%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM612+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 : n022.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 11:48:58 EDT 2023 % Result : Theorem 143.52s 19.42s % Output : Proof 143.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM612+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 10:33:55 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.64 ________ _____ % 0.19/0.64 ___ __ \_________(_)________________________________ % 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.64 % 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.64 (2023-06-19) % 0.19/0.64 % 0.19/0.64 (c) Philipp Rümmer, 2009-2023 % 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.64 Amanda Stjerna. % 0.19/0.64 Free software under BSD-3-Clause. % 0.19/0.64 % 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.64 % 0.19/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.66 Running up to 7 provers in parallel. % 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.86/1.73 Prover 4: Preprocessing ... % 6.86/1.73 Prover 1: Preprocessing ... % 7.58/1.77 Prover 3: Preprocessing ... % 7.58/1.77 Prover 6: Preprocessing ... % 7.58/1.77 Prover 5: Preprocessing ... % 7.58/1.77 Prover 0: Preprocessing ... % 7.58/1.77 Prover 2: Preprocessing ... % 18.79/3.39 Prover 3: Constructing countermodel ... % 18.79/3.40 Prover 1: Constructing countermodel ... % 18.79/3.44 Prover 6: Proving ... % 22.49/3.77 Prover 5: Proving ... % 50.50/7.42 Prover 4: Constructing countermodel ... % 56.51/8.18 Prover 2: Proving ... % 60.03/8.62 Prover 0: Proving ... % 101.62/14.01 Prover 5: stopped % 102.14/14.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 103.10/14.21 Prover 7: Preprocessing ... % 108.69/14.98 Prover 7: Constructing countermodel ... % 116.05/15.87 Prover 2: stopped % 116.05/15.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 117.44/16.04 Prover 1: stopped % 117.44/16.05 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.80/16.10 Prover 8: Preprocessing ... % 118.41/16.28 Prover 9: Preprocessing ... % 120.48/16.45 Prover 8: Warning: ignoring some quantifiers % 120.48/16.48 Prover 8: Constructing countermodel ... % 131.73/17.92 Prover 6: stopped % 131.73/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.93/18.08 Prover 10: Preprocessing ... % 135.47/18.42 Prover 9: Constructing countermodel ... % 136.60/18.55 Prover 10: Constructing countermodel ... % 143.20/19.40 Prover 10: Found proof (size 40) % 143.20/19.40 Prover 10: proved (1481ms) % 143.20/19.40 Prover 8: stopped % 143.20/19.40 Prover 0: stopped % 143.20/19.40 Prover 7: stopped % 143.52/19.40 Prover 9: stopped % 143.52/19.41 Prover 4: stopped % 143.52/19.42 Prover 3: stopped % 143.52/19.42 % 143.52/19.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 143.52/19.42 % 143.52/19.42 % SZS output start Proof for theBenchmark % 143.52/19.43 Assumptions after simplification: % 143.52/19.43 --------------------------------- % 143.52/19.43 % 143.52/19.43 (mCardDiff) % 143.66/19.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v0) = % 143.66/19.46 v1) | ~ (sdtmndt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 143.66/19.46 isFinite0(v0) | ~ aElementOf0(v2, v0) | ~ aSet0(v0) | ? [v4: $i] : % 143.66/19.46 (sbrdtbr0(v3) = v4 & szszuzczcdt0(v4) = v1 & $i(v4) & $i(v1))) % 143.66/19.46 % 143.66/19.46 (mCardNum) % 143.66/19.46 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) % 143.66/19.46 | ~ isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0)) & ! [v0: $i] % 143.66/19.46 : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v1, % 143.66/19.46 szNzAzT0) | ~ aSet0(v0) | isFinite0(v0)) % 143.66/19.46 % 143.66/19.46 (mCountNFin_01) % 143.66/19.46 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 143.66/19.46 % 143.66/19.46 (mDefEmp) % 143.66/19.46 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 143.66/19.46 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 143.66/19.46 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 143.66/19.46 % 143.66/19.46 (mSubFSet) % 143.66/19.46 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) | % 143.66/19.46 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1)) % 143.66/19.46 % 143.66/19.46 (m__) % 143.66/19.46 $i(xP) & $i(xQ) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 