TSTP Solution File: NUM633+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM633+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 : n002.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 11:49:07 EDT 2023
% Result : Theorem 27.87s 4.54s
% Output : Proof 37.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM633+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.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 12:03:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 4.77/1.36 Prover 4: Preprocessing ...
% 4.77/1.36 Prover 1: Preprocessing ...
% 4.77/1.40 Prover 3: Preprocessing ...
% 4.77/1.40 Prover 5: Preprocessing ...
% 4.77/1.41 Prover 6: Preprocessing ...
% 4.77/1.41 Prover 0: Preprocessing ...
% 4.77/1.41 Prover 2: Preprocessing ...
% 14.21/2.68 Prover 3: Constructing countermodel ...
% 14.21/2.69 Prover 1: Constructing countermodel ...
% 14.77/2.71 Prover 6: Proving ...
% 14.90/2.81 Prover 5: Proving ...
% 16.10/2.92 Prover 2: Proving ...
% 19.50/3.36 Prover 4: Constructing countermodel ...
% 21.29/3.60 Prover 0: Proving ...
% 27.87/4.54 Prover 3: proved (3916ms)
% 27.87/4.54
% 27.87/4.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.87/4.54
% 27.87/4.54 Prover 6: stopped
% 28.46/4.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 28.46/4.54 Prover 2: stopped
% 28.46/4.54 Prover 0: stopped
% 28.46/4.56 Prover 5: stopped
% 28.46/4.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.46/4.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 28.46/4.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.46/4.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 30.41/4.81 Prover 7: Preprocessing ...
% 30.41/4.81 Prover 10: Preprocessing ...
% 30.41/4.85 Prover 11: Preprocessing ...
% 30.89/4.85 Prover 13: Preprocessing ...
% 31.33/4.91 Prover 8: Preprocessing ...
% 32.31/5.05 Prover 10: Constructing countermodel ...
% 32.73/5.09 Prover 7: Constructing countermodel ...
% 33.59/5.23 Prover 8: Warning: ignoring some quantifiers
% 33.84/5.24 Prover 8: Constructing countermodel ...
% 34.22/5.31 Prover 13: Warning: ignoring some quantifiers
% 34.22/5.33 Prover 13: Constructing countermodel ...
% 35.20/5.43 Prover 10: Found proof (size 31)
% 35.20/5.43 Prover 10: proved (889ms)
% 35.20/5.43 Prover 7: stopped
% 35.20/5.43 Prover 8: stopped
% 35.20/5.44 Prover 1: stopped
% 35.20/5.44 Prover 4: stopped
% 35.20/5.44 Prover 13: stopped
% 36.75/5.79 Prover 11: Constructing countermodel ...
% 36.75/5.81 Prover 11: stopped
% 36.75/5.81
% 36.75/5.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.75/5.81
% 36.75/5.82 % SZS output start Proof for theBenchmark
% 36.99/5.83 Assumptions after simplification:
% 36.99/5.83 ---------------------------------
% 36.99/5.83
% 36.99/5.83 (m__)
% 36.99/5.88 $i(xO) & $i(xd) & $i(xc) & $i(xS) & $i(xK) & $i(xT) & $i(szNzAzT0) &
% 36.99/5.88 $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v2 &
% 36.99/5.88 szDzozmdt0(xc) = v1 & slbdtsldtrb0(xO, xK) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 36.99/5.88 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (slbdtsldtrb0(v4, xK) = v5) |
% 36.99/5.88 ~ $i(v4) | ~ $i(v3) | ~ aSubsetOf0(v4, xS) | ~ isCountable0(v4) | ~
% 36.99/5.89 aElementOf0(v3, xT) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v3) &
% 36.99/5.89 sdtlpdtrp0(xc, v6) = v7 & $i(v7) & $i(v6) & aElementOf0(v6, v5))) & !
