TSTP Solution File: NUM568+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM568+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 : n024.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 11:48:40 EDT 2023
% Result : Theorem 20.61s 3.52s
% Output : Proof 31.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM568+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 15:26:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.23/1.33 Prover 4: Preprocessing ...
% 4.23/1.33 Prover 1: Preprocessing ...
% 4.94/1.36 Prover 6: Preprocessing ...
% 4.94/1.36 Prover 0: Preprocessing ...
% 4.94/1.36 Prover 3: Preprocessing ...
% 4.94/1.36 Prover 2: Preprocessing ...
% 4.94/1.36 Prover 5: Preprocessing ...
% 13.67/2.48 Prover 1: Constructing countermodel ...
% 14.24/2.55 Prover 6: Proving ...
% 14.24/2.56 Prover 3: Constructing countermodel ...
% 15.04/2.66 Prover 5: Proving ...
% 18.25/3.11 Prover 2: Proving ...
% 20.61/3.51 Prover 3: proved (2881ms)
% 20.61/3.51
% 20.61/3.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.61/3.52
% 20.61/3.52 Prover 2: stopped
% 20.61/3.52 Prover 6: stopped
% 21.42/3.52 Prover 5: stopped
% 21.42/3.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.42/3.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.42/3.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.42/3.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.75/3.70 Prover 7: Preprocessing ...
% 22.75/3.72 Prover 10: Preprocessing ...
% 22.75/3.73 Prover 11: Preprocessing ...
% 22.75/3.73 Prover 8: Preprocessing ...
% 23.75/3.82 Prover 4: Constructing countermodel ...
% 25.08/4.04 Prover 7: Constructing countermodel ...
% 25.78/4.05 Prover 8: Warning: ignoring some quantifiers
% 25.78/4.05 Prover 0: Proving ...
% 25.78/4.06 Prover 0: stopped
% 25.78/4.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 25.78/4.06 Prover 10: Constructing countermodel ...
% 25.78/4.07 Prover 8: Constructing countermodel ...
% 26.32/4.15 Prover 13: Preprocessing ...
% 27.77/4.34 Prover 10: Found proof (size 18)
% 27.77/4.34 Prover 10: proved (817ms)
% 27.77/4.34 Prover 7: stopped
% 27.77/4.34 Prover 1: stopped
% 27.77/4.34 Prover 8: stopped
% 27.77/4.35 Prover 4: stopped
% 28.76/4.49 Prover 13: Warning: ignoring some quantifiers
% 28.76/4.51 Prover 13: Constructing countermodel ...
% 28.76/4.53 Prover 13: stopped
% 30.89/4.98 Prover 11: Constructing countermodel ...
% 30.94/5.00 Prover 11: stopped
% 30.94/5.00
% 30.94/5.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.94/5.00
% 30.94/5.00 % SZS output start Proof for theBenchmark
% 31.03/5.01 Assumptions after simplification:
% 31.03/5.01 ---------------------------------
% 31.03/5.01
% 31.03/5.01 (mCountNFin_01)
% 31.07/5.02 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 31.07/5.02
% 31.07/5.02 (mDefEmp)
% 31.07/5.02 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 31.07/5.02 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 31.07/5.02 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 31.07/5.03
% 31.07/5.03 (mNatExtra)
% 31.07/5.06 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 31.07/5.06 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 31.07/5.06 aElementOf0(v1, szNzAzT0)))
% 31.07/5.06
% 31.07/5.06 (m__)
% 31.07/5.06 $i(xK) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) | ~ $i(v0)
% 31.07/5.06 | ~ aElementOf0(v0, szNzAzT0))
% 31.07/5.06
% 31.07/5.06 (m__3418)
% 31.07/5.06 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 31.07/5.06
% 31.07/5.06 (m__3462)
% 31.07/5.06 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 31.07/5.06
% 31.07/5.06 (m__3520)
% 31.07/5.06 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 31.07/5.06
% 31.07/5.06 Further assumptions not needed in the proof:
