TSTP Solution File: NUM624+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM624+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 : n009.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 144.05s 19.68s
% Output : Proof 144.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM624+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 10:05:06 EDT 2023
% 0.13/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.65 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 6.28/1.61 Prover 4: Preprocessing ...
% 6.28/1.61 Prover 1: Preprocessing ...
% 7.01/1.66 Prover 5: Preprocessing ...
% 7.01/1.66 Prover 0: Preprocessing ...
% 7.01/1.66 Prover 6: Preprocessing ...
% 7.01/1.66 Prover 2: Preprocessing ...
% 7.01/1.66 Prover 3: Preprocessing ...
% 20.19/3.42 Prover 1: Constructing countermodel ...
% 20.27/3.43 Prover 3: Constructing countermodel ...
% 20.27/3.50 Prover 6: Proving ...
% 23.69/3.96 Prover 5: Proving ...
% 45.22/6.69 Prover 4: Constructing countermodel ...
% 51.31/7.56 Prover 2: Proving ...
% 53.52/7.87 Prover 0: Proving ...
% 100.32/13.99 Prover 5: stopped
% 100.32/13.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 102.50/14.25 Prover 7: Preprocessing ...
% 105.03/14.58 Prover 2: stopped
% 105.03/14.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 106.82/14.77 Prover 8: Preprocessing ...
% 108.66/15.05 Prover 7: Constructing countermodel ...
% 109.16/15.14 Prover 8: Warning: ignoring some quantifiers
% 109.16/15.15 Prover 8: Constructing countermodel ...
% 116.27/16.01 Prover 1: stopped
% 116.27/16.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.03/16.22 Prover 9: Preprocessing ...
% 130.68/17.90 Prover 6: stopped
% 130.68/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.07/18.14 Prover 10: Preprocessing ...
% 133.57/18.31 Prover 9: Constructing countermodel ...
% 136.20/18.65 Prover 10: Constructing countermodel ...
% 143.41/19.62 Prover 10: Found proof (size 73)
% 143.41/19.63 Prover 10: proved (1719ms)
% 143.41/19.63 Prover 9: stopped
% 143.41/19.63 Prover 8: stopped
% 143.41/19.63 Prover 7: stopped
% 143.41/19.64 Prover 3: stopped
% 143.41/19.64 Prover 4: stopped
% 144.05/19.68 Prover 0: stopped
% 144.05/19.68
% 144.05/19.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 144.05/19.68
% 144.21/19.69 % SZS output start Proof for theBenchmark
% 144.21/19.69 Assumptions after simplification:
% 144.21/19.69 ---------------------------------
% 144.21/19.69
% 144.21/19.69 (mCountNFin_01)
% 144.21/19.70 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 144.21/19.70
% 144.21/19.70 (mDefEmp)
% 144.21/19.70 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 144.21/19.70 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 144.21/19.70 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 144.21/19.70
% 144.21/19.70 (mMinMin)
% 144.21/19.73 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 144.21/19.73 $i] : (v3 = v2 | v1 = slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~
% 144.21/19.73 (szmzizndt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0)
% 144.21/19.73 | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ aElementOf0(v2,
% 144.21/19.73 v1))
% 144.21/19.73
% 144.21/19.73 (m__3671)
% 144.21/19.73 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 144.21/19.73 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) |
% 144.21/19.73 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 144.21/19.73 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 144.21/19.73 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 144.21/19.73 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 144.21/19.73 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 144.21/19.73 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 144.41/19.73
% 144.41/19.73 (m__4660)
% 144.41/19.73 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 144.41/19.73 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 144.41/19.73 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 144.41/19.73 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i]
% 144.41/19.73 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3))))
% 144.41/19.73
% 144.41/19.73 (m__5093)
% 144.41/19.74 $i(xQ) & $i(xO) & $i(slcrc0) & ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) &
% 144.41/19.74 aElementOf0(v0, xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) |
% 144.41/19.74 aElementOf0(v1, xO)))
% 144.41/19.74
% 144.41/19.74 (m__5106)
% 144.41/19.74 $i(xQ) & $i(szNzAzT0) & aSubsetOf0(xQ, szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) |
% 144.41/19.74 ~ aElementOf0(v0, xQ) | aElementOf0(v0, szNzAzT0))
% 144.41/19.74
% 144.41/19.74 (m__5147)
% 144.41/19.74 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : (
% 144.41/19.74 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0))
% 144.41/19.74
% 144.41/19.74 (m__5164)
% 144.45/19.74 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 144.45/19.74 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 144.45/19.74 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP))
% 144.45/19.74 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) &
% 144.45/19.74 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1:
% 144.45/19.74 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 144.45/19.74
% 144.45/19.74 (m__5348)
% 144.45/19.74 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 &
% 144.45/19.74 $i(v0) & aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx))
% 144.45/19.74
% 144.45/19.74 (m__5389)
