%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM623+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 : n019.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 11:49:02 EDT 2023 % Result : Theorem 43.95s 6.66s % Output : Proof 56.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM623+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 18:02:14 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.74/1.47 Prover 4: Preprocessing ... % 4.74/1.47 Prover 1: Preprocessing ... % 5.59/1.51 Prover 2: Preprocessing ... % 5.59/1.51 Prover 5: Preprocessing ... % 5.59/1.51 Prover 0: Preprocessing ... % 5.59/1.51 Prover 6: Preprocessing ... % 5.59/1.51 Prover 3: Preprocessing ... % 14.97/2.82 Prover 1: Constructing countermodel ... % 14.97/2.82 Prover 3: Constructing countermodel ... % 14.97/2.84 Prover 6: Proving ... % 16.70/3.04 Prover 2: Proving ... % 17.45/3.10 Prover 5: Proving ... % 18.99/3.46 Prover 4: Constructing countermodel ... % 23.63/3.97 Prover 0: Proving ... % 43.95/6.65 Prover 0: proved (6008ms) % 43.95/6.66 % 43.95/6.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 43.95/6.67 % 43.95/6.67 Prover 3: stopped % 43.95/6.67 Prover 6: stopped % 43.95/6.67 Prover 5: stopped % 43.95/6.67 Prover 2: stopped % 43.95/6.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 43.95/6.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 43.95/6.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 43.95/6.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 43.95/6.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 46.74/7.00 Prover 7: Preprocessing ... % 46.74/7.01 Prover 10: Preprocessing ... % 46.74/7.01 Prover 8: Preprocessing ... % 46.74/7.01 Prover 13: Preprocessing ... % 46.74/7.01 Prover 11: Preprocessing ... % 49.38/7.36 Prover 13: Warning: ignoring some quantifiers % 49.38/7.37 Prover 10: Constructing countermodel ... % 49.38/7.38 Prover 7: Constructing countermodel ... % 49.38/7.38 Prover 13: Constructing countermodel ... % 49.38/7.39 Prover 8: Warning: ignoring some quantifiers % 49.93/7.41 Prover 8: Constructing countermodel ... % 55.41/8.18 Prover 11: Constructing countermodel ... % 55.97/8.23 Prover 10: Found proof (size 59) % 55.97/8.23 Prover 10: proved (1564ms) % 55.97/8.23 Prover 13: stopped % 55.97/8.23 Prover 7: stopped % 55.97/8.24 Prover 1: stopped % 55.97/8.24 Prover 11: stopped % 55.97/8.24 Prover 8: stopped % 55.97/8.24 Prover 4: stopped % 55.97/8.24 % 55.97/8.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 55.97/8.24 % 55.97/8.25 % SZS output start Proof for theBenchmark % 55.97/8.25 Assumptions after simplification: % 55.97/8.25 --------------------------------- % 55.97/8.26 % 55.97/8.26 (mCountNFin_01) % 55.97/8.26 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 55.97/8.26 % 55.97/8.26 (mDefEmp) % 55.97/8.26 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 55.97/8.26 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 55.97/8.26 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 55.97/8.26 % 55.97/8.26 (mDefMin) % 56.56/8.28 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 % 56.56/8.28 | v0 = slcrc0 | ~ (szmzizndt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 56.56/8.28 aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & % 56.56/8.28 aElementOf0(v3, v0) & ~ sdtlseqdt0(v2, v3))) & ! [v0: $i] : ! [v1: $i] % 56.56/8.28 : ! [v2: $i] : (v0 = slcrc0 | ~ (szmzizndt0(v0) = v1) | ~ $i(v2) | ~ % 56.56/8.28 $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v2, v0) | % 56.56/8.28 sdtlseqdt0(v1, v2)) & ! [v0: $i] : ! [v1: $i] : (v0 = slcrc0 | ~ % 56.56/8.28 (szmzizndt0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v0, szNzAzT0) % 