TSTP Solution File: NUM594+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM594+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 : n020.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 11:48:50 EDT 2023
% Result : Theorem 89.12s 12.53s
% Output : Proof 89.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM594+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 : n020.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 15:42:30 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.27/1.35 Prover 1: Preprocessing ...
% 4.27/1.38 Prover 4: Preprocessing ...
% 4.27/1.40 Prover 3: Preprocessing ...
% 4.27/1.40 Prover 6: Preprocessing ...
% 4.27/1.40 Prover 5: Preprocessing ...
% 4.27/1.40 Prover 0: Preprocessing ...
% 4.27/1.40 Prover 2: Preprocessing ...
% 14.58/2.66 Prover 1: Constructing countermodel ...
% 14.58/2.69 Prover 3: Constructing countermodel ...
% 14.58/2.69 Prover 6: Proving ...
% 14.58/2.77 Prover 5: Proving ...
% 16.72/2.98 Prover 2: Proving ...
% 20.30/3.44 Prover 4: Constructing countermodel ...
% 20.30/3.50 Prover 0: Proving ...
% 72.80/10.34 Prover 2: stopped
% 72.80/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.62/10.46 Prover 7: Preprocessing ...
% 75.07/10.64 Prover 7: Constructing countermodel ...
% 89.12/12.51 Prover 7: Found proof (size 39)
% 89.12/12.51 Prover 7: proved (2173ms)
% 89.12/12.51 Prover 5: stopped
% 89.12/12.51 Prover 6: stopped
% 89.12/12.52 Prover 0: stopped
% 89.12/12.52 Prover 1: stopped
% 89.12/12.52 Prover 4: stopped
% 89.12/12.53 Prover 3: stopped
% 89.12/12.53
% 89.12/12.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 89.12/12.53
% 89.12/12.53 % SZS output start Proof for theBenchmark
% 89.12/12.54 Assumptions after simplification:
% 89.12/12.54 ---------------------------------
% 89.12/12.54
% 89.12/12.54 (mDefSImg)
% 89.60/12.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 89.60/12.57 $i] : ( ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (sdtlpdtrp0(v0, v5) = v4) | ~
% 89.60/12.57 (szDzozmdt0(v0) = v1) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 89.60/12.57 $i(v0) | ~ aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ aElementOf0(v5, v2)
% 89.60/12.57 | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 89.60/12.57 $i] : ! [v4: $i] : (v4 = v3 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~
% 89.60/12.57 (szDzozmdt0(v0) = v1) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~
% 89.60/12.57 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ aSet0(v4) | ? [v5: $i] : ?
% 89.60/12.57 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & ( ~ aElementOf0(v5, v4) | !
% 89.60/12.57 [v8: $i] : ( ~ (sdtlpdtrp0(v0, v8) = v5) | ~ $i(v8) | ~
% 89.60/12.57 aElementOf0(v8, v2))) & (aElementOf0(v5, v4) | (v7 = v5 &
% 89.60/12.57 sdtlpdtrp0(v0, v6) = v5 & aElementOf0(v6, v2))))) & ! [v0: $i] : !
