TSTP Solution File: NUM627+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM627+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 : n027.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 11:49:04 EDT 2023
% Result : Theorem 63.30s 9.24s
% Output : Proof 285.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM627+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n027.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 08:32:18 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.41/1.48 Prover 1: Preprocessing ...
% 4.41/1.49 Prover 4: Preprocessing ...
% 4.41/1.53 Prover 2: Preprocessing ...
% 4.41/1.53 Prover 0: Preprocessing ...
% 4.41/1.53 Prover 6: Preprocessing ...
% 4.41/1.53 Prover 5: Preprocessing ...
% 4.41/1.54 Prover 3: Preprocessing ...
% 15.54/2.92 Prover 3: Constructing countermodel ...
% 16.42/3.03 Prover 1: Constructing countermodel ...
% 16.42/3.04 Prover 6: Proving ...
% 18.75/3.32 Prover 5: Proving ...
% 19.60/3.42 Prover 2: Proving ...
% 23.47/3.99 Prover 4: Constructing countermodel ...
% 26.98/4.38 Prover 0: Proving ...
% 63.30/9.24 Prover 3: proved (8593ms)
% 63.30/9.24
% 63.30/9.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.30/9.24
% 63.30/9.25 Prover 2: stopped
% 63.30/9.25 Prover 6: stopped
% 64.17/9.26 Prover 0: stopped
% 64.17/9.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 64.17/9.28 Prover 5: stopped
% 64.17/9.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 64.17/9.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 64.17/9.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 64.38/9.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 65.85/9.48 Prover 10: Preprocessing ...
% 65.85/9.51 Prover 8: Preprocessing ...
% 65.85/9.53 Prover 7: Preprocessing ...
% 65.85/9.55 Prover 13: Preprocessing ...
% 66.63/9.59 Prover 11: Preprocessing ...
% 67.10/9.67 Prover 10: Constructing countermodel ...
% 67.10/9.73 Prover 7: Constructing countermodel ...
% 68.16/9.85 Prover 8: Warning: ignoring some quantifiers
% 68.16/9.86 Prover 8: Constructing countermodel ...
% 69.64/10.00 Prover 13: Warning: ignoring some quantifiers
% 70.05/10.04 Prover 13: Constructing countermodel ...
% 73.24/10.55 Prover 11: Constructing countermodel ...
% 97.36/13.64 Prover 13: stopped
% 97.80/13.67 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 98.51/13.77 Prover 16: Preprocessing ...
% 99.70/13.95 Prover 16: Warning: ignoring some quantifiers
% 99.70/13.96 Prover 16: Constructing countermodel ...
% 115.08/15.98 Prover 1: stopped
% 115.08/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 116.20/16.15 Prover 19: Preprocessing ...
% 119.01/16.48 Prover 19: Warning: ignoring some quantifiers
% 119.01/16.49 Prover 19: Constructing countermodel ...
% 136.34/18.83 Prover 16: stopped
% 141.80/19.55 Prover 19: stopped
% 192.83/27.97 Prover 4: stopped
% 200.60/29.76 Prover 7: stopped
% 246.32/41.04 Prover 11: stopped
% 248.31/41.77 Prover 8: stopped
% 285.62/75.02 Prover 10: Found proof (size 44)
% 285.62/75.02 Prover 10: proved (65752ms)
% 285.62/75.02
% 285.62/75.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 285.62/75.02
% 285.62/75.03 % SZS output start Proof for theBenchmark
% 285.62/75.04 Assumptions after simplification:
% 285.62/75.04 ---------------------------------
% 285.62/75.04
% 285.62/75.04 (mLessTotal)
% 285.62/75.09 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1)
% 285.62/75.09 = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 285.62/75.09 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1))
% 285.62/75.09
% 285.62/75.09 (mSuccNum)
% 285.62/75.09 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 285.62/75.09 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1,
% 285.62/75.09 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~
% 285.62/75.09 aElementOf0(v0, szNzAzT0))
% 285.62/75.09
% 285.62/75.10 (m__)
% 285.62/75.10 $i(xx) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) =
% 285.62/75.10 v1 & szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & ~ aElementOf0(xx, v1))