% 144.45/19.74 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) &
% 144.45/19.74 aElementOf0(xm, szNzAzT0)
% 144.45/19.74
% 144.45/19.74 (m__5401)
% 144.45/19.74 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) &
% 144.45/19.74 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 144.45/19.74
% 144.45/19.74 (m__5442)
% 144.45/19.75 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 144.45/19.75 $i] : (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn)
% 144.45/19.75 = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~
% 144.45/19.75 aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2))
% 144.45/19.75
% 144.45/19.75 (m__5461)
% 144.45/19.75 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) =
% 144.45/19.75 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & !
% 144.45/19.75 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1)))
% 144.45/19.75
% 144.45/19.75 (m__5481)
% 144.45/19.75 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm)
% 144.45/19.75 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0))
% 144.45/19.75
% 144.45/19.75 (m__5518)
% 144.45/19.75 $i(xm) & $i(xQ) & $i(xN) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 144.45/19.75 $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2,
% 144.45/19.75 xQ) & aElementOf0(v1, v0) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3,
% 144.45/19.75 v0) | aElementOf0(v3, szNzAzT0)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 144.45/19.75 aElementOf0(v3, xQ) | aElementOf0(v3, szNzAzT0)))
% 144.45/19.75
% 144.45/19.75 (function-axioms)
% 144.45/19.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 144.45/19.76 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 144.45/19.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 144.45/19.76 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 144.45/19.76 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 144.45/19.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 144.45/19.76 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 144.45/19.76 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 144.45/19.76 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 144.45/19.76 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 144.45/19.76 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 144.45/19.76 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 144.45/19.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 144.45/19.76 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 144.45/19.76 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 144.45/19.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 144.45/19.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 144.45/19.76 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 144.45/19.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 144.45/19.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 144.45/19.76 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 144.45/19.76 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 144.45/19.76 v0))
% 144.45/19.76
% 144.45/19.76 Further assumptions not needed in the proof:
% 144.45/19.76 --------------------------------------------
% 144.45/19.76 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 144.45/19.76 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 144.45/19.76 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 144.45/19.76 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 144.45/19.76 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 144.45/19.76 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 144.45/19.76 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 144.45/19.76 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 144.45/19.76 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 144.45/19.76 mZeroLess, mZeroNum, m__, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462,
% 144.45/19.76 m__3520, m__3533, m__3623, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331,
% 144.45/19.76 m__4411, m__4618, m__4730, m__4758, m__4854, m__4891, m__4908, m__4982, m__4998,
% 144.45/19.76 m__5078, m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5309,
% 144.45/19.76 m__5321, m__5365
% 144.45/19.76
% 144.45/19.76 Those formulas are unsatisfiable:
% 144.45/19.76 ---------------------------------
% 144.45/19.76
% 144.45/19.76 Begin of proof
% 144.45/19.76 |
% 144.45/19.76 | ALPHA: (mDefEmp) implies:
% 144.45/19.77 | (1) aSet0(slcrc0)
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (mCountNFin_01) implies:
% 144.45/19.77 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (mMinMin) implies:
% 144.45/19.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 =
% 144.45/19.77 | slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ (szmzizndt0(v0)
% 144.45/19.77 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 144.45/19.77 | aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~
% 144.45/19.77 | aElementOf0(v2, v1))
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__3671) implies:
% 144.45/19.77 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 144.45/19.77 | ~ aElementOf0(v0, szNzAzT0) | isCountable0(v1))
% 144.45/19.77 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 144.45/19.77 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0))
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__4660) implies:
% 144.45/19.77 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) |
% 144.45/19.77 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2
% 144.45/19.77 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & !
