TSTP Solution File: NUM599+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM599+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 : n019.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 11:48:52 EDT 2023
% Result : Theorem 133.64s 18.56s
% Output : Proof 134.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM599+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n019.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 13:24:13 EDT 2023
% 0.13/0.34 % 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.
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.33/1.43 Prover 4: Preprocessing ...
% 4.33/1.43 Prover 1: Preprocessing ...
% 5.04/1.50 Prover 6: Preprocessing ...
% 5.04/1.50 Prover 2: Preprocessing ...
% 5.04/1.50 Prover 5: Preprocessing ...
% 5.04/1.50 Prover 0: Preprocessing ...
% 5.04/1.50 Prover 3: Preprocessing ...
% 15.05/2.88 Prover 1: Constructing countermodel ...
% 15.05/2.88 Prover 3: Constructing countermodel ...
% 15.05/2.90 Prover 6: Proving ...
% 15.05/2.94 Prover 5: Proving ...
% 17.38/3.14 Prover 2: Proving ...
% 20.92/3.66 Prover 4: Constructing countermodel ...
% 24.09/4.01 Prover 0: Proving ...
% 71.55/10.33 Prover 2: stopped
% 71.55/10.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 72.88/10.50 Prover 7: Preprocessing ...
% 75.52/10.82 Prover 7: Constructing countermodel ...
% 99.53/13.96 Prover 5: stopped
% 99.53/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.11/14.08 Prover 8: Preprocessing ...
% 102.29/14.37 Prover 8: Warning: ignoring some quantifiers
% 102.29/14.38 Prover 8: Constructing countermodel ...
% 114.46/15.98 Prover 1: stopped
% 114.46/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.41/16.08 Prover 9: Preprocessing ...
% 120.02/16.78 Prover 9: Constructing countermodel ...
% 128.73/17.88 Prover 6: stopped
% 128.73/17.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 129.71/18.03 Prover 10: Preprocessing ...
% 130.40/18.19 Prover 10: Constructing countermodel ...
% 133.64/18.55 Prover 10: Found proof (size 57)
% 133.64/18.55 Prover 10: proved (642ms)
% 133.64/18.55 Prover 0: stopped
% 133.64/18.55 Prover 8: stopped
% 133.64/18.55 Prover 4: stopped
% 133.64/18.55 Prover 9: stopped
% 133.64/18.55 Prover 3: stopped
% 133.64/18.56 Prover 7: stopped
% 133.64/18.56
% 133.64/18.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 133.64/18.56
% 133.64/18.57 % SZS output start Proof for theBenchmark
% 133.64/18.57 Assumptions after simplification:
% 133.64/18.57 ---------------------------------
% 133.64/18.57
% 133.64/18.57 (mImgCount)
% 134.34/18.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlcdtrc0(v0,
% 134.34/18.60 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 134.34/18.60 aFunction0(v0) | ~ aSubsetOf0(v2, v1) | ~ isCountable0(v2) |
% 134.34/18.60 isCountable0(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) &
% 134.34/18.60 sdtlpdtrp0(v0, v5) = v6 & sdtlpdtrp0(v0, v4) = v6 & $i(v6) & $i(v5) &
% 134.34/18.60 $i(v4) & aElementOf0(v5, v1) & aElementOf0(v4, v1)))
% 134.34/18.60
% 134.34/18.60 (mNatExtra)
% 134.34/18.60 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 134.34/18.60 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 134.34/18.60 aElementOf0(v1, szNzAzT0)))
% 134.34/18.60
% 134.34/18.60 (m__)
% 134.34/18.60 $i(xO) & ~ isCountable0(xO)
% 134.34/18.60
% 134.34/18.60 (m__3418)
% 134.34/18.60 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 134.34/18.60
% 134.34/18.61 (m__3462)
% 134.34/18.61 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 134.34/18.61
% 134.34/18.61 (m__3520)
% 134.34/18.61 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 134.34/18.61
% 134.34/18.61 (m__3821)
% 134.43/18.61 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 134.43/18.61 : (v1 = v0 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~
% 134.43/18.61 $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 134.43/18.61 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & szmzizndt0(v3) =
% 134.43/18.61 v5 & szmzizndt0(v2) = v4 & $i(v5) & $i(v4)))
% 134.43/18.61
% 134.43/18.61 (m__3965)
% 134.43/18.61 $i(xN) & $i(xk) & $i(xS) & $i(xK) & $i(szNzAzT0) & ? [v0: $i] :
% 134.43/18.61 (slbdtsldtrb0(xS, xK) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 134.43/18.61 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v2) | ~ (szmzizndt0(v2) = v3) |
% 134.43/18.61 ~ (sdtmndt0(v2, v3) = v4) | ~ $i(v1) | ~ aElementOf0(v1, szNzAzT0) | ?
