TSTP Solution File: NUM612+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM612+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:48:58 EDT 2023
% Result : Theorem 143.52s 19.42s
% Output : Proof 143.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM612+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.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 10:33:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.64 ________ _____
% 0.19/0.64 ___ __ \_________(_)________________________________
% 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.64
% 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.64 (2023-06-19)
% 0.19/0.64
% 0.19/0.64 (c) Philipp Rümmer, 2009-2023
% 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.64 Amanda Stjerna.
% 0.19/0.64 Free software under BSD-3-Clause.
% 0.19/0.64
% 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.64
% 0.19/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.66 Running up to 7 provers in parallel.
% 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.86/1.73 Prover 4: Preprocessing ...
% 6.86/1.73 Prover 1: Preprocessing ...
% 7.58/1.77 Prover 3: Preprocessing ...
% 7.58/1.77 Prover 6: Preprocessing ...
% 7.58/1.77 Prover 5: Preprocessing ...
% 7.58/1.77 Prover 0: Preprocessing ...
% 7.58/1.77 Prover 2: Preprocessing ...
% 18.79/3.39 Prover 3: Constructing countermodel ...
% 18.79/3.40 Prover 1: Constructing countermodel ...
% 18.79/3.44 Prover 6: Proving ...
% 22.49/3.77 Prover 5: Proving ...
% 50.50/7.42 Prover 4: Constructing countermodel ...
% 56.51/8.18 Prover 2: Proving ...
% 60.03/8.62 Prover 0: Proving ...
% 101.62/14.01 Prover 5: stopped
% 102.14/14.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 103.10/14.21 Prover 7: Preprocessing ...
% 108.69/14.98 Prover 7: Constructing countermodel ...
% 116.05/15.87 Prover 2: stopped
% 116.05/15.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 117.44/16.04 Prover 1: stopped
% 117.44/16.05 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.80/16.10 Prover 8: Preprocessing ...
% 118.41/16.28 Prover 9: Preprocessing ...
% 120.48/16.45 Prover 8: Warning: ignoring some quantifiers
% 120.48/16.48 Prover 8: Constructing countermodel ...
% 131.73/17.92 Prover 6: stopped
% 131.73/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.93/18.08 Prover 10: Preprocessing ...
% 135.47/18.42 Prover 9: Constructing countermodel ...
% 136.60/18.55 Prover 10: Constructing countermodel ...
% 143.20/19.40 Prover 10: Found proof (size 40)
% 143.20/19.40 Prover 10: proved (1481ms)
% 143.20/19.40 Prover 8: stopped
% 143.20/19.40 Prover 0: stopped
% 143.20/19.40 Prover 7: stopped
% 143.52/19.40 Prover 9: stopped
% 143.52/19.41 Prover 4: stopped
% 143.52/19.42 Prover 3: stopped
% 143.52/19.42
% 143.52/19.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 143.52/19.42
% 143.52/19.42 % SZS output start Proof for theBenchmark
% 143.52/19.43 Assumptions after simplification:
% 143.52/19.43 ---------------------------------
% 143.52/19.43
% 143.52/19.43 (mCardDiff)
% 143.66/19.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sbrdtbr0(v0) =
% 143.66/19.46 v1) | ~ (sdtmndt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 143.66/19.46 isFinite0(v0) | ~ aElementOf0(v2, v0) | ~ aSet0(v0) | ? [v4: $i] :
% 143.66/19.46 (sbrdtbr0(v3) = v4 & szszuzczcdt0(v4) = v1 & $i(v4) & $i(v1)))
% 143.66/19.46
% 143.66/19.46 (mCardNum)
% 143.66/19.46 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0)
% 143.66/19.46 | ~ isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0)) & ! [v0: $i]
% 143.66/19.46 : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 143.66/19.46 szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 143.66/19.46
% 143.66/19.46 (mCountNFin_01)
% 143.66/19.46 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 143.66/19.46
% 143.66/19.46 (mDefEmp)
% 143.66/19.46 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 143.66/19.46 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 143.66/19.46 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 143.66/19.46
% 143.66/19.46 (mSubFSet)
% 143.66/19.46 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) |
% 143.66/19.46 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 143.66/19.46
% 143.66/19.46 (m__)
% 143.66/19.46 $i(xP) & $i(xQ) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 143.66/19.46 (sbrdtbr0(xP) = v0 & $i(v0) & ( ~ aElementOf0(v0, szNzAzT0) | ( ~ (v2 = v1) &
% 143.66/19.46 sbrdtbr0(xQ) = v2 & szszuzczcdt0(v0) = v1 & $i(v2) & $i(v1))))
% 143.66/19.46
