TSTP Solution File: NUM632+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM632+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 : 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 11:49:07 EDT 2023
% Result : Theorem 20.89s 3.54s
% Output : Proof 40.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM632+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n004.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 10:05:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.35/1.57 Prover 4: Preprocessing ...
% 6.35/1.57 Prover 1: Preprocessing ...
% 6.35/1.59 Prover 2: Preprocessing ...
% 6.35/1.59 Prover 0: Preprocessing ...
% 6.35/1.59 Prover 3: Preprocessing ...
% 6.35/1.59 Prover 5: Preprocessing ...
% 6.35/1.60 Prover 6: Preprocessing ...
% 20.14/3.40 Prover 3: Constructing countermodel ...
% 20.21/3.41 Prover 6: Proving ...
% 20.21/3.42 Prover 1: Constructing countermodel ...
% 20.89/3.53 Prover 3: proved (2897ms)
% 20.89/3.53
% 20.89/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.89/3.54
% 20.89/3.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 20.89/3.55 Prover 6: proved (2909ms)
% 20.89/3.55
% 20.89/3.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.89/3.55
% 20.89/3.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.08/3.84 Prover 8: Preprocessing ...
% 23.08/3.86 Prover 5: Proving ...
% 23.08/3.86 Prover 5: stopped
% 23.08/3.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.75/3.89 Prover 7: Preprocessing ...
% 23.75/3.90 Prover 1: Found proof (size 47)
% 23.75/3.90 Prover 1: proved (3270ms)
% 23.75/4.06 Prover 7: stopped
% 23.75/4.08 Prover 10: Preprocessing ...
% 25.33/4.15 Prover 10: stopped
% 26.71/4.33 Prover 8: Warning: ignoring some quantifiers
% 26.71/4.35 Prover 8: Constructing countermodel ...
% 26.71/4.38 Prover 8: stopped
% 36.76/5.91 Prover 4: Constructing countermodel ...
% 36.76/5.94 Prover 4: stopped
% 38.85/6.27 Prover 2: Proving ...
% 38.85/6.29 Prover 2: stopped
% 39.17/6.43 Prover 0: Proving ...
% 39.56/6.45 Prover 0: stopped
% 39.56/6.45
% 39.56/6.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.56/6.45
% 39.56/6.47 % SZS output start Proof for theBenchmark
% 39.56/6.48 Assumptions after simplification:
% 39.56/6.48 ---------------------------------
% 39.56/6.48
% 39.56/6.48 (m__)
% 39.82/6.53 $i(xQ) & $i(xd) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 39.82/6.53 szDzizrdt0(xd) = v1 & sdtlpdtrp0(xc, xQ) = v0 & $i(v1) & $i(v0))
% 39.82/6.53
% 39.82/6.53 (m__4854)
% 39.82/6.54 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) =
% 39.82/6.54 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & aSet0(v1) = 0 &
% 39.82/6.54 aElementOf0(v0, xT) = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4:
% 39.82/6.54 int] : (v4 = 0 | ~ (aElementOf0(v3, v1) = v4) | ~ $i(v3) | ? [v5: any]
% 39.82/6.54 : ? [v6: $i] : (sdtlpdtrp0(xd, v3) = v6 & aElementOf0(v3, v2) = v5 &
% 39.82/6.54 $i(v6) & ( ~ (v6 = v0) | ~ (v5 = 0)))) & ! [v3: $i] : ( ~
% 39.82/6.54 (aElementOf0(v3, v1) = 0) | ~ $i(v3) | (sdtlpdtrp0(xd, v3) = v0 &
% 39.82/6.54 aElementOf0(v3, v2) = 0)))
% 39.82/6.54