% 36.99/5.89 [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xc, v3) = v4) | ~ $i(v3)
% 36.99/5.89 | ~ aElementOf0(v3, v0)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 36.99/5.89 (sdtlpdtrp0(xc, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 36.99/5.89 aSubsetOf0(v3, szNzAzT0)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 36.99/5.89 (sdtlpdtrp0(xc, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 36.99/5.89 aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xc, slcrc0) = v3) |
% 36.99/5.89 ~ aElementOf0(slcrc0, v0)))
% 36.99/5.89
% 36.99/5.89 (m__4854)
% 36.99/5.89 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 36.99/5.89 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) &
% 36.99/5.89 aElementOf0(v0, xT))
% 36.99/5.89
% 36.99/5.89 (m__4891)
% 36.99/5.89 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 36.99/5.89 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) &
% 36.99/5.89 aSet0(xO))
% 36.99/5.89
% 36.99/5.89 (m__4908)
% 36.99/5.89 $i(xO) & isCountable0(xO) & aSet0(xO)
% 36.99/5.89
% 36.99/5.89 (m__4982)
% 36.99/5.89 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 36.99/5.89 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 36.99/5.89 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) =
% 36.99/5.89 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 36.99/5.89
% 36.99/5.89 (m__4998)
% 36.99/5.89 $i(xO) & $i(xS) & aSubsetOf0(xO, xS)
% 36.99/5.89
% 36.99/5.89 (function-axioms)
% 36.99/5.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.99/5.89 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 36.99/5.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 36.99/5.89 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 36.99/5.89 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 36.99/5.89 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 36.99/5.89 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 36.99/5.89 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 36.99/5.89 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 36.99/5.89 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 36.99/5.89 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 36.99/5.89 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 36.99/5.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 36.99/5.89 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 36.99/5.89 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 36.99/5.89 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 36.99/5.89 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.99/5.89 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 36.99/5.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 36.99/5.89 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.99/5.89 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 36.99/5.89 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 36.99/5.89 v0))
% 36.99/5.89
% 36.99/5.89 Further assumptions not needed in the proof:
% 36.99/5.89 --------------------------------------------
% 36.99/5.90 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 36.99/5.90 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 36.99/5.90 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 36.99/5.90 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 36.99/5.90 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 36.99/5.90 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 36.99/5.90 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 36.99/5.90 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 36.99/5.90 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 36.99/5.90 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398,
% 36.99/5.90 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754,
% 36.99/5.90 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730,
% 36.99/5.90 m__4758
% 36.99/5.90
% 36.99/5.90 Those formulas are unsatisfiable:
% 36.99/5.90 ---------------------------------
% 36.99/5.90
% 36.99/5.90 Begin of proof
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (m__4854) implies:
% 36.99/5.90 | (1) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 36.99/5.90 | v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT))
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (m__4891) implies:
% 36.99/5.90 | (2) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) =
% 36.99/5.90 | xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO))
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (m__4908) implies:
% 36.99/5.90 | (3) isCountable0(xO)
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (m__4982) implies:
% 36.99/5.90 | (4) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 36.99/5.90 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 36.99/5.90 | xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 & $i(v3) &
% 36.99/5.90 | aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (m__4998) implies:
% 36.99/5.90 | (5) aSubsetOf0(xO, xS)
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (m__) implies:
% 36.99/5.90 | (6) $i(xO)
% 36.99/5.90 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v2 &
% 36.99/5.90 | szDzozmdt0(xc) = v1 & slbdtsldtrb0(xO, xK) = v0 & $i(v2) & $i(v1) &
% 36.99/5.90 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 36.99/5.90 | (slbdtsldtrb0(v4, xK) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 36.99/5.90 | aSubsetOf0(v4, xS) | ~ isCountable0(v4) | ~ aElementOf0(v3, xT) |
% 36.99/5.90 | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v3) & sdtlpdtrp0(xc, v6) = v7
% 36.99/5.90 | & $i(v7) & $i(v6) & aElementOf0(v6, v5))) & ! [v3: $i] : ! [v4:
% 36.99/5.90 | $i] : (v4 = v2 | ~ (sdtlpdtrp0(xc, v3) = v4) | ~ $i(v3) | ~
% 36.99/5.90 | aElementOf0(v3, v0)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 36.99/5.90 | (sdtlpdtrp0(xc, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 36.99/5.90 | aSubsetOf0(v3, szNzAzT0)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 36.99/5.90 | (sdtlpdtrp0(xc, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 36.99/5.90 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xc, slcrc0) =
% 36.99/5.90 | v3) | ~ aElementOf0(slcrc0, v0)))
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (function-axioms) implies:
% 36.99/5.90 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2)
% 36.99/5.90 | = v1) | ~ (szDzizrdt0(v2) = v0))
% 36.99/5.90 |
% 36.99/5.90 | DELTA: instantiating (1) with fresh symbols all_78_0, all_78_1 gives:
% 36.99/5.90 | (9) szDzizrdt0(xd) = all_78_1 & sdtlbdtrb0(xd, all_78_1) = all_78_0 &
% 36.99/5.90 | $i(all_78_0) & $i(all_78_1) & isCountable0(all_78_0) &
% 36.99/5.90 | aElementOf0(all_78_1, xT)
% 36.99/5.90 |
% 36.99/5.90 | ALPHA: (9) implies:
% 36.99/5.90 | (10) aElementOf0(all_78_1, xT)
% 36.99/5.90 | (11) szDzizrdt0(xd) = all_78_1
% 36.99/5.90 |
% 36.99/5.90 | DELTA: instantiating (2) with fresh symbols all_80_0, all_80_1 gives:
% 36.99/5.91 | (12) szDzizrdt0(xd) = all_80_1 & sdtlcdtrc0(xe, all_80_0) = xO &
% 36.99/5.91 | sdtlbdtrb0(xd, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1) &
% 36.99/5.91 | aSet0(xO)
% 36.99/5.91 |
% 36.99/5.91 | ALPHA: (12) implies:
% 36.99/5.91 | (13) $i(all_80_1)
% 36.99/5.91 | (14) szDzizrdt0(xd) = all_80_1
% 36.99/5.91 |
% 36.99/5.91 | DELTA: instantiating (4) with fresh symbols all_84_0, all_84_1 gives:
% 36.99/5.91 | (15) szDzizrdt0(xd) = all_84_1 & sdtlbdtrb0(xd, all_84_1) = all_84_0 &
% 36.99/5.91 | $i(all_84_0) & $i(all_84_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 36.99/5.91 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 36.99/5.91 | $i(v1) & aElementOf0(v1, all_84_0) & aElementOf0(v1, szNzAzT0)))
% 36.99/5.91 |
% 36.99/5.91 | ALPHA: (15) implies:
% 36.99/5.91 | (16) szDzizrdt0(xd) = all_84_1
% 36.99/5.91 |
% 36.99/5.91 | DELTA: instantiating (7) with fresh symbols all_90_0, all_90_1, all_90_2
% 36.99/5.91 | gives:
% 36.99/5.91 | (17) szDzizrdt0(xd) = all_90_0 & szDzozmdt0(xc) = all_90_1 &
% 36.99/5.91 | slbdtsldtrb0(xO, xK) = all_90_2 & $i(all_90_0) & $i(all_90_1) &