% 31.07/5.06 --------------------------------------------
% 31.07/5.06 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 31.07/5.07 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 31.07/5.07 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 31.07/5.07 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 31.07/5.07 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 31.07/5.07 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 31.07/5.07 mMinMin, mNATSet, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc,
% 31.07/5.07 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm,
% 31.07/5.07 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess,
% 31.07/5.07 mZeroNum, m__3291, m__3398, m__3435, m__3453
% 31.07/5.07
% 31.07/5.07 Those formulas are unsatisfiable:
% 31.07/5.07 ---------------------------------
% 31.07/5.07
% 31.07/5.07 Begin of proof
% 31.07/5.07 |
% 31.07/5.07 | ALPHA: (mDefEmp) implies:
% 31.07/5.07 | (1) aSet0(slcrc0)
% 31.07/5.07 |
% 31.07/5.07 | ALPHA: (mCountNFin_01) implies:
% 31.07/5.07 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 31.07/5.07 |
% 31.07/5.07 | ALPHA: (mNatExtra) implies:
% 31.07/5.07 | (3) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 31.07/5.07 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 31.07/5.07 | szNzAzT0)))
% 31.07/5.07 |
% 31.07/5.07 | ALPHA: (m__3418) implies:
% 31.07/5.07 | (4) aElementOf0(xK, szNzAzT0)
% 31.07/5.07 |
% 31.07/5.07 | ALPHA: (m__3520) implies:
% 31.07/5.07 | (5) ~ (xK = sz00)
% 31.07/5.07 |
% 31.07/5.07 | ALPHA: (m__) implies:
% 31.07/5.07 | (6) $i(xK)
% 31.07/5.07 | (7) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xK) | ~ $i(v0) | ~
% 31.07/5.07 | aElementOf0(v0, szNzAzT0))
% 31.07/5.07 |
% 31.07/5.07 | BETA: splitting (2) gives:
% 31.07/5.07 |
% 31.07/5.07 | Case 1:
% 31.07/5.07 | |
% 31.07/5.08 | | (8) ~ aSet0(slcrc0)
% 31.07/5.08 | |
% 31.07/5.08 | | PRED_UNIFY: (1), (8) imply:
% 31.07/5.08 | | (9) $false
% 31.07/5.08 | |
% 31.07/5.08 | | CLOSE: (9) is inconsistent.
% 31.07/5.08 | |
% 31.07/5.08 | Case 2:
% 31.07/5.08 | |
% 31.07/5.08 | |
% 31.07/5.08 | | GROUND_INST: instantiating (3) with xK, simplifying with (4), (6) gives:
% 31.07/5.08 | | (10) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 31.07/5.08 | | aElementOf0(v0, szNzAzT0))
% 31.07/5.08 | |
% 31.07/5.08 | | BETA: splitting (10) gives:
% 31.07/5.08 | |
% 31.07/5.08 | | Case 1:
% 31.07/5.08 | | |
% 31.07/5.08 | | | (11) xK = sz00
% 31.07/5.08 | | |
% 31.07/5.08 | | | REDUCE: (5), (11) imply:
% 31.07/5.08 | | | (12) $false
% 31.07/5.08 | | |
% 31.07/5.08 | | | CLOSE: (12) is inconsistent.
% 31.07/5.08 | | |
% 31.07/5.08 | | Case 2:
% 31.07/5.08 | | |
% 31.07/5.08 | | | (13) ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & aElementOf0(v0,
% 31.07/5.08 | | | szNzAzT0))
% 31.07/5.08 | | |
% 31.07/5.08 | | | DELTA: instantiating (13) with fresh symbol all_91_0 gives:
% 31.07/5.08 | | | (14) szszuzczcdt0(all_91_0) = xK & $i(all_91_0) & aElementOf0(all_91_0,
% 31.07/5.08 | | | szNzAzT0)
% 31.07/5.08 | | |
% 31.07/5.08 | | | ALPHA: (14) implies:
% 31.07/5.08 | | | (15) aElementOf0(all_91_0, szNzAzT0)
% 31.07/5.08 | | | (16) $i(all_91_0)
% 31.07/5.08 | | | (17) szszuzczcdt0(all_91_0) = xK
% 31.07/5.08 | | |
% 31.07/5.08 | | | GROUND_INST: instantiating (7) with all_91_0, simplifying with (15), (16),
% 31.07/5.08 | | | (17) gives:
% 31.07/5.08 | | | (18) $false
% 31.07/5.08 | | |
% 31.07/5.08 | | | CLOSE: (18) is inconsistent.
% 31.07/5.08 | | |
% 31.07/5.08 | | End of split
% 31.07/5.08 | |
% 31.07/5.08 | End of split
% 31.07/5.08 |
% 31.07/5.08 End of proof
% 31.07/5.09 % SZS output end Proof for theBenchmark
% 31.07/5.09
% 31.07/5.09 4476ms
%------------------------------------------------------------------------------