: stopped % 49.72/7.34 Prover 4: stopped % 49.72/7.34 % 49.72/7.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 49.72/7.34 % 49.72/7.36 % SZS output start Proof for theBenchmark % 49.72/7.37 Assumptions after simplification: % 49.72/7.37 --------------------------------- % 49.72/7.37 % 49.72/7.37 (mAddComm) % 50.58/7.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 50.58/7.39 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 50.58/7.39 (sdtpldt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) & % 50.58/7.39 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 50.58/7.39 % 50.58/7.40 (mDefDvs) % 50.58/7.40 ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: % 50.58/7.40 any] : ( ~ (doDivides0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? % 50.58/7.40 [v4: any] : (aDivisorOf0(v1, v0) = v3 & aElement0(v1) = v4 & ( ~ (v3 = % 50.58/7.40 0) | (v4 = 0 & v2 = 0)))) & ! [v1: $i] : ( ~ (doDivides0(v1, v0) % 50.58/7.40 = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v1, v0) % 50.58/7.40 = v3 & aElement0(v1) = v2 & ( ~ (v2 = 0) | v3 = 0))))) % 50.58/7.40 % 50.58/7.40 (mDivision) % 50.58/7.40 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 50.58/7.40 (sbrdtbr0(v1) = v2) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 50.58/7.40 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 50.58/7.40 (iLess0(v6, v2) = v7 & sbrdtbr0(v4) = v6 & sdtasdt0(v3, v1) = v5 & % 50.58/7.40 sdtpldt0(v5, v4) = v0 & aElement0(v4) = 0 & aElement0(v3) = 0 & $i(v6) & % 50.58/7.40 $i(v5) & $i(v4) & $i(v3) & (v7 = 0 | v4 = sz00)) | ? [v3: int] : ( ~ (v3 % 50.58/7.40 = 0) & aElement0(v1) = v3)) % 50.58/7.40 % 50.58/7.40 (mEucSort) % 50.58/7.40 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | % 50.58/7.40 ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 & % 50.58/7.40 aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 50.58/7.40 % 50.58/7.41 (mMulComm) % 50.58/7.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 50.58/7.41 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 50.58/7.41 (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) & % 50.58/7.41 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 50.58/7.41 % 50.58/7.41 (mSortsB) % 50.58/7.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 50.58/7.41 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 50.58/7.41 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0) % 50.58/7.41 | ~ (v3 = 0) | v5 = 0))) % 50.58/7.41 % 50.58/7.41 (mSortsB_02) % 50.58/7.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 50.58/7.41 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 50.58/7.41 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0) % 50.58/7.41 | ~ (v3 = 0) | v5 = 0))) % 50.58/7.41 % 50.58/7.41 (m__) % 50.58/7.41 $i(xu) & $i(xb) & $i(sz00) & ? [v0: $i] : (sbrdtbr0(xu) = v0 & $i(v0) & ! % 50.58/7.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v1, xu) = v3) | ~ % 50.58/7.41 (sdtpldt0(v3, v2) = xb) | ~ $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: % 50.58/7.41 any] : ? [v6: $i] : ? [v7: any] : (iLess0(v6, v0) = v7 & sbrdtbr0(v2) % 50.58/7.42 = v6 & aElement0(v2) = v5 & aElement0(v1) = v4 & $i(v6) & ( ~ (v5 = 0) | % 50.58/7.42 ~ (v4 = 0) | ( ~ (v7 = 0) & ~ (v2 = sz00)))))) % 50.58/7.42 % 50.58/7.42 (m__2091) % 50.58/7.42 aElement0(xb) = 0 & aElement0(xa) = 0 & $i(xb) & $i(xa) % 50.58/7.42 % 50.58/7.42 (m__2174) % 50.58/7.42 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 50.58/7.42 slsdtgt0(xa) = v0 & aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & $i(v1) & % 50.58/7.42 $i(v0)) % 50.58/7.42 % 50.58/7.42 (m__2228) % 50.58/7.42 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 50.58/7.42 (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) & % 50.58/7.42 $i(v1) & $i(v0) & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 & % 50.58/7.42 $i(v3))) % 50.58/7.42 % 50.58/7.42 (m__2273) % 50.58/7.42 $i(xu) & $i(xI) & $i(sz00) & ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 % 50.58/7.42 & aElementOf0(xu, xI) = 0 & $i(v0) & ! [v1: $i] : (v1 = sz00 | ~ % 50.58/7.42 (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~ % 50.58/7.42 (v3 = 0) & iLess0(v2, v0) = v3 & sbrdtbr0(v1) = v2 & $i(v2)))) % 50.58/7.42 % 50.58/7.42 (m__2416) % 50.58/7.42 $i(xu) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 50.58/7.42 $i] : (sdtasdt0(xb, v1) = v3 & sdtasdt0(xa, v0) = v2 & sdtpldt0(v2, v3) = xu % 50.58/7.42 & aElement0(v1) = 0 & aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 50.58/7.42 % 50.58/7.42 (m__2479) % 50.58/7.42 doDivides0(xu, xa) = 0 & $i(xu) & $i(xa) % 50.58/7.42 % 50.58/7.42 (m__2612) % 50.58/7.42 $i(xu) & $i(xb) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xu, xb) = v0) % 50.58/7.42 % 50.58/7.42 (function-axioms) % 50.58/7.43 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 50.58/7.43 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~ % 50.58/7.43 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.58/7.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 50.58/7.43 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, % 50.58/7.43 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 50.58/7.43 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) | % 50.58/7.43 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.58/7.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.58/7.43 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: % 50.58/7.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 50.58/7.43 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 50.58/7.43 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 50.58/7.43 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 50.58/7.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.58/7.43 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 50.58/7.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 50.58/7.43 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.58/7.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.58/7.43 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 50.58/7.43 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 50.58/7.43 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 50.58/7.43 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 50.58/7.43 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) % 50.58/7.43 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 50.58/7.43 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: % 50.58/7.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 50.58/7.43 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0: % 50.58/7.