% 39.82/6.54 (m__4891)
% 39.82/6.55 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 39.82/6.55 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 39.82/6.55 szDzozmdt0(xd) = v2 & aSet0(v1) = 0 & aSet0(xO) = 0 & $i(v2) & $i(v1) &
% 39.82/6.55 $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v1) =
% 39.82/6.55 v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : (sdtlpdtrp0(xd, v3) = v6
% 39.82/6.55 & aElementOf0(v3, v2) = v5 & $i(v6) & ( ~ (v6 = v0) | ~ (v5 = 0)))) &
% 39.82/6.55 ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, xO) = v4) | ~
% 39.82/6.55 $i(v3) | ! [v5: $i] : ( ~ (aElementOf0(v5, v1) = 0) | ~ $i(v5) | ? [v6:
% 39.82/6.55 $i] : ( ~ (v6 = v3) & sdtlpdtrp0(xe, v5) = v6 & $i(v6)))) & ! [v3:
% 39.82/6.55 $i] : ( ~ (aElementOf0(v3, v1) = 0) | ~ $i(v3) | (sdtlpdtrp0(xd, v3) = v0
% 39.82/6.55 & aElementOf0(v3, v2) = 0)) & ! [v3: $i] : ( ~ (aElementOf0(v3, xO) =
% 39.82/6.55 0) | ~ $i(v3) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 39.82/6.55 aElementOf0(v4, v1) = 0 & $i(v4))))
% 39.82/6.55
% 39.82/6.55 (m__4982)
% 40.13/6.56 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 40.13/6.56 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 40.13/6.56 : ! [v3: any] : ( ~ (aElementOf0(v2, xO) = v3) | ~ $i(v2) | ? [v4: $i] :
% 40.13/6.56 (sdtlpdtrp0(xd, v4) = v0 & sdtlpdtrp0(xe, v4) = v2 & aElementOf0(v4, v1) =
% 40.13/6.56 0 & aElementOf0(v4, szNzAzT0) = 0 & $i(v4)) | ( ~ (v3 = 0) & ! [v4: $i]
% 40.13/6.56 : ( ~ (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: $i] : ( ~ (v5 =
% 40.13/6.56 v2) & sdtlpdtrp0(xe, v4) = v5 & $i(v5))))))
% 40.13/6.56
% 40.13/6.56 (m__5182)
% 40.13/6.56 $i(xp) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 40.13/6.56 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (sdtlpdtrp0(xe,
% 40.13/6.56 v2) = xp & aElementOf0(v2, v1) = 0 & $i(v2)))
% 40.13/6.56
% 40.13/6.56 (m__5309)
% 40.13/6.57 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 40.13/6.57 ? [v2: $i] : (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd,
% 40.13/6.57 xn) = v1 & sdtlpdtrp0(xe, xn) = xp & szDzozmdt0(xd) = v0 & aElementOf0(xn,
% 40.13/6.57 v2) = 0 & aElementOf0(xn, v0) = 0 & aElementOf0(xn, szNzAzT0) = 0 & $i(v2)
% 40.13/6.57 & $i(v1) & $i(v0))
% 40.13/6.57
% 40.13/6.57 (m__5321)
% 40.13/6.57 $i(xn) & $i(xd) & ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0
% 40.13/6.57 & $i(v0))
% 40.13/6.57
% 40.13/6.57 (m__5568)
% 40.13/6.57 $i(xn) & $i(xQ) & $i(xd) & $i(xc) & ? [v0: $i] : (sdtlpdtrp0(xd, xn) = v0 &
% 40.13/6.57 sdtlpdtrp0(xc, xQ) = v0 & $i(v0))
% 40.13/6.57
% 40.13/6.57 (function-axioms)
% 40.13/6.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.13/6.58 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 40.13/6.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 40.13/6.58 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 40.13/6.58 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 40.13/6.58 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 40.13/6.58 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 40.13/6.58 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 40.13/6.58 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 40.13/6.58 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.13/6.58 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0:
