TSTP Solution File: NUM588+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM588+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 : n022.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 11:48:48 EDT 2023
% Result : Theorem 22.16s 3.84s
% Output : Proof 39.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM588+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.37 % Computer : n022.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Fri Aug 25 13:47:55 EDT 2023
% 0.13/0.37 % CPUTime :
% 0.22/0.67 ________ _____
% 0.22/0.67 ___ __ \_________(_)________________________________
% 0.22/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.67
% 0.22/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.67 (2023-06-19)
% 0.22/0.67
% 0.22/0.67 (c) Philipp Rümmer, 2009-2023
% 0.22/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.67 Amanda Stjerna.
% 0.22/0.67 Free software under BSD-3-Clause.
% 0.22/0.67
% 0.22/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.67
% 0.22/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.69 Running up to 7 provers in parallel.
% 0.22/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 5.78/1.60 Prover 1: Preprocessing ...
% 5.78/1.61 Prover 4: Preprocessing ...
% 5.78/1.64 Prover 0: Preprocessing ...
% 5.78/1.64 Prover 5: Preprocessing ...
% 5.78/1.64 Prover 6: Preprocessing ...
% 5.78/1.64 Prover 3: Preprocessing ...
% 5.78/1.64 Prover 2: Preprocessing ...
% 17.35/3.19 Prover 3: Constructing countermodel ...
% 17.35/3.19 Prover 1: Constructing countermodel ...
% 17.35/3.21 Prover 6: Proving ...
% 19.13/3.49 Prover 5: Proving ...
% 22.16/3.84 Prover 3: proved (3115ms)
% 22.16/3.84
% 22.16/3.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.16/3.84
% 22.16/3.84 Prover 5: stopped
% 22.16/3.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.16/3.85 Prover 6: stopped
% 22.16/3.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.16/3.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.21/4.19 Prover 2: Proving ...
% 24.21/4.20 Prover 2: stopped
% 24.21/4.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.21/4.21 Prover 7: Preprocessing ...
% 24.21/4.26 Prover 8: Preprocessing ...
% 24.21/4.30 Prover 10: Preprocessing ...
% 26.26/4.44 Prover 11: Preprocessing ...
% 28.55/4.77 Prover 8: Warning: ignoring some quantifiers
% 28.55/4.78 Prover 8: Constructing countermodel ...
% 29.34/4.85 Prover 10: Constructing countermodel ...
% 30.09/4.90 Prover 7: Constructing countermodel ...
% 33.55/5.39 Prover 10: Found proof (size 6)
% 33.55/5.39 Prover 10: proved (1520ms)
% 33.55/5.39 Prover 7: stopped
% 33.55/5.39 Prover 8: stopped
% 33.55/5.39 Prover 1: stopped
% 33.55/5.45 Prover 4: Constructing countermodel ...
% 34.18/5.48 Prover 4: stopped
% 35.26/5.85 Prover 0: Proving ...
% 36.02/5.86 Prover 0: stopped
% 38.69/6.54 Prover 11: Constructing countermodel ...
