TSTP Solution File: NUM625+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM625+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 : n025.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 39.44s 5.96s
% Output : Proof 50.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM625+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.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 11:07:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.04/1.38 Prover 1: Preprocessing ...
% 5.04/1.38 Prover 4: Preprocessing ...
% 5.04/1.42 Prover 2: Preprocessing ...
% 5.04/1.42 Prover 3: Preprocessing ...
% 5.04/1.42 Prover 6: Preprocessing ...
% 5.04/1.42 Prover 0: Preprocessing ...
% 5.04/1.42 Prover 5: Preprocessing ...
% 14.03/2.64 Prover 1: Constructing countermodel ...
% 14.73/2.68 Prover 3: Constructing countermodel ...
% 14.99/2.74 Prover 6: Proving ...
% 16.09/2.87 Prover 5: Proving ...
% 16.96/2.98 Prover 2: Proving ...
% 20.69/3.53 Prover 4: Constructing countermodel ...
% 22.09/3.66 Prover 0: Proving ...
% 39.44/5.96 Prover 0: proved (5319ms)
% 39.44/5.96
% 39.44/5.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.44/5.96
% 39.44/5.96 Prover 2: stopped
% 39.44/5.96 Prover 6: stopped
% 39.92/5.98 Prover 5: stopped
% 39.92/5.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 39.92/5.99 Prover 3: stopped
% 39.92/6.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 39.92/6.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 39.92/6.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 39.92/6.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 42.28/6.35 Prover 7: Preprocessing ...
% 43.02/6.38 Prover 8: Preprocessing ...
% 43.02/6.39 Prover 10: Preprocessing ...
% 43.02/6.43 Prover 11: Preprocessing ...
% 43.02/6.46 Prover 13: Preprocessing ...
% 44.86/6.63 Prover 7: Constructing countermodel ...
% 44.86/6.64 Prover 10: Constructing countermodel ...
% 45.61/6.74 Prover 8: Warning: ignoring some quantifiers
% 45.61/6.75 Prover 8: Constructing countermodel ...
% 46.29/6.82 Prover 13: Warning: ignoring some quantifiers
% 46.29/6.84 Prover 13: Constructing countermodel ...
% 48.68/7.18 Prover 10: Found proof (size 33)
% 48.68/7.18 Prover 10: proved (1203ms)
% 48.68/7.18 Prover 13: stopped
% 48.68/7.18 Prover 8: stopped
% 48.68/7.18 Prover 7: stopped
% 48.68/7.18 Prover 1: stopped
% 48.68/7.18 Prover 4: stopped
% 49.90/7.33 Prover 11: Constructing countermodel ...
% 49.90/7.36 Prover 11: stopped
% 49.90/7.36
% 49.90/7.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.90/7.36
% 49.90/7.36 % SZS output start Proof for theBenchmark
% 49.90/7.37 Assumptions after simplification:
% 49.90/7.37 ---------------------------------
% 49.90/7.37
% 49.90/7.37 (mDefDiff)
% 49.90/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 49.90/7.40 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 49.90/7.40 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 =
% 49.90/7.40 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4))
% 49.90/7.40 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) &
% 49.90/7.40 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 49.90/7.40 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 49.90/7.40 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~
% 49.90/7.40 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 49.90/7.40 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) |
% 49.90/7.40 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1)
% 49.90/7.40 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 49.90/7.40 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 49.90/7.40 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~
% 49.90/7.40 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 49.90/7.40 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 49.90/7.40 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : !
