TSTP Solution File: NUM584+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM584+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 : n013.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 11:48:46 EDT 2023
% Result : Theorem 37.20s 5.70s
% Output : Proof 44.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM584+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n013.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 16:24:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.34/1.36 Prover 1: Preprocessing ...
% 4.34/1.36 Prover 4: Preprocessing ...
% 4.34/1.39 Prover 6: Preprocessing ...
% 4.34/1.39 Prover 5: Preprocessing ...
% 4.34/1.39 Prover 0: Preprocessing ...
% 4.34/1.39 Prover 2: Preprocessing ...
% 4.34/1.39 Prover 3: Preprocessing ...
% 13.21/2.51 Prover 3: Constructing countermodel ...
% 13.21/2.51 Prover 6: Proving ...
% 13.52/2.53 Prover 5: Proving ...
% 13.52/2.53 Prover 1: Constructing countermodel ...
% 15.31/2.82 Prover 2: Proving ...
% 21.89/3.65 Prover 4: Constructing countermodel ...
% 24.17/4.01 Prover 0: Proving ...
% 37.20/5.70 Prover 3: proved (5073ms)
% 37.20/5.70
% 37.20/5.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.20/5.70
% 37.20/5.71 Prover 5: stopped
% 37.20/5.71 Prover 2: stopped
% 37.20/5.72 Prover 0: stopped
% 37.20/5.73 Prover 6: stopped
% 37.20/5.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 37.20/5.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 37.20/5.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 37.20/5.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 37.20/5.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 38.97/5.91 Prover 8: Preprocessing ...
% 38.97/5.91 Prover 7: Preprocessing ...
% 38.97/5.93 Prover 13: Preprocessing ...
% 38.97/5.94 Prover 10: Preprocessing ...
% 38.97/5.95 Prover 11: Preprocessing ...
% 40.45/6.17 Prover 10: Constructing countermodel ...
% 40.45/6.19 Prover 7: Constructing countermodel ...
% 40.45/6.20 Prover 8: Warning: ignoring some quantifiers
% 41.14/6.22 Prover 8: Constructing countermodel ...
% 41.44/6.27 Prover 13: Warning: ignoring some quantifiers
% 41.44/6.30 Prover 13: Constructing countermodel ...
% 43.11/6.46 Prover 10: Found proof (size 57)
% 43.13/6.47 Prover 10: proved (740ms)
% 43.13/6.47 Prover 13: stopped
% 43.13/6.47 Prover 8: stopped
% 43.13/6.47 Prover 7: stopped
% 43.13/6.47 Prover 1: stopped
% 43.13/6.47 Prover 4: stopped
% 43.88/6.66 Prover 11: Constructing countermodel ...
% 43.88/6.68 Prover 11: stopped
% 43.88/6.68
% 43.88/6.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.88/6.68
% 44.12/6.70 % SZS output start Proof for theBenchmark
% 44.12/6.71 Assumptions after simplification:
% 44.12/6.71 ---------------------------------
% 44.12/6.71
% 44.12/6.71 (mDefSel)
% 44.12/6.75 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 44.12/6.75 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) |
% 44.12/6.75 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 44.12/6.75 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 44.12/6.75 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~
% 44.12/6.75 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 44.12/6.75 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 44.12/6.75 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 44.12/6.75 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 44.12/6.75 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ?
% 44.12/6.75 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~
% 44.12/6.75 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) &
% 44.12/6.75 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4,
% 44.12/6.75 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 44.12/6.75 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~
% 44.12/6.75 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1,
% 44.12/6.75 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 44.12/6.75 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1)
% 44.12/6.75 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 44.12/6.75
% 44.12/6.75 (mDefSub)
% 44.12/6.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 44.12/6.75 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 44.12/6.75 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 44.12/6.75 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 44.12/6.75 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 44.12/6.75 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 44.12/6.75
% 44.12/6.75 (mNATSet)
% 44.12/6.75 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 44.12/6.75
% 44.12/6.75 (m__)
% 44.12/6.75 $i(xQ) & $i(xi) & $i(xN) & $i(xS) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ?
