TSTP Solution File: NUM618+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM618+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 : n020.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 11:49:00 EDT 2023
% Result : Theorem 47.27s 7.01s
% Output : Proof 56.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM618+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 12:46:00 EDT 2023
% 0.13/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.68/1.41 Prover 1: Preprocessing ...
% 4.68/1.41 Prover 4: Preprocessing ...
% 4.68/1.45 Prover 0: Preprocessing ...
% 4.68/1.45 Prover 2: Preprocessing ...
% 4.68/1.45 Prover 5: Preprocessing ...
% 4.68/1.45 Prover 6: Preprocessing ...
% 4.68/1.45 Prover 3: Preprocessing ...
% 13.48/2.58 Prover 1: Constructing countermodel ...
% 13.48/2.58 Prover 3: Constructing countermodel ...
% 13.83/2.60 Prover 6: Proving ...
% 14.29/2.73 Prover 5: Proving ...
% 15.17/2.90 Prover 2: Proving ...
% 18.37/3.28 Prover 4: Constructing countermodel ...
% 20.74/3.56 Prover 0: Proving ...
% 47.27/7.01 Prover 3: proved (6365ms)
% 47.27/7.01
% 47.27/7.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.27/7.01
% 47.27/7.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 47.27/7.01 Prover 2: stopped
% 47.27/7.01 Prover 0: stopped
% 47.27/7.01 Prover 5: stopped
% 47.27/7.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 47.27/7.02 Prover 6: stopped
% 47.27/7.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 47.27/7.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 47.27/7.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 49.17/7.23 Prover 7: Preprocessing ...
% 49.17/7.29 Prover 8: Preprocessing ...
% 49.86/7.31 Prover 10: Preprocessing ...
% 49.86/7.33 Prover 11: Preprocessing ...
% 49.86/7.36 Prover 13: Preprocessing ...
% 50.51/7.47 Prover 7: Constructing countermodel ...
% 51.27/7.49 Prover 10: Constructing countermodel ...
% 52.13/7.64 Prover 8: Warning: ignoring some quantifiers
% 52.13/7.66 Prover 8: Constructing countermodel ...
% 53.16/7.74 Prover 13: Warning: ignoring some quantifiers
% 53.16/7.78 Prover 13: Constructing countermodel ...
% 55.34/8.03 Prover 10: Found proof (size 11)
% 55.34/8.03 Prover 10: proved (1013ms)
% 55.34/8.03 Prover 13: stopped
% 55.34/8.03 Prover 7: stopped
% 55.34/8.03 Prover 8: stopped
% 55.34/8.03 Prover 1: stopped
% 55.49/8.03 Prover 4: stopped
% 55.83/8.18 Prover 11: Constructing countermodel ...
