TSTP Solution File: NUM618+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM618+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 : n011.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 11:49:00 EDT 2023
% Result : Theorem 26.80s 4.39s
% Output : Proof 53.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM618+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n011.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 17:02:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.25/1.65 Prover 1: Preprocessing ...
% 6.25/1.67 Prover 4: Preprocessing ...
% 6.85/1.72 Prover 0: Preprocessing ...
% 6.85/1.72 Prover 3: Preprocessing ...
% 6.85/1.72 Prover 6: Preprocessing ...
% 6.85/1.72 Prover 5: Preprocessing ...
% 6.85/1.72 Prover 2: Preprocessing ...
% 18.95/3.36 Prover 3: Constructing countermodel ...
% 18.95/3.36 Prover 6: Proving ...
% 18.95/3.38 Prover 1: Constructing countermodel ...
% 21.82/3.75 Prover 5: Proving ...
% 26.80/4.39 Prover 3: proved (3755ms)
% 26.80/4.39
% 26.80/4.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.80/4.39
% 26.80/4.39 Prover 5: stopped
% 26.80/4.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.80/4.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.80/4.39 Prover 6: stopped
% 26.80/4.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.77/4.69 Prover 10: Preprocessing ...
% 29.33/4.71 Prover 8: Preprocessing ...
% 29.83/4.77 Prover 7: Preprocessing ...
% 32.90/5.26 Prover 8: Warning: ignoring some quantifiers
% 33.52/5.27 Prover 8: Constructing countermodel ...
% 35.40/5.56 Prover 10: Constructing countermodel ...
% 39.36/6.03 Prover 7: Constructing countermodel ...
% 45.84/6.85 Prover 4: Constructing countermodel ...
% 50.72/7.49 Prover 2: Proving ...
% 50.72/7.52 Prover 2: stopped
% 50.72/7.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 50.72/7.52 Prover 10: Found proof (size 25)
% 50.72/7.52 Prover 10: proved (3124ms)
% 50.72/7.52 Prover 4: stopped
% 50.72/7.52 Prover 7: stopped
% 50.72/7.53 Prover 8: stopped
% 51.09/7.54 Prover 1: stopped
% 52.06/7.74 Prover 11: Preprocessing ...
% 53.18/7.94 Prover 11: stopped
% 53.39/8.01 Prover 0: Proving ...
% 53.39/8.04 Prover 0: stopped
% 53.39/8.04
% 53.39/8.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.39/8.04
% 53.39/8.04 % SZS output start Proof for theBenchmark
% 53.65/8.05 Assumptions after simplification:
% 53.65/8.05 ---------------------------------
% 53.65/8.05
% 53.65/8.05 (mCountNFin_01)
% 53.65/8.06 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 53.65/8.06
% 53.65/8.06 (mDefEmp)
% 53.65/8.06 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 53.65/8.06 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 53.65/8.06 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 53.71/8.06
% 53.71/8.06 (mDefSub)
% 53.71/8.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 53.71/8.07 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 53.71/8.07 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 53.71/8.07 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 53.71/8.07 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 53.71/8.07 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 53.71/8.07
% 53.71/8.07 (m__)
% 53.71/8.09 $i(xx) & $i(xe) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) |
% 53.71/8.09 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0))
% 53.71/8.09
% 53.71/8.09 (m__4891)
% 53.71/8.10 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 53.71/8.10 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 53.71/8.10 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & !
% 53.71/8.10 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 53.71/8.10 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 53.71/8.10 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 53.71/8.10 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4)
% 53.71/8.10 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3,
% 53.71/8.10 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~
% 53.71/8.10 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 53.71/8.10 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) &
% 53.71/8.10 aElementOf0(v4, v1))))
% 53.71/8.10
% 53.71/8.10 (m__4982)
% 53.71/8.10 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 53.71/8.10 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 53.71/8.10 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 53.71/8.10 aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 &
% 53.71/8.10 sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) & aElementOf0(v4,
% 53.71/8.10 szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ?
