TSTP Solution File: NUM609+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM609+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n008.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 11:48:57 EDT 2023

% Result   : Theorem 25.67s 4.21s
% Output   : Proof 44.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM609+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Aug 25 17:37:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.85/1.57  Prover 0: Preprocessing ...
% 6.25/1.64  Prover 5: Preprocessing ...
% 6.91/1.65  Prover 1: Preprocessing ...
% 6.91/1.68  Prover 6: Preprocessing ...
% 6.91/1.70  Prover 4: Preprocessing ...
% 6.91/1.70  Prover 2: Preprocessing ...
% 6.91/1.70  Prover 3: Preprocessing ...
% 19.54/3.43  Prover 1: Constructing countermodel ...
% 19.54/3.44  Prover 6: Proving ...
% 20.21/3.50  Prover 3: Constructing countermodel ...
% 21.28/3.80  Prover 5: Proving ...
% 25.67/4.21  Prover 3: proved (3563ms)
% 25.67/4.21  
% 25.67/4.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.67/4.21  
% 25.67/4.23  Prover 6: stopped
% 25.78/4.23  Prover 5: stopped
% 25.78/4.23  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.78/4.23  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.78/4.28  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.93/4.61  Prover 10: Preprocessing ...
% 26.93/4.62  Prover 8: Preprocessing ...
% 26.93/4.62  Prover 7: Preprocessing ...
% 32.24/5.16  Prover 8: Warning: ignoring some quantifiers
% 32.24/5.18  Prover 8: Constructing countermodel ...
% 34.92/5.49  Prover 10: Constructing countermodel ...
% 36.54/5.70  Prover 7: Constructing countermodel ...
% 37.87/5.99  Prover 10: Found proof (size 9)
% 37.87/5.99  Prover 10: proved (1758ms)
% 37.87/5.99  Prover 7: stopped
% 37.87/5.99  Prover 8: stopped
% 37.87/5.99  Prover 1: stopped
% 40.15/6.24  Prover 4: Constructing countermodel ...
% 40.67/6.27  Prover 4: stopped
% 43.08/6.83  Prover 2: Proving ...
% 43.55/6.85  Prover 2: stopped
% 43.74/6.92  Prover 0: Proving ...
% 43.74/6.94  Prover 0: stopped
% 43.74/6.94  
% 43.95/6.94  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.95/6.94  
% 43.95/6.95  % SZS output start Proof for theBenchmark
% 43.98/6.96  Assumptions after simplification:
% 43.98/6.96  ---------------------------------
% 43.98/6.96  
% 43.98/6.96    (m__)
% 43.98/6.97    $i(xP) & $i(xQ) &  ? [v0: $i] : ($i(v0) & aElementOf0(v0, xP) &  ~
% 43.98/6.97      aSubsetOf0(xP, xQ) &  ~ aElementOf0(v0, xQ))
% 43.98/6.97  
% 43.98/6.97    (m__5164)
% 44.21/7.01    $i(xP) & $i(xQ) &  ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 44.21/7.01      $i(v0) & aSet0(xP) &  ~ aElementOf0(v0, xP) &  ! [v1: $i] : (v1 = v0 |  ~
% 44.21/7.01        $i(v1) |  ~ aElementOf0(v1, xQ) |  ~ aElement0(v1) | aElementOf0(v1, xP))
% 44.21/7.01      &  ! [v1: $i] : ( ~ $i(v1) |  ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) &
% 44.21/7.02       ! [v1: $i] : ( ~ $i(v1) |  ~ aElementOf0(v1, xP) | aElement0(v1)) &  ! [v1:
% 44.21/7.02        $i] : ( ~ $i(v1) |  ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 44.21/7.02  
% 44.21/7.02  Further assumptions not needed in the proof:
% 44.21/7.02  --------------------------------------------