56.56/8.28 | aElementOf0(v1, v0)) % 56.56/8.28 % 56.56/8.28 (mMinMin) % 56.56/8.28 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 56.56/8.28 $i] : (v3 = v2 | v1 = slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ % 56.56/8.28 (szmzizndt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) % 56.56/8.28 | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ aElementOf0(v2, % 56.56/8.28 v1)) % 56.56/8.29 % 56.56/8.29 (m__) % 56.56/8.29 ~ (xx = xp) & $i(xx) & $i(xp) % 56.56/8.29 % 56.56/8.29 (m__3671) % 56.56/8.29 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 56.56/8.29 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 56.56/8.29 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ % 56.56/8.29 aElementOf0(v0, szNzAzT0) | isCountable0(v1)) % 56.56/8.29 % 56.56/8.29 (m__5093) % 56.56/8.29 ~ (xQ = slcrc0) & $i(xQ) & $i(xO) & $i(slcrc0) & aSubsetOf0(xQ, xO) % 56.56/8.29 % 56.56/8.29 (m__5106) % 56.56/8.29 $i(xQ) & $i(szNzAzT0) & aSubsetOf0(xQ, szNzAzT0) % 56.56/8.29 % 56.56/8.29 (m__5147) % 56.56/8.29 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) % 56.56/8.29 % 56.56/8.29 (m__5164) % 56.56/8.29 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 56.56/8.29 $i(v0) & aSet0(xP)) % 56.56/8.29 % 56.56/8.29 (m__5389) % 56.56/8.29 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 56.56/8.29 aElementOf0(xm, szNzAzT0) % 56.56/8.29 % 56.56/8.29 (m__5401) % 56.56/8.29 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & % 56.56/8.29 szmzizndt0(v0) = xx & $i(v0)) % 56.56/8.29 % 56.56/8.29 (m__5442) % 56.56/8.29 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 56.56/8.29 (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & % 56.56/8.29 $i(v2) & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v2)) % 56.56/8.29 % 56.56/8.29 (m__5461) % 56.56/8.29 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = % 56.56/8.29 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1)) % 56.56/8.29 % 56.56/8.29 (m__5481) % 56.56/8.29 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) % 56.56/8.29 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0)) % 56.56/8.29 % 56.56/8.29 (function-axioms) % 56.56/8.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.56/8.29 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 56.56/8.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 56.56/8.29 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 56.56/8.29 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 56.56/8.29 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 56.56/8.29 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 56.56/8.29 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 56.56/8.29 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 56.56/8.29 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 56.56/8.29 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 56.56/8.29 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 56.56/8.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 56.56/8.29 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 56.56/8.29 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 56.56/8.29 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 56.56/8.29 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 56.56/8.29 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 56.56/8.29 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 56.56/8.29 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 56.56/8.29 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 56.56/8.29 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 56.56/8.29 v0)) % 56.56/8.29 % 56.56/8.29 Further