TSTP Solution File: NUM547+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM547+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 : n005.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 11:48:32 EDT 2023

% Result   : Theorem 84.05s 11.86s
% Output   : Proof 84.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n005.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 17:02:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.62  ________       _____
% 0.19/0.62  ___  __ \_________(_)________________________________
% 0.19/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62  
% 0.19/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62  (2023-06-19)
% 0.19/0.62  
% 0.19/0.62  (c) Philipp Rümmer, 2009-2023
% 0.19/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62                Amanda Stjerna.
% 0.19/0.62  Free software under BSD-3-Clause.
% 0.19/0.62  
% 0.19/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62  
% 0.19/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63  Running up to 7 provers in parallel.
% 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 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 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 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 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 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.58/1.26  Prover 1: Preprocessing ...
% 3.58/1.27  Prover 4: Preprocessing ...
% 3.58/1.31  Prover 6: Preprocessing ...
% 3.58/1.31  Prover 3: Preprocessing ...
% 3.58/1.31  Prover 5: Preprocessing ...
% 3.58/1.31  Prover 0: Preprocessing ...
% 3.58/1.31  Prover 2: Preprocessing ...
% 10.82/2.26  Prover 1: Constructing countermodel ...
% 10.82/2.26  Prover 3: Constructing countermodel ...
% 11.50/2.37  Prover 6: Proving ...
% 11.98/2.42  Prover 5: Constructing countermodel ...
% 11.98/2.43  Prover 2: Proving ...
% 15.74/2.91  Prover 4: Constructing countermodel ...
% 16.55/3.06  Prover 0: Proving ...
% 72.06/10.36  Prover 2: stopped
% 72.06/10.38  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.74/10.51  Prover 7: Preprocessing ...
% 74.46/10.67  Prover 7: Constructing countermodel ...
% 84.05/11.84  Prover 7: Found proof (size 47)
% 84.05/11.84  Prover 7: proved (1464ms)
% 84.05/11.84  Prover 6: stopped
% 84.05/11.85  Prover 3: stopped
% 84.05/11.85  Prover 0: stopped
% 84.05/11.85  Prover 1: stopped
% 84.05/11.85  Prover 4: stopped
% 84.05/11.86  Prover 5: stopped
% 84.05/11.86  
% 84.05/11.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 84.05/11.86  
% 84.05/11.87  % SZS output start Proof for theBenchmark
% 84.05/11.87  Assumptions after simplification:
% 84.05/11.87  ---------------------------------
% 84.05/11.87  
% 84.05/11.87    (mCountNFin_01)
% 84.21/11.88    $i(slcrc0) & ( ~ isCountable0(slcrc0) |  ~ aSet0(slcrc0))
% 84.21/11.88  
% 84.21/11.88    (mDefEmp)
% 84.21/11.88    $i(slcrc0) & aSet0(slcrc0) &  ! [v0: $i] : (v0 = slcrc0 |  ~ $i(v0) |  ~
% 84.21/11.88      aSet0(v0) |  ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) &  ! [v0: $i] : (
% 84.21/11.88      ~ $i(v0) |  ~ aElementOf0(v0, slcrc0))
% 84.21/11.88  
% 84.21/11.88    (mDefSeg)
% 84.21/11.90    $i(szNzAzT0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 84.21/11.90      (slbdtrb0(v0) = v1) |  ~ (szszuzczcdt0(v2) = v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 84.21/11.90      ~ $i(v0) |  ~ sdtlseqdt0(v3, v0) |  ~ aElementOf0(v2, szNzAzT0) |  ~
% 84.21/11.90      aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) &  ! [v0: $i] :  ! [v1: $i]
% 84.21/11.90    :  ! [v2: $i] :  ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) |  ~ (szszuzczcdt0(v2) =
% 84.21/11.91        v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2, v1) |  ~
% 84.21/11.91      aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) &  ! [v0: $i] :  ! [v1: $i]
% 84.21/11.91    :  ! [v2: $i] :  ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) |  ~ (szszuzczcdt0(v2) =
% 84.21/11.91        v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v2, v1) |  ~
% 84.21/11.91      aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) &  ! [v0: $i] :  !