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 50.58/7.43 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] : % 50.58/7.43 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 50.58/7.43 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 50.58/7.43 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 50.58/7.43 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 50.58/7.43 ~ (aElement0(v2) = v0)) % 50.58/7.43 % 50.58/7.43 Further assumptions not needed in the proof: % 50.58/7.43 -------------------------------------------- % 50.58/7.43 mAMDistr, mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv, % 50.58/7.43 mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, mDefSSum, mEOfElem, % 50.58/7.43 mElmSort, mIdeInt, mIdeSum, mMulAsso, mMulMnOne, mMulUnit, mMulZero, mNatLess, % 50.58/7.43 mNatSort, mPrIdeal, mSetEq, mSetSort, mSortsC, mSortsC_01, mSortsU, mUnNeZr, % 50.58/7.43 m__2110, m__2129, m__2203, m__2383 % 50.58/7.43 % 50.58/7.43 Those formulas are unsatisfiable: % 50.58/7.43 --------------------------------- % 50.58/7.43 % 50.58/7.43 Begin of proof % 50.58/7.43 | % 50.58/7.43 | ALPHA: (mEucSort) implies: % 50.58/7.44 | (1) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ % 50.58/7.44 | $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 & % 50.58/7.44 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 50.58/7.44 | % 50.58/7.44 | ALPHA: (mDivision) implies: % 50.58/7.44 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (sbrdtbr0(v1) % 50.58/7.44 | = v2) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 50.58/7.44 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 50.58/7.44 | (iLess0(v6, v2) = v7 & sbrdtbr0(v4) = v6 & sdtasdt0(v3, v1) = v5 & % 50.58/7.44 | sdtpldt0(v5, v4) = v0 & aElement0(v4) = 0 & aElement0(v3) = 0 & % 50.58/7.44 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & (v7 = 0 | v4 = sz00)) | ? [v3: % 50.58/7.44 | int] : ( ~ (v3 = 0) & aElement0(v1) = v3)) % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__2091) implies: % 50.58/7.44 | (3) aElement0(xa) = 0 % 50.58/7.44 | (4) aElement0(xb) = 0 % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__2174) implies: % 50.58/7.44 | (5) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 50.58/7.44 | aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0)) % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__2228) implies: % 50.58/7.44 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slsdtgt0(xb) = v1 & % 50.58/7.44 | slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) % 50.58/7.44 | & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 & $i(v3))) % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__2273) implies: % 50.58/7.44 | (7) ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 & aElementOf0(xu, xI) % 50.58/7.44 | = 0 & $i(v0) & ! [v1: $i] : (v1 = sz00 | ~ (aElementOf0(v1, xI) = % 50.58/7.44 | 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 50.58/7.44 | iLess0(v2, v0) = v3 & sbrdtbr0(v1) = v2 & $i(v2)))) % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__2416) implies: % 50.58/7.44 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(xb, % 50.58/7.44 | v1) = v3 & sdtasdt0(xa, v0) = v2 & sdtpldt0(v2, v3) = xu & % 50.58/7.44 | aElement0(v1) = 0 & aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) & % 50.58/7.44 | $i(v0)) % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__2479) implies: % 50.58/7.44 | (9) $i(xa) % 50.58/7.44 | (10) doDivides0(xu, xa) = 0 % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__2612) implies: % 50.58/7.44 | (11) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xu, xb) = v0) % 50.58/7.44 | % 50.58/7.44 | ALPHA: (m__) implies: % 50.58/7.44 | (12) $i(xb) % 50.58/7.44 | (13) $i(xu) % 50.58/7.45 | (14) ? [v0: $i] : (sbrdtbr0(xu) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] % 50.58/7.45 | : ! [v3: $i] : ( ~ (sdtasdt0(v1, xu) = v3) | ~ (sdtpldt0(v3, v2) = % 50.58/7.45 | xb) | ~ $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: any] : ? % 50.58/7.45 | [v6: $i] : ? [v7: any] : (iLess0(v6, v0) = v7 & sbrdtbr0(v2) = v6 % 50.58/7.45 | & aElement0(v2) = v5 & aElement0(v1) = v4 & $i(v6) & ( ~ (v5 = % 50.58/7.45 | 0) | ~ (v4 = 0) | ( ~ (v7 = 0) & ~ (v2 = sz00)))))) % 50.58/7.45 | % 50.58/7.45 | ALPHA: (function-axioms) implies: % 50.58/7.45 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 50.58/7.45 | : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 50.58/7.45 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) % 50.58/7.45 | = v1) | ~ (sbrdtbr0(v2) = v0)) % 50.58/7.45 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) % 50.58/7.45 | = v1) | ~ (slsdtgt0(v2) = v0)) % 50.58/7.45 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.58/7.45 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) % 50.58/7.45 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 50.58/7.45 | : ! [v3: $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, % 50.58/7.45 | v2) = v0)) % 50.58/7.45 | % 50.58/7.45 | DELTA: instantiating (11) with fresh symbol all_34_0 gives: % 50.58/7.45 | (20) ~ (all_34_0 = 0) & doDivides0(xu, xb) = all_34_0 % 50.58/7.45 | % 50.58/7.45 | ALPHA: (20) implies: % 50.58/7.45 | (21) doDivides0(xu, xb) = all_34_0 % 50.58/7.45 | % 50.58/7.45 | DELTA: instantiating (5) with fresh symbols all_38_0, all_38_1 gives: % 50.58/7.45 | (22) slsdtgt0(xb) = all_38_0 & slsdtgt0(xa) = all_38_1 & aIdeal0(xI) = 0 & % 50.58/7.45 | sdtpldt1(all_38_1, all_38_0) = xI & $i(all_38_0) & $i(all_38_1) % 50.58/7.45 | % 50.58/7.45 | ALPHA: (22) implies: % 51.02/7.45 | (23) sdtpldt1(all_38_1, all_38_0) = xI % 51.02/7.45 | (24) slsdtgt0(xa) = all_38_1 % 51.02/7.45 | (25) slsdtgt0(xb) = all_38_0 % 51.02/7.45 | % 51.02/7.45 | DELTA: instantiating (6) with fresh symbols all_42_0, all_42_1, all_42_2 % 51.02/7.45 | gives: % 51.02/7.45 | (26) slsdtgt0(xb) = all_42_1 & slsdtgt0(xa) = all_42_2 & sdtpldt1(all_42_2, % 51.02/7.45 | all_42_1) = all_42_0 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & % 51.02/7.45 | ? [v0: $i] : ( ~ (v0 = sz00) & aElementOf0(v0, all_42_0) = 0 & $i(v0)) % 51.02/7.45 | % 51.02/7.45 | ALPHA: (26) implies: % 51.02/7.45 | (27) sdtpldt1(all_42_2, all_42_1) = all_42_0 % 51.02/7.45 | (28) slsdtgt0(xa) = all_42_2 % 51.02/7.45 | (29) slsdtgt0(xb) = all_42_1 % 51.02/7.45 | (30) ? [v0: $i] : ( ~ (v0 = sz00) & aElementOf0(v0, all_42_0) = 0 & % 51.02/7.45 | $i(v0)) % 51.02/7.45 | % 51.02/7.45 | DELTA: instantiating (8) with fresh symbols all_44_0, all_44_1, all_44_2, % 51.02/7.45 | all_44_3 gives: % 51.02/7.45 | (31) sdtasdt0(xb, all_44_2) = all_44_0 & sdtasdt0(xa, all_44_3) = all_44_1 % 51.02/7.45 | & sdtpldt0(all_44_1, all_44_0) = xu & aElement0(all_44_2) = 0 & % 51.02/7.45 | aElement0(all_44_3) = 0 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & % 51.02/7.45 | $i(all_44_3) % 51.02/7.45 | % 51.02/7.45 | ALPHA: (31) implies: % 51.02/7.45 | (32) $i(all_44_3) % 51.02/7.45 | (33) $i(all_44_2) % 51.02/7.45 | (34) $i(all_44_1) % 51.02/7.45 | (35) $i(all_44_0) % 51.02/7.45 | (36) aElement0(all_44_3) = 0 % 51.02/7.45 | (37) aElement0(all_44_2) = 0 % 51.02/7.45 | (38) sdtpldt0(all_44_1, all_44_0) = xu % 51.02/7.46 | (39) sdtasdt0(xa, all_44_3) = all_44_1 % 51.02/7.46 | (40) sdtasdt0(xb, all_44_2) = all_44_0 % 51.02/7.46 | % 51.02/7.46 | DELTA: instantiating (7) with fresh symbol all_46_0 gives: % 51.02/7.46 | (41) ~ (xu = sz00) & sbrdtbr0(xu) = all_46_0 & aElementOf0(xu, xI) = 0 & % 51.02/7.46 | $i(all_46_0) & ! [v0: $i] : (v0 = sz00 | ~ (aElementOf0(v0, xI) = 0) % 51.02/7.46 | | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & iLess0(v1, % 51.02/7.46 | all_46_0) = v2 & sbrdtbr0(v0) = v1 & $i(v1))) % 51.02/7.46 | % 51.02/7.46 | ALPHA: (41) implies: % 51.02/7.46 | (42) ~ (xu = sz00) % 51.02/7.46 | (43) sbrdtbr0(xu) = all_46_0 % 51.02/7.46 | (44) ! [v0: $i] : (v0 = sz00 | ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | % 51.02/7.46 | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & iLess0(v1, all_46_0) = v2 % 51.02/7.46 | & sbrdtbr0(v0) = v1 & $i(v1))) % 51.02/7.46 | % 51.02/7.46 | DELTA: instantiating (14) with fresh symbol all_52_0 gives: % 51.02/7.46 | (45) sbrdtbr0(xu) = all_52_0 & $i(all_52_0) & ! [v0: $i] : ! [v1: $i] : % 51.02/7.46 | ! [v2: $i] : ( ~ (sdtasdt0(v0, xu) = v2) | ~ (sdtpldt0(v2, v1) = xb) % 51.02/7.46 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] % 51.02/7.46 | : ? [v6: any] : (iLess0(v5, all_52_0) = v6 & sbrdtbr0(v1) = v5 & % 51.02/7.46 | aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | % 51.02/7.46 | ~ (v3 = 0) | ( ~ (v6 = 0) & ~ (v1 = sz00))))) % 51.02/7.46 | % 51.02/7.46 | ALPHA: (45) implies: % 51.02/7.46 | (46) sbrdtbr0(xu) = all_52_0 % 51.02/7.46 | (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, xu) = v2) % 51.02/7.46 | | ~ (sdtpldt0(v2, v1) = xb) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] % 51.02/7.46 | : ? [v4: any] : ? [v5: $i] : ? [v6: any] : (iLess0(v5, all_52_0) % 51.02/7.46 | = v6 & sbrdtbr0(v1) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 % 51.02/7.46 | & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | ( ~ (v6 = 0) & ~ (v1 = % 51.02/7.46 | sz00))))) % 51.02/7.46 | % 51.02/7.46 | DELTA: instantiating (30) with fresh symbol all_55_0 gives: % 51.02/7.46 | (48) ~ (all_55_0 = sz00) & aElementOf0(all_55_0, all_42_0) = 0 & % 51.02/7.46 | $i(all_55_0) % 51.02/7.46 | % 51.02/7.46 | ALPHA: (48) implies: % 51.02/7.46 | (49) ~ (all_55_0 = sz00) % 51.02/7.46 | (50) $i(all_55_0) % 51.02/7.46 | (51) aElementOf0(all_55_0, all_42_0) = 0 % 51.02/7.46 | % 51.02/7.46 | GROUND_INST: instantiating (16) with all_46_0, all_52_0, xu, simplifying with % 51.02/7.46 | (43), (46) gives: % 51.02/7.46 | (52) all_52_0 = all_46_0 % 51.02/7.46 | % 51.02/7.46 | GROUND_INST: instantiating (17) with all_38_1, all_42_2, xa, simplifying with % 51.02/7.46 | (24), (28) gives: % 51.02/7.46 | (53) all_42_2 = all_38_1 % 51.02/7.46 | % 51.02/7.46 | GROUND_INST: instantiating (17) with all_38_0, all_42_1, xb, simplifying with % 51.02/7.46 | (25), (29) gives: % 51.02/7.46 | (54) all_42_1 = all_38_0 % 51.02/7.46 | % 51.02/7.46 | REDUCE: (27), (53), (54) imply: % 51.02/7.46 | (55) sdtpldt1(all_38_1, all_38_0) = all_42_0 % 51.02/7.46 | % 51.02/7.46 | GROUND_INST: instantiating (18) with xI, all_42_0, all_38_0, all_38_1, % 51.02/7.46 | simplifying with (23), (55) gives: % 51.02/7.46 | (56) all_42_0 = xI % 51.02/7.47 | % 51.02/7.47 | REDUCE: (51), (56) imply: % 51.02/7.47 | (57) aElementOf0(all_55_0, xI) = 0 % 51.02/7.47 | % 51.02/7.47 | GROUND_INST: instantiating (mDefDvs) with xa, simplifying with (3), (9) gives: % 51.02/7.47 | (58) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xa) = v1) | ~ $i(v0) % 51.02/7.47 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xa) = v2 & % 51.02/7.47 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 51.02/7.47 | $i] : ( ~ (doDivides0(v0, xa) = 0) | ~ $i(v0) | ? [v1: any] : ? % 51.02/7.47 | [v2: any] : (aDivisorOf0(v0, xa) = v2 & aElement0(v0) = v1 & ( ~ (v1 % 51.02/7.47 | = 0) | v2 = 0))) % 51.02/7.47 | % 51.02/7.47 | ALPHA: (58) implies: % 51.02/7.47 | (59) ! [v0: $i] : ( ~ (doDivides0(v0, xa) = 0) | ~ $i(v0) | ? [v1: any] % 51.02/7.47 | : ? [v2: any] : (aDivisorOf0(v0, xa) = v2 & aElement0(v0) = v1 & ( % 51.02/7.47 | ~ (v1 = 0) | v2 = 0))) % 51.02/7.47 | (60) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xa) = v1) | ~ $i(v0) % 51.02/7.47 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xa) = v2 & % 51.02/7.47 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 51.02/7.47 | % 51.02/7.47 | GROUND_INST: instantiating (mDefDvs) with xb, simplifying with (4), (12) % 51.02/7.47 | gives: % 51.02/7.47 | (61) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xb) = v1) | ~ $i(v0) % 51.02/7.47 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xb) = v2 & % 51.02/7.47 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 51.02/7.47 | $i] : ( ~ (doDivides0(v0, xb) = 0) | ~ $i(v0) | ? [v1: any] : ? % 51.02/7.47 | [v2: any] : (aDivisorOf0(v0, xb) = v2 & aElement0(v0) = v1 & ( ~ (v1 % 51.02/7.47 | = 0) | v2 = 0))) % 51.02/7.47 | % 51.02/7.47 | ALPHA: (61) implies: % 51.02/7.47 | (62) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xb) = v1) | ~ $i(v0) % 51.02/7.47 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xb) = v2 & % 51.02/7.47 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 51.02/7.47 | % 51.02/7.47 | GROUND_INST: instantiating (mAddComm) with all_44_1, all_44_0, xu, simplifying % 51.02/7.47 | with (34), (35), (38) gives: % 51.02/7.47 | (63) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_44_0, % 51.02/7.47 | all_44_1) = v2 & aElement0(all_44_0) = v1 & aElement0(all_44_1) = % 51.02/7.47 | v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xu)) % 51.02/7.47 | % 51.02/7.47 | GROUND_INST: instantiating (mSortsB) with all_44_1, all_44_0, xu, simplifying % 51.02/7.47 | with (34), (35), (38) gives: % 51.02/7.47 | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_44_0) = v1 % 51.02/7.47 | & aElement0(all_44_1) = v0 & aElement0(xu) = v2 & ( ~ (v1 = 0) | ~ % 51.02/7.47 | (v0 = 0) | v2 = 0)) % 51.02/7.47 | % 51.02/7.47 | GROUND_INST: instantiating (mMulComm) with xa, all_44_3, all_44_1, simplifying % 51.02/7.47 | with (9), (32), (39) gives: % 51.02/7.47 | (65) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_44_3, xa) = % 51.02/7.47 | v2 & aElement0(all_44_3) = v1 & aElement0(xa) = v0 & $i(v2) & ( ~ % 51.02/7.48 | (v1 = 0) | ~ (v0 = 0) | v2 = all_44_1)) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (mSortsB_02) with xa, all_44_3, all_44_1, % 51.02/7.48 | simplifying with (9), (32), (39) gives: % 51.02/7.48 | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_44_1) = v2 % 51.02/7.48 | & aElement0(all_44_3) = v1 & aElement0(xa) = v0 & ( ~ (v1 = 0) | ~ % 51.02/7.48 | (v0 = 0) | v2 = 0)) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (mMulComm) with xb, all_44_2, all_44_0, simplifying % 51.02/7.48 | with (12), (33), (40) gives: % 51.02/7.48 | (67) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_44_2, xb) = % 51.02/7.48 | v2 & aElement0(all_44_2) = v1 & aElement0(xb) = v0 & $i(v2) & ( ~ % 51.02/7.48 | (v1 = 0) | ~ (v0 = 0) | v2 = all_44_0)) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (mSortsB_02) with xb, all_44_2, all_44_0, % 51.02/7.48 | simplifying with (12), (33), (40) gives: % 51.02/7.48 | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_44_0) = v2 % 51.02/7.48 | & aElement0(all_44_2) = v1 & aElement0(xb) = v0 & ( ~ (v1 = 0) | ~ % 51.02/7.48 | (v0 = 0) | v2 = 0)) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (44) with all_55_0, simplifying with (50), (57) % 