% 143.66/19.46 (m__3418)
% 143.66/19.46 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 143.66/19.46
% 143.66/19.47 (m__5078)
% 143.66/19.47 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 &
% 143.66/19.47 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) &
% 143.66/19.47 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) |
% 143.66/19.47 aElementOf0(v1, xO)))
% 143.66/19.47
% 143.66/19.47 (m__5147)
% 143.66/19.47 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : (
% 143.66/19.47 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0))
% 143.66/19.47
% 143.66/19.47 (m__5164)
% 143.66/19.47 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 143.66/19.47 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 143.66/19.47 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP))
% 143.66/19.47 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) &
% 143.66/19.47 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1:
% 143.66/19.47 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 143.66/19.47
% 143.66/19.47 (m__5173)
% 143.66/19.47 $i(xp) & $i(xQ) & aElementOf0(xp, xQ)
% 143.66/19.47
% 143.66/19.47 (m__5195)
% 143.66/19.47 $i(xP) & $i(xQ) & aSubsetOf0(xP, xQ) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.66/19.47 aElementOf0(v0, xP) | aElementOf0(v0, xQ))
% 143.66/19.47
% 143.66/19.47 (function-axioms)
% 143.66/19.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.66/19.48 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 143.66/19.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 143.66/19.48 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 143.66/19.48 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 143.66/19.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 143.66/19.48 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 143.66/19.48 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 143.66/19.48 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 143.66/19.48 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 143.66/19.48 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 143.66/19.48 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 143.66/19.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 143.66/19.48 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 143.66/19.48 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 143.66/19.48 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 143.66/19.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.66/19.48 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 143.66/19.48 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 143.66/19.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.66/19.48 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 143.66/19.48 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 143.66/19.48 v0))
% 143.66/19.48
% 143.66/19.48 Further assumptions not needed in the proof:
% 143.66/19.48 --------------------------------------------
% 143.66/19.48 mCConsSet, mCDiffSet, mCardCons, mCardEmpty, mCardS, mCardSeg, mCardSub,
% 143.66/19.48 mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff, mDefMax,
% 143.66/19.48 mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, mDefSub, mDiffCons,
% 143.66/19.48 mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel,
% 143.66/19.48 mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm,
% 143.66/19.48 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet,
% 143.66/19.48 mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc,
% 143.66/19.48 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm,
% 143.66/19.48 mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum,
% 143.66/19.48 m__3291, m__3398, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671,
% 143.66/19.48 m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660,
% 143.66/19.48 m__4730, m__4758, m__4854, m__4891, m__4908, m__4982, m__4998, m__5093, m__5106,
% 143.66/19.48 m__5116, m__5182, m__5208
% 143.66/19.48
% 143.66/19.48 Those formulas are unsatisfiable:
% 143.66/19.48 ---------------------------------
% 143.66/19.48
% 143.66/19.48 Begin of proof
% 143.66/19.48 |
% 143.66/19.48 | ALPHA: (mDefEmp) implies:
% 143.66/19.48 | (1) aSet0(slcrc0)
% 143.66/19.48 |
% 143.66/19.48 | ALPHA: (mCountNFin_01) implies:
% 143.66/19.48 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 143.66/19.48 |
% 143.66/19.48 | ALPHA: (mCardNum) implies:
% 143.66/19.49 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 143.66/19.49 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 143.66/19.49 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 143.66/19.49 | isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0))