% 40.13/6.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 40.13/6.58 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 40.13/6.58 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.13/6.58 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 40.13/6.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 40.13/6.58 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.13/6.58 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.13/6.58 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 40.13/6.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 40.13/6.58 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 40.13/6.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 40.13/6.58 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.13/6.58 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~
% 40.13/6.58 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 40.13/6.58 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 40.13/6.58 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 40.13/6.58 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 40.13/6.58 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 40.13/6.58 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 40.13/6.58 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 40.13/6.58 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 40.13/6.58 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 40.13/6.58 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 40.13/6.58 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) &
% 40.13/6.58 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 40.13/6.58 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 40.13/6.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 40.13/6.58 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 40.13/6.58 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 40.13/6.58 ~ (aElement0(v2) = v0))
% 40.13/6.58
% 40.13/6.58 Further assumptions not needed in the proof:
% 40.13/6.58 --------------------------------------------
% 40.13/6.58 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 40.13/6.58 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 40.13/6.58 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 40.13/6.58 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 40.13/6.58 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 40.13/6.58 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 40.13/6.58 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 40.13/6.58 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 40.13/6.58 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 40.13/6.58 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398,
% 40.13/6.58 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754,
% 40.13/6.58 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730,
% 40.13/6.58 m__4758, m__4908, m__4998, m__5078, m__5093, m__5106, m__5116, m__5147, m__5164,