% 44.21/7.02  mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 44.21/7.02  mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 44.21/7.02  mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 44.21/7.02  mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 44.21/7.02  mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 44.21/7.02  mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 44.21/7.02  mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 44.21/7.02  mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 44.21/7.02  mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 44.21/7.02  mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398,
% 44.21/7.02  m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754,
% 44.21/7.02  m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730,
% 44.21/7.02  m__4758, m__4854, m__4891, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106,
% 44.21/7.02  m__5116, m__5147, m__5173, m__5182
% 44.21/7.02  
% 44.21/7.02  Those formulas are unsatisfiable:
% 44.21/7.02  ---------------------------------
% 44.21/7.02  
% 44.21/7.02  Begin of proof
% 44.21/7.02  | 
% 44.21/7.02  | ALPHA: (m__5164) implies:
% 44.21/7.03  |   (1)   ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 44.21/7.03  |          aSet0(xP) &  ~ aElementOf0(v0, xP) &  ! [v1: $i] : (v1 = v0 |  ~
% 44.21/7.03  |            $i(v1) |  ~ aElementOf0(v1, xQ) |  ~ aElement0(v1) |
% 44.21/7.03  |            aElementOf0(v1, xP)) &  ! [v1: $i] : ( ~ $i(v1) |  ~
% 44.21/7.03  |            aElementOf0(v1, xP) | aElementOf0(v1, xQ)) &  ! [v1: $i] : ( ~
% 44.21/7.03  |            $i(v1) |  ~ aElementOf0(v1, xP) | aElement0(v1)) &  ! [v1: $i] : (
% 44.21/7.03  |            ~ $i(v1) |  ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 44.21/7.03  | 
% 44.21/7.03  | ALPHA: (m__) implies:
% 44.21/7.03  |   (2)   ? [v0: $i] : ($i(v0) & aElementOf0(v0, xP) &  ~ aSubsetOf0(xP, xQ) & 
% 44.21/7.03  |          ~ aElementOf0(v0, xQ))
% 44.21/7.03  | 
% 44.21/7.03  | DELTA: instantiating (2) with fresh symbol all_80_0 gives:
% 44.21/7.03  |   (3)  $i(all_80_0) & aElementOf0(all_80_0, xP) &  ~ aSubsetOf0(xP, xQ) &  ~
% 44.21/7.03  |        aElementOf0(all_80_0, xQ)
% 44.21/7.03  | 
% 44.21/7.03  | ALPHA: (3) implies:
% 44.21/7.03  |   (4)   ~ aElementOf0(all_80_0, xQ)
% 44.21/7.03  |   (5)  aElementOf0(all_80_0, xP)
% 44.21/7.03  |   (6)  $i(all_80_0)
% 44.21/7.03  | 
% 44.21/7.03  | DELTA: instantiating (1) with fresh symbol all_93_0 gives:
% 44.21/7.04  |   (7)  szmzizndt0(xQ) = all_93_0 & sdtmndt0(xQ, all_93_0) = xP & $i(all_93_0)
% 44.21/7.04  |        & aSet0(xP) &  ~ aElementOf0(all_93_0, xP) &  ! [v0: any] : (v0 =
% 44.21/7.04  |          all_93_0 |  ~ $i(v0) |  ~ aElementOf0(v0, xQ) |  ~ aElement0(v0) |
% 44.21/7.04  |          aElementOf0(v0, xP)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0,
% 44.21/7.04  |            xP) | aElementOf0(v0, xQ)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 44.21/7.04  |          aElementOf0(v0, xP) | aElement0(v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 44.21/7.04  |          aElementOf0(v0, xQ) | sdtlseqdt0(all_93_0, v0))
% 44.21/7.04  | 
% 44.21/7.04  | ALPHA: (7) implies:
% 44.21/7.04  |   (8)   ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, xP) | aElementOf0(v0,
% 44.21/7.04  |            xQ))
% 44.21/7.04  | 
% 44.21/7.04  | GROUND_INST: instantiating (8) with all_80_0, simplifying with (4), (5), (6)
% 44.21/7.04  |              gives:
% 44.21/7.04  |   (9)  $false
% 44.21/7.04  | 
% 44.21/7.04  | CLOSE: (9) is inconsistent.
% 44.21/7.04  | 
% 44.21/7.04  End of proof
% 44.21/7.04  % SZS output end Proof for theBenchmark
% 44.21/7.04  
% 44.21/7.04  6427ms
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