% 285.62/75.10
% 285.62/75.10 (m__3754)
% 285.62/75.10 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 285.62/75.10 : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1) |
% 285.62/75.10 ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 285.62/75.10 aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 285.62/75.10
% 285.62/75.10 (m__5309)
% 285.62/75.10 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 285.62/75.10 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, xn) = xp &
% 285.62/75.10 $i(v1) & $i(v0) & aElementOf0(xn, v1) & aElementOf0(xn, szNzAzT0))
% 285.62/75.11
% 285.96/75.11 (m__5389)
% 285.96/75.11 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) &
% 285.96/75.11 aElementOf0(xm, szNzAzT0)
% 285.96/75.11
% 285.96/75.11 (m__5401)
% 285.96/75.11 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 &
% 285.96/75.11 szmzizndt0(v0) = xx & $i(v0))
% 285.96/75.11
% 285.96/75.11 (m__5442)
% 285.96/75.11 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 285.96/75.11 (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 &
% 285.96/75.11 $i(v2) & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v2))
% 285.96/75.11
% 285.96/75.11 (m__5461)
% 285.96/75.11 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) =
% 285.96/75.11 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v1))
% 285.96/75.11
% 285.96/75.12 (function-axioms)
% 285.96/75.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 285.96/75.13 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 285.96/75.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 285.96/75.13 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 285.96/75.13 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 285.96/75.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 285.96/75.13 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 285.96/75.13 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 285.96/75.13 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 285.96/75.13 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 285.96/75.13 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 285.96/75.13 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 285.96/75.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 285.96/75.13 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 285.96/75.13 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 285.96/75.13 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 285.96/75.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 285.96/75.13 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 285.96/75.13 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 285.96/75.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 285.96/75.13 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 285.96/75.13 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 285.96/75.13 v0))
% 285.96/75.13
% 285.96/75.13 Further assumptions not needed in the proof:
% 285.96/75.13 --------------------------------------------
% 285.96/75.14 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 285.96/75.14 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 285.96/75.14 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 285.96/75.14 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 285.96/75.14 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 285.96/75.14 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 285.96/75.14 mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet,
% 285.96/75.14 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet,
% 285.96/75.14 mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc,
% 285.96/75.14 mSuccLess, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453,
% 285.96/75.14 m__3462, m__3520, m__3533, m__3623, m__3671, m__3821, m__3965, m__4151, m__4182,
% 285.96/75.14 m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891, m__4908,
% 285.96/75.14 m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, m__5147, m__5164, m__5173,
% 285.96/75.14 m__5182, m__5195, m__5208, m__5217, m__5270, m__5321, m__5348, m__5365
