%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM615+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 : n002.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 11:48:59 EDT 2023 % Result : Theorem 34.36s 5.26s % Output : Proof 86.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM615+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n002.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 11:24:02 EDT 2023 % 0.14/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 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 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 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 % 4.61/1.36 Prover 4: Preprocessing ... % 4.61/1.37 Prover 1: Preprocessing ... % 5.13/1.40 Prover 5: Preprocessing ... % 5.13/1.40 Prover 0: Preprocessing ... % 5.13/1.40 Prover 3: Preprocessing ... % 5.13/1.40 Prover 6: Preprocessing ... % 5.13/1.40 Prover 2: Preprocessing ... % 14.34/2.66 Prover 1: Constructing countermodel ... % 14.74/2.71 Prover 3: Constructing countermodel ... % 15.37/2.81 Prover 6: Proving ... % 15.95/2.91 Prover 5: Proving ... % 17.55/3.06 Prover 2: Proving ... % 21.70/3.61 Prover 4: Constructing countermodel ... % 23.15/3.88 Prover 0: Proving ... % 34.36/5.26 Prover 3: proved (4625ms) % 34.36/5.26 % 34.36/5.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 34.36/5.26 % 34.36/5.26 Prover 0: stopped % 34.36/5.26 Prover 2: stopped % 34.36/5.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 34.36/5.27 Prover 6: stopped % 34.36/5.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 34.36/5.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 34.36/5.29 Prover 5: stopped % 34.36/5.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 34.36/5.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 35.50/5.41 Prover 8: Preprocessing ... % 35.50/5.44 Prover 7: Preprocessing ... % 36.36/5.52 Prover 10: Preprocessing ... % 36.36/5.54 Prover 11: Preprocessing ... % 36.36/5.56 Prover 13: Preprocessing ... % 37.83/5.71 Prover 7: Constructing countermodel ... % 38.59/5.79 Prover 10: Constructing countermodel ... % 38.81/5.81 Prover 8: Warning: ignoring some quantifiers % 38.94/5.83 Prover 8: Constructing countermodel ... % 39.62/5.94 Prover 13: Warning: ignoring some quantifiers % 39.62/5.95 Prover 13: Constructing countermodel ... % 46.75/6.88 Prover 11: Constructing countermodel ... % 73.24/10.30 Prover 13: stopped % 73.75/10.32 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 74.09/10.41 Prover 16: Preprocessing ... % 75.47/10.55 Prover 16: Warning: ignoring some quantifiers % 75.47/10.56 Prover 16: Constructing countermodel ... % 85.74/11.93 Prover 7: Found proof (size 48) % 85.74/11.93 Prover 7: proved (6622ms) % 85.74/11.94 Prover 1: stopped % 85.74/11.94 Prover 16: stopped % 85.74/11.94 Prover 4: stopped % 85.74/11.94 Prover 11: stopped % 85.74/11.94 Prover 10: stopped % 85.74/11.94 Prover 8: stopped % 85.74/11.94 % 85.74/11.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 85.74/11.94 % 86.36/11.95 % SZS output start Proof for theBenchmark % 86.36/11.95 Assumptions after simplification: % 86.36/11.95 --------------------------------- % 86.36/11.95 % 86.36/11.95 (m__) % 86.52/11.98 $i(xp) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 86.52/11.98 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ % 86.52/11.98 (sdtlpdtrp0(xe, v2) = xp) | ~ $i(v2) | ~ aElementOf0(v2, v1))) % 86.52/11.98 % 86.52/11.98 (m__4854) % 86.52/11.98 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 86.52/11.98 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) & % 86.52/11.98 aElementOf0(v0, xT)) % 86.52/11.98 % 86.52/11.98 (m__4891) % 86.52/11.98 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 86.52/11.98 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & % 86.52/11.98 aSet0(xO)) % 86.52/11.98 % 86.52/11.98 (m__4982) % 86.52/11.98 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 86.52/11.98 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 86.52/11.98 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = % 86.52/11.98 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 86.52/11.98 % 86.52/11.98 (m__5147) % 86.52/11.98 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) % 86.52/11.98 % 86.52/11.98 (m__5164) % 86.52/11.98 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & % 86.52/11.98 $i(v0) & aSet0(xP)) % 86.52/11.98 % 86.52/11.98 (m__5182) % 86.52/11.98 $i(xp) & $i(xO) & aElementOf0(xp, xO) % 86.52/11.98 % 86.52/11.98 (function-axioms) % 86.52/11.