% 84.21/11.91    [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (slbdtrb0(v0) = v1) |  ~ $i(v2) |  ~
% 84.21/11.91      $i(v0) |  ~ aElementOf0(v0, szNzAzT0) |  ~ aSet0(v2) |  ? [v3: $i] :  ? [v4:
% 84.21/11.91        $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) |  ~ aElementOf0(v3, szNzAzT0) |
% 84.21/11.91          (szszuzczcdt0(v3) = v4 & $i(v4) &  ~ sdtlseqdt0(v4, v0))) &
% 84.21/11.91        (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 84.21/11.91              v0) & aElementOf0(v3, szNzAzT0))))) &  ! [v0: $i] :  ! [v1: $i] : (
% 84.21/11.91      ~ (slbdtrb0(v0) = v1) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v0, szNzAzT0)
% 84.21/11.91      | aSet0(v1))
% 84.21/11.91  
% 84.21/11.91    (mDefSel)
% 84.21/11.91    $i(szNzAzT0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 84.21/11.91      $i] : (v4 = v1 |  ~ (slbdtsldtrb0(v0, v1) = v2) |  ~ (sbrdtbr0(v3) = v4) | 
% 84.21/11.91      ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~
% 84.21/11.91      aElementOf0(v1, szNzAzT0) |  ~ aSet0(v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 84.21/11.91    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) |  ~
% 84.21/11.91      (sbrdtbr0(v3) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 84.21/11.91      aElementOf0(v3, v2) |  ~ aElementOf0(v1, szNzAzT0) |  ~ aSet0(v0) |
% 84.21/11.91      aSubsetOf0(v3, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 84.21/11.91    : (v3 = v2 |  ~ (slbdtsldtrb0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~
% 84.21/11.91      $i(v0) |  ~ aElementOf0(v1, szNzAzT0) |  ~ aSet0(v3) |  ~ aSet0(v0) |  ?
% 84.21/11.91      [v4: $i] :  ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) |  ~
% 84.21/11.91          aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) &
% 84.21/11.91        (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4,
% 84.21/11.91              v0))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (
% 84.21/11.91      ~ (slbdtsldtrb0(v0, v1) = v2) |  ~ (sbrdtbr0(v3) = v1) |  ~ $i(v3) |  ~
% 84.21/11.91      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aSubsetOf0(v3, v0) |  ~ aElementOf0(v1,
% 84.21/11.91        szNzAzT0) |  ~ aSet0(v0) | aElementOf0(v3, v2)) &  ! [v0: $i] :  ! [v1:
% 84.21/11.91      $i] :  ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) |  ~ $i(v2) |  ~ $i(v1)
% 84.21/11.91      |  ~ $i(v0) |  ~ aElementOf0(v1, szNzAzT0) |  ~ aSet0(v0) | aSet0(v2))
% 84.21/11.91  
% 84.21/11.91    (mNATSet)
% 84.21/11.91    $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 84.21/11.91  
% 84.21/11.91    (mSegZero)
% 84.21/11.91    slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 84.21/11.91  
% 84.21/11.91    (mZeroNum)
% 84.21/11.91    $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 84.21/11.91  
% 84.21/11.91    (m__)
% 84.21/11.92    $i(xS) & $i(xk) &  ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) &  ! [v1:
% 84.21/11.92        $i] : ( ~ $i(v1) |  ~ aElementOf0(v1, v0)))
% 84.21/11.92  
% 84.21/11.92    (m__2202)
% 84.21/11.92    $i(xk) & $i(szNzAzT0) & aElementOf0(xk, szNzAzT0)
% 84.21/11.92  
% 84.21/11.92    (m__2202_02)
% 84.21/11.92     ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS)
% 84.21/11.92  
% 84.21/11.92    (m__2227)
% 84.21/11.92    $i(xT) & $i(xS) & $i(xk) & $i(slcrc0) &  ? [v0: $i] :  ? [v1: $i] : ( ~ (v0 =
% 84.21/11.92        slcrc0) & slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) &
% 84.21/11.92      $i(v0) & aSubsetOf0(v0, v1))
% 84.21/11.92  
% 84.21/11.92    (m__2256)
% 84.21/11.92    $i(xx) & $i(xS) & aElementOf0(xx, xS)
% 84.21/11.92  
% 84.21/11.92    (function-axioms)
% 84.21/11.92     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 84.21/11.92      (slbdtsldtrb0(v3, v2) = v1) |  ~ (slbdtsldtrb0(v3, v2) = v0)) &  ! [v0: $i]
% 84.21/11.92    :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) =
% 84.21/11.92        v1) |  ~ (sdtmndt0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 84.21/11.92      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3,
% 84.21/11.92          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 84.21/11.92      (slbdtrb0(v2) = v1) |  ~ (slbdtrb0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 84.21/11.92    ! [v2: $i] : (v1 = v0 |  ~ (szmzazxdt0(v2) = v1) |  ~ (szmzazxdt0(v2) = v0)) &
% 84.21/11.92     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (szmzizndt0(v2) = v1)
% 84.21/11.92      |  ~ (szmzizndt0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1
% 84.21/11.92      = v0 |  ~ (sbrdtbr0(v2) = v1) |  ~ (sbrdtbr0(v2) = v0)) &  ! [v0: $i] :  !