% 44.12/6.75 [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(xS, xK) = v3
% 44.12/6.75 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 44.12/6.75 $i(v0) & ~ aElementOf0(v2, v3))
% 44.12/6.75
% 44.12/6.75 (m__3418)
% 44.12/6.75 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 44.12/6.75
% 44.12/6.75 (m__3435)
% 44.12/6.76 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS)
% 44.12/6.76
% 44.12/6.76 (m__3453)
% 44.12/6.76 $i(xc) & $i(xS) & $i(xK) & $i(xT) & ? [v0: $i] : ? [v1: $i] :
% 44.12/6.76 (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) = v0 & slbdtsldtrb0(xS, xK) = v0 &
% 44.12/6.76 $i(v1) & $i(v0) & aFunction0(xc) & aSubsetOf0(v1, xT))
% 44.12/6.76
% 44.12/6.76 (m__3989)
% 44.12/6.76 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0)
% 44.12/6.76
% 44.12/6.76 (m__3989_02)
% 44.12/6.76 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 44.12/6.76 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 &
% 44.12/6.76 szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 44.12/6.76 $i(v0) & aElementOf0(xQ, v3))
% 44.12/6.76
% 44.12/6.76 (m__4007)
% 44.12/6.76 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 44.12/6.76 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK &
% 44.12/6.76 sdtpldt0(xQ, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 44.12/6.76
% 44.12/6.76 (m__4024)
% 44.12/6.76 $i(xQ) & $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 44.12/6.76 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2 &
% 44.12/6.76 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v2, xS))
% 44.12/6.76
% 44.12/6.76 (function-axioms)
% 44.12/6.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.12/6.76 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 44.12/6.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 44.12/6.76 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 44.12/6.76 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 44.12/6.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 44.12/6.76 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 44.12/6.76 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 44.12/6.76 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 44.12/6.76 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 44.12/6.76 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 44.12/6.76 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 44.12/6.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 44.12/6.76 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 44.12/6.77 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 44.12/6.77 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 44.12/6.77 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.12/6.77 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 44.12/6.77 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 44.12/6.77 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.12/6.77 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 44.12/6.77 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 44.12/6.77 v0))
% 44.12/6.77
% 44.12/6.77 Further assumptions not needed in the proof:
% 44.12/6.77 --------------------------------------------
% 44.12/6.77 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 44.12/6.77 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 44.12/6.77 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 44.12/6.77 mDefSeg, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 44.12/6.77 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 44.12/6.77 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 44.12/6.77 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 44.12/6.77 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 44.12/6.77 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 44.12/6.77 mZeroLess, mZeroNum, m__3291, m__3398, m__3462, m__3520, m__3533, m__3623,