51.02/7.48 | gives: % 51.02/7.48 | (69) all_55_0 = sz00 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 51.02/7.48 | iLess0(v0, all_46_0) = v1 & sbrdtbr0(all_55_0) = v0 & $i(v0)) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (2) with xb, xu, all_46_0, simplifying with (4), % 51.02/7.48 | (12), (13), (43) gives: % 51.02/7.48 | (70) xu = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 51.02/7.48 | [v4: any] : (iLess0(v3, all_46_0) = v4 & sbrdtbr0(v1) = v3 & % 51.02/7.48 | sdtasdt0(v0, xu) = v2 & sdtpldt0(v2, v1) = xb & aElement0(v1) = 0 & % 51.02/7.48 | aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v4 = 0 | v1 % 51.02/7.48 | = sz00)) | ? [v0: int] : ( ~ (v0 = 0) & aElement0(xu) = v0) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (1) with xu, all_46_0, simplifying with (13), (43) % 51.02/7.48 | gives: % 51.02/7.48 | (71) xu = sz00 | ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_46_0) = % 51.02/7.48 | v1 & aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (62) with xu, all_34_0, simplifying with (13), (21) % 51.02/7.48 | gives: % 51.02/7.48 | (72) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xb) = v0 & % 51.02/7.48 | aElement0(xu) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_34_0 = 0))) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (59) with xu, simplifying with (10), (13) gives: % 51.02/7.48 | (73) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xa) = v1 & % 51.02/7.48 | aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 51.02/7.48 | % 51.02/7.48 | GROUND_INST: instantiating (60) with xu, 0, simplifying with (10), (13) gives: % 51.02/7.48 | (74) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xa) = v0 & % 51.02/7.48 | aElement0(xu) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 51.02/7.48 | % 51.02/7.48 | DELTA: instantiating (68) with fresh symbols all_126_0, all_126_1, all_126_2 % 51.02/7.48 | gives: % 51.02/7.48 | (75) aElement0(all_44_0) = all_126_0 & aElement0(all_44_2) = all_126_1 & % 51.02/7.48 | aElement0(xb) = all_126_2 & ( ~ (all_126_1 = 0) | ~ (all_126_2 = 0) | % 51.02/7.48 | all_126_0 = 0) % 51.02/7.48 | % 51.02/7.48 | ALPHA: (75) implies: % 51.02/7.48 | (76) aElement0(xb) = all_126_2 % 51.02/7.48 | (77) aElement0(all_44_2) = all_126_1 % 51.02/7.48 | (78) aElement0(all_44_0) = all_126_0 % 51.02/7.48 | (79) ~ (all_126_1 = 0) | ~ (all_126_2 = 0) | all_126_0 = 0 % 51.02/7.48 | % 51.02/7.48 | DELTA: instantiating (66) with fresh symbols all_128_0, all_128_1, all_128_2 % 51.02/7.48 | gives: % 51.02/7.49 | (80) aElement0(all_44_1) = all_128_0 & aElement0(all_44_3) = all_128_1 & % 51.02/7.49 | aElement0(xa) = all_128_2 & ( ~ (all_128_1 = 0) | ~ (all_128_2 = 0) | % 51.02/7.49 | all_128_0 = 0) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (80) implies: % 51.02/7.49 | (81) aElement0(xa) = all_128_2 % 51.02/7.49 | (82) aElement0(all_44_3) = all_128_1 % 51.02/7.49 | (83) aElement0(all_44_1) = all_128_0 % 51.02/7.49 | (84) ~ (all_128_1 = 0) | ~ (all_128_2 = 0) | all_128_0 = 0 % 51.02/7.49 | % 51.02/7.49 | DELTA: instantiating (64) with fresh symbols all_130_0, all_130_1, all_130_2 % 51.02/7.49 | gives: % 51.02/7.49 | (85) aElement0(all_44_0) = all_130_1 & aElement0(all_44_1) = all_130_2 & % 51.02/7.49 | aElement0(xu) = all_130_0 & ( ~ (all_130_1 = 0) | ~ (all_130_2 = 0) | % 51.02/7.49 | all_130_0 = 0) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (85) implies: % 51.02/7.49 | (86) aElement0(xu) = all_130_0 % 51.02/7.49 | (87) aElement0(all_44_1) = all_130_2 % 51.02/7.49 | (88) aElement0(all_44_0) = all_130_1 % 51.02/7.49 | (89) ~ (all_130_1 = 0) | ~ (all_130_2 = 0) | all_130_0 = 0 % 51.02/7.49 | % 51.02/7.49 | DELTA: instantiating (67) with fresh symbols all_132_0, all_132_1, all_132_2 % 51.02/7.49 | gives: % 51.02/7.49 | (90) sdtasdt0(all_44_2, xb) = all_132_0 & aElement0(all_44_2) = all_132_1 & % 51.02/7.49 | aElement0(xb) = all_132_2 & $i(all_132_0) & ( ~ (all_132_1 = 0) | ~ % 51.02/7.49 | (all_132_2 = 0) | all_132_0 = all_44_0) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (90) implies: % 51.02/7.49 | (91) aElement0(xb) = all_132_2 % 51.02/7.49 | (92) aElement0(all_44_2) = all_132_1 % 51.02/7.49 | % 51.02/7.49 | DELTA: instantiating (63) with fresh symbols all_134_0, all_134_1, all_134_2 % 51.02/7.49 | gives: % 51.02/7.49 | (93) sdtpldt0(all_44_0, all_44_1) = all_134_0 & aElement0(all_44_0) = % 51.02/7.49 | all_134_1 & aElement0(all_44_1) = all_134_2 & $i(all_134_0) & ( ~ % 51.02/7.49 | (all_134_1 = 0) | ~ (all_134_2 = 0) | all_134_0 = xu) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (93) implies: % 51.02/7.49 | (94) aElement0(all_44_1) = all_134_2 % 51.02/7.49 | (95) aElement0(all_44_0) = all_134_1 % 51.02/7.49 | % 51.02/7.49 | DELTA: instantiating (65) with fresh symbols all_136_0, all_136_1, all_136_2 % 51.02/7.49 | gives: % 51.02/7.49 | (96) sdtasdt0(all_44_3, xa) = all_136_0 & aElement0(all_44_3) = all_136_1 & % 51.02/7.49 | aElement0(xa) = all_136_2 & $i(all_136_0) & ( ~ (all_136_1 = 0) | ~ % 51.02/7.49 | (all_136_2 = 0) | all_136_0 = all_44_1) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (96) implies: % 51.02/7.49 | (97) aElement0(xa) = all_136_2 % 51.02/7.49 | (98) aElement0(all_44_3) = all_136_1 % 51.02/7.49 | % 51.02/7.49 | DELTA: instantiating (72) with fresh symbols all_138_0, all_138_1 gives: % 51.02/7.49 | (99) aDivisorOf0(xu, xb) = all_138_1 & aElement0(xu) = all_138_0 & ( ~ % 51.02/7.49 | (all_138_1 = 0) | (all_138_0 = 0 & all_34_0 = 0)) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (99) implies: % 51.02/7.49 | (100) aElement0(xu) = all_138_0 % 51.02/7.49 | % 51.02/7.49 | DELTA: instantiating (74) with fresh symbols all_140_0, all_140_1 gives: % 51.02/7.49 | (101) aDivisorOf0(xu, xa) = all_140_1 & aElement0(xu) = all_140_0 & ( ~ % 51.02/7.49 | (all_140_1 = 0) | all_140_0 = 0) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (101) implies: % 51.02/7.49 | (102) aElement0(xu) = all_140_0 % 51.02/7.49 | % 51.02/7.49 | DELTA: instantiating (73) with fresh symbols all_142_0, all_142_1 gives: % 51.02/7.49 | (103) aDivisorOf0(xu, xa) = all_142_0 & aElement0(xu) = all_142_1 & ( ~ % 51.02/7.49 | (all_142_1 = 0) | all_142_0 = 0) % 51.02/7.49 | % 51.02/7.49 | ALPHA: (103) implies: % 51.02/7.49 | (104) aElement0(xu) = all_142_1 % 51.02/7.49 | % 51.02/7.49 | BETA: splitting (71) gives: % 51.02/7.49 | % 51.02/7.49 | Case 1: % 51.02/7.49 | | % 51.02/7.49 | | (105) xu = sz00 % 51.02/7.49 | | % 51.02/7.49 | | REDUCE: (42), (105) imply: % 51.02/7.49 | | (106) $false % 51.02/7.49 | | % 51.02/7.49 | | CLOSE: (106) is inconsistent. % 51.02/7.49 | | % 51.02/7.49 | Case 2: % 51.02/7.49 | | % 51.02/7.49 | | (107) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_46_0) = v1 & % 51.02/7.49 | | aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 51.02/7.49 | | % 51.02/7.49 | | DELTA: instantiating (107) with fresh symbols all_156_0, all_156_1 gives: % 51.02/7.49 | | (108) aNaturalNumber0(all_46_0) = all_156_0 & aElement0(xu) = all_156_1 & % 51.02/7.49 | | ( ~ (all_156_1 = 0) | all_156_0 = 0) % 51.02/7.49 | | % 51.02/7.49 | | ALPHA: (108) implies: % 51.02/7.49 | | (109) aElement0(xu) = all_156_1 % 51.02/7.49 | | % 51.02/7.49 | | BETA: splitting (69) gives: % 51.02/7.49 | | % 51.02/7.49 | | Case 1: % 51.02/7.49 | | | % 51.02/7.49 | | | (110) all_55_0 = sz00 % 51.02/7.49 | | | % 51.02/7.49 | | | REDUCE: (49), (110) imply: % 51.02/7.49 | | | (111) $false % 51.02/7.49 | | | % 51.02/7.49 | | | CLOSE: (111) is inconsistent. % 51.02/7.49 | | | % 51.02/7.49 | | Case 2: % 51.02/7.49 | | | % 51.02/7.50 | | | (112) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & iLess0(v0, all_46_0) % 51.02/7.50 | | | = v1 & sbrdtbr0(all_55_0) = v0 & $i(v0)) % 51.02/7.50 | | | % 51.02/7.50 | | | DELTA: instantiating (112) with fresh symbols all_161_0, all_161_1 gives: % 51.02/7.50 | | | (113) ~ (all_161_0 = 0) & iLess0(all_161_1, all_46_0) = all_161_0 & % 51.02/7.50 | | | sbrdtbr0(all_55_0) = all_161_1 & $i(all_161_1) % 51.02/7.50 | | | % 51.02/7.50 | | | ALPHA: (113) implies: % 51.02/7.50 | | | (114) sbrdtbr0(all_55_0) = all_161_1 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with 0, all_136_2, xa, simplifying with % 51.02/7.50 | | | (3), (97) gives: % 51.02/7.50 | | | (115) all_136_2 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_128_2, all_136_2, xa, simplifying % 51.02/7.50 | | | with (81), (97) gives: % 51.02/7.50 | | | (116) all_136_2 = all_128_2 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with 0, all_132_2, xb, simplifying with % 51.02/7.50 | | | (4), (91) gives: % 51.02/7.50 | | | (117) all_132_2 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_126_2, all_132_2, xb, simplifying % 51.02/7.50 | | | with (76), (91) gives: % 51.02/7.50 | | | (118) all_132_2 = all_126_2 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_140_0, all_142_1, xu, simplifying % 51.02/7.50 | | | with (102), (104) gives: % 51.02/7.50 | | | (119) all_142_1 = all_140_0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_138_0, all_142_1, xu, simplifying % 51.02/7.50 | | | with (100), (104) gives: % 51.02/7.50 | | | (120) all_142_1 = all_138_0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_140_0, all_156_1, xu, simplifying % 51.02/7.50 | | | with (102), (109) gives: % 51.02/7.50 | | | (121) all_156_1 = all_140_0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_130_0, all_156_1, xu, simplifying % 51.02/7.50 | | | with (86), (109) gives: % 51.02/7.50 | | | (122) all_156_1 = all_130_0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with 0, all_136_1, all_44_3, simplifying % 51.02/7.50 | | | with (36), (98) gives: % 51.02/7.50 | | | (123) all_136_1 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_128_1, all_136_1, all_44_3, % 51.02/7.50 | | | simplifying with (82), (98) gives: % 51.02/7.50 | | | (124) all_136_1 = all_128_1 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with 0, all_132_1, all_44_2, simplifying % 51.02/7.50 | | | with (37), (92) gives: % 51.02/7.50 | | | (125) all_132_1 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_126_1, all_132_1, all_44_2, % 51.02/7.50 | | | simplifying with (77), (92) gives: % 51.02/7.50 | | | (126) all_132_1 = all_126_1 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_130_2, all_134_2, all_44_1, % 51.02/7.50 | | | simplifying with (87), (94) gives: % 51.02/7.50 | | | (127) all_134_2 = all_130_2 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_128_0, all_134_2, all_44_1, % 51.02/7.50 | | | simplifying with (83), (94) gives: % 51.02/7.50 | | | (128) all_134_2 = all_128_0 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_130_1, all_134_1, all_44_0, % 51.02/7.50 | | | simplifying with (88), (95) gives: % 51.02/7.50 | | | (129) all_134_1 = all_130_1 % 51.02/7.50 | | | % 51.02/7.50 | | | GROUND_INST: instantiating (15) with all_126_0, all_134_1, all_44_0, % 51.02/7.50 | | | simplifying with (78), (95) gives: % 51.02/7.50 | | | (130) all_134_1 = all_126_0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (121), (122) imply: % 51.02/7.50 | | | (131) all_140_0 = all_130_0 % 51.02/7.50 | | | % 51.02/7.50 | | | SIMP: (131) implies: % 51.02/7.50 | | | (132) all_140_0 = all_130_0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (119), (120) imply: % 51.02/7.50 | | | (133) all_140_0 = all_138_0 % 51.02/7.50 | | | % 51.02/7.50 | | | SIMP: (133) implies: % 51.02/7.50 | | | (134) all_140_0 = all_138_0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (132), (134) imply: % 51.02/7.50 | | | (135) all_138_0 = all_130_0 % 51.02/7.50 | | | % 51.02/7.50 | | | SIMP: (135) implies: % 51.02/7.50 | | | (136) all_138_0 = all_130_0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (123), (124) imply: % 51.02/7.50 | | | (137) all_128_1 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | SIMP: (137) implies: % 51.02/7.50 | | | (138) all_128_1 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (115), (116) imply: % 51.02/7.50 | | | (139) all_128_2 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (129), (130) imply: % 51.02/7.50 | | | (140) all_130_1 = all_126_0 % 51.02/7.50 | | | % 51.02/7.50 | | | SIMP: (140) implies: % 51.02/7.50 | | | (141) all_130_1 = all_126_0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (127), (128) imply: % 51.02/7.50 | | | (142) all_130_2 = all_128_0 % 51.02/7.50 | | | % 51.02/7.50 | | | SIMP: (142) implies: % 51.02/7.50 | | | (143) all_130_2 = all_128_0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (125), (126) imply: % 51.02/7.50 | | | (144) all_126_1 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | SIMP: (144) implies: % 51.02/7.50 | | | (145) all_126_1 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | COMBINE_EQS: (117), (118) imply: % 51.02/7.50 | | | (146) all_126_2 = 0 % 51.02/7.50 | | | % 51.02/7.50 | | | BETA: splitting (84) gives: % 51.02/7.50 | | | % 51.02/7.50 | | | Case 1: % 51.02/7.50 | | | | % 51.02/7.50 | | | | (147) ~ (all_128_1 = 0) % 51.02/7.50 | | | | % 51.02/7.50 | | | | REDUCE: (138), (147) imply: % 51.02/7.50 | | | | (148) $false % 51.02/7.50 | | | | % 51.02/7.50 | | | | CLOSE: (148) is inconsistent. % 51.02/7.50 | | | | % 51.02/7.50 | | | Case 2: % 51.02/7.50 | | | | % 51.02/7.50 | | | | (149) ~ (all_128_2 = 0) | all_128_0 = 0 % 51.02/7.50 | | | | % 51.02/7.50 | | | | BETA: splitting (79) gives: % 51.02/7.50 | | | | % 51.02/7.50 | | | | Case 1: % 51.02/7.50 | | | | | % 51.02/7.50 | | | | | (150) ~ (all_126_1 = 0) % 51.02/7.50 | | | | | % 51.02/7.50 | | | | | REDUCE: (145), (150) imply: % 51.02/7.50 | | | | | (151) $false % 51.02/7.50 | | | | | % 51.02/7.50 | | | | | CLOSE: (151) is inconsistent. % 51.02/7.50 | | | | | % 51.02/7.50 | | | | Case 2: % 51.02/7.50 | | | | | % 51.02/7.50 | | | | | (152) ~ (all_126_2 = 0) | all_126_0 = 0 % 51.02/7.50 | | | | | % 51.02/7.50 | | | | | BETA: splitting (152) gives: % 51.02/7.50 | | | | | % 51.02/7.50 | | | | | Case 1: % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | | (153) ~ (all_126_2 = 0) % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | | REDUCE: (146), (153) imply: % 51.02/7.50 | | | | | | (154) $false % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | | CLOSE: (154) is inconsistent. % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | Case 2: % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | | (155) all_126_0 = 0 % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | | COMBINE_EQS: (141), (155) imply: % 51.02/7.50 | | | | | | (156) all_130_1 = 0 % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | | BETA: splitting (149) gives: % 51.02/7.50 | | | | | | % 51.02/7.50 | | | | | | Case 1: % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | | (157) ~ (all_128_2 = 0) % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | | REDUCE: (139), (157) imply: % 51.02/7.50 | | | | | | | (158) $false % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | | CLOSE: (158) is inconsistent. % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | Case 2: % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | | (159) all_128_0 = 0 % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | | COMBINE_EQS: (143), (159) imply: % 51.02/7.50 | | | | | | | (160) all_130_2 = 0 % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | | BETA: splitting (89) gives: % 51.02/7.50 | | | | | | | % 51.02/7.50 | | | | | | | Case 1: % 51.02/7.50 | | | | | | | | % 51.02/7.50 | | | | | | | | (161) ~ (all_130_1 = 0) % 51.02/7.50 | | | | | | | | % 51.02/7.50 | | | | | | | | REDUCE: (156), (161) imply: % 51.02/7.51 | | | | | | | | (162) $false % 51.02/7.51 | | | | | | | | % 51.02/7.51 | | | | | | | | CLOSE: (162) is inconsistent. % 51.02/7.51 | | | | | | | | % 51.02/7.51 | | | | | | | Case 2: % 51.02/7.51 | | | | | | | | % 51.02/7.51 | | | | | | | | (163) ~ (all_130_2 = 0) | all_130_0 = 0 % 51.02/7.51 | | | | | | | | % 51.02/7.51 | | | | | | | | BETA: splitting (163) gives: % 51.02/7.51 | | | | | | | | % 51.02/7.51 | | | | | | | | Case 1: % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | | (164) ~ (all_130_2 = 0) % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | | REDUCE: (160), (164) imply: % 51.02/7.51 | | | | | | | | | (165) $false % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | | CLOSE: (165) is inconsistent. % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | Case 2: % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | | (166) all_130_0 = 0 % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | | REDUCE: (86), (166) imply: % 51.02/7.51 | | | | | | | | | (167) aElement0(xu) = 0 % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | | BETA: splitting (70) gives: % 51.02/7.51 | | | | | | | | | % 51.02/7.51 | | | | | | | | | Case 1: % 51.02/7.51 | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | (168) xu = sz00 % 51.02/7.51 | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | REDUCE: (42), (168) imply: % 51.02/7.51 | | | | | | | | | | (169) $false % 51.02/7.51 | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | CLOSE: (169) is inconsistent. % 51.02/7.51 | | | | | | | | | | % 51.02/7.51 | | | | | | | | | Case 2: % 51.02/7.51 | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | (170) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 51.02/7.51 | | | | | | | | | | $i] : ? [v4: any] : (iLess0(v3, all_46_0) = v4 & % 51.02/7.51 | | | | | | | | | | sbrdtbr0(v1) = v3 & sdtasdt0(v0, xu) = v2 & % 51.02/7.51 | | | | | | | | | | sdtpldt0(v2, v1) = xb & aElement0(v1) = 0 & % 51.02/7.51 | | | | | | | | | | aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) & % 51.02/7.51 | | | | | | | | | | $i(v0) & (v4 = 0 | v1 = sz00)) | ? [v0: int] : ( % 51.02/7.51 | | | | | | | | | | ~ (v0 = 0) & aElement0(xu) = v0) % 51.02/7.51 | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | BETA: splitting (170) gives: % 51.02/7.51 | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | Case 1: % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | (171) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 51.02/7.51 | | | | | | | | | | | $i] : ? [v4: any] : (iLess0(v3, all_46_0) = v4 % 51.02/7.51 | | | | | | | | | | | & sbrdtbr0(v1) = v3 & sdtasdt0(v0, xu) = v2 & % 51.02/7.51 | | | | | | | | | | | sdtpldt0(v2, v1) = xb & aElement0(v1) = 0 & % 51.02/7.51 | | | | | | | | | | | aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) & % 51.02/7.51 | | | | | | | | | | | $i(v0) & (v4 = 0 | v1 = sz00)) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | DELTA: instantiating (171) with fresh symbols all_281_0, % 51.02/7.51 | | | | | | | | | | | all_281_1, all_281_2, all_281_3, all_281_4 gives: % 51.02/7.51 | | | | | | | | | | | (172) iLess0(all_281_1, all_46_0) = all_281_0 & % 51.02/7.51 | | | | | | | | | | | sbrdtbr0(all_281_3) = all_281_1 & % 51.02/7.51 | | | | | | | | | | | sdtasdt0(all_281_4, xu) = all_281_2 & % 51.02/7.51 | | | | | | | | | | | sdtpldt0(all_281_2, all_281_3) = xb & % 51.02/7.51 | | | | | | | | | | | aElement0(all_281_3) = 0 & aElement0(all_281_4) = % 51.02/7.51 | | | | | | | | | | | 0 & $i(all_281_1) & $i(all_281_2) & $i(all_281_3) % 51.02/7.51 | | | | | | | | | | | & $i(all_281_4) & (all_281_0 = 0 | all_281_3 = % 51.02/7.51 | | | | | | | | | | | sz00) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | ALPHA: (172) implies: % 51.02/7.51 | | | | | | | | | | | (173) $i(all_281_4) % 51.02/7.51 | | | | | | | | | | | (174) $i(all_281_3) % 51.02/7.51 | | | | | | | | | | | (175) $i(all_281_2) % 51.02/7.51 | | | | | | | | | | | (176) aElement0(all_281_4) = 0 % 51.02/7.51 | | | | | | | | | | | (177) aElement0(all_281_3) = 0 % 51.02/7.51 | | | | | | | | | | | (178) sdtpldt0(all_281_2, all_281_3) = xb % 51.02/7.51 | | | | | | | | | | | (179) sdtasdt0(all_281_4, xu) = all_281_2 % 51.02/7.51 | | | | | | | | | | | (180) sbrdtbr0(all_281_3) = all_281_1 % 51.02/7.51 | | | | | | | | | | | (181) iLess0(all_281_1, all_46_0) = all_281_0 % 51.02/7.51 | | | | | | | | | | | (182) all_281_0 = 0 | all_281_3 = sz00 % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with all_281_2, % 51.02/7.51 | | | | | | | | | | | all_281_3, xb, simplifying with (174), (175), % 51.02/7.51 | | | | | | | | | | | (178) gives: % 51.02/7.51 | | | | | | | | | | | (183) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 51.02/7.51 | | | | | | | | | | | (sdtpldt0(all_281_3, all_281_2) = v2 & % 51.02/7.51 | | | | | | | | | | | aElement0(all_281_2) = v0 & aElement0(all_281_3) % 51.02/7.51 | | | | | | | | | | | = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 51.02/7.51 | | | | | | | | | | | = xb)) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with all_281_2, all_281_3, % 51.02/7.51 | | | | | | | | | | | xb, simplifying with (174), (175), (178) gives: % 51.02/7.51 | | | | | | | | | | | (184) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 51.02/7.51 | | | | | | | | | | | (aElement0(all_281_2) = v0 & aElement0(all_281_3) % 51.02/7.51 | | | | | | | | | | | = v1 & aElement0(xb) = v2 & ( ~ (v1 = 0) | ~ % 51.02/7.51 | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | GROUND_INST: instantiating (47) with all_281_4, all_281_3, % 51.02/7.51 | | | | | | | | | | | all_281_2, simplifying with (173), (174), (178), % 51.02/7.51 | | | | | | | | | | | (179) gives: % 51.02/7.51 | | | | | | | | | | | (185) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 51.02/7.51 | | | | | | | | | | | [v3: any] : (iLess0(v2, all_52_0) = v3 & % 51.02/7.51 | | | | | | | | | | | sbrdtbr0(all_281_3) = v2 & aElement0(all_281_3) % 51.02/7.51 | | | | | | | | | | | = v1 & aElement0(all_281_4) = v0 & $i(v2) & ( ~ % 51.02/7.51 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = 0) & ~ % 51.02/7.51 | | | | | | | | | | | (all_281_3 = sz00)))) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_281_4, xu, % 51.02/7.51 | | | | | | | | | | | all_281_2, simplifying with (13), (173), (179) % 51.02/7.51 | | | | | | | | | | | gives: % 51.02/7.51 | | | | | | | | | | | (186) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 51.02/7.51 | | | | | | | | | | | (sdtasdt0(xu, all_281_4) = v2 & % 51.02/7.51 | | | | | | | | | | | aElement0(all_281_4) = v0 & aElement0(xu) = v1 & % 51.02/7.51 | | | | | | | | | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 51.02/7.51 | | | | | | | | | | | all_281_2)) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_281_4, xu, % 51.02/7.51 | | | | | | | | | | | all_281_2, simplifying with (13), (173), (179) % 51.02/7.51 | | | | | | | | | | | gives: % 51.02/7.51 | | | | | | | | | | | (187) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 51.02/7.51 | | | | | | | | | | | (aElement0(all_281_2) = v2 & aElement0(all_281_4) % 51.02/7.51 | | | | | | | | | | | = v0 & aElement0(xu) = v1 & ( ~ (v1 = 0) | ~ % 51.02/7.51 | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_55_0, all_161_1, % 51.02/7.51 | | | | | | | | | | | simplifying with (50), (114) gives: % 51.02/7.51 | | | | | | | | | | | (188) all_55_0 = sz00 | ? [v0: any] : ? [v1: any] : % 51.02/7.51 | | | | | | | | | | | (aNaturalNumber0(all_161_1) = v1 & % 51.02/7.51 | | | | | | | | | | | aElement0(all_55_0) = v0 & ( ~ (v0 = 0) | v1 = % 51.02/7.51 | | | | | | | | | | | 0)) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | DELTA: instantiating (187) with fresh symbols all_819_0, % 51.02/7.51 | | | | | | | | | | | all_819_1, all_819_2 gives: % 51.02/7.51 | | | | | | | | | | | (189) aElement0(all_281_2) = all_819_0 & % 51.02/7.51 | | | | | | | | | | | aElement0(all_281_4) = all_819_2 & aElement0(xu) = % 51.02/7.51 | | | | | | | | | | | all_819_1 & ( ~ (all_819_1 = 0) | ~ (all_819_2 = % 51.02/7.51 | | | | | | | | | | | 0) | all_819_0 = 0) % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | ALPHA: (189) implies: % 51.02/7.51 | | | | | | | | | | | (190) aElement0(all_281_4) = all_819_2 % 51.02/7.51 | | | | | | | | | | | % 51.02/7.51 | | | | | | | | | | | DELTA: instantiating (184) with fresh symbols all_827_0, % 51.02/7.51 | | | | | | | | | | | all_827_1, all_827_2 gives: % 51.02/7.52 | | | | | | | | | | | (191) aElement0(all_281_2) = all_827_2 & % 51.02/7.52 | | | | | | | | | | | aElement0(all_281_3) = all_827_1 & aElement0(xb) = % 51.02/7.52 | | | | | | | | | | | all_827_0 & ( ~ (all_827_1 = 0) | ~ (all_827_2 = % 51.02/7.52 | | | | | | | | | | | 0) | all_827_0 = 0) % 51.02/7.52 | | | | | | | | | | | % 51.02/7.52 | | | | | | | | | | | ALPHA: (191) implies: % 51.02/7.52 | | | | | | | | | | | (192) aElement0(all_281_3) = all_827_1 % 51.02/7.52 | | | | | | | | | | | % 51.02/7.52 | | | | | | | | | | | DELTA: instantiating (186) with fresh symbols all_841_0, % 51.02/7.52 | | | | | | | | | | | all_841_1, all_841_2 gives: % 51.02/7.52 | | | | | | | | | | | (193) sdtasdt0(xu, all_281_4) = all_841_0 & % 51.02/7.52 | | | | | | | | | | | aElement0(all_281_4) = all_841_2 & aElement0(xu) = % 51.02/7.52 | | | | | | | | | | | all_841_1 & $i(all_841_0) & ( ~ (all_841_1 = 0) | % 51.02/7.52 | | | | | | | | | | | ~ (all_841_2 = 0) | all_841_0 = all_281_2) % 51.02/7.52 | | | | | | | | | | | % 51.02/7.52 | | | | | | | | | | | ALPHA: (193) implies: % 51.02/7.52 | | | | | | | | | | | (194) aElement0(all_281_4) = all_841_2 % 51.02/7.52 | | | | | | | | | | | % 51.02/7.52 | | | | | | | | | | | DELTA: instantiating (183) with fresh symbols all_845_0, % 51.02/7.52 | | | | | | | | | | | all_845_1, all_845_2 gives: % 51.02/7.52 | | | | | | | | | | | (195) sdtpldt0(all_281_3, all_281_2) = all_845_0 & % 51.02/7.52 | | | | | | | | | | | aElement0(all_281_2) = all_845_2 & % 51.02/7.52 | | | | | | | | | | | aElement0(all_281_3) = all_845_1 & $i(all_845_0) & % 51.02/7.52 | | | | | | | | | | | ( ~ (all_845_1 = 0) | ~ (all_845_2 = 0) | % 51.02/7.52 | | | | | | | | | | | all_845_0 = xb) % 51.02/7.52 | | | | | | | | | | | % 51.02/7.52 | | | | | | | | | | | ALPHA: (195) implies: % 51.02/7.52 | | | | | | | | | | | (196) aElement0(all_281_3) = all_845_1 % 51.02/7.52 | | | | | | | | | | | % 51.02/7.52 | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_865_0, % 51.02/7.52 | | | | | | | | | | | all_865_1, all_865_2, all_865_3 gives: % 51.02/7.52 | | | | | | | | | | | (197) iLess0(all_865_1, all_52_0) = all_865_0 & % 51.02/7.52 | | | | | | | | | | | sbrdtbr0(all_281_3) = all_865_1 & % 51.02/7.52 | | | | | | | | | | | aElement0(all_281_3) = all_865_2 & % 51.02/7.52 | | | | | | | | | | | aElement0(all_281_4) = all_865_3 & $i(all_865_1) & % 51.02/7.52 | | | | | | | | | | | ( ~ (all_865_2 = 0) | ~ (all_865_3 = 0) | ( ~ % 51.02/7.52 | | | | | | | | | | | (all_865_0 = 0) & ~ (all_281_3 = sz00))) % 51.02/7.52 | | | | | | | | | | | % 51.02/7.52 | | | | | | | | | | | ALPHA: (197) implies: % 51.02/7.52 | | | | | | | | | | | (198) aElement0(all_281_4) = all_865_3 % 51.35/7.52 | | | | | | | | | | | (199) aElement0(all_281_3) = all_865_2 % 51.35/7.52 | | | | | | | | | | | (200) sbrdtbr0(all_281_3) = all_865_1 % 51.35/7.52 | | | | | | | | | | | (201) iLess0(all_865_1, all_52_0) = all_865_0 % 51.35/7.52 | | | | | | | | | | | (202) ~ (all_865_2 = 0) | ~ (all_865_3 = 0) | ( ~ % 51.35/7.52 | | | | | | | | | | | (all_865_0 = 0) & ~ (all_281_3 = sz00)) % 51.35/7.52 | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | REDUCE: (52), (201) imply: % 51.35/7.52 | | | | | | | | | | | (203) iLess0(all_865_1, all_46_0) = all_865_0 % 51.35/7.52 | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | BETA: splitting (188) gives: % 51.35/7.52 | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | Case 1: % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | (204) all_55_0 = sz00 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | REDUCE: (49), (204) imply: % 51.35/7.52 | | | | | | | | | | | | (205) $false % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | Case 2: % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_841_2, all_281_4, % 51.35/7.52 | | | | | | | | | | | | simplifying with (176), (194) gives: % 51.35/7.52 | | | | | | | | | | | | (206) all_841_2 = 0 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_841_2, all_865_3, % 51.35/7.52 | | | | | | | | | | | | all_281_4, simplifying with (194), (198) gives: % 51.35/7.52 | | | | | | | | | | | | (207) all_865_3 = all_841_2 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_819_2, all_865_3, % 51.35/7.52 | | | | | | | | | | | | all_281_4, simplifying with (190), (198) gives: % 51.35/7.52 | | | | | | | | | | | | (208) all_865_3 = all_819_2 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_845_1, all_281_3, % 51.35/7.52 | | | | | | | | | | | | simplifying with (177), (196) gives: % 51.35/7.52 | | | | | | | | | | | | (209) all_845_1 = 0 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_845_1, all_865_2, % 51.35/7.52 | | | | | | | | | | | | all_281_3, simplifying with (196), (199) gives: % 51.35/7.52 | | | | | | | | | | | | (210) all_865_2 = all_845_1 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_827_1, all_865_2, % 51.35/7.52 | | | | | | | | | | | | all_281_3, simplifying with (192), (199) gives: % 51.35/7.52 | | | | | | | | | | | | (211) all_865_2 = all_827_1 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_281_1, all_865_1, % 51.35/7.52 | | | | | | | | | | | | all_281_3, simplifying with (180), (200) gives: % 51.35/7.52 | | | | | | | | | | | | (212) all_865_1 = all_281_1 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | COMBINE_EQS: (210), (211) imply: % 51.35/7.52 | | | | | | | | | | | | (213) all_845_1 = all_827_1 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | SIMP: (213) implies: % 51.35/7.52 | | | | | | | | | | | | (214) all_845_1 = all_827_1 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | COMBINE_EQS: (207), (208) imply: % 51.35/7.52 | | | | | | | | | | | | (215) all_841_2 = all_819_2 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | SIMP: (215) implies: % 51.35/7.52 | | | | | | | | | | | | (216) all_841_2 = all_819_2 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | COMBINE_EQS: (209), (214) imply: % 51.35/7.52 | | | | | | | | | | | | (217) all_827_1 = 0 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | COMBINE_EQS: (206), (216) imply: % 51.35/7.52 | | | | | | | | | | | | (218) all_819_2 = 0 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | COMBINE_EQS: (208), (218) imply: % 51.35/7.52 | | | | | | | | | | | | (219) all_865_3 = 0 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | COMBINE_EQS: (211), (217) imply: % 51.35/7.52 | | | | | | | | | | | | (220) all_865_2 = 0 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | REDUCE: (203), (212) imply: % 51.35/7.52 | | | | | | | | | | | | (221) iLess0(all_281_1, all_46_0) = all_865_0 % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | BETA: splitting (202) gives: % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | Case 1: % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | (222) ~ (all_865_2 = 0) % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | REDUCE: (220), (222) imply: % 51.35/7.52 | | | | | | | | | | | | | (223) $false % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | Case 2: % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | (224) ~ (all_865_3 = 0) | ( ~ (all_865_0 = 0) & ~ % 51.35/7.52 | | | | | | | | | | | | | (all_281_3 = sz00)) % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | BETA: splitting (224) gives: % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | Case 1: % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | (225) ~ (all_865_3 = 0) % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | REDUCE: (219), (225) imply: % 51.35/7.52 | | | | | | | | | | | | | | (226) $false % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | Case 2: % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | (227) ~ (all_865_0 = 0) & ~ (all_281_3 = sz00) % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | ALPHA: (227) implies: % 51.35/7.52 | | | | | | | | | | | | | | (228) ~ (all_281_3 = sz00) % 51.35/7.52 | | | | | | | | | | | | | | (229) ~ (all_865_0 = 0) % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | BETA: splitting (182) gives: % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | Case 1: % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | (230) all_281_3 = sz00 % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | REDUCE: (228), (230) imply: % 51.35/7.52 | | | | | | | | | | | | | | | (231) $false % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent. % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | Case 2: % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | (232) all_281_0 = 0 % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | REDUCE: (181), (232) imply: % 51.35/7.52 | | | | | | | | | | | | | | | (233) iLess0(all_281_1, all_46_0) = 0 % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_865_0, all_46_0, % 51.35/7.52 | | | | | | | | | | | | | | | all_281_1, simplifying with (221), (233) gives: % 51.35/7.52 | | | | | | | | | | | | | | | (234) all_865_0 = 0 % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | REDUCE: (229), (234) imply: % 51.35/7.52 | | | | | | | | | | | | | | | (235) $false % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent. % 51.35/7.52 | | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | | End of split % 51.35/7.52 | | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | | End of split % 51.35/7.52 | | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | | End of split % 51.35/7.52 | | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | End of split % 51.35/7.52 | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | Case 2: % 51.35/7.52 | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | (236) ? [v0: int] : ( ~ (v0 = 0) & aElement0(xu) = v0) % 51.35/7.52 | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | DELTA: instantiating (236) with fresh symbol all_281_0 % 51.35/7.52 | | | | | | | | | | | gives: % 51.35/7.52 | | | | | | | | | | | (237) ~ (all_281_0 = 0) & aElement0(xu) = all_281_0 % 51.35/7.52 | | | | | | | | | | | % 51.35/7.52 | | | | | | | | | | | ALPHA: (237) implies: % 51.35/7.53 | | | | | | | | | | | (238) ~ (all_281_0 = 0) % 51.35/7.53 | | | | | | | | | | | (239) aElement0(xu) = all_281_0 % 51.35/7.53 | | | | | | | | | | | % 51.35/7.53 | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_281_0, xu, % 51.35/7.53 | | | | | | | | | | | simplifying with (167), (239) gives: % 51.35/7.53 | | | | | | | | | | | (240) all_281_0 = 0 % 51.35/7.53 | | | | | | | | | | | % 51.35/7.53 | | | | | | | | | | | REDUCE: (238), (240) imply: % 51.35/7.53 | | | | | | | | | | | (241) $false % 51.35/7.53 | | | | | | | | | | | % 51.35/7.53 | | | | | | | | | | | CLOSE: (241) is inconsistent. % 51.35/7.53 | | | | | | | | | | | % 51.35/7.53 | | | | | | | | | | End of split % 51.35/7.53 | | | | | | | | | | % 51.35/7.53 | | | | | | | | | End of split % 51.35/7.53 | | | | | | | | | % 51.35/7.53 | | | | | | | | End of split % 51.35/7.53 | | | | | | | | % 51.35/7.53 | | | | | | | End of split % 51.35/7.53 | | | | | | | % 51.35/7.53 | | | | | | End of split % 51.35/7.53 | | | | | | % 51.35/7.53 | | | | | End of split % 51.35/7.53 | | | | | % 51.35/7.53 | | | | End of split % 51.35/7.53 | | | | % 51.35/7.53 | | | End of split % 51.35/7.53 | | | % 51.35/7.53 | | End of split % 51.35/7.53 | | % 51.35/7.53 | End of split % 51.35/7.53 | % 51.35/7.53 End of proof % 51.35/7.53 % SZS output end Proof for theBenchmark % 51.35/7.53 % 51.35/7.53 6893ms %------------------------------------------------------------------------------