143.66/19.46 (sbrdtbr0(xP) = v0 & $i(v0) & ( ~ aElementOf0(v0, szNzAzT0) | ( ~ (v2 = v1) & % 143.66/19.46 sbrdtbr0(xQ) = v2 & szszuzczcdt0(v0) = v1 & $i(v2) & $i(v1)))) % 143.66/19.46 % 143.66/19.46 (m__3418) % 143.66/19.46 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 143.66/19.46 % 143.66/19.47 (m__5078) % 143.66/19.47 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & % 143.66/19.47 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & % 143.66/19.47 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 143.66/19.47 aElementOf0(v1, xO))) % 143.66/19.47 % 143.66/19.47 (m__5147) % 143.66/19.47 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : ( % 143.66/19.47 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0)) % 143.66/19.47 % 143.66/19.47 (m__5164) % 143.66/19.47 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 143.66/19.47 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 143.66/19.47 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP)) % 143.66/19.47 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & % 143.66/19.47 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: % 143.66/19.47 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 143.66/19.47 % 143.66/19.47 (m__5173) % 143.66/19.47 $i(xp) & $i(xQ) & aElementOf0(xp, xQ) % 143.66/19.47 % 143.66/19.47 (m__5195) % 143.66/19.47 $i(xP) & $i(xQ) & aSubsetOf0(xP, xQ) & ! [v0: $i] : ( ~ $i(v0) | ~ % 143.66/19.47 aElementOf0(v0, xP) | aElementOf0(v0, xQ)) % 143.66/19.47 % 143.66/19.47 (function-axioms) % 143.66/19.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 143.66/19.48 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 143.66/19.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 143.66/19.48 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 143.66/19.48 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 143.66/19.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 143.66/19.48 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 143.66/19.48 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 143.66/19.48 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 143.66/19.48 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 143.66/19.48 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 143.66/19.48 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 143.66/19.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 143.66/19.48 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 143.66/19.48 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 143.66/19.48 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 143.66/19.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 143.66/19.48 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 143.66/19.48 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 143.66/19.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 143.66/19.48 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 143.66/19.48 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 143.66/19.48 v0)) % 143.66/19.48 % 143.66/19.48 Further assumptions not needed in the proof: % 143.66/19.48 -------------------------------------------- % 143.66/19.48 mCConsSet, mCDiffSet, mCardCons, mCardEmpty, mCardS, mCardSeg, mCardSub, % 143.66/19.48 mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff, mDefMax, % 143.66/19.48 mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, mDefSub, mDiffCons, % 143.66/19.48 mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, % 143.66/19.48 mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm, % 143.66/19.48 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, % 143.66/19.48 mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc, % 143.66/19.48 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, % 143.66/19.48 mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, % 143.66/19.48 m__3291, m__3398, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, % 143.66/19.48 m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, % 143.66/19.48 m__4730, m__4758, m__4854, m__4891, m__4908, m__4982, m__4998, m__5093, m__5106, % 143.66/19.48 m__5116, m__5182, m__5208 % 143.66/19.48 % 143.66/19.48 Those formulas are unsatisfiable: % 143.66/19.48 --------------------------------- % 143.66/19.48 % 143.66/19.48 Begin of proof % 143.66/19.48 | % 143.66/19.48 | ALPHA: (mDefEmp) implies: % 143.66/19.48 | (1) aSet0(slcrc0) % 143.66/19.48 | % 143.66/19.48 | ALPHA: (mCountNFin_01) implies: % 143.66/19.48 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 143.66/19.48 | % 143.66/19.48 | ALPHA: (mCardNum) implies: % 143.66/19.49 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 143.66/19.49 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | isFinite0(v0)) % 143.66/19.49 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 143.66/19.49 | isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0)) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (m__3418) implies: % 143.66/19.49 | (5) aElementOf0(xK, szNzAzT0) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (m__5078) implies: % 143.66/19.49 | (6) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0) & % 143.66/19.49 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] : % 143.66/19.49 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO))) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (m__5147) implies: % 143.66/19.49 | (7) szmzizndt0(xQ) = xp % 143.66/19.49 | % 143.66/19.49 | ALPHA: (m__5164) implies: % 143.66/19.49 | (8) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 143.66/19.49 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~ % 143.66/19.49 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | % 143.66/19.49 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 143.66/19.49 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~ % 143.66/19.49 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : ( % 143.66/19.49 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1))) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (m__5173) implies: % 143.66/19.49 | (9) aElementOf0(xp, xQ) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (m__5195) implies: % 143.66/19.49 | (10) aSubsetOf0(xP, xQ) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (m__) implies: % 143.66/19.49 | (11) $i(xQ) % 143.66/19.49 | (12) $i(xP) % 143.66/19.49 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sbrdtbr0(xP) = v0 & $i(v0) % 143.66/19.49 | & ( ~ aElementOf0(v0, szNzAzT0) | ( ~ (v2 = v1) & sbrdtbr0(xQ) = v2 % 143.66/19.49 | & szszuzczcdt0(v0) = v1 & $i(v2) & $i(v1)))) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (function-axioms) implies: % 143.66/19.49 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 143.66/19.49 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 143.66/19.49 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) % 143.66/19.49 | = v1) | ~ (sbrdtbr0(v2) = v0)) % 143.66/19.49 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 143.66/19.49 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 143.66/19.49 | % 143.66/19.49 | DELTA: instantiating (13) with fresh symbols all_90_0, all_90_1, all_90_2 % 143.66/19.49 | gives: % 143.66/19.49 | (17) sbrdtbr0(xP) = all_90_2 & $i(all_90_2) & ( ~ aElementOf0(all_90_2, % 143.66/19.49 | szNzAzT0) | ( ~ (all_90_0 = all_90_1) & sbrdtbr0(xQ) = all_90_0 & % 143.66/19.49 | szszuzczcdt0(all_90_2) = all_90_1 & $i(all_90_0) & $i(all_90_1))) % 143.66/19.49 | % 143.66/19.49 | ALPHA: (17) implies: % 143.66/19.49 | (18) sbrdtbr0(xP) = all_90_2 % 143.66/19.50 | (19) ~ aElementOf0(all_90_2, szNzAzT0) | ( ~ (all_90_0 = all_90_1) & % 143.66/19.50 | sbrdtbr0(xQ) = all_90_0 & szszuzczcdt0(all_90_2) = all_90_1 & % 143.66/19.50 | $i(all_90_0) & $i(all_90_1)) % 143.66/19.50 | % 143.66/19.50 | DELTA: instantiating (6) with fresh symbol all_92_0 gives: % 143.66/19.50 | (20) slbdtsldtrb0(xO, xK) = all_92_0 & sbrdtbr0(xQ) = xK & $i(all_92_0) & % 143.66/19.50 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_92_0) & aSet0(xQ) & ! [v0: % 143.66/19.50 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 143.66/19.50 | % 143.66/19.50 | ALPHA: (20) implies: % 143.66/19.50 | (21) aSet0(xQ) % 143.66/19.50 | (22) sbrdtbr0(xQ) = xK % 143.66/19.50 | % 143.66/19.50 | DELTA: instantiating (8) with fresh symbol all_95_0 gives: % 143.66/19.50 | (23) szmzizndt0(xQ) = all_95_0 & sdtmndt0(xQ, all_95_0) = xP & $i(all_95_0) % 143.66/19.50 | & aSet0(xP) & ~ aElementOf0(all_95_0, xP) & ! [v0: any] : (v0 = % 143.66/19.50 | all_95_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0) | % 143.66/19.50 | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 143.66/19.50 | xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 