TSTP Solution File: NUM605+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM605+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 : n004.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 11:48:55 EDT 2023
% Result : Theorem 32.91s 5.11s
% Output : Proof 41.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM605+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 08:36:38 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.16/1.35 Prover 4: Preprocessing ...
% 4.16/1.36 Prover 1: Preprocessing ...
% 5.05/1.41 Prover 5: Preprocessing ...
% 5.05/1.41 Prover 6: Preprocessing ...
% 5.05/1.41 Prover 2: Preprocessing ...
% 5.05/1.41 Prover 3: Preprocessing ...
% 5.05/1.41 Prover 0: Preprocessing ...
% 13.80/2.66 Prover 1: Constructing countermodel ...
% 14.95/2.77 Prover 6: Proving ...
% 14.95/2.78 Prover 3: Constructing countermodel ...
% 16.68/2.97 Prover 5: Proving ...
% 18.14/3.17 Prover 2: Proving ...
% 23.34/3.88 Prover 4: Constructing countermodel ...
% 26.91/4.32 Prover 0: Proving ...
% 32.91/5.10 Prover 2: proved (4494ms)
% 32.91/5.11
% 32.91/5.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.91/5.11
% 32.91/5.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 32.91/5.12 Prover 3: stopped
% 32.91/5.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 32.91/5.12 Prover 5: stopped
% 32.91/5.12 Prover 6: stopped
% 32.91/5.12 Prover 0: stopped
% 32.91/5.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 32.91/5.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 32.91/5.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 34.13/5.33 Prover 11: Preprocessing ...
% 34.13/5.34 Prover 8: Preprocessing ...
% 34.13/5.35 Prover 7: Preprocessing ...
% 34.13/5.35 Prover 13: Preprocessing ...
% 34.13/5.38 Prover 10: Preprocessing ...
% 36.79/5.61 Prover 7: Constructing countermodel ...
% 37.50/5.71 Prover 10: Constructing countermodel ...
% 37.50/5.73 Prover 8: Warning: ignoring some quantifiers
% 37.50/5.74 Prover 8: Constructing countermodel ...
% 38.16/5.86 Prover 13: Warning: ignoring some quantifiers
% 38.96/5.89 Prover 13: Constructing countermodel ...
% 40.48/6.12 Prover 10: Found proof (size 21)
% 40.48/6.12 Prover 10: proved (984ms)
% 40.48/6.12 Prover 8: stopped
% 40.48/6.12 Prover 7: stopped
% 40.48/6.12 Prover 1: stopped
% 40.48/6.12 Prover 13: stopped
% 40.48/6.12 Prover 4: stopped
% 41.43/6.35 Prover 11: Constructing countermodel ...
% 41.43/6.38 Prover 11: stopped
% 41.43/6.38
% 41.43/6.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.43/6.38
% 41.43/6.39 % SZS output start Proof for theBenchmark
% 41.80/6.40 Assumptions after simplification:
% 41.80/6.40 ---------------------------------
% 41.80/6.40
% 41.80/6.40 (mCardSeg)
% 41.80/6.44 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0)
% 41.80/6.44 | ~ aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 41.80/6.44
% 41.80/6.44 (mDefSel)
% 41.80/6.45 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 41.80/6.45 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) |
% 41.80/6.45 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 41.80/6.45 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 41.80/6.45 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~
% 41.80/6.45 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 41.80/6.45 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 41.80/6.45 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 41.80/6.45 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 41.80/6.45 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ?
% 41.80/6.45 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~
% 41.80/6.45 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) &
% 41.80/6.45 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4,
% 41.80/6.45 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 41.80/6.45 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~
% 41.80/6.45 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1,
% 41.80/6.45 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 41.80/6.45 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1)
% 41.80/6.45 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 41.80/6.45
% 41.80/6.45 (mSegZero)
% 41.80/6.45 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 41.80/6.45
% 41.80/6.45 (mZeroNum)
% 41.80/6.45 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 41.80/6.45
% 41.80/6.45 (m__)
% 41.80/6.45 xQ = slcrc0 & $i(slcrc0)
% 41.80/6.45
% 41.80/6.45 (m__3418)
% 41.80/6.45 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 41.80/6.45
% 41.80/6.45 (m__3462)
% 41.80/6.45 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 41.80/6.45
% 41.80/6.45 (m__3520)
% 41.80/6.46 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 41.80/6.46
% 41.80/6.46 (m__3623)
% 41.80/6.46 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 41.80/6.46 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 41.80/6.46 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2)