% 144.45/19.77 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1,
% 144.45/19.77 | v3))))
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__5093) implies:
% 144.45/19.77 | (7) ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & aElementOf0(v0, xQ) & !
% 144.45/19.77 | [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1,
% 144.45/19.77 | xO)))
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__5106) implies:
% 144.45/19.77 | (8) aSubsetOf0(xQ, szNzAzT0)
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__5147) implies:
% 144.45/19.77 | (9) szmzizndt0(xQ) = xp
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__5164) implies:
% 144.45/19.77 | (10) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 144.45/19.77 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 144.45/19.77 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) |
% 144.45/19.77 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 144.45/19.77 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~
% 144.45/19.77 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : (
% 144.45/19.77 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__5348) implies:
% 144.45/19.77 | (11) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & $i(v0) &
% 144.45/19.77 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx))
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__5389) implies:
% 144.45/19.77 | (12) aElementOf0(xm, szNzAzT0)
% 144.45/19.77 | (13) sdtlpdtrp0(xe, xm) = xx
% 144.45/19.77 |
% 144.45/19.77 | ALPHA: (m__5401) implies:
% 144.45/19.78 | (14) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 144.45/19.78 | $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (m__5442) implies:
% 144.45/19.78 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 144.45/19.78 | (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn)
% 144.45/19.78 | = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~
% 144.45/19.78 | aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2))
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (m__5461) implies:
% 144.45/19.78 | (16) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN,
% 144.45/19.78 | xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : (
% 144.45/19.78 | ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1)))
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (m__5481) implies:
% 144.45/19.78 | (17) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & aElementOf0(xx, xQ)
% 144.45/19.78 | & aElementOf0(xp, v0))
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (m__5518) implies:
% 144.45/19.78 | (18) $i(xQ)
% 144.45/19.78 | (19) $i(xm)
% 144.45/19.78 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xm) = v0 &
% 144.45/19.78 | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, xQ) & aElementOf0(v1, v0)
% 144.45/19.78 | & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 144.45/19.78 | aElementOf0(v3, szNzAzT0)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 144.45/19.78 | aElementOf0(v3, xQ) | aElementOf0(v3, szNzAzT0)))
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (function-axioms) implies:
% 144.45/19.78 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 144.45/19.78 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 144.45/19.78 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 144.45/19.78 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 144.45/19.78 |
% 144.45/19.78 | DELTA: instantiating (17) with fresh symbol all_86_0 gives:
% 144.45/19.78 | (23) sdtlpdtrp0(xN, xm) = all_86_0 & $i(all_86_0) & aElementOf0(xx, xQ) &
% 144.45/19.78 | aElementOf0(xp, all_86_0)
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (23) implies:
% 144.45/19.78 | (24) aElementOf0(xp, all_86_0)
% 144.45/19.78 | (25) sdtlpdtrp0(xN, xm) = all_86_0
% 144.45/19.78 |
% 144.45/19.78 | DELTA: instantiating (14) with fresh symbol all_88_0 gives:
% 144.45/19.78 | (26) sdtlpdtrp0(xN, xm) = all_88_0 & $i(all_88_0) & ! [v0: $i] : ( ~
% 144.45/19.78 | $i(v0) | ~ aElementOf0(v0, all_88_0) | sdtlseqdt0(xx, v0))
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (26) implies:
% 144.45/19.78 | (27) sdtlpdtrp0(xN, xm) = all_88_0
% 144.45/19.78 |
% 144.45/19.78 | DELTA: instantiating (11) with fresh symbol all_91_0 gives:
% 144.45/19.78 | (28) ~ (all_91_0 = xx) & szmzizndt0(xQ) = all_91_0 & $i(all_91_0) &
% 144.45/19.78 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)
% 144.45/19.78 |
% 144.45/19.78 | ALPHA: (28) implies:
% 144.45/19.78 | (29) ~ (all_91_0 = xx)
% 144.45/19.78 | (30) aElementOf0(xx, xQ)
% 144.45/19.78 | (31) szmzizndt0(xQ) = all_91_0
% 144.45/19.78 |
% 144.45/19.78 | DELTA: instantiating (7) with fresh symbol all_93_0 gives:
% 144.45/19.78 | (32) ~ (xQ = slcrc0) & $i(all_93_0) & aElementOf0(all_93_0, xQ) & ! [v0:
% 144.45/19.78 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO))
% 144.45/19.79 |
% 144.45/19.79 | ALPHA: (32) implies:
% 144.45/19.79 | (33) ~ (xQ = slcrc0)
% 144.45/19.79 |
% 144.45/19.79 | DELTA: instantiating (16) with fresh symbols all_103_0, all_103_1 gives:
% 144.45/19.79 | (34) sdtlpdtrp0(xN, xm) = all_103_0 & sdtlpdtrp0(xN, xn) = all_103_1 &
% 144.45/19.79 | $i(all_103_0) & $i(all_103_1) & aSubsetOf0(all_103_1, all_103_0) & !