% 38.69/6.56 Prover 11: stopped
% 38.69/6.57
% 38.69/6.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.69/6.57
% 38.69/6.57 % SZS output start Proof for theBenchmark
% 38.69/6.58 Assumptions after simplification:
% 38.69/6.58 ---------------------------------
% 38.69/6.58
% 38.69/6.58 (mSubTrans)
% 38.69/6.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 38.69/6.59 ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1)
% 38.69/6.59 | ~ aSet0(v0) | aSubsetOf0(v0, v2))
% 38.69/6.59
% 38.69/6.59 (m__)
% 39.41/6.64 $i(xN) & $i(xk) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 39.41/6.64 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 39.41/6.64 : (sdtlpdtrp0(xN, v0) = v1 & slbdtsldtrb0(v5, xk) = v6 & slbdtsldtrb0(v3, xk)
% 39.41/6.64 = v4 & szmzizndt0(v1) = v2 & sbrdtbr0(v7) = xk & sdtmndt0(v1, v2) = v3 &
% 39.41/6.64 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 39.41/6.64 $i(v0) & aSubsetOf0(v7, v5) & aSubsetOf0(v5, v3) & isCountable0(v5) &
% 39.41/6.64 aElementOf0(v8, v7) & aElementOf0(v7, v6) & aElementOf0(v2, v1) &
% 39.41/6.64 aElementOf0(v0, szNzAzT0) & aSet0(v7) & aSet0(v5) & aSet0(v3) & ~
% 39.41/6.64 aSubsetOf0(v7, v3) & ~ aElementOf0(v8, v3) & ~ aElementOf0(v7, v4) & ~
% 39.41/6.64 aElementOf0(v2, v3) & ! [v9: $i] : (v9 = v2 | ~ $i(v9) | ~
% 39.41/6.64 aElementOf0(v9, v1) | ~ aElement0(v9) | aElementOf0(v9, v3)) & ! [v9:
% 39.41/6.64 $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v7) | aElementOf0(v9, v5)) & ! [v9:
% 39.41/6.64 $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v5) | aElementOf0(v9, v3)) & ! [v9:
% 39.41/6.64 $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v3) | aElementOf0(v9, v1)) & ! [v9:
% 39.41/6.64 $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v3) | aElement0(v9)) & ! [v9: $i] :
% 39.41/6.64 ( ~ $i(v9) | ~ aElementOf0(v9, v1) | sdtlseqdt0(v2, v9)))
% 39.41/6.64
% 39.41/6.64 Further assumptions not needed in the proof:
% 39.41/6.64 --------------------------------------------
% 39.41/6.64 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 39.41/6.64 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 39.41/6.64 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 39.41/6.64 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 39.41/6.64 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 39.41/6.64 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 39.41/6.64 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 39.41/6.64 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 39.41/6.64 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSuccEquSucc,
% 39.41/6.64 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435,
% 39.41/6.64 m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965,
% 39.41/6.64 m__4151, m__4182
% 39.41/6.64
% 39.41/6.64 Those formulas are unsatisfiable:
% 39.41/6.64 ---------------------------------
% 39.41/6.64
% 39.41/6.64 Begin of proof
% 39.41/6.64 |
% 39.41/6.64 | ALPHA: (m__) implies:
% 39.62/6.65 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 39.62/6.65 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtlpdtrp0(xN,
% 39.62/6.65 | v0) = v1 & slbdtsldtrb0(v5, xk) = v6 & slbdtsldtrb0(v3, xk) = v4 &
% 39.62/6.65 | szmzizndt0(v1) = v2 & sbrdtbr0(v7) = xk & sdtmndt0(v1, v2) = v3 &
% 39.62/6.65 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 39.62/6.65 | & $i(v0) & aSubsetOf0(v7, v5) & aSubsetOf0(v5, v3) & isCountable0(v5)
% 39.62/6.65 | & aElementOf0(v8, v7) & aElementOf0(v7, v6) & aElementOf0(v2, v1) &
% 39.62/6.65 | aElementOf0(v0, szNzAzT0) & aSet0(v7) & aSet0(v5) & aSet0(v3) & ~
% 39.62/6.65 | aSubsetOf0(v7, v3) & ~ aElementOf0(v8, v3) & ~ aElementOf0(v7, v4)
% 39.62/6.65 | & ~ aElementOf0(v2, v3) & ! [v9: $i] : (v9 = v2 | ~ $i(v9) | ~
% 39.62/6.65 | aElementOf0(v9, v1) | ~ aElement0(v9) | aElementOf0(v9, v3)) & !
