TSTP Solution File: NUM568+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM568+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 : n010.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 11:48:39 EDT 2023

% Result   : Theorem 20.45s 3.50s
% Output   : Proof 29.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM568+1 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri Aug 25 11:49:05 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.62  ________       _____
% 0.22/0.62  ___  __ \_________(_)________________________________
% 0.22/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.22/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.22/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62  
% 0.22/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62  (2023-06-19)
% 0.22/0.62  
% 0.22/0.62  (c) Philipp Rümmer, 2009-2023
% 0.22/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62                Amanda Stjerna.
% 0.22/0.62  Free software under BSD-3-Clause.
% 0.22/0.62  
% 0.22/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62  
% 0.22/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.64  Running up to 7 provers in parallel.
% 0.22/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.55/1.36  Prover 4: Preprocessing ...
% 4.55/1.36  Prover 1: Preprocessing ...
% 4.55/1.41  Prover 0: Preprocessing ...
% 4.55/1.41  Prover 6: Preprocessing ...
% 4.55/1.41  Prover 3: Preprocessing ...
% 4.55/1.41  Prover 5: Preprocessing ...
% 4.55/1.41  Prover 2: Preprocessing ...
% 12.92/2.55  Prover 6: Proving ...
% 12.92/2.55  Prover 1: Constructing countermodel ...
% 12.92/2.56  Prover 3: Constructing countermodel ...
% 12.92/2.59  Prover 5: Proving ...
% 15.20/2.85  Prover 2: Proving ...
% 18.35/3.24  Prover 0: Proving ...
% 18.95/3.30  Prover 4: Constructing countermodel ...
% 20.26/3.49  Prover 3: proved (2847ms)
% 20.26/3.50  
% 20.45/3.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.45/3.50  
% 20.45/3.51  Prover 2: stopped
% 20.45/3.51  Prover 6: stopped
% 20.45/3.51  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 20.45/3.51  Prover 5: stopped
% 20.45/3.51  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.45/3.52  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.45/3.52  Prover 0: stopped
% 20.45/3.52  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.60/3.52  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.35/3.69  Prover 11: Preprocessing ...
% 22.51/3.78  Prover 8: Preprocessing ...
% 22.51/3.78  Prover 10: Preprocessing ...
% 22.51/3.78  Prover 7: Preprocessing ...
% 22.51/3.79  Prover 13: Preprocessing ...
% 23.66/3.98  Prover 10: Constructing countermodel ...
% 24.34/4.03  Prover 7: Constructing countermodel ...
% 24.34/4.07  Prover 8: Warning: ignoring some quantifiers
% 24.34/4.08  Prover 8: Constructing countermodel ...
% 24.95/4.12  Prover 13: Warning: ignoring some quantifiers
% 24.95/4.15  Prover 13: Constructing countermodel ...
% 26.62/4.32  Prover 10: Found proof (size 13)
% 26.62/4.32  Prover 10: proved (807ms)
% 26.62/4.32  Prover 8: stopped
% 26.62/4.32  Prover 1: stopped
% 26.62/4.32  Prover 7: stopped
% 26.62/4.33  Prover 4: stopped
% 26.62/4.33  Prover 13: stopped
% 28.62/4.84  Prover 11: Constructing countermodel ...