% 40.13/6.58 m__5173, m__5195, m__5208, m__5217, m__5270, m__5334
% 40.13/6.58
% 40.13/6.58 Those formulas are unsatisfiable:
% 40.13/6.58 ---------------------------------
% 40.13/6.58
% 40.13/6.58 Begin of proof
% 40.13/6.58 |
% 40.13/6.58 | ALPHA: (m__4854) implies:
% 40.13/6.59 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 40.13/6.59 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & aSet0(v1) = 0 &
% 40.13/6.59 | aElementOf0(v0, xT) = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : !
% 40.13/6.59 | [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v1) = v4) | ~ $i(v3) | ?
% 40.13/6.59 | [v5: any] : ? [v6: $i] : (sdtlpdtrp0(xd, v3) = v6 &
% 40.13/6.59 | aElementOf0(v3, v2) = v5 & $i(v6) & ( ~ (v6 = v0) | ~ (v5 =
% 40.13/6.59 | 0)))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v1) = 0) | ~
% 40.13/6.59 | $i(v3) | (sdtlpdtrp0(xd, v3) = v0 & aElementOf0(v3, v2) = 0)))
% 40.13/6.59 |
% 40.13/6.59 | ALPHA: (m__4891) implies:
% 40.13/6.59 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 40.13/6.59 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 40.13/6.59 | v2 & aSet0(v1) = 0 & aSet0(xO) = 0 & $i(v2) & $i(v1) & $i(v0) & !
% 40.13/6.59 | [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v1) = v4) |
% 40.13/6.59 | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : (sdtlpdtrp0(xd, v3) = v6 &
% 40.13/6.59 | aElementOf0(v3, v2) = v5 & $i(v6) & ( ~ (v6 = v0) | ~ (v5 =
% 40.13/6.59 | 0)))) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 40.13/6.59 | (aElementOf0(v3, xO) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 40.13/6.59 | (aElementOf0(v5, v1) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 =
% 40.13/6.59 | v3) & sdtlpdtrp0(xe, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 40.13/6.59 | (aElementOf0(v3, v1) = 0) | ~ $i(v3) | (sdtlpdtrp0(xd, v3) = v0 &
% 40.13/6.59 | aElementOf0(v3, v2) = 0)) & ! [v3: $i] : ( ~ (aElementOf0(v3,
% 40.13/6.59 | xO) = 0) | ~ $i(v3) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 40.13/6.59 | aElementOf0(v4, v1) = 0 & $i(v4))))
% 40.13/6.59 |
% 40.13/6.59 | ALPHA: (m__4982) implies:
% 40.13/6.59 | (3) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 40.13/6.59 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: any] : ( ~
% 40.13/6.59 | (aElementOf0(v2, xO) = v3) | ~ $i(v2) | ? [v4: $i] :
% 40.13/6.59 | (sdtlpdtrp0(xd, v4) = v0 & sdtlpdtrp0(xe, v4) = v2 &
% 40.13/6.59 | aElementOf0(v4, v1) = 0 & aElementOf0(v4, szNzAzT0) = 0 & $i(v4))
% 40.13/6.59 | | ( ~ (v3 = 0) & ! [v4: $i] : ( ~ (aElementOf0(v4, v1) = 0) | ~
% 40.13/6.59 | $i(v4) | ? [v5: $i] : ( ~ (v5 = v2) & sdtlpdtrp0(xe, v4) = v5
% 40.13/6.59 | & $i(v5))))))
% 40.13/6.59 |
% 40.13/6.59 | ALPHA: (m__5182) implies:
% 40.13/6.59 | (4) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 40.13/6.59 | v1 & $i(v1) & $i(v0) & ? [v2: $i] : (sdtlpdtrp0(xe, v2) = xp &
% 40.13/6.59 | aElementOf0(v2, v1) = 0 & $i(v2)))
% 40.13/6.59 |
% 40.13/6.59 | ALPHA: (m__5309) implies:
% 40.13/6.59 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 &
% 40.13/6.59 | sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xe,