143.66/19.50 | aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 143.66/19.50 | aElementOf0(v0, xQ) | sdtlseqdt0(all_95_0, v0)) % 143.66/19.50 | % 143.66/19.50 | ALPHA: (23) implies: % 143.66/19.50 | (24) aSet0(xP) % 143.66/19.50 | (25) $i(all_95_0) % 143.66/19.50 | (26) sdtmndt0(xQ, all_95_0) = xP % 143.66/19.50 | (27) szmzizndt0(xQ) = all_95_0 % 143.66/19.50 | % 143.66/19.50 | BETA: splitting (2) gives: % 143.66/19.50 | % 143.66/19.50 | Case 1: % 143.66/19.50 | | % 143.66/19.50 | | (28) ~ aSet0(slcrc0) % 143.66/19.50 | | % 143.66/19.50 | | PRED_UNIFY: (1), (28) imply: % 143.66/19.50 | | (29) $false % 143.66/19.50 | | % 143.66/19.50 | | CLOSE: (29) is inconsistent. % 143.66/19.50 | | % 143.66/19.50 | Case 2: % 143.66/19.50 | | % 143.66/19.50 | | % 143.66/19.50 | | GROUND_INST: instantiating (16) with xp, all_95_0, xQ, simplifying with (7), % 143.66/19.50 | | (27) gives: % 143.66/19.50 | | (30) all_95_0 = xp % 143.66/19.50 | | % 143.66/19.50 | | REDUCE: (26), (30) imply: % 143.66/19.50 | | (31) sdtmndt0(xQ, xp) = xP % 143.66/19.50 | | % 143.66/19.50 | | REDUCE: (25), (30) imply: % 143.66/19.50 | | (32) $i(xp) % 143.66/19.50 | | % 143.66/19.50 | | GROUND_INST: instantiating (3) with xQ, xK, simplifying with (5), (11), % 143.66/19.50 | | (21), (22) gives: % 143.66/19.50 | | (33) isFinite0(xQ) % 143.66/19.50 | | % 143.66/19.50 | | GROUND_INST: instantiating (mCardDiff) with xQ, xK, xp, xP, simplifying with % 143.66/19.50 | | (9), (11), (21), (22), (31), (32), (33) gives: % 143.66/19.51 | | (34) ? [v0: $i] : (sbrdtbr0(xP) = v0 & szszuzczcdt0(v0) = xK & $i(v0) & % 143.66/19.51 | | $i(xK)) % 143.66/19.51 | | % 143.66/19.51 | | GROUND_INST: instantiating (mSubFSet) with xQ, xP, simplifying with (10), % 143.66/19.51 | | (11), (12), (21), (33) gives: % 143.66/19.51 | | (35) isFinite0(xP) % 143.66/19.51 | | % 143.66/19.51 | | DELTA: instantiating (34) with fresh symbol all_186_0 gives: % 143.66/19.51 | | (36) sbrdtbr0(xP) = all_186_0 & szszuzczcdt0(all_186_0) = xK & % 143.66/19.51 | | $i(all_186_0) & $i(xK) % 143.66/19.51 | | % 143.66/19.51 | | ALPHA: (36) implies: % 143.66/19.51 | | (37) szszuzczcdt0(all_186_0) = xK % 143.66/19.51 | | (38) sbrdtbr0(xP) = all_186_0 % 143.66/19.51 | | % 143.66/19.51 | | GROUND_INST: instantiating (15) with all_90_2, all_186_0, xP, simplifying % 143.66/19.51 | | with (18), (38) gives: % 143.66/19.51 | | (39) all_186_0 = all_90_2 % 143.66/19.51 | | % 143.66/19.51 | | REDUCE: (37), (39) imply: % 143.66/19.51 | | (40) szszuzczcdt0(all_90_2) = xK % 143.66/19.51 | | % 143.66/19.51 | | BETA: splitting (19) gives: % 143.66/19.51 | | % 143.66/19.51 | | Case 1: % 143.66/19.51 | | | % 143.66/19.51 | | | (41) ~ aElementOf0(all_90_2, szNzAzT0) % 143.66/19.51 | | | % 143.66/19.51 | | | GROUND_INST: instantiating (4) with xP, all_90_2, simplifying with (12), % 143.66/19.51 | | | (18), (24), (35), (41) gives: % 143.66/19.51 | | | (42) $false % 143.66/19.51 | | | % 143.66/19.51 | | | CLOSE: (42) is inconsistent. % 143.66/19.51 | | | % 143.66/19.51 | | Case 2: % 143.66/19.51 | | | % 143.66/19.51 | | | (43) ~ (all_90_0 = all_90_1) & sbrdtbr0(xQ) = all_90_0 & % 143.66/19.51 | | | szszuzczcdt0(all_90_2) = all_90_1 & $i(all_90_0) & $i(all_90_1) % 143.66/19.51 | | | % 143.66/19.51 | | | ALPHA: (43) implies: % 143.66/19.51 | | | (44) ~ (all_90_0 = all_90_1) % 143.66/19.51 | | | (45) szszuzczcdt0(all_90_2) = all_90_1 % 143.66/19.51 | | | (46) sbrdtbr0(xQ) = all_90_0 % 143.66/19.51 | | | % 143.66/19.51 | | | GROUND_INST: instantiating (14) with xK, all_90_1, all_90_2, simplifying % 143.66/19.51 | | | with (40), (45) gives: % 143.66/19.51 | | | (47) all_90_1 = xK % 143.66/19.51 | | | % 143.66/19.51 | | | GROUND_INST: instantiating (15) with xK, all_90_0, xQ, simplifying with % 143.66/19.51 | | | (22), (46) gives: % 143.66/19.51 | | | (48) all_90_0 = xK % 143.66/19.51 | | | % 143.66/19.51 | | | REDUCE: (44), (47), (48) imply: % 143.66/19.51 | | | (49) $false % 143.66/19.51 | | | % 143.66/19.51 | | | CLOSE: (49) is inconsistent. % 143.66/19.51 | | | % 143.66/19.51 | | End of split % 143.66/19.51 | | % 143.66/19.51 | End of split % 143.66/19.51 | % 143.66/19.51 End of proof % 143.66/19.51 % SZS output end Proof for theBenchmark % 143.66/19.51 % 143.66/19.51 18873ms %------------------------------------------------------------------------------