%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM627+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 : n027.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 11:49:04 EDT 2023 % Result : Theorem 63.30s 9.24s % Output : Proof 285.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM627+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n027.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Aug 25 08:32:18 EDT 2023 % 0.15/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.41/1.48 Prover 1: Preprocessing ... % 4.41/1.49 Prover 4: Preprocessing ... % 4.41/1.53 Prover 2: Preprocessing ... % 4.41/1.53 Prover 0: Preprocessing ... % 4.41/1.53 Prover 6: Preprocessing ... % 4.41/1.53 Prover 5: Preprocessing ... % 4.41/1.54 Prover 3: Preprocessing ... % 15.54/2.92 Prover 3: Constructing countermodel ... % 16.42/3.03 Prover 1: Constructing countermodel ... % 16.42/3.04 Prover 6: Proving ... % 18.75/3.32 Prover 5: Proving ... % 19.60/3.42 Prover 2: Proving ... % 23.47/3.99 Prover 4: Constructing countermodel ... % 26.98/4.38 Prover 0: Proving ... % 63.30/9.24 Prover 3: proved (8593ms) % 63.30/9.24 % 63.30/9.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 63.30/9.24 % 63.30/9.25 Prover 2: stopped % 63.30/9.25 Prover 6: stopped % 64.17/9.26 Prover 0: stopped % 64.17/9.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 64.17/9.28 Prover 5: stopped % 64.17/9.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 64.17/9.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 64.17/9.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 64.38/9.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 65.85/9.48 Prover 10: Preprocessing ... % 65.85/9.51 Prover 8: Preprocessing ... % 65.85/9.53 Prover 7: Preprocessing ... % 65.85/9.55 Prover 13: Preprocessing ... % 66.63/9.59 Prover 11: Preprocessing ... % 67.10/9.67 Prover 10: Constructing countermodel ... % 67.10/9.73 Prover 7: Constructing countermodel ... % 68.16/9.85 Prover 8: Warning: ignoring some quantifiers % 68.16/9.86 Prover 8: Constructing countermodel ... % 69.64/10.00 Prover 13: Warning: ignoring some quantifiers % 70.05/10.04 Prover 13: Constructing countermodel ... % 73.24/10.55 Prover 11: Constructing countermodel ... % 97.36/13.64 Prover 13: stopped % 97.80/13.67 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 98.51/13.77 Prover 16: Preprocessing ... % 99.70/13.95 Prover 16: Warning: ignoring some quantifiers % 99.70/13.96 Prover 16: Constructing countermodel ... % 115.08/15.98 Prover 1: stopped % 115.08/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 116.20/16.15 Prover 19: Preprocessing ... % 119.01/16.48 Prover 19: Warning: ignoring some quantifiers % 119.01/16.49 Prover 19: Constructing countermodel ... % 136.34/18.83 Prover 16: stopped % 141.80/19.55 Prover 19: stopped % 192.83/27.97 Prover 4: stopped % 200.60/29.76 Prover 7: stopped % 246.32/41.04 Prover 11: stopped % 248.31/41.77 Prover 8: stopped % 285.62/75.02 Prover 10: Found proof (size 44) % 285.62/75.02 Prover 10: proved (65752ms) % 285.62/75.02 % 285.62/75.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 285.62/75.02 % 285.62/75.03 % SZS output start Proof for theBenchmark % 285.62/75.04 Assumptions after simplification: % 285.62/75.04 --------------------------------- % 285.62/75.04 % 285.62/75.04 (mLessTotal) % 285.62/75.09 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1) % 285.62/75.09 = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 285.62/75.09 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1)) % 285.62/75.09 % 285.62/75.09 (mSuccNum) % 285.62/75.09 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 285.62/75.09 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, % 285.62/75.09 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~ % 285.62/75.09 aElementOf0(v0, szNzAzT0)) % 285.62/75.09 % 285.62/75.10 (m__) % 285.62/75.10 $i(xx) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) = % 285.62/75.10 v1 & szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & ~ aElementOf0(xx, v1)) % 