TSTP Solution File: NUM611+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM611+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 : n016.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 11:48:58 EDT 2023
% Result : Theorem 143.81s 19.94s
% Output : Proof 143.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM611+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 14:03:10 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.05/1.63 Prover 4: Preprocessing ...
% 5.05/1.63 Prover 1: Preprocessing ...
% 5.74/1.67 Prover 2: Preprocessing ...
% 5.74/1.67 Prover 0: Preprocessing ...
% 5.74/1.67 Prover 6: Preprocessing ...
% 5.74/1.67 Prover 3: Preprocessing ...
% 5.74/1.67 Prover 5: Preprocessing ...
% 20.36/3.52 Prover 3: Constructing countermodel ...
% 20.36/3.54 Prover 6: Proving ...
% 20.86/3.62 Prover 1: Constructing countermodel ...
% 23.17/3.94 Prover 5: Proving ...
% 43.30/6.67 Prover 4: Constructing countermodel ...
% 52.74/7.85 Prover 2: Proving ...
% 53.43/7.94 Prover 0: Proving ...
% 98.54/13.98 Prover 5: stopped
% 98.54/13.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 99.04/14.19 Prover 7: Preprocessing ...
% 105.28/14.97 Prover 7: Constructing countermodel ...
% 108.12/15.26 Prover 2: stopped
% 108.12/15.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 109.50/15.44 Prover 8: Preprocessing ...
% 111.20/15.71 Prover 8: Warning: ignoring some quantifiers
% 111.20/15.73 Prover 8: Constructing countermodel ...
% 113.51/15.98 Prover 1: stopped
% 113.51/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 114.76/16.13 Prover 9: Preprocessing ...
% 128.53/17.89 Prover 6: stopped
% 128.53/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.49/18.22 Prover 10: Preprocessing ...
% 130.49/18.22 Prover 9: Constructing countermodel ...
% 133.75/18.68 Prover 10: Constructing countermodel ...
% 143.53/19.90 Prover 10: Found proof (size 57)
% 143.53/19.90 Prover 10: proved (1991ms)
% 143.53/19.90 Prover 9: stopped
% 143.53/19.90 Prover 3: stopped
% 143.53/19.91 Prover 7: stopped
% 143.53/19.91 Prover 8: stopped
% 143.53/19.91 Prover 4: stopped
% 143.81/19.94 Prover 0: stopped
% 143.81/19.94
% 143.81/19.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 143.81/19.94
% 143.81/19.95 % SZS output start Proof for theBenchmark
% 143.81/19.95 Assumptions after simplification:
% 143.81/19.95 ---------------------------------
% 143.81/19.95
% 143.81/19.95 (mCardCons)
% 143.81/19.98 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 143.81/19.98 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2)
% 143.81/19.98 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~
% 143.81/19.98 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0))))
% 143.81/19.98
% 143.81/19.98 (mCardDiff)
% 143.81/19.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v0) =
% 143.81/19.98 v1) | ~ (sdtmndt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 143.81/19.98 isFinite0(v0) | ~ aElementOf0(v2, v0) | ~ aSet0(v0) | ? [v4: $i] :
% 143.81/19.98 (sbrdtbr0(v3) = v4 & szszuzczcdt0(v4) = v1 & $i(v4) & $i(v1)))
% 143.81/19.98
% 143.81/19.98 (mCardNum)
% 143.81/19.98 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0)
% 143.81/19.98 | ~ isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0)) & ! [v0: $i]
% 143.81/19.98 : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 143.81/19.98 szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 143.81/19.98
% 143.81/19.98 (mCountNFin_01)
% 143.81/19.98 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 143.81/19.98
% 143.81/19.98 (mDefEmp)
% 143.81/19.99 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 143.81/19.99 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 143.81/19.99 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 143.81/19.99
% 143.81/19.99 (mNatExtra)
% 143.81/19.99 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 143.81/19.99 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 143.81/19.99 aElementOf0(v1, szNzAzT0)))
% 143.81/19.99
% 143.81/19.99 (mSubFSet)
% 143.81/19.99 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) |
% 143.81/19.99 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 143.81/19.99
% 143.81/19.99 (mSuccEquSucc)
% 143.81/19.99 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.81/19.99 (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 143.81/19.99 | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 143.81/19.99
% 143.81/19.99 (m__)
% 143.81/19.99 $i(xP) & $i(xk) & ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0))
% 143.81/19.99
% 143.81/19.99 (m__3418)
% 143.81/19.99 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 143.81/19.99
% 143.81/19.99 (m__3462)
% 143.81/19.99 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 143.81/19.99