% 40.13/6.59 | xn) = xp & szDzozmdt0(xd) = v0 & aElementOf0(xn, v2) = 0 &
% 40.13/6.59 | aElementOf0(xn, v0) = 0 & aElementOf0(xn, szNzAzT0) = 0 & $i(v2) &
% 40.13/6.59 | $i(v1) & $i(v0))
% 40.13/6.59 |
% 40.13/6.59 | ALPHA: (m__5321) implies:
% 40.13/6.60 | (6) ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0 & $i(v0))
% 40.13/6.60 |
% 40.13/6.60 | ALPHA: (m__5568) implies:
% 40.13/6.60 | (7) ? [v0: $i] : (sdtlpdtrp0(xd, xn) = v0 & sdtlpdtrp0(xc, xQ) = v0 &
% 40.13/6.60 | $i(v0))
% 40.13/6.60 |
% 40.13/6.60 | ALPHA: (m__) implies:
% 40.13/6.60 | (8) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & szDzizrdt0(xd) = v1 &
% 40.13/6.60 | sdtlpdtrp0(xc, xQ) = v0 & $i(v1) & $i(v0))
% 40.13/6.60 |
% 40.13/6.60 | ALPHA: (function-axioms) implies:
% 40.13/6.60 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2)
% 40.13/6.60 | = v1) | ~ (szDzizrdt0(v2) = v0))
% 40.13/6.60 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.13/6.60 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 40.13/6.60 |
% 40.13/6.60 | DELTA: instantiating (7) with fresh symbol all_85_0 gives:
% 40.13/6.60 | (11) sdtlpdtrp0(xd, xn) = all_85_0 & sdtlpdtrp0(xc, xQ) = all_85_0 &
% 40.13/6.60 | $i(all_85_0)
% 40.13/6.60 |
% 40.13/6.60 | ALPHA: (11) implies:
% 40.13/6.60 | (12) sdtlpdtrp0(xc, xQ) = all_85_0
% 40.13/6.60 | (13) sdtlpdtrp0(xd, xn) = all_85_0
% 40.13/6.60 |
% 40.13/6.60 | DELTA: instantiating (6) with fresh symbol all_87_0 gives:
% 40.13/6.60 | (14) szDzizrdt0(xd) = all_87_0 & sdtlpdtrp0(xd, xn) = all_87_0 &
% 40.13/6.60 | $i(all_87_0)
% 40.13/6.60 |
% 40.13/6.60 | ALPHA: (14) implies:
% 40.13/6.60 | (15) szDzizrdt0(xd) = all_87_0
% 40.13/6.60 |
% 40.13/6.60 | DELTA: instantiating (8) with fresh symbols all_91_0, all_91_1 gives:
% 40.13/6.60 | (16) ~ (all_91_0 = all_91_1) & szDzizrdt0(xd) = all_91_0 & sdtlpdtrp0(xc,
% 40.13/6.60 | xQ) = all_91_1 & $i(all_91_0) & $i(all_91_1)
% 40.13/6.60 |
% 40.13/6.60 | ALPHA: (16) implies:
% 40.13/6.60 | (17) ~ (all_91_0 = all_91_1)
% 40.13/6.60 | (18) sdtlpdtrp0(xc, xQ) = all_91_1
% 40.13/6.60 | (19) szDzizrdt0(xd) = all_91_0
% 40.13/6.60 |
% 40.13/6.60 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives:
% 40.13/6.60 | (20) szDzizrdt0(xd) = all_93_1 & sdtlbdtrb0(xd, all_93_1) = all_93_0 &
% 40.13/6.60 | $i(all_93_0) & $i(all_93_1) & ? [v0: $i] : (sdtlpdtrp0(xe, v0) = xp &
% 40.13/6.60 | aElementOf0(v0, all_93_0) = 0 & $i(v0))
% 40.13/6.60 |
% 40.13/6.60 | ALPHA: (20) implies:
% 40.13/6.60 | (21) szDzizrdt0(xd) = all_93_1
% 40.13/6.60 |
% 40.13/6.60 | DELTA: instantiating (5) with fresh symbols all_104_0, all_104_1, all_104_2
% 40.13/6.60 | gives:
% 40.13/6.61 | (22) szDzizrdt0(xd) = all_104_1 & sdtlbdtrb0(xd, all_104_1) = all_104_0 &
% 40.13/6.61 | sdtlpdtrp0(xd, xn) = all_104_1 & sdtlpdtrp0(xe, xn) = xp &
% 40.13/6.61 | szDzozmdt0(xd) = all_104_2 & aElementOf0(xn, all_104_0) = 0 &
% 40.13/6.61 | aElementOf0(xn, all_104_2) = 0 & aElementOf0(xn, szNzAzT0) = 0 &
% 40.13/6.61 | $i(all_104_0) & $i(all_104_1) & $i(all_104_2)
% 40.13/6.61 |
% 40.13/6.61 | ALPHA: (22) implies:
% 40.13/6.61 | (23) sdtlpdtrp0(xd, xn) = all_104_1