% 44.12/6.77 m__3671, m__3754, m__3821
% 44.12/6.77
% 44.12/6.77 Those formulas are unsatisfiable:
% 44.12/6.77 ---------------------------------
% 44.12/6.77
% 44.12/6.77 Begin of proof
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (mDefSub) implies:
% 44.12/6.77 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1,
% 44.12/6.77 | v0) | ~ aSet0(v0) | aSet0(v1))
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (mNATSet) implies:
% 44.12/6.77 | (2) aSet0(szNzAzT0)
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (mDefSel) implies:
% 44.12/6.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 44.12/6.77 | (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~
% 44.12/6.77 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~
% 44.12/6.77 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__3418) implies:
% 44.12/6.77 | (4) aElementOf0(xK, szNzAzT0)
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__3435) implies:
% 44.12/6.77 | (5) aSubsetOf0(xS, szNzAzT0)
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__3453) implies:
% 44.12/6.77 | (6) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) =
% 44.12/6.77 | v0 & slbdtsldtrb0(xS, xK) = v0 & $i(v1) & $i(v0) & aFunction0(xc) &
% 44.12/6.77 | aSubsetOf0(v1, xT))
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__3989) implies:
% 44.12/6.77 | (7) $i(szNzAzT0)
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__3989_02) implies:
% 44.12/6.77 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xN,
% 44.12/6.77 | xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0) = v1 &
% 44.12/6.77 | sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 44.12/6.77 | aElementOf0(xQ, v3))
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__4007) implies:
% 44.12/6.77 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 &
% 44.12/6.77 | szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & sdtpldt0(xQ, v1) = v2 &
% 44.12/6.77 | $i(v2) & $i(v1) & $i(v0))
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__4024) implies:
% 44.12/6.77 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 &
% 44.12/6.77 | szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2 & $i(v2) & $i(v1) &
% 44.12/6.77 | $i(v0) & aSubsetOf0(v2, xS))
% 44.12/6.77 |
% 44.12/6.77 | ALPHA: (m__) implies:
% 44.12/6.77 | (11) $i(xK)
% 44.12/6.77 | (12) $i(xS)
% 44.12/6.78 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 44.12/6.78 | (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(xS, xK) = v3 & szmzizndt0(v0)
% 44.12/6.78 | = v1 & sdtpldt0(xQ, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 44.12/6.78 | ~ aElementOf0(v2, v3))
% 44.12/6.78 |
% 44.12/6.78 | ALPHA: (function-axioms) implies:
% 44.12/6.78 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.12/6.78 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 44.12/6.78 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.12/6.78 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 44.12/6.78 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.12/6.78 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0))
% 44.12/6.78 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.12/6.78 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 44.12/6.78 |
% 44.12/6.78 | DELTA: instantiating (9) with fresh symbols all_69_0, all_69_1, all_69_2
% 44.12/6.78 | gives:
% 44.12/6.78 | (18) sdtlpdtrp0(xN, xi) = all_69_2 & szmzizndt0(all_69_2) = all_69_1 &
% 44.12/6.78 | sbrdtbr0(all_69_0) = xK & sdtpldt0(xQ, all_69_1) = all_69_0 &
% 44.12/6.78 | $i(all_69_0) & $i(all_69_1) & $i(all_69_2)
% 44.12/6.78 |
% 44.12/6.78 | ALPHA: (18) implies:
% 44.12/6.78 | (19) sdtpldt0(xQ, all_69_1) = all_69_0
% 44.12/6.78 | (20) sbrdtbr0(all_69_0) = xK
% 44.12/6.78 | (21) szmzizndt0(all_69_2) = all_69_1
% 44.12/6.78 | (22) sdtlpdtrp0(xN, xi) = all_69_2
% 44.12/6.78 |
% 44.12/6.78 | DELTA: instantiating (10) with fresh symbols all_71_0, all_71_1, all_71_2
% 44.12/6.78 | gives:
% 44.12/6.78 | (23) sdtlpdtrp0(xN, xi) = all_71_2 & szmzizndt0(all_71_2) = all_71_1 &
% 44.12/6.78 | sdtpldt0(xQ, all_71_1) = all_71_0 & $i(all_71_0) & $i(all_71_1) &
% 44.12/6.78 | $i(all_71_2) & aSubsetOf0(all_71_0, xS)
% 44.12/6.78 |
% 44.12/6.78 | ALPHA: (23) implies:
% 44.12/6.78 | (24) aSubsetOf0(all_71_0, xS)
% 44.12/6.78 | (25) $i(all_71_0)
% 44.12/6.78 | (26) sdtpldt0(xQ, all_71_1) = all_71_0
% 44.12/6.78 | (27) szmzizndt0(all_71_2) = all_71_1
% 44.12/6.78 | (28) sdtlpdtrp0(xN, xi) = all_71_2
% 44.12/6.78 |
% 44.12/6.78 | DELTA: instantiating (6) with fresh symbols all_73_0, all_73_1 gives:
% 44.12/6.78 | (29) sdtlcdtrc0(xc, all_73_1) = all_73_0 & szDzozmdt0(xc) = all_73_1 &
% 44.12/6.78 | slbdtsldtrb0(xS, xK) = all_73_1 & $i(all_73_0) & $i(all_73_1) &
% 44.12/6.78 | aFunction0(xc) & aSubsetOf0(all_73_0, xT)
% 44.12/6.78 |
% 44.12/6.78 | ALPHA: (29) implies:
% 44.12/6.78 | (30) slbdtsldtrb0(xS, xK) = all_73_1
% 44.12/6.78 |
% 44.12/6.78 | DELTA: instantiating (8) with fresh symbols all_75_0, all_75_1, all_75_2,
% 44.12/6.78 | all_75_3 gives:
% 44.12/6.78 | (31) sdtlpdtrp0(xN, xi) = all_75_3 & slbdtsldtrb0(all_75_1, xk) = all_75_0
% 44.12/6.78 | & szmzizndt0(all_75_3) = all_75_2 & sdtmndt0(all_75_3, all_75_2) =
% 44.12/6.78 | all_75_1 & $i(all_75_0) & $i(all_75_1) & $i(all_75_2) & $i(all_75_3) &
% 44.12/6.78 | aElementOf0(xQ, all_75_0)
% 44.12/6.78 |
% 44.12/6.78 | ALPHA: (31) implies:
% 44.12/6.78 | (32) szmzizndt0(all_75_3) = all_75_2
% 44.12/6.78 | (33) sdtlpdtrp0(xN, xi) = all_75_3
% 44.12/6.78 |
% 44.12/6.78 | DELTA: instantiating (13) with fresh symbols all_77_0, all_77_1, all_77_2,
% 44.12/6.78 | all_77_3 gives:
% 44.12/6.78 | (34) sdtlpdtrp0(xN, xi) = all_77_3 & slbdtsldtrb0(xS, xK) = all_77_0 &
% 44.12/6.78 | szmzizndt0(all_77_3) = all_77_2 & sdtpldt0(xQ, all_77_2) = all_77_1 &
% 44.12/6.78 | $i(all_77_0) & $i(all_77_1) & $i(all_77_2) & $i(all_77_3) & ~
% 44.12/6.78 | aElementOf0(all_77_1, all_77_0)
% 44.12/6.78 |
% 44.12/6.78 | ALPHA: (34) implies:
% 44.12/6.78 | (35) ~ aElementOf0(all_77_1, all_77_0)
% 44.12/6.78 | (36) $i(all_77_0)
% 44.12/6.78 | (37) sdtpldt0(xQ, all_77_2) = all_77_1
% 44.12/6.79 | (38) szmzizndt0(all_77_3) = all_77_2
% 44.12/6.79 | (39) slbdtsldtrb0(xS, xK) = all_77_0
% 44.12/6.79 | (40) sdtlpdtrp0(xN, xi) = all_77_3
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (16) with all_73_1, all_77_0, xK, xS, simplifying
% 44.12/6.79 | with (30), (39) gives:
% 44.12/6.79 | (41) all_77_0 = all_73_1
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (17) with all_71_2, all_75_3, xi, xN, simplifying
% 44.12/6.79 | with (28), (33) gives:
% 44.12/6.79 | (42) all_75_3 = all_71_2
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (17) with all_75_3, all_77_3, xi, xN, simplifying
% 44.12/6.79 | with (33), (40) gives:
% 44.12/6.79 | (43) all_77_3 = all_75_3
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (17) with all_69_2, all_77_3, xi, xN, simplifying
% 44.12/6.79 | with (22), (40) gives:
% 44.12/6.79 | (44) all_77_3 = all_69_2
% 44.12/6.79 |