% 143.81/19.99 (m__3520)
% 143.81/19.99 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 143.81/19.99
% 143.81/19.99 (m__3533)
% 143.81/19.99 szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk,
% 143.81/19.99 szNzAzT0)
% 143.81/19.99
% 143.81/19.99 (m__5078)
% 143.81/19.99 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 &
% 143.81/19.99 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) &
% 143.81/19.99 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) |
% 143.81/19.99 aElementOf0(v1, xO)))
% 143.81/19.99
% 143.81/19.99 (m__5147)
% 143.81/19.99 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : (
% 143.81/19.99 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0))
% 143.81/19.99
% 143.81/19.99 (m__5164)
% 143.81/20.00 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 143.81/20.00 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 143.81/20.00 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP))
% 143.81/20.00 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) &
% 143.81/20.00 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1:
% 143.81/20.00 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 143.81/20.00
% 143.81/20.00 (m__5173)
% 143.81/20.00 $i(xp) & $i(xQ) & aElementOf0(xp, xQ)
% 143.81/20.00
% 143.81/20.00 (m__5195)
% 143.81/20.00 $i(xP) & $i(xQ) & aSubsetOf0(xP, xQ) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.81/20.00 aElementOf0(v0, xP) | aElementOf0(v0, xQ))
% 143.81/20.00
% 143.81/20.00 (function-axioms)
% 143.81/20.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.81/20.00 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 143.81/20.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 143.81/20.01 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 143.81/20.01 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 143.81/20.01 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 143.81/20.01 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 143.81/20.01 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 143.81/20.01 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 143.81/20.01 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 143.81/20.01 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 143.81/20.01 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 143.81/20.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 143.81/20.01 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 143.81/20.01 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 143.81/20.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 143.81/20.01 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.81/20.01 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 143.81/20.01 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 143.81/20.01 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.81/20.01 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 143.81/20.01 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 143.81/20.01 v0))
% 143.81/20.01
% 143.81/20.01 Further assumptions not needed in the proof:
% 143.81/20.01 --------------------------------------------
% 143.81/20.01 mCConsSet, mCDiffSet, mCardEmpty, mCardS, mCardSeg, mCardSub, mCardSubEx,
% 143.81/20.01 mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff, mDefMax, mDefMin, mDefPtt,
% 143.81/20.01 mDefRst, mDefSImg, mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet,
% 143.81/20.01 mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg,
% 143.81/20.01 mFunSort, mIH, mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl,
% 143.81/20.01 mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, mNatNSucc,
% 143.81/20.01 mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet,
% 143.81/20.01 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubRefl,
% 143.81/20.01 mSubTrans, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3435,
% 143.81/20.01 m__3453, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331,
% 143.81/20.01 m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891, m__4908, m__4982,
% 143.81/20.01 m__4998, m__5093, m__5106, m__5116, m__5182, m__5208
% 143.81/20.01
% 143.81/20.01 Those formulas are unsatisfiable:
% 143.81/20.01 ---------------------------------
% 143.81/20.01
% 143.81/20.01 Begin of proof
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (mDefEmp) implies:
% 143.81/20.01 | (1) aSet0(slcrc0)
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (mCountNFin_01) implies:
% 143.81/20.01 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (mSuccEquSucc) implies:
% 143.81/20.01 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.81/20.01 | (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~
% 143.81/20.01 | $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (mNatExtra) implies:
% 143.81/20.01 | (4) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 143.81/20.01 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 143.81/20.01 | szNzAzT0)))
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (mCardNum) implies:
% 143.81/20.01 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 143.81/20.01 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 143.81/20.01 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 143.81/20.01 | isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0))
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (m__3418) implies:
% 143.81/20.01 | (7) aElementOf0(xK, szNzAzT0)
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (m__3520) implies:
% 143.81/20.01 | (8) ~ (xK = sz00)
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (m__3533) implies:
% 143.81/20.01 | (9) aElementOf0(xk, szNzAzT0)
% 143.81/20.01 | (10) szszuzczcdt0(xk) = xK
% 143.81/20.01 |
% 143.81/20.01 | ALPHA: (m__5078) implies:
% 143.81/20.01 | (11) $i(xK)
% 143.81/20.02 | (12) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0)
% 143.81/20.02 | & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i]
% 143.81/20.02 | : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO)))
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (m__5147) implies:
% 143.81/20.02 | (13) szmzizndt0(xQ) = xp
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (m__5164) implies:
% 143.81/20.02 | (14) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 143.81/20.02 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 143.81/20.02 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) |
% 143.81/20.02 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 143.81/20.02 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~
% 143.81/20.02 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : (
% 143.81/20.02 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (m__5173) implies:
% 143.81/20.02 | (15) aElementOf0(xp, xQ)
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (m__5195) implies:
% 143.81/20.02 | (16) aSubsetOf0(xP, xQ)
% 143.81/20.02 | (17) $i(xQ)
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (m__) implies:
% 143.81/20.02 | (18) $i(xk)
% 143.81/20.02 | (19) $i(xP)
% 143.81/20.02 | (20) ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0))
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (function-axioms) implies:
% 143.81/20.02 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.81/20.02 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 143.81/20.02 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2)
% 143.81/20.02 | = v1) | ~ (sbrdtbr0(v2) = v0))
% 143.81/20.02 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.81/20.02 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 143.81/20.02 |
% 143.81/20.02 | DELTA: instantiating (20) with fresh symbol all_82_0 gives:
% 143.81/20.02 | (24) ~ (all_82_0 = xk) & sbrdtbr0(xP) = all_82_0 & $i(all_82_0)
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (24) implies:
% 143.81/20.02 | (25) ~ (all_82_0 = xk)
% 143.81/20.02 | (26) sbrdtbr0(xP) = all_82_0
% 143.81/20.02 |
% 143.81/20.02 | DELTA: instantiating (12) with fresh symbol all_92_0 gives:
% 143.81/20.02 | (27) slbdtsldtrb0(xO, xK) = all_92_0 & sbrdtbr0(xQ) = xK & $i(all_92_0) &
% 143.81/20.02 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_92_0) & aSet0(xQ) & ! [v0:
% 143.81/20.02 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO))
% 143.81/20.02 |
% 143.81/20.02 | ALPHA: (27) implies:
% 143.81/20.02 | (28) aSet0(xQ)
% 143.81/20.02 | (29) sbrdtbr0(xQ) = xK
% 143.81/20.02 |
% 143.81/20.02 | DELTA: instantiating (14) with fresh symbol all_95_0 gives:
% 143.81/20.03 | (30) szmzizndt0(xQ) = all_95_0 & sdtmndt0(xQ, all_95_0) = xP & $i(all_95_0)
% 143.81/20.03 | & aSet0(xP) & ~ aElementOf0(all_95_0, xP) & ! [v0: any] : (v0 =
% 143.81/20.03 | all_95_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0) |
% 143.81/20.03 | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 143.81/20.03 | xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.81/20.03 | aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.81/20.03 | aElementOf0(v0, xQ) | sdtlseqdt0(all_95_0, v0))
% 143.81/20.03 |
% 143.81/20.03 | ALPHA: (30) implies:
% 143.81/20.03 | (31) aSet0(xP)
% 143.81/20.03 | (32) $i(all_95_0)
% 143.81/20.03 | (33) sdtmndt0(xQ, all_95_0) = xP
% 143.81/20.03 | (34) szmzizndt0(xQ) = all_95_0
% 143.81/20.03 |
% 143.81/20.03 | BETA: splitting (2) gives:
% 143.81/20.03 |
% 143.81/20.03 | Case 1:
% 143.81/20.03 | |
% 143.81/20.03 | | (35) ~ aSet0(slcrc0)
% 143.81/20.03 | |
% 143.81/20.03 | | PRED_UNIFY: (1), (35) imply:
% 143.81/20.03 | | (36) $false
% 143.81/20.03 | |
% 143.81/20.03 | | CLOSE: (36) is inconsistent.