% 144.45/19.79 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_103_1) |
% 144.45/19.79 | aElementOf0(v0, all_103_0))
% 144.45/19.79 |
% 144.45/19.79 | ALPHA: (34) implies:
% 144.45/19.79 | (35) sdtlpdtrp0(xN, xm) = all_103_0
% 144.45/19.79 |
% 144.45/19.79 | DELTA: instantiating (15) with fresh symbols all_109_0, all_109_1, all_109_2,
% 144.45/19.79 | all_109_3 gives:
% 144.45/19.79 | (36) sdtlpdtrp0(xN, all_109_2) = all_109_1 & sdtlpdtrp0(xN, xm) = all_109_3
% 144.45/19.79 | & szszuzczcdt0(xn) = all_109_2 & $i(all_109_0) & $i(all_109_1) &
% 144.45/19.79 | $i(all_109_2) & $i(all_109_3) & aElementOf0(all_109_0, all_109_3) & ~
% 144.45/19.79 | aSubsetOf0(all_109_3, all_109_1) & ~ aElementOf0(all_109_0,
% 144.45/19.79 | all_109_1)
% 144.45/19.79 |
% 144.45/19.79 | ALPHA: (36) implies:
% 144.45/19.79 | (37) sdtlpdtrp0(xN, xm) = all_109_3
% 144.45/19.79 |
% 144.45/19.79 | DELTA: instantiating (20) with fresh symbols all_113_0, all_113_1, all_113_2
% 144.45/19.79 | gives:
% 144.45/19.79 | (38) sdtlpdtrp0(xN, xm) = all_113_2 & $i(all_113_0) & $i(all_113_1) &
% 144.45/19.79 | $i(all_113_2) & aElementOf0(all_113_0, xQ) & aElementOf0(all_113_1,
% 144.45/19.79 | all_113_2) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 144.45/19.79 | all_113_2) | aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ( ~ $i(v0)
% 144.45/19.79 | | ~ aElementOf0(v0, xQ) | aElementOf0(v0, szNzAzT0))
% 144.45/19.79 |
% 144.45/19.79 | ALPHA: (38) implies:
% 144.45/19.79 | (39) sdtlpdtrp0(xN, xm) = all_113_2
% 144.45/19.79 |
% 144.45/19.79 | DELTA: instantiating (10) with fresh symbol all_116_0 gives:
% 144.45/19.79 | (40) szmzizndt0(xQ) = all_116_0 & sdtmndt0(xQ, all_116_0) = xP &
% 144.45/19.79 | $i(all_116_0) & aSet0(xP) & ~ aElementOf0(all_116_0, xP) & ! [v0:
% 144.45/19.79 | any] : (v0 = all_116_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~
% 144.45/19.79 | aElement0(v0) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 144.45/19.79 | aElementOf0(v0, xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~
% 144.45/19.79 | $i(v0) | ~ aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~
% 144.45/19.79 | $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(all_116_0, v0))
% 144.45/19.79 |
% 144.45/19.79 | ALPHA: (40) implies:
% 144.45/19.79 | (41) szmzizndt0(xQ) = all_116_0
% 144.45/19.79 |
% 144.45/19.79 | BETA: splitting (2) gives:
% 144.45/19.79 |
% 144.45/19.79 | Case 1:
% 144.45/19.79 | |
% 144.45/19.79 | | (42) ~ aSet0(slcrc0)
% 144.45/19.79 | |
% 144.45/19.79 | | PRED_UNIFY: (1), (42) imply:
% 144.45/19.79 | | (43) $false
% 144.45/19.79 | |
% 144.45/19.79 | | CLOSE: (43) is inconsistent.