% 285.96/75.14
% 285.96/75.14 Those formulas are unsatisfiable:
% 285.96/75.14 ---------------------------------
% 285.96/75.14
% 285.96/75.14 Begin of proof
% 285.96/75.14 |
% 285.96/75.14 | ALPHA: (mSuccNum) implies:
% 285.96/75.14 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 285.96/75.14 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0))
% 285.96/75.14 |
% 285.96/75.14 | ALPHA: (mLessTotal) implies:
% 285.96/75.14 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1) = v2) |
% 285.96/75.14 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 285.96/75.14 | aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1))
% 285.96/75.14 |
% 285.96/75.14 | ALPHA: (m__3754) implies:
% 285.96/75.15 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 285.96/75.15 | (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~ $i(v1)
% 285.96/75.15 | | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0) |
% 285.96/75.15 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 285.96/75.15 |
% 285.96/75.15 | ALPHA: (m__5309) implies:
% 285.96/75.15 | (4) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 285.96/75.15 | v1 & sdtlpdtrp0(xe, xn) = xp & $i(v1) & $i(v0) & aElementOf0(xn, v1)
% 285.96/75.15 | & aElementOf0(xn, szNzAzT0))
% 285.96/75.15 |
% 285.96/75.15 | ALPHA: (m__5389) implies:
% 285.96/75.15 | (5) aElementOf0(xm, szNzAzT0)
% 285.96/75.15 |
% 285.96/75.15 | ALPHA: (m__5401) implies:
% 285.96/75.15 | (6) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & $i(v0))
% 285.96/75.15 |
% 285.96/75.15 | ALPHA: (m__5442) implies:
% 285.96/75.15 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, v1) = v2 &
% 285.96/75.15 | sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & $i(v2) & $i(v1) &
% 285.96/75.15 | $i(v0) & ~ aSubsetOf0(v0, v2))
% 285.96/75.15 |
% 285.96/75.15 | ALPHA: (m__5461) implies:
% 285.96/75.15 | (8) $i(xm)
% 285.96/75.15 | (9) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN,
% 285.96/75.15 | xn) = v0 & $i(v1) & $i(v0) & ~ aSubsetOf0(v0, v1))
% 285.96/75.15 |
% 285.96/75.15 | ALPHA: (m__) implies:
% 285.96/75.15 | (10) $i(xn)
% 285.96/75.15 | (11) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, v0) = v1 &
% 285.96/75.15 | szszuzczcdt0(xn) = v0 & $i(v1) & $i(v0) & ~ aElementOf0(xx, v1))
% 285.96/75.15 |
% 285.96/75.15 | ALPHA: (function-axioms) implies:
% 285.96/75.16 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 285.96/75.16 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 285.96/75.16 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 285.96/75.16 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 285.96/75.16 |
% 285.96/75.16 | DELTA: instantiating (6) with fresh symbol all_82_0 gives:
% 285.96/75.16 | (14) sdtlpdtrp0(xN, xm) = all_82_0 & szmzizndt0(all_82_0) = xx &
% 285.96/75.16 | $i(all_82_0)
% 285.96/75.16 |
% 285.96/75.16 | ALPHA: (14) implies:
% 285.96/75.16 | (15) sdtlpdtrp0(xN, xm) = all_82_0
% 285.96/75.16 |
% 285.96/75.16 | DELTA: instantiating (11) with fresh symbols all_90_0, all_90_1 gives:
% 285.96/75.16 | (16) sdtlpdtrp0(xN, all_90_1) = all_90_0 & szszuzczcdt0(xn) = all_90_1 &
% 285.96/75.16 | $i(all_90_0) & $i(all_90_1) & ~ aElementOf0(xx, all_90_0)
% 285.96/75.16 |
% 285.96/75.16 | ALPHA: (16) implies:
% 285.96/75.16 | (17) szszuzczcdt0(xn) = all_90_1
% 285.96/75.16 | (18) sdtlpdtrp0(xN, all_90_1) = all_90_0
% 285.96/75.16 |
% 285.96/75.16 | DELTA: instantiating (9) with fresh symbols all_92_0, all_92_1 gives:
% 285.96/75.16 | (19) sdtlpdtrp0(xN, xm) = all_92_0 & sdtlpdtrp0(xN, xn) = all_92_1 &
% 285.96/75.16 | $i(all_92_0) & $i(all_92_1) & ~ aSubsetOf0(all_92_1, all_92_0)
% 285.96/75.16 |
% 285.96/75.16 | ALPHA: (19) implies:
% 285.96/75.16 | (20) ~ aSubsetOf0(all_92_1, all_92_0)
% 285.96/75.16 | (21) sdtlpdtrp0(xN, xn) = all_92_1
% 285.96/75.16 | (22) sdtlpdtrp0(xN, xm) = all_92_0
% 285.96/75.16 |
% 285.96/75.16 | DELTA: instantiating (4) with fresh symbols all_98_0, all_98_1 gives:
% 285.96/75.16 | (23) szDzizrdt0(xd) = all_98_1 & sdtlbdtrb0(xd, all_98_1) = all_98_0 &