% 36.99/5.91 | $i(all_90_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 36.99/5.91 | (slbdtsldtrb0(v1, xK) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 36.99/5.91 | aSubsetOf0(v1, xS) | ~ isCountable0(v1) | ~ aElementOf0(v0, xT) |
% 36.99/5.91 | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v0) & sdtlpdtrp0(xc, v3) = v4 &
% 36.99/5.91 | $i(v4) & $i(v3) & aElementOf0(v3, v2))) & ! [v0: $i] : ! [v1:
% 36.99/5.91 | int] : (v1 = all_90_0 | ~ (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) |
% 36.99/5.91 | ~ aElementOf0(v0, all_90_2)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 36.99/5.91 | (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_90_2)
% 36.99/5.91 | | aSubsetOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 36.99/5.91 | (sdtlpdtrp0(xc, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_90_2)
% 36.99/5.91 | | aElementOf0(v0, all_90_1)) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xc,
% 36.99/5.91 | slcrc0) = v0) | ~ aElementOf0(slcrc0, all_90_2))
% 36.99/5.91 |
% 36.99/5.91 | ALPHA: (17) implies:
% 36.99/5.91 | (18) slbdtsldtrb0(xO, xK) = all_90_2
% 36.99/5.91 | (19) szDzizrdt0(xd) = all_90_0
% 36.99/5.91 | (20) ! [v0: $i] : ! [v1: int] : (v1 = all_90_0 | ~ (sdtlpdtrp0(xc, v0) =
% 36.99/5.91 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_90_2))
% 36.99/5.91 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xK) =
% 36.99/5.91 | v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, xS) | ~
% 36.99/5.91 | isCountable0(v1) | ~ aElementOf0(v0, xT) | ? [v3: $i] : ? [v4:
% 36.99/5.91 | $i] : ( ~ (v4 = v0) & sdtlpdtrp0(xc, v3) = v4 & $i(v4) & $i(v3) &
% 36.99/5.91 | aElementOf0(v3, v2)))
% 36.99/5.91 |
% 36.99/5.91 | GROUND_INST: instantiating (8) with all_80_1, all_84_1, xd, simplifying with
% 36.99/5.91 | (14), (16) gives:
% 36.99/5.91 | (22) all_84_1 = all_80_1
% 36.99/5.91 |
% 36.99/5.91 | GROUND_INST: instantiating (8) with all_84_1, all_90_0, xd, simplifying with
% 36.99/5.91 | (16), (19) gives:
% 36.99/5.91 | (23) all_90_0 = all_84_1
% 36.99/5.91 |
% 36.99/5.91 | GROUND_INST: instantiating (8) with all_78_1, all_90_0, xd, simplifying with
% 36.99/5.91 | (11), (19) gives:
% 36.99/5.91 | (24) all_90_0 = all_78_1
% 36.99/5.91 |
% 36.99/5.91 | COMBINE_EQS: (23), (24) imply:
% 36.99/5.91 | (25) all_84_1 = all_78_1
% 36.99/5.91 |
% 36.99/5.91 | SIMP: (25) implies:
% 36.99/5.91 | (26) all_84_1 = all_78_1
% 36.99/5.91 |
% 36.99/5.91 | COMBINE_EQS: (22), (26) imply:
% 36.99/5.91 | (27) all_80_1 = all_78_1
% 36.99/5.91 |
% 36.99/5.91 | SIMP: (27) implies:
% 36.99/5.91 | (28) all_80_1 = all_78_1
% 36.99/5.91 |
% 36.99/5.91 | REDUCE: (13), (28) imply:
% 36.99/5.91 | (29) $i(all_78_1)
% 36.99/5.91 |
% 37.40/5.91 | GROUND_INST: instantiating (21) with all_78_1, xO, all_90_2, simplifying with
% 37.40/5.91 | (3), (5), (6), (10), (18), (29) gives:
% 37.40/5.92 | (30) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_78_1) & sdtlpdtrp0(xc, v0)
% 37.40/5.92 | = v1 & $i(v1) & $i(v0) & aElementOf0(v0, all_90_2))
% 37.40/5.92 |
% 37.40/5.92 | DELTA: instantiating (30) with fresh symbols all_113_0, all_113_1 gives:
% 37.40/5.92 | (31) ~ (all_113_0 = all_78_1) & sdtlpdtrp0(xc, all_113_1) = all_113_0 &
% 37.40/5.92 | $i(all_113_0) & $i(all_113_1) & aElementOf0(all_113_1, all_90_2)
% 37.40/5.92 |
% 37.40/5.92 | ALPHA: (31) implies:
% 37.40/5.92 | (32) ~ (all_113_0 = all_78_1)
% 37.40/5.92 | (33) aElementOf0(all_113_1, all_90_2)
% 37.40/5.92 | (34) $i(all_113_1)
% 37.40/5.92 | (35) sdtlpdtrp0(xc, all_113_1) = all_113_0
% 37.40/5.92 |
% 37.40/5.92 | GROUND_INST: instantiating (20) with all_113_1, all_113_0, simplifying with
% 37.40/5.92 | (33), (34), (35) gives:
% 37.40/5.92 | (36) all_113_0 = all_90_0
% 37.40/5.92 |
% 37.40/5.92 | COMBINE_EQS: (24), (36) imply:
% 37.40/5.92 | (37) all_113_0 = all_78_1
% 37.40/5.92 |
% 37.40/5.92 | REDUCE: (32), (37) imply:
% 37.40/5.92 | (38) $false
% 37.40/5.92 |
% 37.40/5.92 | CLOSE: (38) is inconsistent.
% 37.40/5.92 |
% 37.40/5.92 End of proof
% 37.40/5.92 % SZS output end Proof for theBenchmark
% 37.40/5.92
% 37.40/5.92 5321ms
%------------------------------------------------------------------------------