assumptions not needed in the proof: % 56.56/8.29 -------------------------------------------- % 56.56/8.30 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 56.56/8.30 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 56.56/8.30 mDefDiff, mDefMax, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, mDefSub, % 56.56/8.30 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 56.56/8.30 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 56.56/8.30 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 56.56/8.30 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 56.56/8.30 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 56.56/8.30 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 56.56/8.30 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 56.56/8.30 m__3520, m__3533, m__3623, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, % 56.56/8.30 m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891, m__4908, m__4982, % 56.56/8.30 m__4998, m__5078, m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, % 56.56/8.30 m__5309, m__5321, m__5348, m__5365 % 56.56/8.30 % 56.56/8.30 Those formulas are unsatisfiable: % 56.56/8.30 --------------------------------- % 56.56/8.30 % 56.56/8.30 Begin of proof % 56.56/8.30 | % 56.56/8.30 | ALPHA: (mDefEmp) implies: % 56.56/8.30 | (1) aSet0(slcrc0) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (mCountNFin_01) implies: % 56.56/8.30 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (mDefMin) implies: % 56.56/8.30 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v0 = slcrc0 | ~ % 56.56/8.30 | (szmzizndt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aSubsetOf0(v0, % 56.56/8.30 | szNzAzT0) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & % 56.56/8.30 | aElementOf0(v3, v0) & ~ sdtlseqdt0(v2, v3))) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (mMinMin) implies: % 56.56/8.30 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = % 56.56/8.30 | slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ (szmzizndt0(v0) % 56.56/8.30 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 56.56/8.30 | aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ % 56.56/8.30 | aElementOf0(v2, v1)) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__3671) implies: % 56.56/8.30 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 56.56/8.30 | ~ aElementOf0(v0, szNzAzT0) | isCountable0(v1)) % 56.56/8.30 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 56.56/8.30 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5093) implies: % 56.56/8.30 | (7) ~ (xQ = slcrc0) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5106) implies: % 56.56/8.30 | (8) aSubsetOf0(xQ, szNzAzT0) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5147) implies: % 56.56/8.30 | (9) szmzizndt0(xQ) = xp % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5164) implies: % 56.56/8.30 | (10) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 56.56/8.30 | aSet0(xP)) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5389) implies: % 56.56/8.30 | (11) aElementOf0(xm, szNzAzT0) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5401) implies: % 56.56/8.30 | (12) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & $i(v0)) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5442) implies: % 56.56/8.30 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, v1) = v2 & % 56.56/8.30 | sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & $i(v2) & $i(v1) & % 56.56/8.30 | $i(v0) & ~ aSubsetOf0(v0, v2)) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5461) implies: % 56.56/8.30 | (14) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN, % 