%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM610+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 11:48:57 EDT 2023 % Result : Theorem 22.85s 3.75s % Output : Proof 44.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : NUM610+3 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n009.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 : Fri Aug 25 10:55:50 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.42/1.60 Prover 4: Preprocessing ... % 6.42/1.61 Prover 1: Preprocessing ... % 7.17/1.64 Prover 2: Preprocessing ... % 7.17/1.64 Prover 6: Preprocessing ... % 7.17/1.64 Prover 0: Preprocessing ... % 7.17/1.64 Prover 3: Preprocessing ... % 7.17/1.64 Prover 5: Preprocessing ... % 17.09/3.07 Prover 6: Proving ... % 18.14/3.13 Prover 1: Constructing countermodel ... % 18.14/3.14 Prover 3: Constructing countermodel ... % 20.32/3.36 Prover 5: Proving ... % 22.85/3.75 Prover 3: proved (3117ms) % 22.85/3.75 % 22.85/3.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.85/3.75 % 22.85/3.76 Prover 6: stopped % 22.85/3.76 Prover 5: stopped % 22.85/3.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.85/3.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.65/3.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 24.95/3.98 Prover 7: Preprocessing ... % 24.95/4.04 Prover 8: Preprocessing ... % 24.95/4.05 Prover 10: Preprocessing ... % 28.64/4.46 Prover 8: Warning: ignoring some quantifiers % 28.92/4.48 Prover 8: Constructing countermodel ... % 31.88/4.93 Prover 10: Constructing countermodel ... % 33.88/5.14 Prover 7: Constructing countermodel ... % 37.41/5.56 Prover 10: Found proof (size 16) % 37.41/5.56 Prover 10: proved (1760ms) % 37.41/5.56 Prover 7: stopped % 37.41/5.56 Prover 8: stopped % 37.41/5.56 Prover 1: stopped % 40.82/6.16 Prover 4: Constructing countermodel ... % 40.82/6.19 Prover 4: stopped % 42.95/6.50 Prover 2: Proving ... % 43.07/6.52 Prover 2: stopped % 44.09/6.78 Prover 0: Proving ... % 44.09/6.80 Prover 0: stopped % 44.09/6.81 % 44.09/6.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 44.09/6.81 % 44.09/6.81 % SZS output start Proof for theBenchmark % 44.09/6.82 Assumptions after simplification: % 44.09/6.82 --------------------------------- % 44.09/6.82 % 44.09/6.82 (mSubTrans) % 44.09/6.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 44.09/6.83 ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) % 44.09/6.83 | ~ aSet0(v0) | aSubsetOf0(v0, v2)) % 44.09/6.83 % 44.09/6.84 (m__) % 44.09/6.84 $i(xP) & $i(xO) & ? [v0: $i] : ($i(v0) & aElementOf0(v0, xP) & ~ % 44.09/6.84 aSubsetOf0(xP, xO) & ~ aElementOf0(v0, xO)) % 44.09/6.84 % 44.09/6.84 (m__4891) % 44.51/6.89 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 44.51/6.89 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 44.51/6.89 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 44.51/6.89 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 44.51/6.89 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 44.51/6.89 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 44.51/6.89 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 44.51/6.89 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 44.51/6.89 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 44.51/6.89 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 44.51/6.89 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 44.51/6.89 aElementOf0(v4, v1)))) % 44.51/6.89 % 44.51/6.89 (m__5078) % 44.51/6.89 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & % 44.51/6.89 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & % 44.51/6.89 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 44.51/6.89 aElementOf0(v1, xO))) % 44.51/6.89 % 44.51/6.89 (m__5164) % 44.62/6.90 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 44.62/6.90 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 44.62/6.90 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP)) % 44.62/6.90 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & % 44.62/6.90 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: % 44.62/6.90 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 44.62/6.90 % 44.62/6.90 (m__5195) % 44.62/6.90 $i(xP) & $i(xQ) & aSubsetOf0(xP, xQ) & ! [v0: $i] : ( ~ $i(v0) | ~ % 44.62/6.90 aElementOf0(v0, xP) | aElementOf0(v0, xQ)) % 44.62/6.90 % 44.62/6.90 Further assumptions not needed in the proof: % 44.62/6.90 -------------------------------------------- % 44.62/6.90 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 44.62/6.90 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 44.62/6.90 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 44.62/6.90 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 44.62/6.90 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 44.62/6.90 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 44.62/6.90 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 44.62/6.90 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 44.62/6.90 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSuccEquSucc, % 44.62/6.90 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, % 44.62/6.90 m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, % 44.62/6.90 m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, % 44.62/6.90 m__4908, m__4982, m__4998, m__5093, m__5106, m__5116, m__5147, m__5173, m__5182 % 44.62/6.90 % 44.62/6.90 Those formulas