% 84.21/11.92    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (szszuzczcdt0(v2) = v1) |  ~
% 84.21/11.92      (szszuzczcdt0(v2) = v0))
% 84.21/11.92  
% 84.21/11.92  Further assumptions not needed in the proof:
% 84.21/11.92  --------------------------------------------
% 84.21/11.92  mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 84.21/11.92  mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 84.21/11.92  mDefDiff, mDefMax, mDefMin, mDefSub, mDiffCons, mEOfElem, mElmSort, mEmpFin,
% 84.21/11.92  mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, mIHSort, mLessASymm, mLessRefl,
% 84.21/11.92  mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatExtra, mNatNSucc,
% 84.21/11.92  mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSelCSet, mSelFSet, mSelNSet,
% 84.21/11.92  mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess,
% 84.21/11.92  mSuccNum, mZeroLess
% 84.21/11.92  
% 84.21/11.92  Those formulas are unsatisfiable:
% 84.21/11.92  ---------------------------------
% 84.21/11.92  
% 84.21/11.92  Begin of proof
% 84.21/11.92  | 
% 84.21/11.92  | ALPHA: (mDefEmp) implies:
% 84.21/11.92  |   (1)  aSet0(slcrc0)
% 84.21/11.92  |   (2)   ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, slcrc0))
% 84.21/11.92  |   (3)   ! [v0: $i] : (v0 = slcrc0 |  ~ $i(v0) |  ~ aSet0(v0) |  ? [v1: $i] :
% 84.21/11.92  |          ($i(v1) & aElementOf0(v1, v0)))
% 84.21/11.92  | 
% 84.21/11.92  | ALPHA: (mCountNFin_01) implies:
% 84.21/11.92  |   (4)   ~ isCountable0(slcrc0) |  ~ aSet0(slcrc0)
% 84.21/11.92  | 
% 84.21/11.92  | ALPHA: (mNATSet) implies:
% 84.21/11.92  |   (5)  aSet0(szNzAzT0)
% 84.21/11.92  |   (6)  isCountable0(szNzAzT0)
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (mZeroNum) implies:
% 84.21/11.93  |   (7)  aElementOf0(sz00, szNzAzT0)
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (mDefSeg) implies:
% 84.21/11.93  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (slbdtrb0(v0) =
% 84.21/11.93  |            v1) |  ~ $i(v2) |  ~ $i(v0) |  ~ aElementOf0(v0, szNzAzT0) |  ~
% 84.21/11.93  |          aSet0(v2) |  ? [v3: $i] :  ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3,
% 84.21/11.93  |                v2) |  ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 &
% 84.21/11.93  |                $i(v4) &  ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) |
% 84.21/11.93  |              (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) &
% 84.21/11.93  |                aElementOf0(v3, szNzAzT0)))))
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (mSegZero) implies:
% 84.21/11.93  |   (9)  slbdtrb0(sz00) = slcrc0
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (mDefSel) implies:
% 84.21/11.93  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) =
% 84.21/11.93  |             v2) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v1,
% 84.21/11.93  |             szNzAzT0) |  ~ aSet0(v0) | aSet0(v2))
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (m__2202) implies:
% 84.21/11.93  |   (11)  aElementOf0(xk, szNzAzT0)
% 84.21/11.93  |   (12)  $i(szNzAzT0)
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (m__2202_02) implies:
% 84.21/11.93  |   (13)  aSet0(xS)
% 84.21/11.93  |   (14)  $i(sz00)
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (m__2227) implies:
% 84.21/11.93  |   (15)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v0 = slcrc0) & slbdtsldtrb0(xT, xk) =
% 84.21/11.93  |           v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0,
% 84.21/11.93  |             v1))
% 84.21/11.93  | 
% 84.21/11.93  | ALPHA: (m__2256) implies:
% 84.21/11.93  |   (16)  aElementOf0(xx, xS)
% 84.49/11.93  |   (17)  $i(xx)
% 84.49/11.93  | 
% 84.49/11.93  | ALPHA: (m__) implies:
% 84.49/11.93  |   (18)  $i(xk)
% 84.49/11.93  |   (19)  $i(xS)
