TSTP Solution File: NUM624+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM624+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 : 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 11:49:03 EDT 2023
% Result : Theorem 23.53s 4.01s
% Output : Proof 30.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM624+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 14:52:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.95/1.52 Prover 4: Preprocessing ...
% 5.61/1.55 Prover 1: Preprocessing ...
% 5.61/1.58 Prover 0: Preprocessing ...
% 5.61/1.58 Prover 3: Preprocessing ...
% 5.61/1.58 Prover 6: Preprocessing ...
% 5.61/1.58 Prover 2: Preprocessing ...
% 5.61/1.58 Prover 5: Preprocessing ...
% 15.49/2.94 Prover 1: Constructing countermodel ...
% 16.47/3.04 Prover 3: Constructing countermodel ...
% 16.69/3.07 Prover 6: Proving ...
% 17.79/3.20 Prover 5: Proving ...
% 18.35/3.26 Prover 2: Proving ...
% 22.94/3.89 Prover 4: Constructing countermodel ...
% 23.53/4.01 Prover 3: proved (3351ms)
% 23.53/4.01
% 23.53/4.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.53/4.01
% 23.53/4.01 Prover 2: stopped
% 23.53/4.01 Prover 5: stopped
% 23.99/4.02 Prover 6: stopped
% 23.99/4.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.99/4.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.99/4.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.99/4.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.99/4.19 Prover 7: Preprocessing ...
% 23.99/4.23 Prover 0: Proving ...
% 23.99/4.24 Prover 10: Preprocessing ...
% 25.09/4.25 Prover 0: stopped
% 25.09/4.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.16/4.33 Prover 11: Preprocessing ...
% 26.44/4.40 Prover 8: Preprocessing ...
% 26.97/4.45 Prover 13: Preprocessing ...
% 27.23/4.53 Prover 10: Constructing countermodel ...
% 27.93/4.59 Prover 7: Constructing countermodel ...
% 29.59/4.85 Prover 8: Warning: ignoring some quantifiers
% 29.59/4.86 Prover 8: Constructing countermodel ...
% 29.59/4.89 Prover 10: Found proof (size 49)
% 29.59/4.89 Prover 10: proved (851ms)
% 29.59/4.90 Prover 7: stopped
% 29.59/4.90 Prover 1: stopped
% 29.59/4.90 Prover 4: stopped
% 29.59/4.90 Prover 11: stopped
% 29.59/4.90 Prover 8: stopped
% 29.59/4.92 Prover 13: Warning: ignoring some quantifiers
% 29.59/4.95 Prover 13: Constructing countermodel ...
% 29.59/4.97 Prover 13: stopped
% 29.59/4.97
% 29.59/4.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.59/4.97
% 30.62/4.98 % SZS output start Proof for theBenchmark
% 30.62/4.98 Assumptions after simplification:
% 30.62/4.98 ---------------------------------
% 30.62/4.98
% 30.62/4.98 (mMinMin)
% 30.87/5.01 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 30.87/5.01 $i] : (v3 = v2 | v1 = slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~
% 30.87/5.01 (szmzizndt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0)
% 30.87/5.01 | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ aElementOf0(v2,
% 30.87/5.01 v1))
% 30.87/5.01
% 30.87/5.01 (m__)
% 30.87/5.01 ~ (xx = xp) & $i(xx) & $i(xp)
% 30.87/5.01
% 30.87/5.01 (m__5147)
% 30.87/5.01 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ)
% 30.87/5.01
% 30.87/5.01 (m__5164)
% 30.87/5.01 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 30.87/5.01 $i(v0) & aSet0(xP))
% 30.87/5.01
% 30.87/5.01 (m__5401)
% 30.87/5.01 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 &
% 30.87/5.01 szmzizndt0(v0) = xx & $i(v0))
% 30.87/5.01
% 30.87/5.01 (m__5442)
% 30.87/5.01 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 30.87/5.01 (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 &
% 30.87/5.01 $i(v2) & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v2))
% 30.87/5.01
% 30.87/5.01 (m__5461)
% 30.87/5.01 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) =
% 30.87/5.01 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1))