% 285.96/75.16 | sdtlpdtrp0(xe, xn) = xp & $i(all_98_0) & $i(all_98_1) &
% 285.96/75.16 | aElementOf0(xn, all_98_0) & aElementOf0(xn, szNzAzT0)
% 285.96/75.16 |
% 285.96/75.16 | ALPHA: (23) implies:
% 285.96/75.16 | (24) aElementOf0(xn, szNzAzT0)
% 285.96/75.16 |
% 285.96/75.16 | DELTA: instantiating (7) with fresh symbols all_102_0, all_102_1, all_102_2
% 285.96/75.16 | gives:
% 285.96/75.16 | (25) sdtlpdtrp0(xN, all_102_1) = all_102_0 & sdtlpdtrp0(xN, xm) = all_102_2
% 285.96/75.16 | & szszuzczcdt0(xn) = all_102_1 & $i(all_102_0) & $i(all_102_1) &
% 285.96/75.16 | $i(all_102_2) & ~ aSubsetOf0(all_102_2, all_102_0)
% 285.96/75.16 |
% 285.96/75.16 | ALPHA: (25) implies:
% 285.96/75.16 | (26) ~ aSubsetOf0(all_102_2, all_102_0)
% 285.96/75.16 | (27) $i(all_102_1)
% 285.96/75.17 | (28) szszuzczcdt0(xn) = all_102_1
% 285.96/75.17 | (29) sdtlpdtrp0(xN, xm) = all_102_2
% 285.96/75.17 | (30) sdtlpdtrp0(xN, all_102_1) = all_102_0
% 285.96/75.17 |
% 285.96/75.17 | GROUND_INST: instantiating (12) with all_90_1, all_102_1, xn, simplifying with
% 285.96/75.17 | (17), (28) gives:
% 285.96/75.17 | (31) all_102_1 = all_90_1
% 285.96/75.17 |
% 285.96/75.17 | GROUND_INST: instantiating (13) with all_92_0, all_102_2, xm, xN, simplifying
% 285.96/75.17 | with (22), (29) gives:
% 285.96/75.17 | (32) all_102_2 = all_92_0
% 285.96/75.17 |
% 285.96/75.17 | GROUND_INST: instantiating (13) with all_82_0, all_102_2, xm, xN, simplifying
% 285.96/75.17 | with (15), (29) gives:
% 285.96/75.17 | (33) all_102_2 = all_82_0
% 285.96/75.17 |
% 285.96/75.17 | COMBINE_EQS: (32), (33) imply:
% 285.96/75.17 | (34) all_92_0 = all_82_0
% 285.96/75.17 |
% 285.96/75.17 | SIMP: (34) implies:
% 285.96/75.17 | (35) all_92_0 = all_82_0
% 285.96/75.17 |
% 285.96/75.17 | REDUCE: (30), (31) imply:
% 285.96/75.17 | (36) sdtlpdtrp0(xN, all_90_1) = all_102_0
% 285.96/75.17 |
% 285.96/75.17 | REDUCE: (27), (31) imply:
% 285.96/75.17 | (37) $i(all_90_1)
% 285.96/75.17 |
% 285.96/75.17 | REDUCE: (26), (33) imply:
% 285.96/75.17 | (38) ~ aSubsetOf0(all_82_0, all_102_0)
% 285.96/75.17 |
% 285.96/75.17 | REDUCE: (20), (35) imply:
% 285.96/75.17 | (39) ~ aSubsetOf0(all_92_1, all_82_0)
% 285.96/75.17 |
% 285.96/75.17 | GROUND_INST: instantiating (13) with all_90_0, all_102_0, all_90_1, xN,
% 285.96/75.17 | simplifying with (18), (36) gives:
% 285.96/75.17 | (40) all_102_0 = all_90_0
% 285.96/75.17 |
% 285.96/75.17 | REDUCE: (38), (40) imply:
% 285.96/75.17 | (41) ~ aSubsetOf0(all_82_0, all_90_0)
% 285.96/75.17 |
% 285.96/75.17 | GROUND_INST: instantiating (2) with xm, xn, all_90_1, simplifying with (5),
% 285.96/75.17 | (8), (10), (17), (24) gives:
% 285.96/75.17 | (42) sdtlseqdt0(all_90_1, xm) | sdtlseqdt0(xm, xn)
% 285.96/75.17 |
% 285.96/75.17 | GROUND_INST: instantiating (1) with xn, all_90_1, simplifying with (10), (17),
% 285.96/75.17 | (24) gives:
% 285.96/75.17 | (43) aElementOf0(all_90_1, szNzAzT0)
% 285.96/75.17 |
% 285.96/75.18 | BETA: splitting (42) gives:
% 285.96/75.18 |
% 285.96/75.18 | Case 1:
% 285.96/75.18 | |
% 285.96/75.18 | | (44) sdtlseqdt0(all_90_1, xm)
% 285.96/75.18 | |
% 285.96/75.18 | | GROUND_INST: instantiating (3) with xm, all_90_1, all_82_0, all_90_0,
% 285.96/75.18 | | simplifying with (5), (8), (15), (18), (37), (41), (43), (44)
% 285.96/75.18 | | gives:
% 285.96/75.18 | | (45) $false
% 285.96/75.18 | |
% 285.96/75.18 | | CLOSE: (45) is inconsistent.
% 285.96/75.18 | |
% 285.96/75.18 | Case 2:
% 285.96/75.18 | |
% 285.96/75.18 | | (46) sdtlseqdt0(xm, xn)
% 285.96/75.18 | |
% 285.96/75.18 | | GROUND_INST: instantiating (3) with xn, xm, all_92_1, all_82_0, simplifying
% 285.96/75.18 | | with (5), (8), (10), (15), (21), (24), (39), (46) gives:
% 285.96/75.18 | | (47) $false
% 285.96/75.18 | |
% 285.96/75.18 | | CLOSE: (47) is inconsistent.
% 285.96/75.18 | |
% 285.96/75.18 | End of split
% 285.96/75.18 |
% 285.96/75.18 End of proof
% 285.96/75.18 % SZS output end Proof for theBenchmark
% 285.96/75.18
% 285.96/75.18 74568ms
%------------------------------------------------------------------------------