% 134.43/18.61 [v5: $i] : (slbdtsldtrb0(v4, xk) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i]
% 134.43/18.61 : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | ~
% 134.43/18.61 aSet0(v6) | aElementOf0(v7, v0)))))
% 134.43/18.61
% 134.43/18.61 (m__4660)
% 134.45/18.61 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 134.45/18.61 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 134.45/18.61 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 134.45/18.61 szmzizndt0(v2) = v1 & $i(v2) & $i(v1)))
% 134.45/18.61
% 134.45/18.62 (m__4854)
% 134.45/18.62 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 134.45/18.62 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) &
% 134.45/18.62 aElementOf0(v0, xT))
% 134.45/18.62
% 134.45/18.62 (m__4891)
% 134.45/18.62 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 134.45/18.62 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) &
% 134.45/18.62 aSet0(xO))
% 134.45/18.62
% 134.45/18.62 (m__4930)
% 134.45/18.62 $i(xd) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 134.45/18.62 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSubsetOf0(v1, szNzAzT0) &
% 134.45/18.62 isCountable0(v1))
% 134.45/18.62
% 134.45/18.62 (function-axioms)
% 134.45/18.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 134.45/18.63 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 134.45/18.63 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 134.45/18.63 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 134.45/18.63 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 134.45/18.63 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 134.45/18.63 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 134.45/18.63 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 134.45/18.63 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 134.45/18.63 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 134.45/18.63 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 134.45/18.63 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 134.45/18.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 134.45/18.63 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 134.45/18.63 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 134.45/18.63 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 134.45/18.63 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 134.45/18.63 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 134.45/18.63 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 134.45/18.63 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 134.45/18.63 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 134.45/18.63 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 134.45/18.63 v0))
% 134.45/18.63
% 134.45/18.63 Further assumptions not needed in the proof:
% 134.45/18.63 --------------------------------------------
% 134.45/18.63 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 134.45/18.63 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 134.45/18.63 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 134.45/18.63 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 134.45/18.63 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 134.45/18.63 mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal,