% 89.60/12.57 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlcdtrc0(v0, v2) =
% 89.60/12.57 v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 89.60/12.57 $i(v0) | ~ aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ aElementOf0(v4, v3)
% 89.60/12.57 | ? [v5: $i] : (sdtlpdtrp0(v0, v5) = v4 & $i(v5) & aElementOf0(v5, v2))) &
% 89.60/12.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlcdtrc0(v0, v2)
% 89.60/12.57 = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 89.60/12.57 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | aSet0(v3))
% 89.60/12.57
% 89.60/12.57 (mDefSub)
% 89.60/12.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 89.60/12.57 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 89.60/12.57 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 89.60/12.57 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 89.60/12.57 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 89.60/12.57 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 89.60/12.57
% 89.60/12.57 (mNATSet)
% 89.60/12.58 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 89.60/12.58
% 89.60/12.58 (m__)
% 89.60/12.58 $i(xx) & $i(xd) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = xx) |
% 89.60/12.58 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0))
% 89.60/12.58
% 89.60/12.58 (m__4730)
% 89.60/12.58 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 89.60/12.58 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) |
% 89.60/12.58 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 89.60/12.58 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 89.60/12.58 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 89.60/12.58 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~
% 89.60/12.58 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~
% 89.60/12.58 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1)
% 89.60/12.58 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 89.60/12.58 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 89.60/12.58 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 89.60/12.58 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 89.60/12.58 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~
% 89.60/12.58 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) |
% 89.60/12.58 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 89.60/12.58 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v4 & sdtlpdtrp0(xC, v0) = v5
% 89.60/12.58 & sdtlpdtrp0(xN, v1) = v2 & slbdtsldtrb0(v2, xk) = v3 & $i(v5) & $i(v4) &
% 89.60/12.58 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v4 | ~
% 89.60/12.58 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v3) | ~
% 89.60/12.58 aSet0(v6))))
% 89.60/12.58
% 89.60/12.58 (m__4769)
% 89.60/12.58 $i(xd) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd)
% 89.60/12.58 = v0 & $i(v1) & $i(v0) & aSet0(v1))
% 89.60/12.58
% 89.60/12.58 (m__4781)
% 89.60/12.58 $i(xx) & $i(xd) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 89.60/12.58 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aElementOf0(xx, v1))
% 89.60/12.58
% 89.60/12.59 (function-axioms)
% 89.60/12.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 89.60/12.59 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 89.60/12.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 89.60/12.59 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 89.60/12.59 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 89.60/12.59 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 89.60/12.59 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 89.60/12.59 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 89.60/12.59 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 89.60/12.59 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 89.60/12.59 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 89.60/12.59 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 89.60/12.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 89.60/12.59 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 89.60/12.59 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 89.60/12.59 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 89.60/12.59 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 89.60/12.59 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 89.60/12.59 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 89.60/12.59 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 89.60/12.59 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 89.60/12.59 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 89.60/12.59 v0))
% 89.60/12.59
% 89.60/12.59 Further assumptions not needed in the proof:
% 89.60/12.59 --------------------------------------------
% 89.60/12.59 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 89.60/12.59 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 89.60/12.59 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSeg,
