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