% 44.12/6.79 | COMBINE_EQS: (43), (44) imply:
% 44.12/6.79 | (45) all_75_3 = all_69_2
% 44.12/6.79 |
% 44.12/6.79 | SIMP: (45) implies:
% 44.12/6.79 | (46) all_75_3 = all_69_2
% 44.12/6.79 |
% 44.12/6.79 | COMBINE_EQS: (42), (46) imply:
% 44.12/6.79 | (47) all_71_2 = all_69_2
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (38), (44) imply:
% 44.12/6.79 | (48) szmzizndt0(all_69_2) = all_77_2
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (32), (46) imply:
% 44.12/6.79 | (49) szmzizndt0(all_69_2) = all_75_2
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (27), (47) imply:
% 44.12/6.79 | (50) szmzizndt0(all_69_2) = all_71_1
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (36), (41) imply:
% 44.12/6.79 | (51) $i(all_73_1)
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (35), (41) imply:
% 44.12/6.79 | (52) ~ aElementOf0(all_77_1, all_73_1)
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (14) with all_69_1, all_75_2, all_69_2, simplifying
% 44.12/6.79 | with (21), (49) gives:
% 44.12/6.79 | (53) all_75_2 = all_69_1
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (14) with all_75_2, all_77_2, all_69_2, simplifying
% 44.12/6.79 | with (48), (49) gives:
% 44.12/6.79 | (54) all_77_2 = all_75_2
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (14) with all_71_1, all_77_2, all_69_2, simplifying
% 44.12/6.79 | with (48), (50) gives:
% 44.12/6.79 | (55) all_77_2 = all_71_1
% 44.12/6.79 |
% 44.12/6.79 | COMBINE_EQS: (54), (55) imply:
% 44.12/6.79 | (56) all_75_2 = all_71_1
% 44.12/6.79 |
% 44.12/6.79 | SIMP: (56) implies:
% 44.12/6.79 | (57) all_75_2 = all_71_1
% 44.12/6.79 |
% 44.12/6.79 | COMBINE_EQS: (53), (57) imply:
% 44.12/6.79 | (58) all_71_1 = all_69_1
% 44.12/6.79 |
% 44.12/6.79 | SIMP: (58) implies:
% 44.12/6.79 | (59) all_71_1 = all_69_1
% 44.12/6.79 |
% 44.12/6.79 | COMBINE_EQS: (55), (59) imply:
% 44.12/6.79 | (60) all_77_2 = all_69_1
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (37), (60) imply:
% 44.12/6.79 | (61) sdtpldt0(xQ, all_69_1) = all_77_1
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (26), (59) imply:
% 44.12/6.79 | (62) sdtpldt0(xQ, all_69_1) = all_71_0
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (15) with all_69_0, all_77_1, all_69_1, xQ,
% 44.12/6.79 | simplifying with (19), (61) gives:
% 44.12/6.79 | (63) all_77_1 = all_69_0
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (15) with all_71_0, all_77_1, all_69_1, xQ,
% 44.12/6.79 | simplifying with (61), (62) gives:
% 44.12/6.79 | (64) all_77_1 = all_71_0
% 44.12/6.79 |
% 44.12/6.79 | COMBINE_EQS: (63), (64) imply:
% 44.12/6.79 | (65) all_71_0 = all_69_0
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (25), (65) imply:
% 44.12/6.79 | (66) $i(all_69_0)
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (24), (65) imply:
% 44.12/6.79 | (67) aSubsetOf0(all_69_0, xS)
% 44.12/6.79 |
% 44.12/6.79 | REDUCE: (52), (63) imply:
% 44.12/6.79 | (68) ~ aElementOf0(all_69_0, all_73_1)
% 44.12/6.79 |
% 44.12/6.79 | GROUND_INST: instantiating (1) with szNzAzT0, xS, simplifying with (2), (5),
% 44.12/6.79 | (7), (12) gives:
% 44.12/6.79 | (69) aSet0(xS)
% 44.12/6.79 |
% 44.12/6.80 | GROUND_INST: instantiating (3) with xS, xK, all_73_1, all_69_0, simplifying
% 44.12/6.80 | with (4), (11), (12), (20), (30), (51), (66), (67), (68), (69)
% 44.12/6.80 | gives:
% 44.12/6.80 | (70) $false
% 44.12/6.80 |
% 44.12/6.80 | CLOSE: (70) is inconsistent.
% 44.12/6.80 |
% 44.12/6.80 End of proof
% 44.12/6.80 % SZS output end Proof for theBenchmark
% 44.12/6.80
% 44.12/6.80 6195ms
%------------------------------------------------------------------------------