% 56.09/8.21 Prover 11: stopped
% 56.09/8.21
% 56.09/8.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.09/8.21
% 56.09/8.21 % SZS output start Proof for theBenchmark
% 56.09/8.21 Assumptions after simplification:
% 56.09/8.21 ---------------------------------
% 56.09/8.21
% 56.09/8.21 (m__)
% 56.09/8.24 $i(xx) & $i(xe) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) |
% 56.09/8.24 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0))
% 56.09/8.24
% 56.09/8.24 (m__4982)
% 56.09/8.24 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 56.09/8.24 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 56.09/8.24 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) =
% 56.09/8.24 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 56.09/8.24
% 56.09/8.24 (m__5365)
% 56.09/8.24 $i(xx) & $i(xO) & $i(szNzAzT0) & aElementOf0(xx, xO) & aElementOf0(xx,
% 56.09/8.24 szNzAzT0)
% 56.09/8.24
% 56.09/8.24 Further assumptions not needed in the proof:
% 56.09/8.24 --------------------------------------------
% 56.09/8.24 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 56.09/8.24 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 56.09/8.24 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 56.09/8.24 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 56.09/8.24 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 56.09/8.24 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 56.09/8.24 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 56.09/8.24 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 56.09/8.24 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 56.09/8.24 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398,
% 56.09/8.24 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754,
% 56.09/8.24 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730,
% 56.09/8.24 m__4758, m__4854, m__4891, m__4908, m__4998, m__5078, m__5093, m__5106, m__5116,
% 56.09/8.24 m__5147, m__5164, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5309,
% 56.09/8.24 m__5321, m__5348
% 56.09/8.24
% 56.09/8.24 Those formulas are unsatisfiable:
% 56.09/8.24 ---------------------------------
% 56.09/8.24
% 56.09/8.24 Begin of proof
% 56.09/8.24 |
% 56.09/8.24 | ALPHA: (m__4982) implies:
% 56.09/8.25 | (1) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 56.09/8.25 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 56.09/8.25 | xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 & $i(v3) &
% 56.09/8.25 | aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 56.09/8.25 |
% 56.09/8.25 | ALPHA: (m__5365) implies:
% 56.09/8.25 | (2) aElementOf0(xx, xO)
% 56.09/8.25 |
% 56.09/8.25 | ALPHA: (m__) implies:
% 56.09/8.25 | (3) $i(xx)
% 56.09/8.25 | (4) ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) | ~ $i(v0) | ~
% 56.09/8.25 | aElementOf0(v0, szNzAzT0))
% 56.09/8.25 |
% 56.09/8.25 | DELTA: instantiating (1) with fresh symbols all_97_0, all_97_1 gives:
% 56.09/8.25 | (5) szDzizrdt0(xd) = all_97_1 & sdtlbdtrb0(xd, all_97_1) = all_97_0 &
% 56.09/8.25 | $i(all_97_0) & $i(all_97_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 56.09/8.25 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 & $i(v1)
% 56.09/8.25 | & aElementOf0(v1, all_97_0) & aElementOf0(v1, szNzAzT0)))
% 56.09/8.25 |
% 56.09/8.25 | ALPHA: (5) implies:
% 56.09/8.25 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] :
% 56.09/8.25 | (sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1, all_97_0) &
% 56.09/8.25 | aElementOf0(v1, szNzAzT0)))
% 56.09/8.25 |
% 56.09/8.25 | GROUND_INST: instantiating (6) with xx, simplifying with (2), (3) gives:
% 56.09/8.25 | (7) ? [v0: $i] : (sdtlpdtrp0(xe, v0) = xx & $i(v0) & aElementOf0(v0,
% 56.09/8.25 | all_97_0) & aElementOf0(v0, szNzAzT0))
% 56.09/8.25 |
% 56.09/8.25 | DELTA: instantiating (7) with fresh symbol all_123_0 gives:
% 56.09/8.25 | (8) sdtlpdtrp0(xe, all_123_0) = xx & $i(all_123_0) & aElementOf0(all_123_0,
% 56.09/8.25 | all_97_0) & aElementOf0(all_123_0, szNzAzT0)
% 56.09/8.25 |
% 56.09/8.25 | ALPHA: (8) implies:
% 56.09/8.25 | (9) aElementOf0(all_123_0, szNzAzT0)
% 56.09/8.25 | (10) $i(all_123_0)
% 56.09/8.25 | (11) sdtlpdtrp0(xe, all_123_0) = xx
% 56.09/8.25 |
% 56.09/8.25 | GROUND_INST: instantiating (4) with all_123_0, simplifying with (9), (10),
% 56.09/8.25 | (11) gives:
% 56.09/8.25 | (12) $false
% 56.09/8.26 |
% 56.09/8.26 | CLOSE: (12) is inconsistent.
% 56.09/8.26 |
% 56.09/8.26 End of proof
% 56.09/8.26 % SZS output end Proof for theBenchmark
% 56.09/8.26
% 56.09/8.26 7644ms
%------------------------------------------------------------------------------