% 134.45/18.63 mLessTrans, mMinMin, mNATSet, mNatNSucc, mNoScLessZr, mPttSet, mSegFin,
% 134.45/18.63 mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub,
% 134.45/18.63 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess,
% 134.45/18.63 mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3435, m__3453, m__3533,
% 134.45/18.63 m__3623, m__3671, m__3754, m__4151, m__4182, m__4331, m__4411, m__4618, m__4730,
% 134.45/18.63 m__4758
% 134.45/18.63
% 134.45/18.63 Those formulas are unsatisfiable:
% 134.45/18.63 ---------------------------------
% 134.45/18.63
% 134.45/18.63 Begin of proof
% 134.45/18.63 |
% 134.45/18.64 | ALPHA: (mNatExtra) implies:
% 134.45/18.64 | (1) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 134.45/18.64 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 134.45/18.64 | szNzAzT0)))
% 134.45/18.64 |
% 134.45/18.64 | ALPHA: (m__3418) implies:
% 134.45/18.64 | (2) aElementOf0(xK, szNzAzT0)
% 134.45/18.64 |
% 134.45/18.64 | ALPHA: (m__3520) implies:
% 134.45/18.64 | (3) ~ (xK = sz00)
% 134.45/18.64 |
% 134.45/18.64 | ALPHA: (m__3821) implies:
% 134.45/18.64 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 134.45/18.64 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1)
% 134.45/18.64 | | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 134.45/18.64 | szNzAzT0) | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) &
% 134.45/18.64 | szmzizndt0(v3) = v5 & szmzizndt0(v2) = v4 & $i(v5) & $i(v4)))
% 134.45/18.64 |
% 134.45/18.64 | ALPHA: (m__3965) implies:
% 134.45/18.64 | (5) $i(xK)
% 134.45/18.64 |
% 134.45/18.64 | ALPHA: (m__4660) implies:
% 134.45/18.64 | (6) aFunction0(xe)
% 134.45/18.64 | (7) szDzozmdt0(xe) = szNzAzT0
% 134.45/18.64 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) |
% 134.45/18.64 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2
% 134.45/18.64 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1)))
% 134.45/18.64 |
% 134.45/18.64 | ALPHA: (m__4854) implies:
% 134.45/18.64 | (9) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 134.45/18.64 | v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT))
% 134.45/18.64 |
% 134.45/18.64 | ALPHA: (m__4891) implies:
% 134.45/18.64 | (10) $i(xe)
% 134.45/18.64 | (11) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1)
% 134.45/18.65 | = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO))
% 134.45/18.65 |
% 134.45/18.65 | ALPHA: (m__4930) implies:
% 134.45/18.65 | (12) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 134.45/18.65 | = v1 & $i(v1) & $i(v0) & aSubsetOf0(v1, szNzAzT0) &
% 134.45/18.65 | isCountable0(v1))
% 134.45/18.65 |
% 134.45/18.65 | ALPHA: (m__) implies:
% 134.45/18.65 | (13) ~ isCountable0(xO)
% 134.45/18.65 |
% 134.45/18.65 | ALPHA: (function-axioms) implies:
% 134.45/18.65 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 134.45/18.65 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 134.45/18.65 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 134.45/18.65 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0))