285.62/75.10 % 285.62/75.10 (m__3754) % 285.62/75.10 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 285.62/75.10 : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) | % 285.62/75.10 ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 285.62/75.10 aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 285.62/75.10 % 285.62/75.10 (m__5309) % 285.62/75.10 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 285.62/75.10 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, xn) = xp & % 285.62/75.10 $i(v1) & $i(v0) & aElementOf0(xn, v1) & aElementOf0(xn, szNzAzT0)) % 285.62/75.11 % 285.96/75.11 (m__5389) % 285.96/75.11 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 285.96/75.11 aElementOf0(xm, szNzAzT0) % 285.96/75.11 % 285.96/75.11 (m__5401) % 285.96/75.11 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & % 285.96/75.11 szmzizndt0(v0) = xx & $i(v0)) % 285.96/75.11 % 285.96/75.11 (m__5442) % 285.96/75.11 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 285.96/75.11 (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & % 285.96/75.11 $i(v2) & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v2)) % 285.96/75.11 % 285.96/75.11 (m__5461) % 285.96/75.11 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = % 285.96/75.11 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v1)) % 285.96/75.11 % 285.96/75.12 (function-axioms) % 285.96/75.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 285.96/75.13 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 285.96/75.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 285.96/75.13 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 285.96/75.13 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 285.96/75.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 285.96/75.13 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 285.96/75.13 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 285.96/75.13 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 285.96/75.13 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 285.96/75.13 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 285.96/75.13 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 285.96/75.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 285.96/75.13 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 285.96/75.13 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 285.96/75.13 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 285.96/75.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 285.96/75.13 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 285.96/75.13 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 285.96/75.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 285.96/75.13 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 285.96/75.13 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 285.96/75.13 v0)) % 285.96/75.13 % 285.96/75.13 Further assumptions not needed in the proof: % 285.96/75.13 -------------------------------------------- % 285.96/75.14 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 285.96/75.14 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 285.96/75.14 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 285.96/75.14 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 285.96/75.14 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 285.96/75.14 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 285.96/75.14 mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, % 285.96/75.14 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, % 285.96/75.14 mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, % 285.96/75.14 mSuccLess, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, % 285.96/75.14 m__3462, m__3520, m__3533, m__3623, m__3671, m__3821, m__3965, m__4151, m__4182, % 285.96/75.14 m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891, m__4908, % 285.96/75.14 m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, m__5147, m__5164, m__5173, % 285.96/75.14 m__5182, m__5195, m__5208, m__5217, m__5270, m__5321, m__5348, m__5365 % 