% 89.60/12.59 mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 89.60/12.59 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 89.60/12.59 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 89.60/12.59 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 89.60/12.59 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 89.60/12.59 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 89.60/12.59 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462,
% 89.60/12.59 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182,
% 89.60/12.59 m__4331, m__4411, m__4618, m__4660
% 89.60/12.59
% 89.60/12.59 Those formulas are unsatisfiable:
% 89.60/12.59 ---------------------------------
% 89.60/12.59
% 89.60/12.59 Begin of proof
% 89.60/12.59 |
% 89.60/12.59 | ALPHA: (mDefSub) implies:
% 89.60/12.59 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~
% 89.60/12.59 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) &
% 89.60/12.59 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 89.60/12.59 |
% 89.60/12.59 | ALPHA: (mNATSet) implies:
% 89.60/12.59 | (2) aSet0(szNzAzT0)
% 89.60/12.59 |
% 89.60/12.59 | ALPHA: (mDefSImg) implies:
% 89.60/12.59 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 89.60/12.59 | ~ (sdtlcdtrc0(v0, v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v4) |
% 89.60/12.59 | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ aFunction0(v0) | ~
% 89.60/12.59 | aSubsetOf0(v2, v1) | ~ aElementOf0(v4, v3) | ? [v5: $i] :
% 89.60/12.59 | (sdtlpdtrp0(v0, v5) = v4 & $i(v5) & aElementOf0(v5, v2)))
% 89.60/12.59 |
% 89.60/12.59 | ALPHA: (m__4730) implies:
% 89.60/12.60 | (4) aFunction0(xd)
% 89.60/12.60 | (5) szDzozmdt0(xd) = szNzAzT0
% 89.60/12.60 |
% 89.60/12.60 | ALPHA: (m__4769) implies:
% 89.60/12.60 | (6) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) =
% 89.60/12.60 | v0 & $i(v1) & $i(v0) & aSet0(v1))
% 89.60/12.60 |
% 89.60/12.60 | ALPHA: (m__4781) implies:
% 89.60/12.60 | (7) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) =
% 89.60/12.60 | v0 & $i(v1) & $i(v0) & aElementOf0(xx, v1))
% 89.60/12.60 |
% 89.60/12.60 | ALPHA: (m__) implies:
% 89.60/12.60 | (8) $i(xd)
% 89.60/12.60 | (9) $i(xx)
% 89.60/12.60 | (10) ! [v0: $i] : ( ~ (sdtlpdtrp0(xd, v0) = xx) | ~ $i(v0) | ~
% 89.60/12.60 | aElementOf0(v0, szNzAzT0))
% 89.60/12.60 |
% 89.60/12.60 | ALPHA: (function-axioms) implies:
% 89.60/12.60 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 89.60/12.60 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 89.60/12.60 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 89.60/12.60 | (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0))
% 89.60/12.60 |
% 89.60/12.60 | DELTA: instantiating (6) with fresh symbols all_77_0, all_77_1 gives:
% 89.60/12.60 | (13) sdtlcdtrc0(xd, all_77_1) = all_77_0 & szDzozmdt0(xd) = all_77_1 &
% 89.60/12.60 | $i(all_77_0) & $i(all_77_1) & aSet0(all_77_0)
% 89.60/12.60 |
% 89.60/12.60 | ALPHA: (13) implies:
% 89.60/12.60 | (14) $i(all_77_1)
% 89.60/12.60 | (15) szDzozmdt0(xd) = all_77_1
% 89.60/12.60 | (16) sdtlcdtrc0(xd, all_77_1) = all_77_0
% 89.60/12.60 |
% 89.60/12.60 | DELTA: instantiating (7) with fresh symbols all_79_0, all_79_1 gives:
% 89.60/12.60 | (17) sdtlcdtrc0(xd, all_79_1) = all_79_0 & szDzozmdt0(xd) = all_79_1 &
% 89.60/12.60 | $i(all_79_0) & $i(all_79_1) & aElementOf0(xx, all_79_0)
% 89.60/12.60 |
% 89.60/12.60 | ALPHA: (17) implies:
% 89.60/12.60 | (18) aElementOf0(xx, all_79_0)
% 89.60/12.60 | (19) $i(all_79_0)
% 89.60/12.60 | (20) szDzozmdt0(xd) = all_79_1
% 89.60/12.60 | (21) sdtlcdtrc0(xd, all_79_1) = all_79_0
% 89.60/12.60 |
% 89.60/12.60 | GROUND_INST: instantiating (11) with all_77_1, all_79_1, xd, simplifying with
% 89.60/12.60 | (15), (20) gives:
% 89.60/12.60 | (22) all_79_1 = all_77_1
% 89.60/12.60 |
% 89.60/12.60 | GROUND_INST: instantiating (11) with szNzAzT0, all_79_1, xd, simplifying with
% 89.60/12.60 | (5), (20) gives:
% 89.60/12.60 | (23) all_79_1 = szNzAzT0
% 89.60/12.60 |
% 89.60/12.60 | GROUND_INST: instantiating (12) with all_77_0, all_79_0, all_77_1, xd,
% 89.60/12.60 | simplifying with (16) gives:
% 89.60/12.60 | (24) all_79_0 = all_77_0 | ~ (sdtlcdtrc0(xd, all_77_1) = all_79_0)
% 89.60/12.60 |
% 89.60/12.60 | COMBINE_EQS: (22), (23) imply:
% 89.60/12.60 | (25) all_77_1 = szNzAzT0
% 89.60/12.60 |
% 89.60/12.60 | SIMP: (25) implies:
% 89.60/12.60 | (26) all_77_1 = szNzAzT0
% 89.60/12.60 |
% 89.60/12.60 | REDUCE: (21), (23) imply:
% 89.60/12.60 | (27) sdtlcdtrc0(xd, szNzAzT0) = all_79_0
% 89.60/12.60 |
% 89.60/12.60 | REDUCE: (14), (26) imply:
% 89.60/12.60 | (28) $i(szNzAzT0)
% 89.60/12.60 |
% 89.60/12.60 | BETA: splitting (24) gives:
% 89.60/12.60 |
% 89.60/12.60 | Case 1:
% 89.60/12.60 | |
% 89.60/12.60 | | (29) ~ (sdtlcdtrc0(xd, all_77_1) = all_79_0)
% 89.60/12.60 | |
% 89.60/12.61 | | REDUCE: (26), (29) imply:
% 89.60/12.61 | | (30) ~ (sdtlcdtrc0(xd, szNzAzT0) = all_79_0)
% 89.60/12.61 | |
% 89.60/12.61 | | PRED_UNIFY: (27), (30) imply:
% 89.60/12.61 | | (31) $false
% 89.60/12.61 | |
% 89.60/12.61 | | CLOSE: (31) is inconsistent.