% 134.45/18.65 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 134.45/18.65 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 134.45/18.65 |
% 134.45/18.65 | DELTA: instantiating (9) with fresh symbols all_78_0, all_78_1 gives:
% 134.45/18.65 | (17) szDzizrdt0(xd) = all_78_1 & sdtlbdtrb0(xd, all_78_1) = all_78_0 &
% 134.45/18.65 | $i(all_78_0) & $i(all_78_1) & isCountable0(all_78_0) &
% 134.45/18.65 | aElementOf0(all_78_1, xT)
% 134.45/18.65 |
% 134.45/18.65 | ALPHA: (17) implies:
% 134.45/18.65 | (18) sdtlbdtrb0(xd, all_78_1) = all_78_0
% 134.45/18.65 | (19) szDzizrdt0(xd) = all_78_1
% 134.45/18.65 |
% 134.45/18.65 | DELTA: instantiating (12) with fresh symbols all_80_0, all_80_1 gives:
% 134.45/18.65 | (20) szDzizrdt0(xd) = all_80_1 & sdtlbdtrb0(xd, all_80_1) = all_80_0 &
% 134.45/18.65 | $i(all_80_0) & $i(all_80_1) & aSubsetOf0(all_80_0, szNzAzT0) &
% 134.45/18.65 | isCountable0(all_80_0)
% 134.45/18.65 |
% 134.45/18.65 | ALPHA: (20) implies:
% 134.45/18.65 | (21) isCountable0(all_80_0)
% 134.45/18.65 | (22) aSubsetOf0(all_80_0, szNzAzT0)
% 134.45/18.65 | (23) $i(all_80_0)
% 134.45/18.65 | (24) sdtlbdtrb0(xd, all_80_1) = all_80_0
% 134.45/18.65 | (25) szDzizrdt0(xd) = all_80_1
% 134.45/18.65 |
% 134.45/18.65 | DELTA: instantiating (11) with fresh symbols all_82_0, all_82_1 gives:
% 134.45/18.65 | (26) szDzizrdt0(xd) = all_82_1 & sdtlcdtrc0(xe, all_82_0) = xO &
% 134.45/18.65 | sdtlbdtrb0(xd, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1) &
% 134.45/18.65 | aSet0(xO)
% 134.45/18.65 |
% 134.45/18.65 | ALPHA: (26) implies:
% 134.45/18.65 | (27) sdtlbdtrb0(xd, all_82_1) = all_82_0
% 134.45/18.65 | (28) sdtlcdtrc0(xe, all_82_0) = xO
% 134.45/18.65 | (29) szDzizrdt0(xd) = all_82_1
% 134.45/18.65 |
% 134.45/18.66 | GROUND_INST: instantiating (15) with all_80_1, all_82_1, xd, simplifying with
% 134.45/18.66 | (25), (29) gives:
% 134.45/18.66 | (30) all_82_1 = all_80_1
% 134.45/18.66 |
% 134.45/18.66 | GROUND_INST: instantiating (15) with all_78_1, all_82_1, xd, simplifying with
% 134.45/18.66 | (19), (29) gives:
% 134.45/18.66 | (31) all_82_1 = all_78_1
% 134.45/18.66 |
% 134.45/18.66 | COMBINE_EQS: (30), (31) imply:
% 134.45/18.66 | (32) all_80_1 = all_78_1
% 134.45/18.66 |
% 134.45/18.66 | REDUCE: (27), (31) imply:
% 134.45/18.66 | (33) sdtlbdtrb0(xd, all_78_1) = all_82_0
% 134.45/18.66 |
% 134.45/18.66 | REDUCE: (24), (32) imply:
% 134.45/18.66 | (34) sdtlbdtrb0(xd, all_78_1) = all_80_0
% 134.45/18.66 |
% 134.45/18.66 | GROUND_INST: instantiating (16) with all_78_0, all_82_0, all_78_1, xd,
% 134.45/18.66 | simplifying with (18), (33) gives:
% 134.45/18.66 | (35) all_82_0 = all_78_0
% 134.45/18.66 |
% 134.45/18.66 | GROUND_INST: instantiating (16) with all_80_0, all_82_0, all_78_1, xd,
% 134.45/18.66 | simplifying with (33), (34) gives:
% 134.45/18.66 | (36) all_82_0 = all_80_0
% 134.45/18.66 |
% 134.45/18.66 | COMBINE_EQS: (35), (36) imply:
% 134.45/18.66 | (37) all_80_0 = all_78_0
% 134.45/18.66 |
% 134.45/18.66 | REDUCE: (28), (35) imply:
% 134.45/18.66 | (38) sdtlcdtrc0(xe, all_78_0) = xO
% 134.45/18.66 |
% 134.45/18.66 | REDUCE: (23), (37) imply:
% 134.45/18.66 | (39) $i(all_78_0)
% 134.45/18.66 |
% 134.45/18.66 | REDUCE: (22), (37) imply:
% 134.45/18.66 | (40) aSubsetOf0(all_78_0, szNzAzT0)
% 134.45/18.66 |
% 134.45/18.66 | REDUCE: (21), (37) imply:
% 134.45/18.66 | (41) isCountable0(all_78_0)
% 134.45/18.66 |
% 134.45/18.66 | GROUND_INST: instantiating (1) with xK, simplifying with (2), (5) gives:
% 134.45/18.66 | (42) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 134.45/18.66 | aElementOf0(v0, szNzAzT0))
% 134.45/18.66 |
% 134.45/18.66 | GROUND_INST: instantiating (mImgCount) with xe, szNzAzT0, all_78_0, xO,
% 134.45/18.66 | simplifying with (6), (7), (10), (13), (38), (39), (40), (41)
% 134.45/18.66 | gives:
% 134.45/18.66 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 134.45/18.66 | sdtlpdtrp0(xe, v1) = v2 & sdtlpdtrp0(xe, v0) = v2 & $i(v2) & $i(v1)
% 134.45/18.66 | & $i(v0) & aElementOf0(v1, szNzAzT0) & aElementOf0(v0, szNzAzT0))
% 134.45/18.66 |
% 134.45/18.66 | DELTA: instantiating (43) with fresh symbols all_109_0, all_109_1, all_109_2
% 134.45/18.66 | gives:
% 134.45/18.66 | (44) ~ (all_109_1 = all_109_2) & sdtlpdtrp0(xe, all_109_1) = all_109_0 &
% 134.45/18.66 | sdtlpdtrp0(xe, all_109_2) = all_109_0 & $i(all_109_0) & $i(all_109_1)
% 134.45/18.66 | & $i(all_109_2) & aElementOf0(all_109_1, szNzAzT0) &
% 134.45/18.66 | aElementOf0(all_109_2, szNzAzT0)
% 134.45/18.66 |
% 134.45/18.66 | ALPHA: (44) implies:
% 134.45/18.66 | (45) ~ (all_109_1 = all_109_2)
% 134.45/18.66 | (46) aElementOf0(all_109_2, szNzAzT0)
% 134.45/18.66 | (47) aElementOf0(all_109_1, szNzAzT0)
% 134.45/18.66 | (48) $i(all_109_2)
% 134.45/18.66 | (49) $i(all_109_1)
% 134.45/18.66 | (50) sdtlpdtrp0(xe, all_109_2) = all_109_0
% 134.45/18.66 | (51) sdtlpdtrp0(xe, all_109_1) = all_109_0
% 134.45/18.66 |
% 134.45/18.66 | BETA: splitting (42) gives:
% 134.45/18.66 |
% 134.45/18.66 | Case 1:
% 134.45/18.66 | |
% 134.45/18.66 | | (52) xK = sz00
% 134.45/18.66 | |
% 134.45/18.66 | | REDUCE: (3), (52) imply:
% 134.45/18.66 | | (53) $false
% 134.45/18.67 | |
% 134.45/18.67 | | CLOSE: (53) is inconsistent.
% 134.45/18.67 | |
% 134.45/18.67 | Case 2:
% 134.45/18.67 | |
% 134.45/18.67 | |
% 134.45/18.67 | | GROUND_INST: instantiating (8) with all_109_2, all_109_0, simplifying with
% 134.45/18.67 | | (46), (48), (50) gives:
% 134.45/18.67 | | (54) ? [v0: $i] : (sdtlpdtrp0(xN, all_109_2) = v0 & szmzizndt0(v0) =
% 134.45/18.67 | | all_109_0 & $i(v0) & $i(all_109_0))
% 134.45/18.67 | |
% 134.45/18.67 | | GROUND_INST: instantiating (8) with all_109_1, all_109_0, simplifying with
% 134.45/18.67 | | (47), (49), (51) gives:
% 134.45/18.67 | | (55) ? [v0: $i] : (sdtlpdtrp0(xN, all_109_1) = v0 & szmzizndt0(v0) =
% 134.45/18.67 | | all_109_0 & $i(v0) & $i(all_109_0))
% 134.45/18.67 | |
% 134.45/18.67 | | DELTA: instantiating (55) with fresh symbol all_127_0 gives:
% 134.45/18.67 | | (56) sdtlpdtrp0(xN, all_109_1) = all_127_0 & szmzizndt0(all_127_0) =
% 134.45/18.67 | | all_109_0 & $i(all_127_0) & $i(all_109_0)