285.96/75.14 % 285.96/75.14 Those formulas are unsatisfiable: % 285.96/75.14 --------------------------------- % 285.96/75.14 % 285.96/75.14 Begin of proof % 285.96/75.14 | % 285.96/75.14 | ALPHA: (mSuccNum) implies: % 285.96/75.14 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | % 285.96/75.14 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0)) % 285.96/75.14 | % 285.96/75.14 | ALPHA: (mLessTotal) implies: % 285.96/75.14 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1) = v2) | % 285.96/75.14 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 285.96/75.14 | aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1)) % 285.96/75.14 | % 285.96/75.14 | ALPHA: (m__3754) implies: % 285.96/75.15 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 285.96/75.15 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) % 285.96/75.15 | | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) | % 285.96/75.15 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3)) % 285.96/75.15 | % 285.96/75.15 | ALPHA: (m__5309) implies: % 285.96/75.15 | (4) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = % 285.96/75.15 | v1 & sdtlpdtrp0(xe, xn) = xp & $i(v1) & $i(v0) & aElementOf0(xn, v1) % 285.96/75.15 | & aElementOf0(xn, szNzAzT0)) % 285.96/75.15 | % 285.96/75.15 | ALPHA: (m__5389) implies: % 285.96/75.15 | (5) aElementOf0(xm, szNzAzT0) % 285.96/75.15 | % 285.96/75.15 | ALPHA: (m__5401) implies: % 285.96/75.15 | (6) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & $i(v0)) % 285.96/75.15 | % 285.96/75.15 | ALPHA: (m__5442) implies: % 285.96/75.15 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, v1) = v2 & % 285.96/75.15 | sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & $i(v2) & $i(v1) & % 285.96/75.15 | $i(v0) & ~ aSubsetOf0(v0, v2)) % 285.96/75.15 | % 285.96/75.15 | ALPHA: (m__5461) implies: % 285.96/75.15 | (8) $i(xm) % 285.96/75.15 | (9) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN, % 285.96/75.15 | xn) = v0 & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v1)) % 285.96/75.15 | % 285.96/75.15 | ALPHA: (m__) implies: % 285.96/75.15 | (10) $i(xn) % 285.96/75.15 | (11) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) = v1 & % 285.96/75.15 | szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & ~ aElementOf0(xx, v1)) % 285.96/75.15 | % 285.96/75.15 | ALPHA: (function-axioms) implies: % 285.96/75.16 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 285.96/75.16 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 285.96/75.16 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 285.96/75.16 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 285.96/75.16 | % 285.96/75.16 | DELTA: instantiating (6) with fresh symbol all_82_0 gives: % 285.96/75.16 | (14) sdtlpdtrp0(xN, xm) = all_82_0 & szmzizndt0(all_82_0) = xx & % 285.96/75.16 | $i(all_82_0) % 285.96/75.16 | % 285.96/75.16 | ALPHA: (14) implies: % 285.96/75.16 | (15) sdtlpdtrp0(xN, xm) = all_82_0 % 285.96/75.16 | % 285.96/75.16 | DELTA: instantiating (11) with fresh symbols all_90_0, all_90_1 gives: % 285.96/75.16 | (16) sdtlpdtrp0(xN, all_90_1) = all_90_0 & szszuzczcdt0(xn) = all_90_1 & % 285.96/75.16 | $i(all_90_0) & $i(all_90_1) & ~ aElementOf0(xx, all_90_0) % 285.96/75.16 | % 285.96/75.16 | ALPHA: (16) implies: % 285.96/75.16 | (17) szszuzczcdt0(xn) = all_90_1 % 285.96/75.16 | (18) sdtlpdtrp0(xN, all_90_1) = all_90_0 % 285.96/75.16 | % 285.96/75.16 | DELTA: instantiating (9) with fresh symbols all_92_0, all_92_1 gives: % 285.96/75.16 | (19) sdtlpdtrp0(xN, xm) = all_92_0 & sdtlpdtrp0(xN, xn) = all_92_1 & % 285.96/75.16 | $i(all_92_0) & $i(all_92_1) & ~ aSubsetOf0(all_92_1, all_92_0) % 285.96/75.16 | % 285.96/75.16 | ALPHA: (19) implies: % 285.96/75.16 | (20) ~ aSubsetOf0(all_92_1, all_92_0) % 285.96/75.16 | (21) sdtlpdtrp0(xN, xn) = all_92_1 % 285.96/75.16 | (22) sdtlpdtrp0(xN, xm) = all_92_0 % 285.96/75.16 | % 285.96/75.16 | DELTA: instantiating (4) with fresh symbols all_98_0, all_98_1 gives: % 285.96/75.16 | (23) szDzizrdt0(xd) = all_98_1 & sdtlbdtrb0(xd, all_98_1) = all_98_0 & % 285.96/75.16 | sdtlpdtrp0(xe, xn) = xp & $i(all_98_0) & $i(all_98_1) & % 285.96/75.16 | aElementOf0(xn, all_98_0) & aElementOf0(xn, szNzAzT0) % 285.96/75.16 | % 285.96/75.16 | ALPHA: (23) implies: % 285.96/75.16 | (24) aElementOf0(xn, szNzAzT0) % 285.96/75.16 | % 285.96/75.16 | DELTA: instantiating (7) with fresh symbols all_102_0, all_102_1, all_102_2 % 285.96/75.16 | gives: % 285.96/75.16 | (25) sdtlpdtrp0(xN, all_102_1) = all_102_0 & sdtlpdtrp0(xN, xm) = all_102_2 % 285.96/75.16 | & szszuzczcdt0(xn) = all_102_1 & $i(all_102_0) & $i(all_102_1) & % 285.96/75.16 | $i(all_102_2) & ~ aSubsetOf0(all_102_2, all_102_0) % 285.96/75.16 | % 285.96/75.16 | ALPHA: (25) implies: % 285.96/75.16 | (26) ~ aSubsetOf0(all_102_2, all_102_0) % 285.96/75.16 | (27) $i(all_102_1) % 285.96/75.17 | (28) szszuzczcdt0(xn) = all_102_1 % 285.96/75.17 | (29) sdtlpdtrp0(xN, xm) = all_102_2 % 285.96/75.17 | (30) sdtlpdtrp0(xN, all_102_1) = all_102_0 % 285.96/75.17 | % 285.96/75.17 | GROUND_INST: instantiating (12) with all_90_1, all_102_1, xn, simplifying with % 285.96/75.17 | (17), (28) gives: % 285.96/75.17 | (31) all_102_1 = all_90_1 % 285.96/75.17 | % 285.96/75.17 | GROUND_INST: instantiating (13) with all_92_0, all_102_2, xm, xN, simplifying % 285.96/75.17 | with (22), (29) gives: % 285.96/75.17 | (32) all_102_2 = all_92_0 % 285.96/75.17 | % 285.96/75.17 | GROUND_INST: instantiating (13) with all_82_0, all_102_2, xm, xN, simplifying % 285.96/75.17 | with (15), (29) gives: % 285.96/75.17 | (33) all_102_2 = all_82_0 % 285.96/75.17 | % 285.96/75.17 | COMBINE_EQS: (32), (33) imply: % 285.96/75.17 | (34) all_92_0 = all_82_0 % 285.96/75.17 | % 285.96/75.17 | SIMP: (34) implies: % 285.96/75.17 | (35) all_92_0 = all_82_0 % 285.96/75.17 | % 285.96/75.17 | REDUCE: (30), (31) imply: % 285.96/75.17 | (36) sdtlpdtrp0(xN, all_90_1) = all_102_0 % 285.96/75.17 | % 285.96/75.17 | REDUCE: (27), (31) imply: % 285.96/75.17 | (37) $i(all_90_1) % 285.96/75.17 | % 285.96/75.17 | REDUCE: (26), (33) imply: % 285.96/75.17 | (38) ~ aSubsetOf0(all_82_0, all_102_0) % 285.96/75.17 | % 285.96/75.17 | REDUCE: (20), (35) imply: % 285.96/75.17 | (39) ~ aSubsetOf0(all_92_1, all_82_0) % 285.96/75.17 | % 285.96/75.17 | GROUND_INST: instantiating (13) with all_90_0, all_102_0, all_90_1, xN, % 285.96/75.17 | simplifying with (18), (36) gives: % 285.96/75.17 | (40) all_102_0 = all_90_0 % 285.96/75.17 | % 285.96/75.17 | REDUCE: (38), (40) imply: % 285.96/75.17 | (41) ~ aSubsetOf0(all_82_0, all_90_0) % 285.96/75.17 | % 285.96/75.17 | GROUND_INST: instantiating (2) with xm, xn, all_90_1, simplifying with (5), % 285.96/75.17 | (8), (10), (17), (24) gives: % 285.96/75.17 | (42) sdtlseqdt0(all_90_1, xm) | sdtlseqdt0(xm, xn) % 285.96/75.17 | % 285.96/75.17 | GROUND_INST: instantiating (1) with xn, all_90_1, simplifying with (10), (17), % 285.96/75.17 | (24) gives: % 285.96/75.17 | (43) aElementOf0(all_90_1, szNzAzT0) % 285.96/75.17 | % 285.96/75.18 | BETA: splitting (42) gives: % 285.96/75.18 | % 285.96/75.18 | Case 1: % 285.96/75.18 | | % 285.96/75.18 | | (44) sdtlseqdt0(all_90_1, xm) % 285.96/75.18 | | % 285.96/75.18 | | GROUND_INST: instantiating (3) with xm, all_90_1, all_82_0, all_90_0, % 285.96/75.18 | | simplifying with (5), (8), (15), (18), (37), (41), (43), (44) % 285.96/75.18 | | gives: % 285.96/75.18 | | (45) $false % 285.96/75.18 | | % 285.96/75.18 | | CLOSE: (45) is inconsistent. % 285.96/75.18 | | % 285.96/75.18 | Case 2: % 285.96/75.18 | | % 285.96/75.18 | | (46) sdtlseqdt0(xm, xn) % 285.96/75.18 | | % 285.96/75.18 | | GROUND_INST: instantiating (3) with xn, xm, all_92_1, all_82_0, simplifying % 285.96/75.18 | | with (5), (8), (10), (15), (21), (24), (39), (46) gives: % 285.96/75.18 | | (47) $false % 285.96/75.18 | | % 285.96/75.18 | | CLOSE: (47) is inconsistent. % 285.96/75.18 | | % 285.96/75.18 | End of split % 285.96/75.18 | % 285.96/75.18 End of proof % 285.96/75.18 % SZS output end Proof for theBenchmark % 285.96/75.18 % 285.96/75.18 74568ms %------------------------------------------------------------------------------