% 39.62/6.65 | [v9: $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v7) | aElementOf0(v9, v5))
% 39.62/6.65 | & ! [v9: $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v5) | aElementOf0(v9,
% 39.62/6.65 | v3)) & ! [v9: $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v3) |
% 39.62/6.65 | aElementOf0(v9, v1)) & ! [v9: $i] : ( ~ $i(v9) | ~
% 39.62/6.65 | aElementOf0(v9, v3) | aElement0(v9)) & ! [v9: $i] : ( ~ $i(v9) |
% 39.62/6.65 | ~ aElementOf0(v9, v1) | sdtlseqdt0(v2, v9)))
% 39.62/6.65 |
% 39.62/6.66 | DELTA: instantiating (1) with fresh symbols all_72_0, all_72_1, all_72_2,
% 39.62/6.66 | all_72_3, all_72_4, all_72_5, all_72_6, all_72_7, all_72_8 gives:
% 39.62/6.66 | (2) sdtlpdtrp0(xN, all_72_8) = all_72_7 & slbdtsldtrb0(all_72_3, xk) =
% 39.62/6.66 | all_72_2 & slbdtsldtrb0(all_72_5, xk) = all_72_4 & szmzizndt0(all_72_7)
% 39.62/6.66 | = all_72_6 & sbrdtbr0(all_72_1) = xk & sdtmndt0(all_72_7, all_72_6) =
% 39.62/6.66 | all_72_5 & $i(all_72_0) & $i(all_72_1) & $i(all_72_2) & $i(all_72_3) &
% 39.62/6.66 | $i(all_72_4) & $i(all_72_5) & $i(all_72_6) & $i(all_72_7) &
% 39.62/6.66 | $i(all_72_8) & aSubsetOf0(all_72_1, all_72_3) & aSubsetOf0(all_72_3,
% 39.62/6.66 | all_72_5) & isCountable0(all_72_3) & aElementOf0(all_72_0, all_72_1)
% 39.62/6.66 | & aElementOf0(all_72_1, all_72_2) & aElementOf0(all_72_6, all_72_7) &
% 39.62/6.66 | aElementOf0(all_72_8, szNzAzT0) & aSet0(all_72_1) & aSet0(all_72_3) &
% 39.62/6.66 | aSet0(all_72_5) & ~ aSubsetOf0(all_72_1, all_72_5) & ~
% 39.62/6.66 | aElementOf0(all_72_0, all_72_5) & ~ aElementOf0(all_72_1, all_72_4) &
% 39.62/6.66 | ~ aElementOf0(all_72_6, all_72_5) & ! [v0: any] : (v0 = all_72_6 | ~
% 39.62/6.66 | $i(v0) | ~ aElementOf0(v0, all_72_7) | ~ aElement0(v0) |
% 39.62/6.66 | aElementOf0(v0, all_72_5)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 39.62/6.66 | aElementOf0(v0, all_72_1) | aElementOf0(v0, all_72_3)) & ! [v0: $i]
% 39.62/6.66 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_72_3) | aElementOf0(v0,
% 39.62/6.66 | all_72_5)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 39.62/6.66 | all_72_5) | aElementOf0(v0, all_72_7)) & ! [v0: $i] : ( ~ $i(v0) |
% 39.62/6.66 | ~ aElementOf0(v0, all_72_5) | aElement0(v0)) & ! [v0: $i] : ( ~
% 39.62/6.66 | $i(v0) | ~ aElementOf0(v0, all_72_7) | sdtlseqdt0(all_72_6, v0))
% 39.62/6.66 |
% 39.62/6.66 | ALPHA: (2) implies:
% 39.62/6.66 | (3) ~ aSubsetOf0(all_72_1, all_72_5)
% 39.62/6.66 | (4) aSet0(all_72_5)
% 39.62/6.66 | (5) aSet0(all_72_3)
% 39.62/6.67 | (6) aSet0(all_72_1)
% 39.62/6.67 | (7) aSubsetOf0(all_72_3, all_72_5)
% 39.62/6.67 | (8) aSubsetOf0(all_72_1, all_72_3)
% 39.62/6.67 | (9) $i(all_72_5)
% 39.62/6.67 | (10) $i(all_72_3)
% 39.62/6.67 | (11) $i(all_72_1)
% 39.62/6.67 |
% 39.62/6.67 | GROUND_INST: instantiating (mSubTrans) with all_72_1, all_72_3, all_72_5,
% 39.62/6.67 | simplifying with (3), (4), (5), (6), (7), (8), (9), (10), (11)
% 39.62/6.67 | gives:
% 39.62/6.67 | (12) $false
% 39.62/6.67 |
% 39.62/6.67 | CLOSE: (12) is inconsistent.
% 39.62/6.67 |
% 39.62/6.67 End of proof
% 39.62/6.67 % SZS output end Proof for theBenchmark
% 39.62/6.67
% 39.62/6.67 5994ms
%------------------------------------------------------------------------------