% 134.45/18.67 | |
% 134.45/18.67 | | ALPHA: (56) implies:
% 134.45/18.67 | | (57) szmzizndt0(all_127_0) = all_109_0
% 134.45/18.67 | | (58) sdtlpdtrp0(xN, all_109_1) = all_127_0
% 134.45/18.67 | |
% 134.45/18.67 | | DELTA: instantiating (54) with fresh symbol all_129_0 gives:
% 134.45/18.67 | | (59) sdtlpdtrp0(xN, all_109_2) = all_129_0 & szmzizndt0(all_129_0) =
% 134.45/18.67 | | all_109_0 & $i(all_129_0) & $i(all_109_0)
% 134.45/18.67 | |
% 134.45/18.67 | | ALPHA: (59) implies:
% 134.45/18.67 | | (60) szmzizndt0(all_129_0) = all_109_0
% 134.45/18.67 | | (61) sdtlpdtrp0(xN, all_109_2) = all_129_0
% 134.45/18.67 | |
% 134.45/18.67 | | GROUND_INST: instantiating (4) with all_109_1, all_109_2, all_127_0,
% 134.45/18.67 | | all_129_0, simplifying with (46), (47), (48), (49), (58), (61)
% 134.45/18.67 | | gives:
% 134.45/18.67 | | (62) all_109_1 = all_109_2 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 134.45/18.67 | | szmzizndt0(all_129_0) = v1 & szmzizndt0(all_127_0) = v0 & $i(v1) &
% 134.45/18.67 | | $i(v0))
% 134.45/18.67 | |
% 134.45/18.67 | | BETA: splitting (62) gives:
% 134.45/18.67 | |
% 134.45/18.67 | | Case 1:
% 134.45/18.67 | | |
% 134.45/18.67 | | | (63) all_109_1 = all_109_2
% 134.45/18.67 | | |
% 134.45/18.67 | | | REDUCE: (45), (63) imply:
% 134.45/18.67 | | | (64) $false
% 134.45/18.67 | | |
% 134.45/18.67 | | | CLOSE: (64) is inconsistent.
% 134.45/18.67 | | |
% 134.45/18.67 | | Case 2:
% 134.45/18.67 | | |
% 134.45/18.67 | | | (65) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & szmzizndt0(all_129_0)
% 134.45/18.67 | | | = v1 & szmzizndt0(all_127_0) = v0 & $i(v1) & $i(v0))
% 134.45/18.67 | | |
% 134.45/18.67 | | | DELTA: instantiating (65) with fresh symbols all_166_0, all_166_1 gives:
% 134.45/18.67 | | | (66) ~ (all_166_0 = all_166_1) & szmzizndt0(all_129_0) = all_166_0 &
% 134.45/18.67 | | | szmzizndt0(all_127_0) = all_166_1 & $i(all_166_0) & $i(all_166_1)
% 134.45/18.67 | | |
% 134.45/18.67 | | | ALPHA: (66) implies:
% 134.45/18.67 | | | (67) ~ (all_166_0 = all_166_1)
% 134.45/18.67 | | | (68) szmzizndt0(all_127_0) = all_166_1
% 134.45/18.67 | | | (69) szmzizndt0(all_129_0) = all_166_0
% 134.45/18.67 | | |
% 134.45/18.67 | | | GROUND_INST: instantiating (14) with all_109_0, all_166_1, all_127_0,
% 134.45/18.67 | | | simplifying with (57), (68) gives:
% 134.45/18.67 | | | (70) all_166_1 = all_109_0
% 134.45/18.67 | | |
% 134.45/18.67 | | | GROUND_INST: instantiating (14) with all_109_0, all_166_0, all_129_0,
% 134.45/18.67 | | | simplifying with (60), (69) gives:
% 134.45/18.67 | | | (71) all_166_0 = all_109_0
% 134.45/18.67 | | |
% 134.45/18.67 | | | REDUCE: (67), (70), (71) imply:
% 134.45/18.67 | | | (72) $false
% 134.45/18.67 | | |
% 134.45/18.67 | | | CLOSE: (72) is inconsistent.
% 134.45/18.67 | | |
% 134.45/18.67 | | End of split
% 134.45/18.67 | |
% 134.45/18.67 | End of split
% 134.45/18.67 |
% 134.45/18.67 End of proof
% 134.45/18.67 % SZS output end Proof for theBenchmark
% 134.45/18.68
% 134.45/18.68 18062ms
%------------------------------------------------------------------------------