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (m__3418) implies:
% 143.66/19.49 | (5) aElementOf0(xK, szNzAzT0)
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (m__5078) implies:
% 143.66/19.49 | (6) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0) &
% 143.66/19.49 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] :
% 143.66/19.49 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO)))
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (m__5147) implies:
% 143.66/19.49 | (7) szmzizndt0(xQ) = xp
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (m__5164) implies:
% 143.66/19.49 | (8) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 143.66/19.49 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 143.66/19.49 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) |
% 143.66/19.49 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 143.66/19.49 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~
% 143.66/19.49 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : (
% 143.66/19.49 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (m__5173) implies:
% 143.66/19.49 | (9) aElementOf0(xp, xQ)
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (m__5195) implies:
% 143.66/19.49 | (10) aSubsetOf0(xP, xQ)
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (m__) implies:
% 143.66/19.49 | (11) $i(xQ)
% 143.66/19.49 | (12) $i(xP)
% 143.66/19.49 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sbrdtbr0(xP) = v0 & $i(v0)
% 143.66/19.49 | & ( ~ aElementOf0(v0, szNzAzT0) | ( ~ (v2 = v1) & sbrdtbr0(xQ) = v2
% 143.66/19.49 | & szszuzczcdt0(v0) = v1 & $i(v2) & $i(v1))))
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (function-axioms) implies:
% 143.66/19.49 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.66/19.49 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 143.66/19.49 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2)
% 143.66/19.49 | = v1) | ~ (sbrdtbr0(v2) = v0))
% 143.66/19.49 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.66/19.49 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 143.66/19.49 |
% 143.66/19.49 | DELTA: instantiating (13) with fresh symbols all_90_0, all_90_1, all_90_2
% 143.66/19.49 | gives:
% 143.66/19.49 | (17) sbrdtbr0(xP) = all_90_2 & $i(all_90_2) & ( ~ aElementOf0(all_90_2,
% 143.66/19.49 | szNzAzT0) | ( ~ (all_90_0 = all_90_1) & sbrdtbr0(xQ) = all_90_0 &
% 143.66/19.49 | szszuzczcdt0(all_90_2) = all_90_1 & $i(all_90_0) & $i(all_90_1)))
% 143.66/19.49 |
% 143.66/19.49 | ALPHA: (17) implies:
% 143.66/19.49 | (18) sbrdtbr0(xP) = all_90_2
% 143.66/19.50 | (19) ~ aElementOf0(all_90_2, szNzAzT0) | ( ~ (all_90_0 = all_90_1) &
% 143.66/19.50 | sbrdtbr0(xQ) = all_90_0 & szszuzczcdt0(all_90_2) = all_90_1 &
% 143.66/19.50 | $i(all_90_0) & $i(all_90_1))
% 143.66/19.50 |
% 143.66/19.50 | DELTA: instantiating (6) with fresh symbol all_92_0 gives:
% 143.66/19.50 | (20) slbdtsldtrb0(xO, xK) = all_92_0 & sbrdtbr0(xQ) = xK & $i(all_92_0) &
% 143.66/19.50 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_92_0) & aSet0(xQ) & ! [v0:
% 143.66/19.50 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO))
% 143.66/19.50 |
% 143.66/19.50 | ALPHA: (20) implies:
% 143.66/19.50 | (21) aSet0(xQ)
% 143.66/19.50 | (22) sbrdtbr0(xQ) = xK
% 143.66/19.50 |
% 143.66/19.50 | DELTA: instantiating (8) with fresh symbol all_95_0 gives:
% 143.66/19.50 | (23) szmzizndt0(xQ) = all_95_0 & sdtmndt0(xQ, all_95_0) = xP & $i(all_95_0)
% 143.66/19.50 | & aSet0(xP) & ~ aElementOf0(all_95_0, xP) & ! [v0: any] : (v0 =
% 143.66/19.50 | all_95_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0) |
% 143.66/19.50 | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 143.66/19.50 | xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.66/19.50 | aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 143.66/19.50 | aElementOf0(v0, xQ) | sdtlseqdt0(all_95_0, v0))
% 143.66/19.50 |
% 143.66/19.50 | ALPHA: (23) implies:
% 143.66/19.50 | (24) aSet0(xP)
% 143.66/19.50 | (25) $i(all_95_0)
% 143.66/19.50 | (26) sdtmndt0(xQ, all_95_0) = xP
% 143.66/19.50 | (27) szmzizndt0(xQ) = all_95_0
% 143.66/19.50 |
% 143.66/19.50 | BETA: splitting (2) gives:
% 143.66/19.50 |
% 143.66/19.50 | Case 1:
% 143.66/19.50 | |
% 143.66/19.50 | | (28) ~ aSet0(slcrc0)
% 143.66/19.50 | |
% 143.66/19.50 | | PRED_UNIFY: (1), (28) imply:
% 143.66/19.50 | | (29) $false
% 143.66/19.50 | |
% 143.66/19.50 | | CLOSE: (29) is inconsistent.