% 89.60/12.61 | |
% 89.60/12.61 | Case 2:
% 89.60/12.61 | |
% 89.60/12.61 | | (32) all_79_0 = all_77_0
% 89.60/12.61 | |
% 89.60/12.61 | | REDUCE: (27), (32) imply:
% 89.60/12.61 | | (33) sdtlcdtrc0(xd, szNzAzT0) = all_77_0
% 89.60/12.61 | |
% 89.60/12.61 | | REDUCE: (19), (32) imply:
% 89.60/12.61 | | (34) $i(all_77_0)
% 89.60/12.61 | |
% 89.60/12.61 | | REDUCE: (18), (32) imply:
% 89.60/12.61 | | (35) aElementOf0(xx, all_77_0)
% 89.60/12.61 | |
% 89.60/12.61 | | GROUND_INST: instantiating (1) with szNzAzT0, szNzAzT0, simplifying with
% 89.60/12.61 | | (2), (28) gives:
% 89.60/12.61 | | (36) aSubsetOf0(szNzAzT0, szNzAzT0)
% 89.60/12.61 | |
% 89.60/12.61 | | GROUND_INST: instantiating (3) with xd, szNzAzT0, szNzAzT0, all_77_0, xx,
% 89.60/12.61 | | simplifying with (4), (5), (8), (9), (28), (33), (34), (35)
% 89.81/12.61 | | gives:
% 89.81/12.61 | | (37) ~ aSubsetOf0(szNzAzT0, szNzAzT0) | ? [v0: $i] : (sdtlpdtrp0(xd,
% 89.81/12.61 | | v0) = xx & $i(v0) & aElementOf0(v0, szNzAzT0))
% 89.81/12.61 | |
% 89.81/12.61 | | BETA: splitting (37) gives:
% 89.81/12.61 | |
% 89.81/12.61 | | Case 1:
% 89.81/12.61 | | |
% 89.81/12.61 | | | (38) ~ aSubsetOf0(szNzAzT0, szNzAzT0)
% 89.81/12.61 | | |
% 89.81/12.61 | | | PRED_UNIFY: (36), (38) imply:
% 89.81/12.61 | | | (39) $false
% 89.81/12.61 | | |
% 89.81/12.61 | | | CLOSE: (39) is inconsistent.
% 89.81/12.61 | | |
% 89.81/12.61 | | Case 2:
% 89.81/12.61 | | |
% 89.81/12.61 | | | (40) ? [v0: $i] : (sdtlpdtrp0(xd, v0) = xx & $i(v0) & aElementOf0(v0,
% 89.81/12.61 | | | szNzAzT0))
% 89.81/12.61 | | |
% 89.81/12.61 | | | DELTA: instantiating (40) with fresh symbol all_156_0 gives:
% 89.81/12.61 | | | (41) sdtlpdtrp0(xd, all_156_0) = xx & $i(all_156_0) &
% 89.81/12.61 | | | aElementOf0(all_156_0, szNzAzT0)
% 89.81/12.61 | | |
% 89.81/12.61 | | | ALPHA: (41) implies:
% 89.81/12.61 | | | (42) aElementOf0(all_156_0, szNzAzT0)
% 89.81/12.61 | | | (43) $i(all_156_0)
% 89.81/12.61 | | | (44) sdtlpdtrp0(xd, all_156_0) = xx
% 89.81/12.61 | | |
% 89.81/12.61 | | | GROUND_INST: instantiating (10) with all_156_0, simplifying with (42),
% 89.81/12.61 | | | (43), (44) gives:
% 89.81/12.61 | | | (45) $false
% 89.81/12.61 | | |
% 89.81/12.61 | | | CLOSE: (45) is inconsistent.
% 89.81/12.61 | | |
% 89.81/12.61 | | End of split
% 89.81/12.61 | |
% 89.81/12.61 | End of split
% 89.81/12.61 |
% 89.81/12.61 End of proof
% 89.81/12.61 % SZS output end Proof for theBenchmark
% 89.81/12.61
% 89.81/12.61 12009ms
%------------------------------------------------------------------------------