% 143.81/20.03 | |
% 143.81/20.03 | Case 2:
% 143.81/20.03 | |
% 143.81/20.03 | |
% 143.81/20.03 | | GROUND_INST: instantiating (23) with xp, all_95_0, xQ, simplifying with
% 143.81/20.03 | | (13), (34) gives:
% 143.81/20.03 | | (37) all_95_0 = xp
% 143.81/20.03 | |
% 143.81/20.03 | | REDUCE: (33), (37) imply:
% 143.81/20.03 | | (38) sdtmndt0(xQ, xp) = xP
% 143.81/20.03 | |
% 143.81/20.03 | | REDUCE: (32), (37) imply:
% 143.81/20.03 | | (39) $i(xp)
% 143.81/20.03 | |
% 143.81/20.03 | | GROUND_INST: instantiating (4) with xK, simplifying with (7), (11) gives:
% 143.81/20.03 | | (40) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 143.81/20.03 | | aElementOf0(v0, szNzAzT0))
% 143.81/20.03 | |
% 143.81/20.03 | | GROUND_INST: instantiating (5) with xQ, xK, simplifying with (7), (17),
% 143.81/20.03 | | (28), (29) gives:
% 143.81/20.03 | | (41) isFinite0(xQ)
% 143.81/20.03 | |
% 143.81/20.03 | | BETA: splitting (40) gives:
% 143.81/20.03 | |
% 143.81/20.03 | | Case 1:
% 143.81/20.03 | | |
% 143.81/20.03 | | | (42) xK = sz00
% 143.81/20.03 | | |
% 143.81/20.03 | | | REDUCE: (8), (42) imply:
% 143.81/20.03 | | | (43) $false
% 143.81/20.03 | | |
% 143.81/20.03 | | | CLOSE: (43) is inconsistent.
% 143.81/20.03 | | |
% 143.81/20.03 | | Case 2:
% 143.81/20.03 | | |
% 143.81/20.03 | | | (44) ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & aElementOf0(v0,
% 143.81/20.03 | | | szNzAzT0))
% 143.81/20.03 | | |
% 143.81/20.03 | | | DELTA: instantiating (44) with fresh symbol all_158_0 gives:
% 143.81/20.03 | | | (45) szszuzczcdt0(all_158_0) = xK & $i(all_158_0) &
% 143.81/20.03 | | | aElementOf0(all_158_0, szNzAzT0)
% 143.81/20.03 | | |
% 143.81/20.03 | | | ALPHA: (45) implies:
% 143.81/20.03 | | | (46) aElementOf0(all_158_0, szNzAzT0)
% 143.81/20.03 | | | (47) $i(all_158_0)
% 143.81/20.03 | | | (48) szszuzczcdt0(all_158_0) = xK
% 143.81/20.03 | | |
% 143.81/20.03 | | | GROUND_INST: instantiating (mCardDiff) with xQ, xK, xp, xP, simplifying
% 143.81/20.03 | | | with (15), (17), (28), (29), (38), (39), (41) gives:
% 143.81/20.03 | | | (49) ? [v0: $i] : (sbrdtbr0(xP) = v0 & szszuzczcdt0(v0) = xK & $i(v0)
% 143.81/20.03 | | | & $i(xK))
% 143.81/20.03 | | |
% 143.81/20.04 | | | GROUND_INST: instantiating (mSubFSet) with xQ, xP, simplifying with (16),
% 143.81/20.04 | | | (17), (19), (28), (41) gives:
% 143.81/20.04 | | | (50) isFinite0(xP)
% 143.81/20.04 | | |
% 143.81/20.04 | | | GROUND_INST: instantiating (3) with all_158_0, xk, xK, simplifying with
% 143.81/20.04 | | | (9), (10), (18), (46), (47), (48) gives:
% 143.81/20.04 | | | (51) all_158_0 = xk
% 143.81/20.04 | | |
% 143.81/20.04 | | | DELTA: instantiating (49) with fresh symbol all_185_0 gives:
% 143.81/20.04 | | | (52) sbrdtbr0(xP) = all_185_0 & szszuzczcdt0(all_185_0) = xK &