% 28.89/4.88  Prover 11: stopped
% 28.89/4.88  
% 28.89/4.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.89/4.88  
% 28.89/4.89  % SZS output start Proof for theBenchmark
% 28.89/4.90  Assumptions after simplification:
% 28.89/4.90  ---------------------------------
% 28.89/4.90  
% 28.89/4.90    (mNatExtra)
% 28.89/4.94    $i(sz00) & $i(szNzAzT0) &  ! [v0: $i] : (v0 = sz00 |  ~ $i(v0) |  ~
% 28.89/4.94      aElementOf0(v0, szNzAzT0) |  ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 28.89/4.94        aElementOf0(v1, szNzAzT0)))
% 28.89/4.94  
% 28.89/4.94    (m__)
% 28.89/4.94    $i(xK) & $i(szNzAzT0) &  ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) |  ~ $i(v0)
% 28.89/4.94      |  ~ aElementOf0(v0, szNzAzT0))
% 28.89/4.94  
% 28.89/4.94    (m__3418)
% 28.89/4.94    $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 28.89/4.94  
% 28.89/4.94    (m__3462)
% 28.89/4.94     ~ (xK = sz00) & $i(xK) & $i(sz00)
% 28.89/4.94  
% 28.89/4.94    (m__3520)
% 28.89/4.95     ~ (xK = sz00) & $i(xK) & $i(sz00)
% 28.89/4.95  
% 28.89/4.95  Further assumptions not needed in the proof:
% 28.89/4.95  --------------------------------------------
% 28.89/4.95  mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 28.89/4.95  mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 28.89/4.95  mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 28.89/4.95  mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 28.89/4.95  mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 28.89/4.95  mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 28.89/4.95  mLessTotal, mLessTrans, mMinMin, mNATSet, mNatNSucc, mNoScLessZr, mPttSet,
% 28.89/4.95  mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet,
% 28.89/4.95  mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc,
% 28.89/4.95  mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3435, m__3453
% 28.89/4.95  
% 28.89/4.95  Those formulas are unsatisfiable:
% 28.89/4.95  ---------------------------------
% 28.89/4.95  
% 28.89/4.95  Begin of proof
% 28.89/4.95  | 
% 28.89/4.95  | ALPHA: (mNatExtra) implies:
% 28.89/4.95  |   (1)   ! [v0: $i] : (v0 = sz00 |  ~ $i(v0) |  ~ aElementOf0(v0, szNzAzT0) | 
% 28.89/4.95  |          ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 28.89/4.95  |              szNzAzT0)))
% 28.89/4.95  | 
% 28.89/4.95  | ALPHA: (m__3418) implies:
% 28.89/4.95  |   (2)  aElementOf0(xK, szNzAzT0)
% 28.89/4.95  | 
% 28.89/4.95  | ALPHA: (m__3520) implies:
% 28.89/4.96  |   (3)   ~ (xK = sz00)
% 28.89/4.96  | 
% 28.89/4.96  | ALPHA: (m__) implies:
% 28.89/4.96  |   (4)  $i(xK)
% 28.89/4.96  |   (5)   ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) |  ~ $i(v0) |  ~
% 28.89/4.96  |          aElementOf0(v0, szNzAzT0))
% 28.89/4.96  | 
% 28.89/4.96  | GROUND_INST: instantiating (1) with xK, simplifying with (2), (4) gives:
% 29.25/4.96  |   (6)  xK = sz00 |  ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 29.25/4.96  |          aElementOf0(v0, szNzAzT0))
% 29.25/4.96  | 
% 29.25/4.96  | BETA: splitting (6) gives:
% 29.25/4.96  | 
% 29.25/4.96  | Case 1:
% 29.25/4.96  | | 
% 29.25/4.96  | |   (7)  xK = sz00
% 29.25/4.96  | | 
% 29.25/4.96  | | REDUCE: (3), (7) imply:
% 29.25/4.96  | |   (8)  $false
% 29.25/4.96  | | 
% 29.25/4.96  | | CLOSE: (8) is inconsistent.
% 29.25/4.96  | | 
% 29.25/4.96  | Case 2:
% 29.25/4.96  | | 
% 29.25/4.97  | |   (9)   ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & aElementOf0(v0,
% 29.25/4.97  | |            szNzAzT0))
% 29.25/4.97  | | 
% 29.25/4.97  | | DELTA: instantiating (9) with fresh symbol all_85_0 gives:
% 29.25/4.97  | |   (10)  szszuzczcdt0(all_85_0) = xK & $i(all_85_0) & aElementOf0(all_85_0,
% 29.25/4.97  | |           szNzAzT0)
% 29.25/4.97  | | 
% 29.25/4.97  | | ALPHA: (10) implies:
% 29.25/4.97  | |   (11)  aElementOf0(all_85_0, szNzAzT0)
% 29.25/4.97  | |   (12)  $i(all_85_0)
% 29.25/4.97  | |   (13)  szszuzczcdt0(all_85_0) = xK
% 29.25/4.97  | | 
% 29.25/4.97  | | GROUND_INST: instantiating (5) with all_85_0, simplifying with (11), (12),
% 29.25/4.97  | |              (13) gives:
% 29.25/4.97  | |   (14)  $false
% 29.25/4.97  | | 
% 29.25/4.97  | | CLOSE: (14) is inconsistent.
% 29.25/4.97  | | 
% 29.25/4.97  | End of split
% 29.25/4.97  | 
% 29.25/4.97  End of proof
% 29.25/4.97  % SZS output end Proof for theBenchmark
% 29.25/4.97  
% 29.25/4.97  4345ms
%------------------------------------------------------------------------------