% 40.13/6.61 | (24) szDzizrdt0(xd) = all_104_1
% 40.13/6.61 |
% 40.13/6.61 | DELTA: instantiating (3) with fresh symbols all_106_0, all_106_1 gives:
% 40.13/6.61 | (25) szDzizrdt0(xd) = all_106_1 & sdtlbdtrb0(xd, all_106_1) = all_106_0 &
% 40.13/6.61 | $i(all_106_0) & $i(all_106_1) & ! [v0: $i] : ! [v1: any] : ( ~
% 40.13/6.61 | (aElementOf0(v0, xO) = v1) | ~ $i(v0) | ? [v2: $i] :
% 40.13/6.61 | (sdtlpdtrp0(xd, v2) = all_106_1 & sdtlpdtrp0(xe, v2) = v0 &
% 40.13/6.61 | aElementOf0(v2, all_106_0) = 0 & aElementOf0(v2, szNzAzT0) = 0 &
% 40.13/6.61 | $i(v2)) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ (aElementOf0(v2,
% 40.13/6.61 | all_106_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) &
% 40.13/6.61 | sdtlpdtrp0(xe, v2) = v3 & $i(v3)))))
% 40.13/6.61 |
% 40.13/6.61 | ALPHA: (25) implies:
% 40.13/6.61 | (26) szDzizrdt0(xd) = all_106_1
% 40.13/6.61 |
% 40.13/6.61 | DELTA: instantiating (1) with fresh symbols all_109_0, all_109_1, all_109_2
% 40.13/6.61 | gives:
% 40.13/6.61 | (27) szDzizrdt0(xd) = all_109_2 & sdtlbdtrb0(xd, all_109_2) = all_109_1 &
% 40.13/6.61 | szDzozmdt0(xd) = all_109_0 & aSet0(all_109_1) = 0 &
% 40.13/6.61 | aElementOf0(all_109_2, xT) = 0 & $i(all_109_0) & $i(all_109_1) &
% 40.13/6.61 | $i(all_109_2) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 40.13/6.61 | (aElementOf0(v0, all_109_1) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 40.13/6.61 | [v3: $i] : (sdtlpdtrp0(xd, v0) = v3 & aElementOf0(v0, all_109_0) =
% 40.13/6.61 | v2 & $i(v3) & ( ~ (v3 = all_109_2) | ~ (v2 = 0)))) & ! [v0: $i]
% 40.13/6.61 | : ( ~ (aElementOf0(v0, all_109_1) = 0) | ~ $i(v0) | (sdtlpdtrp0(xd,
% 40.13/6.61 | v0) = all_109_2 & aElementOf0(v0, all_109_0) = 0))
% 40.13/6.61 |
% 40.13/6.61 | ALPHA: (27) implies:
% 40.13/6.61 | (28) szDzizrdt0(xd) = all_109_2
% 40.13/6.61 |
% 40.13/6.61 | DELTA: instantiating (2) with fresh symbols all_118_0, all_118_1, all_118_2
% 40.13/6.61 | gives:
% 40.13/6.61 | (29) szDzizrdt0(xd) = all_118_2 & sdtlcdtrc0(xe, all_118_1) = xO &
% 40.13/6.61 | sdtlbdtrb0(xd, all_118_2) = all_118_1 & szDzozmdt0(xd) = all_118_0 &
% 40.13/6.61 | aSet0(all_118_1) = 0 & aSet0(xO) = 0 & $i(all_118_0) & $i(all_118_1) &
% 40.13/6.61 | $i(all_118_2) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 40.13/6.61 | (aElementOf0(v0, all_118_1) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 40.13/6.61 | [v3: $i] : (sdtlpdtrp0(xd, v0) = v3 & aElementOf0(v0, all_118_0) =
% 40.13/6.61 | v2 & $i(v3) & ( ~ (v3 = all_118_2) | ~ (v2 = 0)))) & ! [v0: $i]
% 40.13/6.61 | : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xO) = v1) | ~ $i(v0) |
% 40.13/6.61 | ! [v2: $i] : ( ~ (aElementOf0(v2, all_118_1) = 0) | ~ $i(v2) | ?
% 40.13/6.61 | [v3: $i] : ( ~ (v3 = v0) & sdtlpdtrp0(xe, v2) = v3 & $i(v3)))) &
% 40.13/6.61 | ! [v0: $i] : ( ~ (aElementOf0(v0, all_118_1) = 0) | ~ $i(v0) |
% 40.13/6.61 | (sdtlpdtrp0(xd, v0) = all_118_2 & aElementOf0(v0, all_118_0) = 0)) &
% 40.13/6.61 | ! [v0: $i] : ( ~ (aElementOf0(v0, xO) = 0) | ~ $i(v0) | ? [v1: $i]
% 40.13/6.61 | : (sdtlpdtrp0(xe, v1) = v0 & aElementOf0(v1, all_118_1) = 0 &