% 144.45/19.79 | |
% 144.45/19.79 | Case 2:
% 144.45/19.79 | |
% 144.45/19.79 | | (44) ~ isCountable0(slcrc0)
% 144.45/19.79 | |
% 144.45/19.79 | | GROUND_INST: instantiating (21) with all_91_0, all_116_0, xQ, simplifying
% 144.45/19.79 | | with (31), (41) gives:
% 144.45/19.79 | | (45) all_116_0 = all_91_0
% 144.45/19.79 | |
% 144.45/19.79 | | GROUND_INST: instantiating (21) with xp, all_116_0, xQ, simplifying with
% 144.45/19.79 | | (9), (41) gives:
% 144.45/19.79 | | (46) all_116_0 = xp
% 144.45/19.79 | |
% 144.45/19.80 | | GROUND_INST: instantiating (22) with all_86_0, all_103_0, xm, xN,
% 144.45/19.80 | | simplifying with (25), (35) gives:
% 144.45/19.80 | | (47) all_103_0 = all_86_0
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (22) with all_103_0, all_109_3, xm, xN,
% 144.45/19.80 | | simplifying with (35), (37) gives:
% 144.45/19.80 | | (48) all_109_3 = all_103_0
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (22) with all_109_3, all_113_2, xm, xN,
% 144.45/19.80 | | simplifying with (37), (39) gives:
% 144.45/19.80 | | (49) all_113_2 = all_109_3
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (22) with all_88_0, all_113_2, xm, xN,
% 144.45/19.80 | | simplifying with (27), (39) gives:
% 144.45/19.80 | | (50) all_113_2 = all_88_0
% 144.45/19.80 | |
% 144.45/19.80 | | COMBINE_EQS: (45), (46) imply:
% 144.45/19.80 | | (51) all_91_0 = xp
% 144.45/19.80 | |
% 144.45/19.80 | | SIMP: (51) implies:
% 144.45/19.80 | | (52) all_91_0 = xp
% 144.45/19.80 | |
% 144.45/19.80 | | COMBINE_EQS: (49), (50) imply:
% 144.45/19.80 | | (53) all_109_3 = all_88_0
% 144.45/19.80 | |
% 144.45/19.80 | | SIMP: (53) implies:
% 144.45/19.80 | | (54) all_109_3 = all_88_0
% 144.45/19.80 | |
% 144.45/19.80 | | COMBINE_EQS: (48), (54) imply:
% 144.45/19.80 | | (55) all_103_0 = all_88_0
% 144.45/19.80 | |
% 144.45/19.80 | | SIMP: (55) implies:
% 144.45/19.80 | | (56) all_103_0 = all_88_0
% 144.45/19.80 | |
% 144.45/19.80 | | COMBINE_EQS: (47), (56) imply:
% 144.45/19.80 | | (57) all_88_0 = all_86_0
% 144.45/19.80 | |
% 144.45/19.80 | | REDUCE: (29), (52) imply:
% 144.45/19.80 | | (58) ~ (xx = xp)
% 144.45/19.80 | |
% 144.45/19.80 | | SIMP: (58) implies:
% 144.45/19.80 | | (59) ~ (xx = xp)
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (5) with xm, all_86_0, simplifying with (12),
% 144.45/19.80 | | (19), (25) gives:
% 144.45/19.80 | | (60) aSubsetOf0(all_86_0, szNzAzT0)
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (4) with xm, all_86_0, simplifying with (12),
% 144.45/19.80 | | (19), (25) gives:
% 144.45/19.80 | | (61) isCountable0(all_86_0)
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (6) with xm, xx, simplifying with (12), (13),
% 144.45/19.80 | | (19) gives:
% 144.45/19.80 | | (62) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx &
% 144.45/19.80 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) |