56.56/8.30 | xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1)) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__5481) implies: % 56.56/8.30 | (15) $i(xQ) % 56.56/8.30 | (16) $i(xm) % 56.56/8.30 | (17) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & aElementOf0(xx, xQ) % 56.56/8.30 | & aElementOf0(xp, v0)) % 56.56/8.30 | % 56.56/8.30 | ALPHA: (m__) implies: % 56.56/8.30 | (18) ~ (xx = xp) % 56.56/8.30 | (19) $i(xx) % 56.56/8.31 | % 56.56/8.31 | ALPHA: (function-axioms) implies: % 56.56/8.31 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 56.56/8.31 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 56.56/8.31 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.56/8.31 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 56.56/8.31 | % 56.56/8.31 | DELTA: instantiating (12) with fresh symbol all_80_0 gives: % 56.56/8.31 | (22) sdtlpdtrp0(xN, xm) = all_80_0 & szmzizndt0(all_80_0) = xx & % 56.56/8.31 | $i(all_80_0) % 56.56/8.31 | % 56.56/8.31 | ALPHA: (22) implies: % 56.56/8.31 | (23) szmzizndt0(all_80_0) = xx % 56.56/8.31 | (24) sdtlpdtrp0(xN, xm) = all_80_0 % 56.56/8.31 | % 56.56/8.31 | DELTA: instantiating (17) with fresh symbol all_86_0 gives: % 56.70/8.31 | (25) sdtlpdtrp0(xN, xm) = all_86_0 & $i(all_86_0) & aElementOf0(xx, xQ) & % 56.70/8.31 | aElementOf0(xp, all_86_0) % 56.70/8.31 | % 56.70/8.31 | ALPHA: (25) implies: % 56.70/8.31 | (26) aElementOf0(xp, all_86_0) % 56.70/8.31 | (27) aElementOf0(xx, xQ) % 56.70/8.31 | (28) $i(all_86_0) % 56.70/8.31 | (29) sdtlpdtrp0(xN, xm) = all_86_0 % 56.70/8.31 | % 56.70/8.31 | DELTA: instantiating (10) with fresh symbol all_88_0 gives: % 56.70/8.31 | (30) szmzizndt0(xQ) = all_88_0 & sdtmndt0(xQ, all_88_0) = xP & $i(all_88_0) % 56.70/8.31 | & aSet0(xP) % 56.70/8.31 | % 56.70/8.31 | ALPHA: (30) implies: % 56.70/8.31 | (31) szmzizndt0(xQ) = all_88_0 % 56.70/8.31 | % 56.70/8.31 | DELTA: instantiating (14) with fresh symbols all_92_0, all_92_1 gives: % 56.70/8.31 | (32) sdtlpdtrp0(xN, xm) = all_92_0 & sdtlpdtrp0(xN, xn) = all_92_1 & % 56.70/8.31 | $i(all_92_0) & $i(all_92_1) & aSubsetOf0(all_92_1, all_92_0) % 56.70/8.31 | % 56.70/8.31 | ALPHA: (32) implies: % 56.70/8.31 | (33) sdtlpdtrp0(xN, xm) = all_92_0 % 56.70/8.31 | % 56.70/8.31 | DELTA: instantiating (13) with fresh symbols all_102_0, all_102_1, all_102_2 % 56.70/8.31 | gives: % 56.70/8.31 | (34) sdtlpdtrp0(xN, all_102_1) = all_102_0 & sdtlpdtrp0(xN, xm) = all_102_2 % 56.70/8.31 | & szszuzczcdt0(xn) = all_102_1 & $i(all_102_0) & $i(all_102_1) & % 56.70/8.31 | $i(all_102_2) & ~ aSubsetOf0(all_102_2, all_102_0) % 56.70/8.31 | % 56.70/8.31 | ALPHA: (34) implies: % 56.70/8.31 | (35) sdtlpdtrp0(xN, xm) = all_102_2 % 56.70/8.31 | % 56.70/8.31 | BETA: splitting (2) gives: % 56.70/8.31 | % 56.70/8.31 | Case 1: % 56.70/8.31 | | % 56.70/8.31 | | (36) ~ isCountable0(slcrc0) % 56.70/8.31 | | % 56.70/8.31 | | GROUND_INST: instantiating (20) with xp, all_88_0, xQ, simplifying with (9), % 56.70/8.31 | | (31) gives: % 56.70/8.31 | | (37) all_88_0 = xp % 56.70/8.31 | | % 56.70/8.31 | | GROUND_INST: instantiating (21) with all_80_0, all_92_0, xm, xN, simplifying % 56.70/8.31 | | with (24), (33) gives: % 56.70/8.31 | | (38) all_92_0 = all_80_0 % 56.70/8.31 | | % 56.70/8.31 | | GROUND_INST: instantiating (21) with all_92_0, all_102_2, xm, xN, % 56.70/8.31 | | simplifying with (33), (35) gives: % 56.70/8.31 | | (39) all_102_2 = all_92_0 % 56.70/8.31 | | % 56.70/8.31 | | GROUND_INST: instantiating (21) with all_86_0, all_102_2, xm, xN, % 56.70/8.31 | | simplifying with (29), (35) gives: % 56.70/8.31 | | (40) all_102_2 = all_86_0 % 56.70/8.31 | | % 56.70/8.31 | | COMBINE_EQS: (39), (40) imply: % 56.70/8.31 | | (41) all_92_0 = all_86_0 % 56.70/8.31 | | % 56.70/8.31 | | SIMP: (41) implies: % 56.70/8.31 | | (42) all_92_0 = all_86_0 % 56.70/8.31 | | % 56.70/8.31 | | COMBINE_EQS: (38), (42) imply: % 56.70/8.31 | | (43) all_86_0 = all_80_0 % 56.70/8.31 | | % 56.70/8.31 | | REDUCE: (28), (43) imply: % 56.70/8.31 | | (44) $i(all_80_0) % 56.70/8.31 | | % 56.70/8.31 | | REDUCE: (26), (43) imply: % 56.70/8.31 | | (45) aElementOf0(xp, all_80_0) % 56.70/8.31 | | % 56.70/8.31 | | GROUND_INST: instantiating (3) with xQ, xp, xx, simplifying with (8), (9), % 56.70/8.31 | | (15), (19), (27) gives: % 56.70/8.31 | | (46) xx = xp | xQ = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, xQ) % 56.70/8.31 | | & ~ sdtlseqdt0(xx, v0)) % 56.70/8.31 | | % 56.70/8.32 | | GROUND_INST: instantiating (6) with xm, all_80_0, simplifying with (11), % 56.70/8.32 | | (16), (24) gives: % 56.70/8.32 | | (47) aSubsetOf0(all_80_0, szNzAzT0) % 56.70/8.32 | | % 56.70/8.32 | | GROUND_INST: instantiating (5) with xm, all_80_0, simplifying with (11), % 56.70/8.32 | | (16), (24) gives: % 56.70/8.32 | | (48) isCountable0(all_80_0) % 56.70/8.32 | | % 56.70/8.32 | | BETA: splitting (46) gives: % 56.70/8.32 | | % 56.70/8.32 | | Case 1: % 56.70/8.32 | | | % 56.70/8.32 | | | (49) xQ = slcrc0 % 56.70/8.32 | | | % 56.70/8.32 | | | REDUCE: (7), (49) imply: % 56.70/8.32 | | | (50) $false % 56.70/8.32 | | | % 56.70/8.32 | | | CLOSE: (50) is inconsistent. % 56.70/8.32 | | | % 56.70/8.32 | | Case 2: % 56.70/8.32 | | | % 56.70/8.32 | | | % 56.70/8.32 | | | GROUND_INST: instantiating (4) with xQ, all_80_0, xp, xx, simplifying with % 56.70/8.32 | | | (8), (9), (15), (23), (27), (44), (45), (47) gives: % 56.70/8.32 | | | (51) all_80_0 = slcrc0 | xx = xp | xQ = slcrc0 % 56.70/8.32 | | | % 56.70/8.32 | | | BETA: splitting (51) gives: % 56.70/8.32 | | | % 56.70/8.32 | | | Case 1: % 56.70/8.32 | | | | % 56.70/8.32 | | | | (52) all_80_0 = slcrc0 % 56.70/8.32 | | | | % 56.70/8.32 | | | | REDUCE: (48), (52) imply: % 56.70/8.32 | | | | (53) isCountable0(slcrc0) % 56.70/8.32 | | | | % 56.70/8.32 | | | | PRED_UNIFY: (36), (53) imply: % 56.70/8.32 | | | | (54) $false % 56.70/8.32 | | | | % 56.70/8.32 | | | | CLOSE: (54) is inconsistent. % 56.70/8.32 | | | | % 56.70/8.32 | | | Case 2: % 56.70/8.32 | | | | % 56.70/8.32 | | | | (55) xx = xp | xQ = slcrc0 % 56.70/8.32 | | | | % 56.70/8.32 | | | | BETA: splitting (55) gives: % 56.70/8.32 | | | | % 56.70/8.32 | | | | Case 1: % 56.70/8.32 | | | | | % 56.70/8.32 | | | | | (56) xQ = slcrc0 % 56.70/8.32 | | | | | % 56.70/8.32 | | | | | REDUCE: (7), (56) imply: % 56.70/8.32 | | | | | (57) $false % 56.70/8.32 | | | | | % 56.70/8.32 | | | | | CLOSE: (57) is inconsistent. % 56.70/8.32 | | | | | % 56.70/8.32 | | | | Case 2: % 56.70/8.32 | | | | | % 56.70/8.32 | | | | | (58) xx = xp % 56.70/8.32 | | | | | % 56.70/8.32 | | | | | REDUCE: (18), (58) imply: % 56.70/8.32 | | | | | (59) $false % 56.70/8.32 | | | | | % 56.70/8.32 | | | | | CLOSE: (59) is inconsistent. % 56.70/8.32 | | | | | % 56.70/8.32 | | | | End of split % 56.70/8.32 | | | | % 56.70/8.32 | | | End of split % 56.70/8.32 | | | % 56.70/8.32 | | End of split % 56.70/8.32 | | % 56.70/8.32 | Case 2: % 56.70/8.32 | | % 56.70/8.32 | | (60) ~ aSet0(slcrc0) % 56.70/8.32 | | % 56.70/8.32 | | PRED_UNIFY: (1), (60) imply: % 56.70/8.32 | | (61) $false % 56.70/8.32 | | % 56.70/8.32 | | CLOSE: (61) is inconsistent. % 56.70/8.32 | | % 56.70/8.32 | End of split % 56.70/8.32 | % 56.70/8.32 End of proof % 56.70/8.32 % SZS output end Proof for theBenchmark % 56.70/8.32 % 56.70/8.32 7713ms %------------------------------------------------------------------------------