are unsatisfiable: % 44.62/6.90 --------------------------------- % 44.62/6.90 % 44.62/6.90 Begin of proof % 44.62/6.90 | % 44.62/6.90 | ALPHA: (m__4891) implies: % 44.62/6.91 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 44.62/6.91 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 44.62/6.91 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 44.62/6.91 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 44.62/6.91 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 44.62/6.92 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 44.62/6.92 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 44.62/6.92 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 44.62/6.92 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 44.62/6.92 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 44.62/6.92 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 44.62/6.92 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 44.62/6.92 | $i(v4) & aElementOf0(v4, v1)))) % 44.62/6.92 | % 44.62/6.92 | ALPHA: (m__5078) implies: % 44.62/6.92 | (2) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0) & % 44.62/6.92 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] : % 44.62/6.92 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO))) % 44.62/6.92 | % 44.62/6.92 | ALPHA: (m__5164) implies: % 44.75/6.92 | (3) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 44.75/6.92 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 44.75/6.92 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | % 44.75/6.92 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 44.75/6.92 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~ % 44.75/6.92 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : ( % 44.75/6.92 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 44.75/6.92 | % 44.75/6.92 | ALPHA: (m__5195) implies: % 44.75/6.92 | (4) aSubsetOf0(xP, xQ) % 44.75/6.92 | (5) $i(xQ) % 44.75/6.92 | % 44.75/6.92 | ALPHA: (m__) implies: % 44.75/6.93 | (6) $i(xO) % 44.75/6.93 | (7) $i(xP) % 44.75/6.93 | (8) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xP) & ~ aSubsetOf0(xP, xO) & % 44.75/6.93 | ~ aElementOf0(v0, xO)) % 44.75/6.93 | % 44.75/6.93 | DELTA: instantiating (8) with fresh symbol all_81_0 gives: % 44.75/6.93 | (9) $i(all_81_0) & aElementOf0(all_81_0, xP) & ~ aSubsetOf0(xP, xO) & ~ % 44.75/6.93 | aElementOf0(all_81_0, xO) % 44.75/6.93 | % 44.75/6.93 | ALPHA: (9) implies: % 44.75/6.93 | (10) ~ aSubsetOf0(xP, xO) % 44.75/6.93 | % 44.75/6.93 | DELTA: instantiating (2) with fresh symbol all_91_0 gives: % 44.75/6.93 | (11) slbdtsldtrb0(xO, xK) = all_91_0 & sbrdtbr0(xQ) = xK & $i(all_91_0) & % 44.75/6.93 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_91_0) & aSet0(xQ) & ! [v0: % 44.75/6.93 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 44.75/6.93 | % 44.75/6.93 | ALPHA: (11) implies: % 44.75/6.93 | (12) aSet0(xQ) % 44.75/6.93 | (13) aSubsetOf0(xQ, xO) % 44.75/6.93 | % 44.75/6.93 | DELTA: instantiating (3) with fresh symbol all_94_0 gives: % 44.75/6.93 | (14) szmzizndt0(xQ) = all_94_0 & sdtmndt0(xQ, all_94_0) = xP & $i(all_94_0) % 44.75/6.93 | & aSet0(xP) & ~ aElementOf0(all_94_0, xP) & ! [v0: any] : (v0 = % 44.75/6.93 | all_94_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0) | % 44.75/6.93 | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 44.75/6.93 | xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 44.75/6.93 | aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 44.75/6.93 | aElementOf0(v0, xQ) | sdtlseqdt0(all_94_0, v0)) % 44.75/6.93 | % 44.75/6.93 | ALPHA: (14) implies: % 44.75/6.93 | (15) aSet0(xP) % 44.75/6.93 | % 44.75/6.93 | DELTA: instantiating (1) with fresh symbols all_106_0, all_106_1, all_106_2 % 44.75/6.93 | gives: % 44.75/6.94 | (16) szDzizrdt0(xd) = all_106_2 & sdtlcdtrc0(xe, all_106_1) = xO & % 44.75/6.94 | sdtlbdtrb0(xd, all_106_2) = all_106_1 & szDzozmdt0(xd) = all_106_0 & % 44.75/6.94 | $i(all_106_0) & $i(all_106_1) & $i(all_106_2) & aSet0(all_106_1) & % 44.75/6.94 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_106_2 | ~ % 44.75/6.94 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 44.75/6.94 | all_106_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 44.75/6.94 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_106_1) | % 44.75/6.94 | aElementOf0(v0, all_106_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 44.75/6.94 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 44.75/6.94 | aElementOf0(v1, all_106_1) | aElementOf0(v0, xO)) & ! [v0: $i] : ( % 44.75/6.94 | ~ (sdtlpdtrp0(xd, v0) = all_106_2) | ~ $i(v0) | ~ aElementOf0(v0, % 44.75/6.94 | all_106_0) | aElementOf0(v0, all_106_1)) & ! [v0: $i] : ( ~ % 44.75/6.94 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) % 44.75/6.94 | = v0 & $i(v1) & aElementOf0(v1, all_106_1))) % 44.75/6.94 | % 44.75/6.94 | ALPHA: (16) implies: % 44.75/6.94 | (17) aSet0(xO) % 44.75/6.94 | % 44.75/6.94 | GROUND_INST: instantiating (mSubTrans) with xP, xQ, xO, simplifying with (4), % 44.75/6.94 | (5), (6), (7), (10), (12), (13), (15), (17) gives: % 44.75/6.94 | (18) $false % 44.75/6.94 | % 44.75/6.94 | CLOSE: (18) is inconsistent. % 44.75/6.94 | % 44.75/6.94 End of proof % 44.75/6.94 % SZS output end Proof for theBenchmark % 44.75/6.94 % 44.75/6.94 6341ms %------------------------------------------------------------------------------