% 84.49/11.93  |   (20)   ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) &  ! [v1: $i] : ( ~
% 84.49/11.93  |             $i(v1) |  ~ aElementOf0(v1, v0)))
% 84.49/11.93  | 
% 84.49/11.93  | ALPHA: (function-axioms) implies:
% 84.49/11.93  |   (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 84.49/11.93  |           (slbdtsldtrb0(v3, v2) = v1) |  ~ (slbdtsldtrb0(v3, v2) = v0))
% 84.49/11.93  | 
% 84.49/11.93  | DELTA: instantiating (20) with fresh symbol all_53_0 gives:
% 84.49/11.93  |   (22)  slbdtsldtrb0(xS, xk) = all_53_0 & $i(all_53_0) &  ! [v0: $i] : ( ~
% 84.49/11.93  |           $i(v0) |  ~ aElementOf0(v0, all_53_0))
% 84.49/11.93  | 
% 84.49/11.93  | ALPHA: (22) implies:
% 84.49/11.93  |   (23)  slbdtsldtrb0(xS, xk) = all_53_0
% 84.49/11.93  |   (24)   ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_53_0))
% 84.49/11.93  | 
% 84.49/11.93  | DELTA: instantiating (15) with fresh symbols all_56_0, all_56_1 gives:
% 84.49/11.93  |   (25)   ~ (all_56_1 = slcrc0) & slbdtsldtrb0(xT, xk) = all_56_0 &
% 84.49/11.93  |         slbdtsldtrb0(xS, xk) = all_56_1 & $i(all_56_0) & $i(all_56_1) &
% 84.49/11.93  |         aSubsetOf0(all_56_1, all_56_0)
% 84.49/11.93  | 
% 84.49/11.93  | ALPHA: (25) implies:
% 84.49/11.93  |   (26)   ~ (all_56_1 = slcrc0)
% 84.49/11.93  |   (27)  $i(all_56_1)
% 84.49/11.93  |   (28)  slbdtsldtrb0(xS, xk) = all_56_1
% 84.49/11.93  | 
% 84.49/11.93  | BETA: splitting (4) gives:
% 84.49/11.93  | 
% 84.49/11.93  | Case 1:
% 84.49/11.93  | | 
% 84.49/11.93  | |   (29)   ~ isCountable0(slcrc0)
% 84.49/11.93  | | 
% 84.49/11.94  | | GROUND_INST: instantiating (21) with all_53_0, all_56_1, xk, xS, simplifying
% 84.49/11.94  | |              with (23), (28) gives:
% 84.49/11.94  | |   (30)  all_56_1 = all_53_0
% 84.49/11.94  | | 
% 84.49/11.94  | | PRED_UNIFY: (6), (29) imply:
% 84.49/11.94  | |   (31)   ~ (szNzAzT0 = slcrc0)
% 84.49/11.94  | | 
% 84.49/11.94  | | REDUCE: (26), (30) imply:
% 84.49/11.94  | |   (32)   ~ (all_53_0 = slcrc0)
% 84.49/11.94  | | 
% 84.49/11.94  | | REDUCE: (27), (30) imply:
% 84.49/11.94  | |   (33)  $i(all_53_0)
% 84.49/11.94  | | 
% 84.49/11.94  | | GROUND_INST: instantiating (3) with szNzAzT0, simplifying with (5), (12)
% 84.49/11.94  | |              gives:
% 84.49/11.94  | |   (34)  szNzAzT0 = slcrc0 |  ? [v0: $i] : ($i(v0) & aElementOf0(v0,
% 84.49/11.94  | |             szNzAzT0))
% 84.49/11.94  | | 
% 84.49/11.94  | | GROUND_INST: instantiating (2) with xx, simplifying with (17) gives:
% 84.49/11.94  | |   (35)   ~ aElementOf0(xx, slcrc0)
% 84.49/11.94  | | 
% 84.49/11.94  | | GROUND_INST: instantiating (8) with sz00, slcrc0, xS, simplifying with (7),
% 84.49/11.94  | |              (9), (13), (14), (19) gives:
% 84.49/11.94  | |   (36)  xS = slcrc0 |  ? [v0: $i] :  ? [v1: $i] : ($i(v0) & ( ~
% 84.49/11.94  | |             aElementOf0(v0, xS) |  ~ aElementOf0(v0, szNzAzT0) |
% 84.49/11.94  | |             (szszuzczcdt0(v0) = v1 & $i(v1) &  ~ sdtlseqdt0(v1, sz00))) &
% 84.49/11.94  | |           (aElementOf0(v0, xS) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 84.49/11.94  | |               sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0))))
% 84.49/11.94  | | 
% 84.49/11.94  | | GROUND_INST: instantiating (10) with xS, xk, all_53_0, simplifying with
% 84.49/11.94  | |              (11), (13), (18), (19), (23), (33) gives:
% 84.49/11.94  | |   (37)  aSet0(all_53_0)
% 84.49/11.94  | | 
% 84.49/11.94  | | BETA: splitting (34) gives:
% 84.49/11.94  | | 
% 84.49/11.94  | | Case 1:
% 84.49/11.94  | | | 
% 84.49/11.94  | | |   (38)  szNzAzT0 = slcrc0
% 84.49/11.94  | | | 
% 84.49/11.94  | | | REDUCE: (31), (38) imply:
% 84.49/11.94  | | |   (39)  $false
% 84.49/11.94  | | | 
% 84.49/11.94  | | | CLOSE: (39) is inconsistent.
