TSTP Solution File: NUM599+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------