% 30.87/5.01
% 30.87/5.01 (m__5481)
% 30.87/5.01 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm)
% 30.87/5.01 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0))
% 30.87/5.01
% 30.87/5.01 (m__5518)
% 30.87/5.01 $i(xm) & $i(xQ) & $i(xN) & $i(szNzAzT0) & $i(slcrc0) & ? [v0: $i] : ( ~ (v0 =
% 30.87/5.01 slcrc0) & ~ (xQ = slcrc0) & sdtlpdtrp0(xN, xm) = v0 & $i(v0) &
% 30.87/5.01 aSubsetOf0(v0, szNzAzT0) & aSubsetOf0(xQ, szNzAzT0))
% 30.87/5.01
% 30.87/5.01 (function-axioms)
% 30.87/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 30.87/5.02 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 30.87/5.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 30.87/5.02 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 30.87/5.02 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 30.87/5.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 30.87/5.02 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 30.87/5.02 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 30.87/5.02 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 30.87/5.02 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 30.87/5.02 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 30.87/5.02 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 30.87/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 30.87/5.02 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 30.87/5.02 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 30.87/5.02 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 30.87/5.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 30.87/5.02 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 30.87/5.02 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 30.87/5.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 30.87/5.02 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 30.87/5.02 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 30.87/5.02 v0))
% 30.87/5.02
% 30.87/5.02 Further assumptions not needed in the proof:
% 30.87/5.02 --------------------------------------------
% 30.87/5.02 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 30.87/5.02 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 30.87/5.02 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 30.87/5.02 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 30.87/5.02 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 30.87/5.02 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 30.87/5.02 mLessTotal, mLessTrans, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet,
% 30.87/5.02 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet,
% 30.87/5.02 mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc,
% 30.87/5.02 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435,
% 30.87/5.02 m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965,
% 30.87/5.02 m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854,
% 30.87/5.02 m__4891, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, m__5173,
% 30.87/5.02 m__5182, m__5195, m__5208, m__5217, m__5270, m__5309, m__5321, m__5348, m__5365,
% 30.87/5.02 m__5389
% 30.87/5.02
% 30.87/5.02 Those formulas are unsatisfiable:
% 30.87/5.02 ---------------------------------
% 30.87/5.02
% 30.87/5.02 Begin of proof
% 30.87/5.02 |
% 30.87/5.02 | ALPHA: (mMinMin) implies:
% 30.87/5.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 =
% 30.87/5.02 | slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ (szmzizndt0(v0)
% 30.87/5.02 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 30.87/5.02 | aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~
% 30.87/5.02 | aElementOf0(v2, v1))
% 30.87/5.02 |
% 30.87/5.02 | ALPHA: (m__5147) implies:
% 30.87/5.02 | (2) szmzizndt0(xQ) = xp
% 30.87/5.02 |
% 30.87/5.02 | ALPHA: (m__5164) implies:
% 30.87/5.03 | (3) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 30.87/5.03 | aSet0(xP))
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (m__5401) implies:
% 30.87/5.03 | (4) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & $i(v0))
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (m__5442) implies:
% 30.87/5.03 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, v1) = v2 &
% 30.87/5.03 | sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & $i(v2) & $i(v1) &
% 30.87/5.03 | $i(v0) & ~ aSubsetOf0(v0, v2))
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (m__5461) implies:
% 30.87/5.03 | (6) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN,
% 30.87/5.03 | xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1))
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (m__5481) implies:
% 30.87/5.03 | (7) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & aElementOf0(xx, xQ) &
% 30.87/5.03 | aElementOf0(xp, v0))
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (m__5518) implies:
% 30.87/5.03 | (8) $i(xQ)
% 30.87/5.03 | (9) ? [v0: $i] : ( ~ (v0 = slcrc0) & ~ (xQ = slcrc0) & sdtlpdtrp0(xN, xm)
% 30.87/5.03 | = v0 & $i(v0) & aSubsetOf0(v0, szNzAzT0) & aSubsetOf0(xQ, szNzAzT0))
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (m__) implies:
% 30.87/5.03 | (10) ~ (xx = xp)
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (function-axioms) implies:
% 30.87/5.03 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 30.87/5.03 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 30.87/5.03 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 30.87/5.03 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 30.87/5.03 |
% 30.87/5.03 | DELTA: instantiating (4) with fresh symbol all_80_0 gives:
% 30.87/5.03 | (13) sdtlpdtrp0(xN, xm) = all_80_0 & szmzizndt0(all_80_0) = xx &
% 30.87/5.03 | $i(all_80_0)
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (13) implies:
% 30.87/5.03 | (14) szmzizndt0(all_80_0) = xx
% 30.87/5.03 | (15) sdtlpdtrp0(xN, xm) = all_80_0
% 30.87/5.03 |
% 30.87/5.03 | DELTA: instantiating (3) with fresh symbol all_86_0 gives:
% 30.87/5.03 | (16) szmzizndt0(xQ) = all_86_0 & sdtmndt0(xQ, all_86_0) = xP & $i(all_86_0)
% 30.87/5.03 | & aSet0(xP)
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (16) implies:
% 30.87/5.03 | (17) szmzizndt0(xQ) = all_86_0
% 30.87/5.03 |
% 30.87/5.03 | DELTA: instantiating (7) with fresh symbol all_88_0 gives:
% 30.87/5.03 | (18) sdtlpdtrp0(xN, xm) = all_88_0 & $i(all_88_0) & aElementOf0(xx, xQ) &
% 30.87/5.03 | aElementOf0(xp, all_88_0)
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (18) implies:
% 30.87/5.03 | (19) aElementOf0(xp, all_88_0)
% 30.87/5.03 | (20) aElementOf0(xx, xQ)
% 30.87/5.03 | (21) $i(all_88_0)
% 30.87/5.03 | (22) sdtlpdtrp0(xN, xm) = all_88_0
% 30.87/5.03 |
% 30.87/5.03 | DELTA: instantiating (6) with fresh symbols all_90_0, all_90_1 gives:
% 30.87/5.03 | (23) sdtlpdtrp0(xN, xm) = all_90_0 & sdtlpdtrp0(xN, xn) = all_90_1 &
% 30.87/5.03 | $i(all_90_0) & $i(all_90_1) & aSubsetOf0(all_90_1, all_90_0)
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (23) implies:
% 30.87/5.03 | (24) sdtlpdtrp0(xN, xm) = all_90_0
% 30.87/5.03 |
% 30.87/5.03 | DELTA: instantiating (9) with fresh symbol all_94_0 gives:
% 30.87/5.03 | (25) ~ (all_94_0 = slcrc0) & ~ (xQ = slcrc0) & sdtlpdtrp0(xN, xm) =
% 30.87/5.03 | all_94_0 & $i(all_94_0) & aSubsetOf0(all_94_0, szNzAzT0) &
% 30.87/5.03 | aSubsetOf0(xQ, szNzAzT0)
% 30.87/5.03 |
% 30.87/5.03 | ALPHA: (25) implies:
% 30.87/5.03 | (26) ~ (xQ = slcrc0)
% 30.87/5.03 | (27) ~ (all_94_0 = slcrc0)
% 30.87/5.03 | (28) aSubsetOf0(xQ, szNzAzT0)
% 30.87/5.03 | (29) aSubsetOf0(all_94_0, szNzAzT0)
% 30.87/5.03 | (30) sdtlpdtrp0(xN, xm) = all_94_0
% 30.87/5.03 |
% 30.87/5.03 | DELTA: instantiating (5) with fresh symbols all_104_0, all_104_1, all_104_2
% 30.87/5.03 | gives:
% 30.87/5.04 | (31) sdtlpdtrp0(xN, all_104_1) = all_104_0 & sdtlpdtrp0(xN, xm) = all_104_2
% 30.87/5.04 | & szszuzczcdt0(xn) = all_104_1 & $i(all_104_0) & $i(all_104_1) &
% 30.87/5.04 | $i(all_104_2) & ~ aSubsetOf0(all_104_2, all_104_0)
% 30.87/5.04 |
% 30.87/5.04 | ALPHA: (31) implies:
% 30.87/5.04 | (32) sdtlpdtrp0(xN, xm) = all_104_2
% 30.87/5.04 |
% 30.87/5.04 | GROUND_INST: instantiating (11) with xp, all_86_0, xQ, simplifying with (2),
% 30.87/5.04 | (17) gives:
% 30.87/5.04 | (33) all_86_0 = xp
% 30.87/5.04 |
% 30.87/5.04 | GROUND_INST: instantiating (12) with all_80_0, all_94_0, xm, xN, simplifying
% 30.87/5.04 | with (15), (30) gives:
% 30.87/5.04 | (34) all_94_0 = all_80_0
% 30.87/5.04 |
% 30.87/5.04 | GROUND_INST: instantiating (12) with all_94_0, all_104_2, xm, xN, simplifying
% 30.87/5.04 | with (30), (32) gives:
% 30.87/5.04 | (35) all_104_2 = all_94_0
% 30.87/5.04 |
% 30.87/5.04 | GROUND_INST: instantiating (12) with all_90_0, all_104_2, xm, xN, simplifying
% 30.87/5.04 | with (24), (32) gives:
% 30.87/5.04 | (36) all_104_2 = all_90_0
% 30.87/5.04 |
% 30.87/5.04 | GROUND_INST: instantiating (12) with all_88_0, all_104_2, xm, xN, simplifying
% 30.87/5.04 | with (22), (32) gives:
% 30.87/5.04 | (37) all_104_2 = all_88_0
% 30.87/5.04 |
% 30.87/5.04 | COMBINE_EQS: (35), (36) imply:
% 30.87/5.04 | (38) all_94_0 = all_90_0
% 30.87/5.04 |
% 30.87/5.04 | SIMP: (38) implies:
% 30.87/5.04 | (39) all_94_0 = all_90_0
% 30.87/5.04 |
% 30.87/5.04 | COMBINE_EQS: (36), (37) imply:
% 30.87/5.04 | (40) all_90_0 = all_88_0
% 30.87/5.04 |
% 30.87/5.04 | COMBINE_EQS: (34), (39) imply:
% 30.87/5.04 | (41) all_90_0 = all_80_0
% 30.87/5.04 |
% 30.87/5.04 | SIMP: (41) implies:
% 30.87/5.04 | (42) all_90_0 = all_80_0
% 30.87/5.04 |
% 30.87/5.04 | COMBINE_EQS: (40), (42) imply:
% 30.87/5.04 | (43) all_88_0 = all_80_0
% 30.87/5.04 |
% 30.87/5.04 | SIMP: (43) implies:
% 30.87/5.04 | (44) all_88_0 = all_80_0
% 30.87/5.04 |
% 30.87/5.04 | REDUCE: (27), (34) imply:
% 30.87/5.04 | (45) ~ (all_80_0 = slcrc0)
% 30.87/5.04 |
% 30.87/5.04 | REDUCE: (21), (44) imply:
% 30.87/5.04 | (46) $i(all_80_0)
% 30.87/5.04 |
% 30.87/5.04 | REDUCE: (29), (34) imply:
% 30.87/5.04 | (47) aSubsetOf0(all_80_0, szNzAzT0)
% 30.87/5.04 |
% 30.87/5.04 | REDUCE: (19), (44) imply:
% 30.87/5.04 | (48) aElementOf0(xp, all_80_0)
% 30.87/5.04 |
% 30.87/5.04 | GROUND_INST: instantiating (1) with xQ, all_80_0, xp, xx, simplifying with
% 30.87/5.04 | (2), (8), (14), (20), (28), (46), (47), (48) gives:
% 30.87/5.04 | (49) all_80_0 = slcrc0 | xx = xp | xQ = slcrc0
% 30.87/5.04 |
% 30.87/5.04 | BETA: splitting (49) gives:
% 30.87/5.04 |
% 30.87/5.04 | Case 1:
% 30.87/5.04 | |
% 30.87/5.04 | | (50) all_80_0 = slcrc0
% 30.87/5.04 | |
% 30.87/5.04 | | REDUCE: (45), (50) imply:
% 30.87/5.04 | | (51) $false
% 30.87/5.04 | |
% 30.87/5.04 | | CLOSE: (51) is inconsistent.
% 30.87/5.04 | |
% 30.87/5.04 | Case 2:
% 30.87/5.04 | |
% 30.87/5.04 | | (52) xx = xp | xQ = slcrc0
% 30.87/5.04 | |
% 30.87/5.04 | | BETA: splitting (52) gives:
% 30.87/5.04 | |
% 30.87/5.04 | | Case 1:
% 30.87/5.04 | | |
% 30.87/5.04 | | | (53) xQ = slcrc0
% 30.87/5.04 | | |
% 30.87/5.04 | | | REDUCE: (26), (53) imply:
% 30.87/5.04 | | | (54) $false
% 30.87/5.04 | | |
% 30.87/5.04 | | | CLOSE: (54) is inconsistent.
% 30.87/5.04 | | |
% 30.87/5.04 | | Case 2:
% 30.87/5.04 | | |
% 30.87/5.04 | | | (55) xx = xp
% 30.87/5.04 | | |
% 30.87/5.04 | | | REDUCE: (10), (55) imply:
% 30.87/5.04 | | | (56) $false
% 30.87/5.04 | | |
% 30.87/5.04 | | | CLOSE: (56) is inconsistent.
% 30.87/5.04 | | |
% 30.87/5.04 | | End of split
% 30.87/5.04 | |
% 30.87/5.04 | End of split
% 30.87/5.04 |
% 30.87/5.04 End of proof
% 30.87/5.04 % SZS output end Proof for theBenchmark
% 30.87/5.04
% 30.87/5.04 4416ms
%------------------------------------------------------------------------------