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 86.52/11.99 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 86.52/11.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 86.52/11.99 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 86.52/11.99 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 86.52/11.99 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 86.52/11.99 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 86.52/11.99 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 86.52/11.99 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 86.52/11.99 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 86.52/11.99 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 86.52/11.99 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 86.52/11.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 86.52/11.99 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 86.52/11.99 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 86.52/11.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 86.52/11.99 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 86.52/11.99 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 86.52/11.99 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 86.52/11.99 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 86.52/11.99 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 86.52/11.99 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 86.52/11.99 v0)) % 86.52/11.99 % 86.52/11.99 Further assumptions not needed in the proof: % 86.52/11.99 -------------------------------------------- % 86.52/11.99 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 86.52/11.99 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 86.52/11.99 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 86.52/11.99 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 86.52/11.99 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 86.52/11.99 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 86.52/11.99 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 86.52/11.99 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 86.52/11.99 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 86.52/11.99 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, % 86.52/11.99 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, % 86.52/11.99 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, % 86.52/11.99 m__4758, m__4908, m__4998, m__5078, m__5093, m__5106, m__5116, m__5173, m__5195, % 86.52/11.99 m__5208, m__5217, m__5270 % 86.52/11.99 % 86.52/11.99 Those formulas are unsatisfiable: % 86.52/11.99 --------------------------------- % 86.52/11.99 % 86.52/11.99 Begin of proof % 86.52/11.99 | % 86.52/11.99 | ALPHA: (m__4854) implies: % 86.52/11.99 | (1) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = % 86.52/11.99 | v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT)) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (m__4891) implies: % 86.52/12.00 | (2) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = % 86.52/12.00 | xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO)) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (m__4982) implies: % 86.52/12.00 | (3) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = % 86.52/12.00 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 86.52/12.00 | xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 & $i(v3) & % 86.52/12.00 | aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (m__5147) implies: % 86.52/12.00 | (4) szmzizndt0(xQ) = xp % 86.52/12.00 | % 86.52/12.00 | ALPHA: (m__5164) implies: % 86.52/12.00 | (5) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) & % 86.52/12.00 | aSet0(xP)) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (m__5182) implies: % 86.52/12.00 | (6) aElementOf0(xp, xO) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (m__) implies: % 86.52/12.00 | (7) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = % 86.52/12.00 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtlpdtrp0(xe, v2) = xp) | % 86.52/12.00 | ~ $i(v2) | ~ aElementOf0(v2, v1))) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (function-axioms) implies: % 86.52/12.00 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) % 86.52/12.00 | = v1) | ~ (szmzizndt0(v2) = v0)) % 86.52/12.00 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) % 86.52/12.00 | = v1) | ~ (szDzizrdt0(v2) = v0)) % 86.52/12.00 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 86.52/12.00 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 86.52/12.00 | % 86.52/12.00 | DELTA: instantiating (5) with fresh symbol all_82_0 gives: % 86.52/12.00 | (11) szmzizndt0(xQ) = all_82_0 & sdtmndt0(xQ, all_82_0) = xP & $i(all_82_0) % 86.52/12.00 | & aSet0(xP) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (11) implies: % 86.52/12.00 | (12) $i(all_82_0) % 86.52/12.00 | (13) szmzizndt0(xQ) = all_82_0 % 86.52/12.00 | % 86.52/12.00 | DELTA: instantiating (2) with fresh symbols all_86_0, all_86_1 gives: % 86.52/12.00 | (14) szDzizrdt0(xd) = all_86_1 & sdtlcdtrc0(xe, all_86_0) = xO & % 86.52/12.00 | sdtlbdtrb0(xd, all_86_1) = all_86_0 & $i(all_86_0) & $i(all_86_1) & % 86.52/12.00 | aSet0(xO) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (14) implies: % 86.52/12.00 | (15) sdtlbdtrb0(xd, all_86_1) = all_86_0 % 86.52/12.00 | (16) szDzizrdt0(xd) = all_86_1 % 86.52/12.00 | % 86.52/12.00 | DELTA: instantiating (1) with fresh symbols all_88_0, all_88_1 gives: % 86.52/12.00 | (17) szDzizrdt0(xd) = all_88_1 & sdtlbdtrb0(xd, all_88_1) = all_88_0 & % 86.52/12.00 | $i(all_88_0) & $i(all_88_1) & isCountable0(all_88_0) & % 86.52/12.00 | aElementOf0(all_88_1, xT) % 86.52/12.00 | % 86.52/12.00 | ALPHA: (17) implies: % 86.52/12.00 | (18) szDzizrdt0(xd) = all_88_1 % 86.52/12.00 | % 86.52/12.00 | DELTA: instantiating (7) with fresh symbols all_90_0, all_90_1 gives: % 86.52/12.01 | (19) szDzizrdt0(xd) = all_90_1 & sdtlbdtrb0(xd, all_90_1) = all_90_0 & % 86.52/12.01 | $i(all_90_0) & $i(all_90_1) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = % 86.52/12.01 | xp) | ~ $i(v0) | ~ aElementOf0(v0, all_90_0)) % 86.52/12.01 | % 86.52/12.01 | ALPHA: (19) implies: % 86.52/12.01 | (20) sdtlbdtrb0(xd, all_90_1) = all_90_0 % 86.52/12.01 | (21) szDzizrdt0(xd) = all_90_1 % 86.52/12.01 | (22) ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xp) | ~ $i(v0) | ~ % 86.52/12.01 | aElementOf0(v0, all_90_0)) % 86.52/12.01 | % 86.52/12.01 | DELTA: instantiating (3) with fresh symbols all_95_0, all_95_1 gives: % 86.52/12.01 | (23) szDzizrdt0(xd) = all_95_1 & sdtlbdtrb0(xd, all_95_1) = all_95_0 & % 86.52/12.01 | $i(all_95_0) & $i(all_95_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 86.52/12.01 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 & % 86.52/12.01 | $i(v1) & aElementOf0(v1, all_95_0) & aElementOf0(v1, szNzAzT0))) % 86.52/12.01 | % 86.52/12.01 | ALPHA: (23) implies: % 86.52/12.01 | (24) sdtlbdtrb0(xd, all_95_1) = all_95_0 % 86.52/12.01 | (25) szDzizrdt0(xd) = all_95_1 % 86.52/12.01 | (26) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : % 86.52/12.01 | (sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1, all_95_0) & % 86.52/12.01 | aElementOf0(v1, szNzAzT0))) % 86.52/12.01 | % 86.52/12.01 | GROUND_INST: instantiating (8) with xp, all_82_0, xQ, simplifying with (4), % 86.52/12.01 | (13) gives: % 86.52/12.01 | (27) all_82_0 = xp % 86.52/12.01 | % 86.52/12.01 | GROUND_INST: instantiating (10) with all_86_0, all_90_0, all_86_1, xd, % 86.52/12.01 | simplifying with (15) gives: % 86.52/12.01 | (28) all_90_0 = all_86_0 | ~ (sdtlbdtrb0(xd, all_86_1) = all_90_0) % 86.52/12.01 | % 86.52/12.01 | GROUND_INST: instantiating (10) with all_86_0, all_95_0, all_86_1, xd, % 86.52/12.01 | simplifying with (15) gives: % 86.52/12.01 | (29) all_95_0 = all_86_0 | ~ (sdtlbdtrb0(xd, all_86_1) = all_95_0) % 86.52/12.01 | % 86.52/12.01 | GROUND_INST: instantiating (9) with all_86_1, all_90_1, xd, simplifying with % 86.52/12.01 | (16), (21) gives: % 86.52/12.01 | (30) all_90_1 = all_86_1 % 86.52/12.01 | % 86.52/12.01 | GROUND_INST: instantiating (9) with all_90_1, all_95_1, xd, simplifying with % 86.52/12.01 | (21), (25) gives: % 86.52/12.01 | (31) all_95_1 = all_90_1 % 86.52/12.01 | % 86.52/12.01 | GROUND_INST: instantiating (9) with all_88_1, all_95_1, xd, simplifying with % 86.52/12.01 | (18), (25) gives: % 86.52/12.01 | (32) all_95_1 = all_88_1 % 86.52/12.01 | % 86.52/12.01 | COMBINE_EQS: (31), (32) imply: % 86.52/12.01 | (33) all_90_1 = all_88_1 % 86.52/12.01 | % 86.52/12.01 | SIMP: (33) implies: % 86.52/12.01 | (34) all_90_1 = all_88_1 % 86.52/12.01 | % 86.52/12.01 | COMBINE_EQS: (30), (34) imply: % 86.52/12.01 | (35) all_88_1 = all_86_1 % 86.52/12.01 | % 86.52/12.01 | COMBINE_EQS: (32), (35) imply: % 86.52/12.01 | (36) all_95_1 = all_86_1 % 86.52/12.01 | % 86.52/12.01 | REDUCE: (24), (36) imply: % 86.52/12.01 | (37) sdtlbdtrb0(xd, all_86_1) = all_95_0 % 86.52/12.01 | % 86.52/12.01 | REDUCE: (20), (30) imply: % 86.52/12.01 | (38) sdtlbdtrb0(xd, all_86_1) = all_90_0 % 86.52/12.01 | % 86.52/12.01 | REDUCE: (12), (27) imply: % 86.52/12.01 | (39) $i(xp) % 86.52/12.01 | % 86.52/12.01 | BETA: splitting (29) gives: % 86.52/12.01 | % 86.52/12.01 | Case 1: % 86.52/12.01 | | % 86.52/12.01 | | (40) ~ (sdtlbdtrb0(xd, all_86_1) = all_95_0) % 86.52/12.01 | | % 86.52/12.01 | | PRED_UNIFY: (37), (40) imply: % 86.52/12.01 | | (41) $false % 86.52/12.02 | | % 86.52/12.02 | | CLOSE: (41) is inconsistent. % 86.52/12.02 | | % 86.52/12.02 | Case 2: % 86.52/12.02 | | % 86.52/12.02 | | (42) all_95_0 = all_86_0 % 86.52/12.02 | | % 86.52/12.02 | | BETA: splitting (28) gives: % 86.52/12.02 | | % 86.52/12.02 | | Case 1: % 86.52/12.02 | | | % 86.52/12.02 | | | (43) ~ (sdtlbdtrb0(xd, all_86_1) = all_90_0) % 86.52/12.02 | | | % 86.52/12.02 | | | PRED_UNIFY: (38), (43) imply: % 86.52/12.02 | | | (44) $false % 86.52/12.02 | | | % 86.52/12.02 | | | CLOSE: (44) is inconsistent. % 86.52/12.02 | | | % 86.52/12.02 | | Case 2: % 86.52/12.02 | | | % 86.52/12.02 | | | (45) all_90_0 = all_86_0 % 86.52/12.02 | | | % 86.52/12.02 | | | GROUND_INST: instantiating (26) with xp, simplifying with (6), (39) gives: % 86.52/12.02 | | | (46) ? [v0: $i] : (sdtlpdtrp0(xe, v0) = xp & $i(v0) & aElementOf0(v0, % 86.52/12.02 | | | all_95_0) & aElementOf0(v0, szNzAzT0)) % 86.52/12.02 | | | % 86.52/12.02 | | | DELTA: instantiating (46) with fresh symbol all_129_0 gives: % 86.52/12.02 | | | (47) sdtlpdtrp0(xe, all_129_0) = xp & $i(all_129_0) & % 86.52/12.02 | | | aElementOf0(all_129_0, all_95_0) & aElementOf0(all_129_0, % 86.52/12.02 | | | szNzAzT0) % 86.52/12.02 | | | % 86.52/12.02 | | | ALPHA: (47) implies: % 86.52/12.02 | | | (48) aElementOf0(all_129_0, all_95_0) % 86.52/12.02 | | | (49) $i(all_129_0) % 86.52/12.02 | | | (50) sdtlpdtrp0(xe, all_129_0) = xp % 86.52/12.02 | | | % 86.52/12.02 | | | REDUCE: (42), (48) imply: % 86.52/12.02 | | | (51) aElementOf0(all_129_0, all_86_0) % 86.52/12.02 | | | % 86.52/12.02 | | | GROUND_INST: instantiating (22) with all_129_0, simplifying with (49), % 86.52/12.02 | | | (50) gives: % 86.52/12.02 | | | (52) ~ aElementOf0(all_129_0, all_90_0) % 86.52/12.02 | | | % 86.52/12.02 | | | REDUCE: (45), (52) imply: % 86.52/12.02 | | | (53) ~ aElementOf0(all_129_0, all_86_0) % 86.52/12.02 | | | % 86.52/12.02 | | | PRED_UNIFY: (51), (53) imply: % 86.52/12.02 | | | (54) $false % 86.52/12.02 | | | % 86.52/12.02 | | | CLOSE: (54) is inconsistent. % 86.52/12.02 | | | % 86.52/12.02 | | End of split % 86.52/12.02 | | % 86.52/12.02 | End of split % 86.52/12.02 | % 86.52/12.02 End of proof % 86.52/12.02 % SZS output end Proof for theBenchmark % 86.52/12.02 % 86.52/12.02 11409ms %------------------------------------------------------------------------------