% 40.13/6.61 | $i(v1)))
% 40.13/6.61 |
% 40.13/6.61 | ALPHA: (29) implies:
% 40.13/6.61 | (30) szDzizrdt0(xd) = all_118_2
% 40.13/6.61 |
% 40.13/6.62 | GROUND_INST: instantiating (10) with all_85_0, all_91_1, xQ, xc, simplifying
% 40.13/6.62 | with (12), (18) gives:
% 40.13/6.62 | (31) all_91_1 = all_85_0
% 40.13/6.62 |
% 40.13/6.62 | GROUND_INST: instantiating (10) with all_85_0, all_104_1, xn, xd, simplifying
% 40.13/6.62 | with (13), (23) gives:
% 40.13/6.62 | (32) all_104_1 = all_85_0
% 40.13/6.62 |
% 40.13/6.62 | GROUND_INST: instantiating (9) with all_93_1, all_104_1, xd, simplifying with
% 40.13/6.62 | (21), (24) gives:
% 40.13/6.62 | (33) all_104_1 = all_93_1
% 40.13/6.62 |
% 40.13/6.62 | GROUND_INST: instantiating (9) with all_87_0, all_104_1, xd, simplifying with
% 40.13/6.62 | (15), (24) gives:
% 40.13/6.62 | (34) all_104_1 = all_87_0
% 40.13/6.62 |
% 40.13/6.62 | GROUND_INST: instantiating (9) with all_93_1, all_106_1, xd, simplifying with
% 40.13/6.62 | (21), (26) gives:
% 40.13/6.62 | (35) all_106_1 = all_93_1
% 40.13/6.62 |
% 40.13/6.62 | GROUND_INST: instantiating (9) with all_106_1, all_109_2, xd, simplifying with
% 40.13/6.62 | (26), (28) gives:
% 40.13/6.62 | (36) all_109_2 = all_106_1
% 40.13/6.62 |
% 40.13/6.62 | GROUND_INST: instantiating (9) with all_109_2, all_118_2, xd, simplifying with
% 40.13/6.62 | (28), (30) gives:
% 40.13/6.62 | (37) all_118_2 = all_109_2
% 40.13/6.62 |
% 40.13/6.62 | GROUND_INST: instantiating (9) with all_91_0, all_118_2, xd, simplifying with
% 40.13/6.62 | (19), (30) gives:
% 40.13/6.62 | (38) all_118_2 = all_91_0
% 40.13/6.62 |
% 40.13/6.62 | COMBINE_EQS: (37), (38) imply:
% 40.13/6.62 | (39) all_109_2 = all_91_0
% 40.13/6.62 |
% 40.13/6.62 | SIMP: (39) implies:
% 40.13/6.62 | (40) all_109_2 = all_91_0
% 40.13/6.62 |
% 40.13/6.62 | COMBINE_EQS: (36), (40) imply:
% 40.13/6.62 | (41) all_106_1 = all_91_0
% 40.13/6.62 |
% 40.13/6.62 | SIMP: (41) implies:
% 40.13/6.62 | (42) all_106_1 = all_91_0
% 40.13/6.62 |
% 40.13/6.62 | COMBINE_EQS: (35), (42) imply:
% 40.13/6.62 | (43) all_93_1 = all_91_0
% 40.13/6.62 |
% 40.13/6.62 | SIMP: (43) implies:
% 40.13/6.62 | (44) all_93_1 = all_91_0
% 40.13/6.62 |
% 40.13/6.62 | COMBINE_EQS: (32), (34) imply:
% 40.13/6.62 | (45) all_87_0 = all_85_0
% 40.13/6.62 |
% 40.13/6.62 | COMBINE_EQS: (33), (34) imply:
% 40.13/6.62 | (46) all_93_1 = all_87_0
% 40.13/6.62 |
% 40.13/6.62 | SIMP: (46) implies:
% 40.13/6.62 | (47) all_93_1 = all_87_0
% 40.13/6.62 |
% 40.13/6.62 | COMBINE_EQS: (44), (47) imply:
% 40.13/6.62 | (48) all_91_0 = all_87_0
% 40.13/6.62 |
% 40.13/6.62 | SIMP: (48) implies:
% 40.13/6.62 | (49) all_91_0 = all_87_0
% 40.13/6.62 |
% 40.13/6.62 | COMBINE_EQS: (45), (49) imply:
% 40.13/6.62 | (50) all_91_0 = all_85_0
% 40.13/6.62 |
% 40.13/6.62 | REDUCE: (17), (31), (50) imply:
% 40.13/6.62 | (51) $false
% 40.13/6.62 |
% 40.13/6.62 | CLOSE: (51) is inconsistent.
% 40.13/6.62 |
% 40.13/6.62 End of proof
% 40.13/6.62 % SZS output end Proof for theBenchmark
% 40.13/6.62
% 40.13/6.62 6011ms
%------------------------------------------------------------------------------