TSTP Solution File: NUM550+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM550+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 : n023.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 11:48:33 EDT 2023

% Result   : Theorem 15.70s 2.85s
% Output   : Proof 26.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : NUM550+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.08/0.30  % Computer : n023.cluster.edu
% 0.08/0.30  % Model    : x86_64 x86_64
% 0.08/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30  % Memory   : 8042.1875MB
% 0.08/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30  % CPULimit : 300
% 0.08/0.30  % WCLimit  : 300
% 0.08/0.30  % DateTime : Fri Aug 25 13:29:57 EDT 2023
% 0.08/0.30  % CPUTime  : 
% 0.15/0.58  ________       _____
% 0.15/0.58  ___  __ \_________(_)________________________________
% 0.15/0.58  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.15/0.58  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.15/0.58  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.15/0.58  
% 0.15/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.58  (2023-06-19)
% 0.15/0.58  
% 0.15/0.58  (c) Philipp Rümmer, 2009-2023
% 0.15/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.58                Amanda Stjerna.
% 0.15/0.58  Free software under BSD-3-Clause.
% 0.15/0.58  
% 0.15/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.58  
% 0.15/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.60  Running up to 7 provers in parallel.
% 0.68/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.61  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.15/1.36  Prover 4: Preprocessing ...
% 4.15/1.36  Prover 1: Preprocessing ...
% 4.62/1.41  Prover 2: Preprocessing ...
% 4.62/1.41  Prover 3: Preprocessing ...
% 4.62/1.41  Prover 5: Preprocessing ...
% 4.62/1.41  Prover 0: Preprocessing ...
% 4.62/1.41  Prover 6: Preprocessing ...
% 14.93/2.73  Prover 2: Constructing countermodel ...
% 14.93/2.76  Prover 1: Constructing countermodel ...
% 14.93/2.78  Prover 3: Constructing countermodel ...
% 15.70/2.84  Prover 2: proved (2206ms)
% 15.70/2.84  
% 15.70/2.85  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.70/2.85  
% 15.70/2.86  Prover 3: stopped
% 15.70/2.87  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.70/2.91  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.25/2.94  Prover 5: Proving ...
% 16.25/2.95  Prover 5: stopped
% 16.25/2.98  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.96/3.01  Prover 6: Proving ...
% 16.96/3.02  Prover 6: stopped
% 16.96/3.03  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.96/3.07  Prover 8: Preprocessing ...
% 17.64/3.13  Prover 10: Preprocessing ...
% 18.37/3.19  Prover 7: Preprocessing ...
% 18.56/3.28  Prover 11: Preprocessing ...
% 21.61/3.62  Prover 10: Constructing countermodel ...
% 21.61/3.65  Prover 4: Constructing countermodel ...
% 21.61/3.65  Prover 7: Constructing countermodel ...
% 22.15/3.76  Prover 8: Warning: ignoring some quantifiers
% 22.87/3.77  Prover 0: Constructing countermodel ...
% 22.87/3.77  Prover 0: stopped
% 22.87/3.78  Prover 8: Constructing countermodel ...
% 22.87/3.79  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.36/3.84  Prover 10: Found proof (size 12)
% 23.36/3.84  Prover 10: proved (865ms)
% 23.36/3.84  Prover 4: stopped
% 23.36/3.84  Prover 8: stopped
% 23.36/3.84  Prover 1: stopped
% 23.36/3.84  Prover 7: stopped
% 23.36/3.90  Prover 13: Preprocessing ...
% 24.23/3.99  Prover 13: stopped
% 25.99/4.37  Prover 11: Constructing countermodel ...