% 41.80/6.46 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 41.80/6.46 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v4: $i] : ? [v5: $i]
% 41.80/6.46 : (sdtlpdtrp0(xN, v4) = v5 & szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) &
% 41.80/6.46 aSubsetOf0(v5, v3) & isCountable0(v5)))
% 41.80/6.46
% 41.80/6.46 (m__4891)
% 41.80/6.46 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 41.80/6.46 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) &
% 41.80/6.46 aSet0(xO))
% 41.80/6.46
% 41.80/6.46 (m__5078)
% 41.80/6.46 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) &
% 41.80/6.46 aElementOf0(xQ, v0))
% 41.80/6.46
% 41.80/6.46 Further assumptions not needed in the proof:
% 41.80/6.46 --------------------------------------------
% 41.80/6.46 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 41.80/6.46 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons,
% 41.80/6.46 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg,
% 41.80/6.46 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 41.80/6.46 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 41.80/6.46 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 41.80/6.46 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 41.80/6.46 mSegSucc, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm,
% 41.80/6.46 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess,
% 41.80/6.46 m__3291, m__3398, m__3435, m__3453, m__3533, m__3671, m__3754, m__3821, m__3965,
% 41.80/6.46 m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854,
% 41.80/6.46 m__4908, m__4982, m__4998
% 41.80/6.46
% 41.80/6.46 Those formulas are unsatisfiable:
% 41.80/6.46 ---------------------------------
% 41.80/6.46
% 41.80/6.46 Begin of proof
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (mZeroNum) implies:
% 41.80/6.46 | (1) aElementOf0(sz00, szNzAzT0)
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (mSegZero) implies:
% 41.80/6.46 | (2) slbdtrb0(sz00) = slcrc0
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (mCardSeg) implies:
% 41.80/6.46 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~
% 41.80/6.46 | aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0)
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (mDefSel) implies:
% 41.80/6.46 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 41.80/6.46 | (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) | ~
% 41.80/6.46 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) |
% 41.80/6.46 | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0))
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (m__3418) implies:
% 41.80/6.46 | (5) aElementOf0(xK, szNzAzT0)
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (m__3520) implies:
% 41.80/6.46 | (6) ~ (xK = sz00)
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (m__3623) implies:
% 41.80/6.46 | (7) $i(sz00)
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (m__4891) implies:
% 41.80/6.46 | (8) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) =
% 41.80/6.46 | xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO))
% 41.80/6.46 |
% 41.80/6.46 | ALPHA: (m__5078) implies:
% 41.80/6.47 | (9) $i(xK)
% 41.80/6.47 | (10) $i(xO)
% 41.80/6.47 | (11) $i(xQ)
% 41.80/6.47 | (12) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) & aElementOf0(xQ,
% 41.80/6.47 | v0))
% 41.80/6.47 |
% 41.80/6.47 | ALPHA: (m__) implies:
% 41.80/6.47 | (13) xQ = slcrc0
% 41.80/6.47 |
% 41.80/6.47 | DELTA: instantiating (12) with fresh symbol all_76_0 gives:
% 41.80/6.47 | (14) slbdtsldtrb0(xO, xK) = all_76_0 & $i(all_76_0) & aElementOf0(xQ,
% 41.80/6.47 | all_76_0)
% 41.80/6.47 |
% 41.80/6.47 | ALPHA: (14) implies:
% 41.80/6.47 | (15) aElementOf0(xQ, all_76_0)
% 41.80/6.47 | (16) $i(all_76_0)
% 41.80/6.47 | (17) slbdtsldtrb0(xO, xK) = all_76_0
% 41.80/6.47 |
% 41.80/6.47 | DELTA: instantiating (8) with fresh symbols all_82_0, all_82_1 gives:
% 41.80/6.47 | (18) szDzizrdt0(xd) = all_82_1 & sdtlcdtrc0(xe, all_82_0) = xO &
% 41.80/6.47 | sdtlbdtrb0(xd, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1) &
% 41.80/6.47 | aSet0(xO)
% 41.80/6.47 |
% 41.80/6.47 | ALPHA: (18) implies:
% 41.80/6.47 | (19) aSet0(xO)
% 41.80/6.47 |
% 41.80/6.47 | REDUCE: (11), (13) imply:
% 41.80/6.47 | (20) $i(slcrc0)
% 41.80/6.47 |
% 41.80/6.47 | REDUCE: (13), (15) imply:
% 41.80/6.47 | (21) aElementOf0(slcrc0, all_76_0)
% 41.80/6.47 |
% 41.80/6.47 | GROUND_INST: instantiating (3) with sz00, slcrc0, simplifying with (1), (2),
% 41.80/6.47 | (7) gives:
% 41.80/6.47 | (22) sbrdtbr0(slcrc0) = sz00
% 41.80/6.47 |
% 41.80/6.47 | GROUND_INST: instantiating (4) with xO, xK, all_76_0, slcrc0, sz00,
% 41.80/6.47 | simplifying with (5), (9), (10), (16), (17), (19), (20), (21),
% 41.80/6.47 | (22) gives:
% 41.80/6.47 | (23) xK = sz00
% 41.80/6.47 |
% 41.80/6.47 | REDUCE: (6), (23) imply:
% 41.80/6.47 | (24) $false
% 41.80/6.47 |
% 41.80/6.47 | CLOSE: (24) is inconsistent.
% 41.80/6.47 |
% 41.80/6.47 End of proof
% 41.80/6.47 % SZS output end Proof for theBenchmark
% 41.80/6.47
% 41.80/6.47 5882ms
%------------------------------------------------------------------------------