% 143.81/20.04 | | | $i(all_185_0) & $i(xK)
% 143.81/20.04 | | |
% 143.81/20.04 | | | ALPHA: (52) implies:
% 143.81/20.04 | | | (53) $i(all_185_0)
% 143.81/20.04 | | | (54) szszuzczcdt0(all_185_0) = xK
% 143.81/20.04 | | | (55) sbrdtbr0(xP) = all_185_0
% 143.81/20.04 | | |
% 143.81/20.04 | | | GROUND_INST: instantiating (22) with all_82_0, all_185_0, xP, simplifying
% 143.81/20.04 | | | with (26), (55) gives:
% 143.81/20.04 | | | (56) all_185_0 = all_82_0
% 143.81/20.04 | | |
% 143.81/20.04 | | | REDUCE: (54), (56) imply:
% 143.81/20.04 | | | (57) szszuzczcdt0(all_82_0) = xK
% 143.81/20.04 | | |
% 143.81/20.04 | | | REDUCE: (53), (56) imply:
% 143.81/20.04 | | | (58) $i(all_82_0)
% 143.81/20.04 | | |
% 143.81/20.04 | | | GROUND_INST: instantiating (6) with xP, all_82_0, simplifying with (19),
% 143.81/20.04 | | | (26), (31), (50) gives:
% 143.81/20.04 | | | (59) aElementOf0(all_82_0, szNzAzT0)
% 143.81/20.04 | | |
% 143.81/20.04 | | | GROUND_INST: instantiating (mCardCons) with xP, all_82_0, simplifying with
% 143.81/20.04 | | | (19), (26), (31), (50) gives:
% 143.81/20.04 | | | (60) ? [v0: $i] : (szszuzczcdt0(all_82_0) = v0 & $i(v0) & ! [v1: $i]
% 143.81/20.04 | | | : ! [v2: $i] : ( ~ (sdtpldt0(xP, v1) = v2) | ~ $i(v1) | ~
% 143.81/20.04 | | | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, xP)))
% 143.81/20.04 | | |
% 143.81/20.04 | | | DELTA: instantiating (60) with fresh symbol all_233_0 gives:
% 143.81/20.04 | | | (61) szszuzczcdt0(all_82_0) = all_233_0 & $i(all_233_0) & ! [v0: $i] :
% 143.81/20.04 | | | ! [v1: $i] : ( ~ (sdtpldt0(xP, v0) = v1) | ~ $i(v0) | ~
% 143.81/20.04 | | | aElement0(v0) | sbrdtbr0(v1) = all_233_0 | aElementOf0(v0, xP))
% 143.81/20.04 | | |
% 143.81/20.04 | | | ALPHA: (61) implies:
% 143.81/20.04 | | | (62) szszuzczcdt0(all_82_0) = all_233_0
% 143.81/20.04 | | |
% 143.81/20.04 | | | GROUND_INST: instantiating (21) with xK, all_233_0, all_82_0, simplifying
% 143.81/20.04 | | | with (57), (62) gives:
% 143.81/20.04 | | | (63) all_233_0 = xK
% 143.81/20.04 | | |
% 143.81/20.04 | | | GROUND_INST: instantiating (3) with xk, all_82_0, xK, simplifying with
% 143.81/20.04 | | | (9), (10), (18), (57), (58), (59) gives:
% 143.81/20.04 | | | (64) all_82_0 = xk
% 143.81/20.04 | | |
% 143.81/20.04 | | | REDUCE: (25), (64) imply:
% 143.81/20.04 | | | (65) $false
% 143.81/20.04 | | |
% 143.81/20.04 | | | CLOSE: (65) is inconsistent.
% 143.81/20.04 | | |
% 143.81/20.04 | | End of split
% 143.81/20.04 | |
% 143.81/20.04 | End of split
% 143.81/20.04 |
% 143.81/20.04 End of proof
% 143.81/20.04 % SZS output end Proof for theBenchmark
% 143.81/20.04
% 143.81/20.04 19426ms
%------------------------------------------------------------------------------