% 53.71/8.10 [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 & sdtlpdtrp0(xe, v3) = v2 & $i(v3) &
% 53.71/8.10 aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 53.71/8.10
% 53.71/8.10 (m__5208)
% 53.71/8.10 $i(xP) & $i(xO) & aSubsetOf0(xP, xO) & ! [v0: $i] : ( ~ $i(v0) | ~
% 53.71/8.10 aElementOf0(v0, xP) | aElementOf0(v0, xO))
% 53.71/8.10
% 53.71/8.10 (m__5270)
% 53.71/8.10 $i(xP) & $i(xO) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xO, xk) = v0 & $i(v0) &
% 53.71/8.10 aElementOf0(xP, v0))
% 53.71/8.10
% 53.71/8.10 (m__5348)
% 53.71/8.11 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 &
% 53.71/8.11 $i(v0) & aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx))
% 53.71/8.11
% 53.71/8.11 Further assumptions not needed in the proof:
% 53.71/8.11 --------------------------------------------
% 53.71/8.11 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 53.71/8.11 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 53.71/8.11 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 53.71/8.11 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 53.71/8.11 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 53.71/8.11 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 53.71/8.11 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 53.71/8.11 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 53.71/8.11 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 53.71/8.11 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462,
% 53.71/8.11 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182,
% 53.71/8.11 m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4908, m__4998,
% 53.71/8.11 m__5078, m__5093, m__5106, m__5116, m__5147, m__5164, m__5173, m__5182, m__5195,
% 53.71/8.11 m__5217, m__5309, m__5321, m__5365
% 53.71/8.11
% 53.71/8.11 Those formulas are unsatisfiable:
% 53.71/8.11 ---------------------------------
% 53.71/8.11
% 53.71/8.11 Begin of proof
% 53.71/8.11 |
% 53.71/8.11 | ALPHA: (mDefEmp) implies:
% 53.71/8.11 | (1) aSet0(slcrc0)
% 53.71/8.11 |
% 53.71/8.11 | ALPHA: (mCountNFin_01) implies:
% 53.71/8.11 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 53.71/8.11 |
% 53.71/8.11 | ALPHA: (mDefSub) implies:
% 53.71/8.11 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 53.71/8.11 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 53.71/8.11 | aSet0(v0) | aElementOf0(v2, v0))
% 53.71/8.11 |
% 53.71/8.11 | ALPHA: (m__4891) implies:
% 53.95/8.11 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 53.95/8.11 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 53.95/8.11 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] :
% 53.95/8.11 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) |
% 53.95/8.11 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 53.95/8.11 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 53.95/8.11 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 53.95/8.11 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 53.95/8.11 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~
% 53.95/8.11 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 53.95/8.11 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 53.95/8.11 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 53.95/8.11 | $i(v4) & aElementOf0(v4, v1))))
% 53.95/8.11 |
% 53.95/8.11 | ALPHA: (m__4982) implies:
% 53.95/8.11 | (5) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 53.95/8.11 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 53.95/8.11 | (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 53.95/8.11 | aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 &
% 53.95/8.12 | sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) &
% 53.95/8.12 | aElementOf0(v4, szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 53.95/8.12 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 &
% 53.95/8.12 | sdtlpdtrp0(xe, v3) = v2 & $i(v3) & aElementOf0(v3, v1) &
% 53.95/8.12 | aElementOf0(v3, szNzAzT0))))
% 53.95/8.12 |
% 53.95/8.12 | ALPHA: (m__5208) implies:
% 53.95/8.12 | (6) aSubsetOf0(xP, xO)
% 53.95/8.12 |
% 53.95/8.12 | ALPHA: (m__5270) implies:
% 53.95/8.12 | (7) $i(xO)
% 53.95/8.12 |
% 53.95/8.12 | ALPHA: (m__5348) implies:
% 53.95/8.12 | (8) $i(xP)
% 53.95/8.12 | (9) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & $i(v0) &
% 53.95/8.12 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx))
% 53.95/8.12 |
% 53.95/8.12 | ALPHA: (m__) implies:
% 53.95/8.12 | (10) $i(xx)
% 53.95/8.12 | (11) ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) | ~ $i(v0) | ~
% 53.95/8.12 | aElementOf0(v0, szNzAzT0))