% 144.45/19.80 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 144.45/19.80 | |
% 144.45/19.80 | | DELTA: instantiating (62) with fresh symbol all_157_0 gives:
% 144.45/19.80 | | (63) sdtlpdtrp0(xN, xm) = all_157_0 & szmzizndt0(all_157_0) = xx &
% 144.45/19.80 | | $i(all_157_0) & $i(xx) & aElementOf0(xx, all_157_0) & ! [v0: $i] :
% 144.45/19.80 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_157_0) | sdtlseqdt0(xx, v0))
% 144.45/19.80 | |
% 144.45/19.80 | | ALPHA: (63) implies:
% 144.45/19.80 | | (64) $i(all_157_0)
% 144.45/19.80 | | (65) szmzizndt0(all_157_0) = xx
% 144.45/19.80 | | (66) sdtlpdtrp0(xN, xm) = all_157_0
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (22) with all_86_0, all_157_0, xm, xN,
% 144.45/19.80 | | simplifying with (25), (66) gives:
% 144.45/19.80 | | (67) all_157_0 = all_86_0
% 144.45/19.80 | |
% 144.45/19.80 | | REDUCE: (65), (67) imply:
% 144.45/19.80 | | (68) szmzizndt0(all_86_0) = xx
% 144.45/19.80 | |
% 144.45/19.80 | | REDUCE: (64), (67) imply:
% 144.45/19.80 | | (69) $i(all_86_0)
% 144.45/19.80 | |
% 144.45/19.80 | | GROUND_INST: instantiating (3) with all_86_0, xQ, xx, xp, simplifying with
% 144.45/19.80 | | (8), (9), (18), (24), (30), (60), (68), (69) gives:
% 144.77/19.80 | | (70) all_86_0 = slcrc0 | xx = xp | xQ = slcrc0
% 144.77/19.80 | |
% 144.77/19.80 | | BETA: splitting (70) gives:
% 144.77/19.80 | |
% 144.77/19.80 | | Case 1:
% 144.77/19.80 | | |
% 144.77/19.80 | | | (71) all_86_0 = slcrc0
% 144.77/19.80 | | |
% 144.77/19.80 | | | REDUCE: (61), (71) imply:
% 144.77/19.81 | | | (72) isCountable0(slcrc0)
% 144.77/19.81 | | |
% 144.77/19.81 | | | PRED_UNIFY: (44), (72) imply:
% 144.77/19.81 | | | (73) $false
% 144.77/19.81 | | |
% 144.77/19.81 | | | CLOSE: (73) is inconsistent.
% 144.77/19.81 | | |
% 144.77/19.81 | | Case 2:
% 144.77/19.81 | | |
% 144.77/19.81 | | | (74) xx = xp | xQ = slcrc0
% 144.77/19.81 | | |
% 144.77/19.81 | | | BETA: splitting (74) gives:
% 144.77/19.81 | | |
% 144.77/19.81 | | | Case 1:
% 144.77/19.81 | | | |
% 144.77/19.81 | | | | (75) xQ = slcrc0
% 144.77/19.81 | | | |
% 144.77/19.81 | | | | REDUCE: (33), (75) imply:
% 144.77/19.81 | | | | (76) $false
% 144.77/19.81 | | | |
% 144.77/19.81 | | | | CLOSE: (76) is inconsistent.
% 144.77/19.81 | | | |
% 144.77/19.81 | | | Case 2:
% 144.77/19.81 | | | |
% 144.77/19.81 | | | | (77) xx = xp
% 144.77/19.81 | | | |
% 144.77/19.81 | | | | REDUCE: (59), (77) imply:
% 144.77/19.81 | | | | (78) $false
% 144.77/19.81 | | | |
% 144.77/19.81 | | | | CLOSE: (78) is inconsistent.
% 144.77/19.81 | | | |
% 144.77/19.81 | | | End of split
% 144.77/19.81 | | |
% 144.77/19.81 | | End of split
% 144.77/19.81 | |
% 144.77/19.81 | End of split
% 144.77/19.81 |
% 144.77/19.81 End of proof
% 144.77/19.81 % SZS output end Proof for theBenchmark
% 144.77/19.81
% 144.77/19.81 19178ms
%------------------------------------------------------------------------------