% 84.49/11.94  | | | 
% 84.49/11.94  | | Case 2:
% 84.49/11.94  | | | 
% 84.49/11.94  | | | 
% 84.49/11.94  | | | PRED_UNIFY: (16), (35) imply:
% 84.49/11.94  | | |   (40)   ~ (xS = slcrc0)
% 84.49/11.94  | | | 
% 84.49/11.94  | | | BETA: splitting (36) gives:
% 84.49/11.94  | | | 
% 84.49/11.94  | | | Case 1:
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | |   (41)  xS = slcrc0
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | | REDUCE: (40), (41) imply:
% 84.49/11.94  | | | |   (42)  $false
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | | CLOSE: (42) is inconsistent.
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | Case 2:
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | | GROUND_INST: instantiating (3) with all_53_0, simplifying with (33),
% 84.49/11.94  | | | |              (37) gives:
% 84.49/11.94  | | | |   (43)  all_53_0 = slcrc0 |  ? [v0: $i] : ($i(v0) & aElementOf0(v0,
% 84.49/11.94  | | | |             all_53_0))
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | | BETA: splitting (43) gives:
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | | Case 1:
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | |   (44)  all_53_0 = slcrc0
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | | REDUCE: (32), (44) imply:
% 84.49/11.94  | | | | |   (45)  $false
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | | CLOSE: (45) is inconsistent.
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | Case 2:
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | |   (46)   ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_53_0))
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | | DELTA: instantiating (46) with fresh symbol all_146_0 gives:
% 84.49/11.94  | | | | |   (47)  $i(all_146_0) & aElementOf0(all_146_0, all_53_0)
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | | ALPHA: (47) implies:
% 84.49/11.94  | | | | |   (48)  aElementOf0(all_146_0, all_53_0)
% 84.49/11.94  | | | | |   (49)  $i(all_146_0)
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | | GROUND_INST: instantiating (24) with all_146_0, simplifying with (48),
% 84.49/11.94  | | | | |              (49) gives:
% 84.49/11.94  | | | | |   (50)  $false
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | | CLOSE: (50) is inconsistent.
% 84.49/11.94  | | | | | 
% 84.49/11.94  | | | | End of split
% 84.49/11.94  | | | | 
% 84.49/11.94  | | | End of split
% 84.49/11.94  | | | 
% 84.49/11.94  | | End of split
% 84.49/11.94  | | 
% 84.49/11.94  | Case 2:
% 84.49/11.94  | | 
% 84.49/11.95  | |   (51)   ~ aSet0(slcrc0)
% 84.49/11.95  | | 
% 84.49/11.95  | | PRED_UNIFY: (1), (51) imply:
% 84.49/11.95  | |   (52)  $false
% 84.49/11.95  | | 
% 84.49/11.95  | | CLOSE: (52) is inconsistent.
% 84.49/11.95  | | 
% 84.49/11.95  | End of split
% 84.49/11.95  | 
% 84.49/11.95  End of proof
% 84.49/11.95  % SZS output end Proof for theBenchmark
% 84.49/11.95  
% 84.49/11.95  11328ms
%------------------------------------------------------------------------------