% 26.20/4.42  Prover 11: stopped
% 26.20/4.42  
% 26.20/4.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.20/4.42  
% 26.20/4.42  % SZS output start Proof for theBenchmark
% 26.20/4.43  Assumptions after simplification:
% 26.20/4.43  ---------------------------------
% 26.20/4.43  
% 26.20/4.43    (mCardEmpty)
% 26.34/4.47    $i(sz00) & $i(slcrc0) &  ! [v0: $i] : (v0 = sz00 |  ~ (sbrdtbr0(slcrc0) = v0)
% 26.34/4.48      |  ~ aSet0(slcrc0)) &  ! [v0: $i] : (v0 = slcrc0 |  ~ (sbrdtbr0(v0) = sz00)
% 26.34/4.48      |  ~ $i(v0) |  ~ aSet0(v0))
% 26.34/4.48  
% 26.34/4.48    (m__)
% 26.34/4.48    xQ = slcrc0 & $i(slcrc0) &  ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0,
% 26.34/4.48        slcrc0))
% 26.34/4.48  
% 26.34/4.48    (m__2202_02)
% 26.34/4.48     ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS)
% 26.34/4.48  
% 26.34/4.48    (m__2270)
% 26.34/4.48    $i(xQ) & $i(xS) & $i(xk) &  ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 &
% 26.34/4.48      sbrdtbr0(xQ) = xk & $i(v0) & aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) &
% 26.34/4.48      aSet0(xQ) &  ! [v1: $i] : ( ~ $i(v1) |  ~ aElementOf0(v1, xQ) |
% 26.34/4.48        aElementOf0(v1, xS)))
% 26.34/4.48  
% 26.34/4.48  Further assumptions not needed in the proof:
% 26.34/4.48  --------------------------------------------
% 26.34/4.48  mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardNum, mCardS, mCardSeg,
% 26.34/4.48  mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons,
% 26.34/4.49  mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDefSub, mDiffCons,
% 26.34/4.49  mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH,
% 26.34/4.49  mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 26.34/4.49  mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess,
% 26.34/4.49  mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet,
% 26.34/4.49  mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum,
% 26.34/4.49  m__2202, m__2227, m__2256, m__2291
% 26.34/4.49  
% 26.34/4.49  Those formulas are unsatisfiable:
% 26.34/4.49  ---------------------------------
% 26.34/4.49  
% 26.34/4.49  Begin of proof
% 26.34/4.49  | 
% 26.34/4.49  | ALPHA: (mCardEmpty) implies:
% 26.34/4.49  |   (1)   ! [v0: $i] : (v0 = sz00 |  ~ (sbrdtbr0(slcrc0) = v0) |  ~
% 26.34/4.49  |          aSet0(slcrc0))
% 26.34/4.49  | 
% 26.34/4.49  | ALPHA: (m__2202_02) implies:
% 26.34/4.49  |   (2)   ~ (xk = sz00)
% 26.34/4.49  | 
% 26.34/4.49  | ALPHA: (m__2270) implies:
% 26.34/4.49  |   (3)   ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & sbrdtbr0(xQ) = xk & $i(v0) &
% 26.34/4.49  |          aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) & aSet0(xQ) &  ! [v1: $i] :
% 26.34/4.49  |          ( ~ $i(v1) |  ~ aElementOf0(v1, xQ) | aElementOf0(v1, xS)))
% 26.34/4.49  | 
% 26.34/4.49  | ALPHA: (m__) implies:
% 26.34/4.50  |   (4)  xQ = slcrc0
% 26.34/4.50  | 
% 26.34/4.50  | DELTA: instantiating (3) with fresh symbol all_54_0 gives:
% 26.34/4.50  |   (5)  slbdtsldtrb0(xS, xk) = all_54_0 & sbrdtbr0(xQ) = xk & $i(all_54_0) &
% 26.34/4.50  |        aSubsetOf0(xQ, xS) & aElementOf0(xQ, all_54_0) & aSet0(xQ) &  ! [v0:
% 26.34/4.50  |          $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, xQ) | aElementOf0(v0, xS))
% 26.34/4.50  | 
% 26.34/4.50  | ALPHA: (5) implies:
% 26.34/4.50  |   (6)  aSet0(xQ)
% 26.34/4.50  |   (7)  sbrdtbr0(xQ) = xk
% 26.34/4.50  | 
% 26.34/4.50  | REDUCE: (4), (7) imply:
% 26.34/4.50  |   (8)  sbrdtbr0(slcrc0) = xk
% 26.34/4.50  | 
% 26.34/4.50  | REDUCE: (4), (6) imply:
% 26.34/4.50  |   (9)  aSet0(slcrc0)
% 26.34/4.50  | 
% 26.34/4.50  | GROUND_INST: instantiating (1) with xk, simplifying with (8), (9) gives:
% 26.34/4.50  |   (10)  xk = sz00
% 26.34/4.50  | 
% 26.34/4.51  | REDUCE: (2), (10) imply:
% 26.34/4.51  |   (11)  $false
% 26.34/4.51  | 
% 26.34/4.51  | CLOSE: (11) is inconsistent.
% 26.34/4.51  | 
% 26.34/4.51  End of proof
% 26.34/4.51  % SZS output end Proof for theBenchmark
% 26.34/4.51  
% 26.34/4.51  3923ms
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