% 143.66/19.50 | |
% 143.66/19.50 | Case 2:
% 143.66/19.50 | |
% 143.66/19.50 | |
% 143.66/19.50 | | GROUND_INST: instantiating (16) with xp, all_95_0, xQ, simplifying with (7),
% 143.66/19.50 | | (27) gives:
% 143.66/19.50 | | (30) all_95_0 = xp
% 143.66/19.50 | |
% 143.66/19.50 | | REDUCE: (26), (30) imply:
% 143.66/19.50 | | (31) sdtmndt0(xQ, xp) = xP
% 143.66/19.50 | |
% 143.66/19.50 | | REDUCE: (25), (30) imply:
% 143.66/19.50 | | (32) $i(xp)
% 143.66/19.50 | |
% 143.66/19.50 | | GROUND_INST: instantiating (3) with xQ, xK, simplifying with (5), (11),
% 143.66/19.50 | | (21), (22) gives:
% 143.66/19.50 | | (33) isFinite0(xQ)
% 143.66/19.50 | |
% 143.66/19.50 | | GROUND_INST: instantiating (mCardDiff) with xQ, xK, xp, xP, simplifying with
% 143.66/19.50 | | (9), (11), (21), (22), (31), (32), (33) gives:
% 143.66/19.51 | | (34) ? [v0: $i] : (sbrdtbr0(xP) = v0 & szszuzczcdt0(v0) = xK & $i(v0) &
% 143.66/19.51 | | $i(xK))
% 143.66/19.51 | |
% 143.66/19.51 | | GROUND_INST: instantiating (mSubFSet) with xQ, xP, simplifying with (10),
% 143.66/19.51 | | (11), (12), (21), (33) gives:
% 143.66/19.51 | | (35) isFinite0(xP)
% 143.66/19.51 | |
% 143.66/19.51 | | DELTA: instantiating (34) with fresh symbol all_186_0 gives:
% 143.66/19.51 | | (36) sbrdtbr0(xP) = all_186_0 & szszuzczcdt0(all_186_0) = xK &
% 143.66/19.51 | | $i(all_186_0) & $i(xK)
% 143.66/19.51 | |
% 143.66/19.51 | | ALPHA: (36) implies:
% 143.66/19.51 | | (37) szszuzczcdt0(all_186_0) = xK
% 143.66/19.51 | | (38) sbrdtbr0(xP) = all_186_0
% 143.66/19.51 | |
% 143.66/19.51 | | GROUND_INST: instantiating (15) with all_90_2, all_186_0, xP, simplifying
% 143.66/19.51 | | with (18), (38) gives:
% 143.66/19.51 | | (39) all_186_0 = all_90_2
% 143.66/19.51 | |
% 143.66/19.51 | | REDUCE: (37), (39) imply:
% 143.66/19.51 | | (40) szszuzczcdt0(all_90_2) = xK
% 143.66/19.51 | |
% 143.66/19.51 | | BETA: splitting (19) gives:
% 143.66/19.51 | |
% 143.66/19.51 | | Case 1:
% 143.66/19.51 | | |
% 143.66/19.51 | | | (41) ~ aElementOf0(all_90_2, szNzAzT0)
% 143.66/19.51 | | |
% 143.66/19.51 | | | GROUND_INST: instantiating (4) with xP, all_90_2, simplifying with (12),
% 143.66/19.51 | | | (18), (24), (35), (41) gives:
% 143.66/19.51 | | | (42) $false
% 143.66/19.51 | | |
% 143.66/19.51 | | | CLOSE: (42) is inconsistent.
% 143.66/19.51 | | |
% 143.66/19.51 | | Case 2:
% 143.66/19.51 | | |
% 143.66/19.51 | | | (43) ~ (all_90_0 = all_90_1) & sbrdtbr0(xQ) = all_90_0 &
% 143.66/19.51 | | | szszuzczcdt0(all_90_2) = all_90_1 & $i(all_90_0) & $i(all_90_1)
% 143.66/19.51 | | |
% 143.66/19.51 | | | ALPHA: (43) implies:
% 143.66/19.51 | | | (44) ~ (all_90_0 = all_90_1)
% 143.66/19.51 | | | (45) szszuzczcdt0(all_90_2) = all_90_1
% 143.66/19.51 | | | (46) sbrdtbr0(xQ) = all_90_0
% 143.66/19.51 | | |
% 143.66/19.51 | | | GROUND_INST: instantiating (14) with xK, all_90_1, all_90_2, simplifying
% 143.66/19.51 | | | with (40), (45) gives:
% 143.66/19.51 | | | (47) all_90_1 = xK
% 143.66/19.51 | | |
% 143.66/19.51 | | | GROUND_INST: instantiating (15) with xK, all_90_0, xQ, simplifying with
% 143.66/19.51 | | | (22), (46) gives:
% 143.66/19.51 | | | (48) all_90_0 = xK
% 143.66/19.51 | | |
% 143.66/19.51 | | | REDUCE: (44), (47), (48) imply:
% 143.66/19.51 | | | (49) $false
% 143.66/19.51 | | |
% 143.66/19.51 | | | CLOSE: (49) is inconsistent.
% 143.66/19.51 | | |
% 143.66/19.51 | | End of split
% 143.66/19.51 | |
% 143.66/19.51 | End of split
% 143.66/19.51 |
% 143.66/19.51 End of proof
% 143.66/19.51 % SZS output end Proof for theBenchmark
% 143.66/19.51
% 143.66/19.51 18873ms
%------------------------------------------------------------------------------