% 53.95/8.12 |
% 53.95/8.12 | DELTA: instantiating (9) with fresh symbol all_87_0 gives:
% 53.95/8.12 | (12) ~ (all_87_0 = xx) & szmzizndt0(xQ) = all_87_0 & $i(all_87_0) &
% 53.95/8.12 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)
% 53.95/8.12 |
% 53.95/8.12 | ALPHA: (12) implies:
% 53.95/8.12 | (13) aElementOf0(xx, xP)
% 53.95/8.12 |
% 53.95/8.12 | DELTA: instantiating (5) with fresh symbols all_113_0, all_113_1 gives:
% 53.95/8.12 | (14) szDzizrdt0(xd) = all_113_1 & sdtlbdtrb0(xd, all_113_1) = all_113_0 &
% 53.95/8.12 | $i(all_113_0) & $i(all_113_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 53.95/8.12 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 53.95/8.12 | aElementOf0(v1, all_113_0) | ? [v2: $i] : (sdtlpdtrp0(xd, v2) =
% 53.95/8.12 | all_113_1 & sdtlpdtrp0(xe, v2) = v0 & $i(v2) & aElementOf0(v2,
% 53.95/8.12 | all_113_0) & aElementOf0(v2, szNzAzT0))) & ! [v0: $i] : ( ~
% 53.95/8.12 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xd, v1)
% 53.95/8.12 | = all_113_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1,
% 53.95/8.12 | all_113_0) & aElementOf0(v1, szNzAzT0)))
% 53.95/8.12 |
% 53.95/8.12 | ALPHA: (14) implies:
% 53.95/8.12 | (15) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] :
% 53.95/8.12 | (sdtlpdtrp0(xd, v1) = all_113_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) &
% 53.95/8.12 | aElementOf0(v1, all_113_0) & aElementOf0(v1, szNzAzT0)))
% 53.95/8.12 |
% 53.95/8.12 | DELTA: instantiating (4) with fresh symbols all_116_0, all_116_1, all_116_2
% 53.95/8.12 | gives:
% 53.95/8.12 | (16) szDzizrdt0(xd) = all_116_2 & sdtlcdtrc0(xe, all_116_1) = xO &
% 53.95/8.12 | sdtlbdtrb0(xd, all_116_2) = all_116_1 & szDzozmdt0(xd) = all_116_0 &
% 53.95/8.12 | $i(all_116_0) & $i(all_116_1) & $i(all_116_2) & aSet0(all_116_1) &
% 53.95/8.12 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_116_2 | ~
% 53.95/8.12 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 53.95/8.12 | all_116_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0)
% 53.95/8.12 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_116_1) |
% 53.95/8.12 | aElementOf0(v0, all_116_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 53.95/8.12 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 53.95/8.12 | aElementOf0(v1, all_116_1) | aElementOf0(v0, xO)) & ! [v0: $i] : (
% 53.95/8.12 | ~ (sdtlpdtrp0(xd, v0) = all_116_2) | ~ $i(v0) | ~ aElementOf0(v0,
% 53.95/8.12 | all_116_0) | aElementOf0(v0, all_116_1)) & ! [v0: $i] : ( ~
% 53.95/8.12 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1)
% 53.95/8.12 | = v0 & $i(v1) & aElementOf0(v1, all_116_1)))
% 53.95/8.12 |
% 53.95/8.12 | ALPHA: (16) implies:
% 53.95/8.12 | (17) aSet0(xO)
% 53.95/8.12 |
% 53.95/8.12 | BETA: splitting (2) gives:
% 53.95/8.12 |
% 53.95/8.13 | Case 1:
% 53.95/8.13 | |
% 53.95/8.13 | | (18) ~ aSet0(slcrc0)
% 53.95/8.13 | |
% 53.95/8.13 | | PRED_UNIFY: (1), (18) imply:
% 53.95/8.13 | | (19) $false
% 53.95/8.13 | |
% 53.95/8.13 | | CLOSE: (19) is inconsistent.
% 53.95/8.13 | |
% 53.95/8.13 | Case 2:
% 53.95/8.13 | |
% 53.95/8.13 | |
% 53.95/8.13 | | GROUND_INST: instantiating (3) with xO, xP, xx, simplifying with (6), (7),
% 53.95/8.13 | | (8), (10), (13), (17) gives:
% 53.95/8.13 | | (20) aElementOf0(xx, xO)
% 53.95/8.13 | |
% 53.95/8.13 | | GROUND_INST: instantiating (15) with xx, simplifying with (10), (20) gives:
% 53.95/8.13 | | (21) ? [v0: $i] : (sdtlpdtrp0(xd, v0) = all_113_1 & sdtlpdtrp0(xe, v0) =
% 53.95/8.13 | | xx & $i(v0) & aElementOf0(v0, all_113_0) & aElementOf0(v0,
% 53.95/8.13 | | szNzAzT0))
% 53.95/8.13 | |
% 53.95/8.13 | | DELTA: instantiating (21) with fresh symbol all_226_0 gives:
% 53.95/8.13 | | (22) sdtlpdtrp0(xd, all_226_0) = all_113_1 & sdtlpdtrp0(xe, all_226_0) =
% 53.95/8.13 | | xx & $i(all_226_0) & aElementOf0(all_226_0, all_113_0) &
% 53.95/8.13 | | aElementOf0(all_226_0, szNzAzT0)
% 53.95/8.13 | |
% 53.95/8.13 | | ALPHA: (22) implies:
% 53.95/8.13 | | (23) aElementOf0(all_226_0, szNzAzT0)
% 53.95/8.13 | | (24) $i(all_226_0)
% 53.95/8.13 | | (25) sdtlpdtrp0(xe, all_226_0) = xx
% 53.95/8.13 | |
% 53.95/8.13 | | GROUND_INST: instantiating (11) with all_226_0, simplifying with (23), (24),
% 53.95/8.13 | | (25) gives:
% 53.95/8.13 | | (26) $false
% 53.95/8.13 | |
% 53.95/8.13 | | CLOSE: (26) is inconsistent.
% 53.95/8.13 | |
% 53.95/8.13 | End of split
% 53.95/8.13 |
% 53.95/8.13 End of proof
% 53.95/8.13 % SZS output end Proof for theBenchmark
% 53.95/8.13
% 53.95/8.13 7519ms
%------------------------------------------------------------------------------