% 49.90/7.40 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) |
% 49.90/7.40 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 49.90/7.40
% 49.90/7.40 (mDefSub)
% 50.30/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 50.30/7.40 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 50.30/7.40 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 50.30/7.40 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 50.30/7.40 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 50.30/7.40 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 50.30/7.40
% 50.30/7.40 (mImgElm)
% 50.30/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(v0,
% 50.30/7.40 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 50.30/7.40 aFunction0(v0) | ~ aElementOf0(v2, v1) | aElement0(v3))
% 50.30/7.40
% 50.30/7.40 (m__4660)
% 50.30/7.41 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 50.30/7.41 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 50.30/7.41 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 50.30/7.41 szmzizndt0(v2) = v1 & $i(v2) & $i(v1)))
% 50.30/7.41
% 50.30/7.41 (m__4891)
% 50.30/7.41 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 50.30/7.41 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) &
% 50.30/7.41 aSet0(xO))
% 50.30/7.41
% 50.30/7.41 (m__5093)
% 50.30/7.41 ~ (xQ = slcrc0) & $i(xQ) & $i(xO) & $i(slcrc0) & aSubsetOf0(xQ, xO)
% 50.30/7.41
% 50.30/7.41 (m__5147)
% 50.30/7.41 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ)
% 50.30/7.41
% 50.30/7.41 (m__5164)
% 50.30/7.41 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 50.30/7.41 $i(v0) & aSet0(xP))
% 50.30/7.41
% 50.30/7.41 (m__5309)
% 50.30/7.41 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 50.30/7.41 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, xn) = xp &
% 50.30/7.41 $i(v1) & $i(v0) & aElementOf0(xn, v1) & aElementOf0(xn, szNzAzT0))
% 50.30/7.41
% 50.30/7.41 (m__5348)
% 50.30/7.41 $i(xx) & $i(xP) & aElementOf0(xx, xP)
% 50.30/7.41
% 50.30/7.41 (m__5365)
% 50.30/7.41 $i(xx) & $i(xO) & $i(szNzAzT0) & aElementOf0(xx, xO) & aElementOf0(xx,
% 50.30/7.41 szNzAzT0)
% 50.30/7.41
% 50.30/7.41 (m__5389)
% 50.30/7.41 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) &
% 50.30/7.41 aElementOf0(xm, szNzAzT0)
% 50.30/7.41
% 50.30/7.41 (m__5461)
% 50.30/7.41 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) =
% 50.30/7.41 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1))
% 50.30/7.41
% 50.30/7.41 (m__5481)
% 50.30/7.41 $i(xm) & $i(xx) & $i(xp) & $i(xQ) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm)
% 50.30/7.41 = v0 & $i(v0) & aElementOf0(xx, xQ) & aElementOf0(xp, v0))
% 50.30/7.41
% 50.30/7.41 (m__5496)
% 50.30/7.41 xx = xp & $i(xp)
% 50.30/7.41
% 50.30/7.41 (function-axioms)
% 50.30/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.30/7.42 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 50.30/7.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 50.30/7.42 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 50.30/7.42 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 50.30/7.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 50.30/7.42 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 50.30/7.42 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 50.30/7.42 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 50.30/7.42 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 50.30/7.42 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 50.30/7.42 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 50.30/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 50.30/7.42 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 50.30/7.42 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 50.30/7.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 50.30/7.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 50.30/7.42 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 50.30/7.42 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 50.30/7.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 50.30/7.42 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 50.30/7.42 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 50.30/7.42 v0))
% 50.30/7.42
% 50.30/7.42 Further assumptions not needed in the proof:
% 50.30/7.42 --------------------------------------------
% 50.30/7.42 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 50.30/7.42 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 50.30/7.42 mDefCons, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg,
% 50.30/7.42 mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 50.30/7.42 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgRng,
% 50.30/7.42 mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin,
% 50.30/7.42 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 50.30/7.42 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 50.30/7.42 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 50.30/7.42 mZeroLess, mZeroNum, m__, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462,
% 50.30/7.42 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182,
% 50.30/7.42 m__4331, m__4411, m__4618, m__4730, m__4758, m__4854, m__4908, m__4982, m__4998,
% 50.30/7.42 m__5078, m__5106, m__5116, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270,
% 50.30/7.42 m__5321, m__5401, m__5442
% 50.30/7.42
% 50.30/7.42 Those formulas are unsatisfiable:
% 50.30/7.42 ---------------------------------
% 50.30/7.42
% 50.30/7.42 Begin of proof
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (mDefSub) implies:
% 50.30/7.42 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1,
% 50.30/7.42 | v0) | ~ aSet0(v0) | aSet0(v1))
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (mDefDiff) implies:
% 50.30/7.42 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) |
% 50.30/7.42 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v2) | ~
% 50.30/7.42 | aElement0(v1) | ~ aSet0(v0))
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (m__4660) implies:
% 50.30/7.42 | (3) aFunction0(xe)
% 50.30/7.42 | (4) szDzozmdt0(xe) = szNzAzT0
% 50.30/7.42 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) |
% 50.30/7.42 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2
% 50.30/7.42 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1)))
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (m__4891) implies:
% 50.30/7.42 | (6) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) =
% 50.30/7.42 | xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO))
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (m__5093) implies:
% 50.30/7.42 | (7) aSubsetOf0(xQ, xO)
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (m__5147) implies:
% 50.30/7.42 | (8) szmzizndt0(xQ) = xp
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (m__5164) implies:
% 50.30/7.42 | (9) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 50.30/7.42 | aSet0(xP))
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (m__5309) implies:
% 50.30/7.42 | (10) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 50.30/7.42 | = v1 & sdtlpdtrp0(xe, xn) = xp & $i(v1) & $i(v0) & aElementOf0(xn,
% 50.30/7.42 | v1) & aElementOf0(xn, szNzAzT0))
% 50.30/7.42 |
% 50.30/7.42 | ALPHA: (m__5348) implies:
% 50.30/7.42 | (11) aElementOf0(xx, xP)
% 50.30/7.42 | (12) $i(xP)
% 50.30/7.42 |
% 50.30/7.43 | ALPHA: (m__5365) implies:
% 50.30/7.43 | (13) $i(xO)
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (m__5389) implies:
% 50.30/7.43 | (14) aElementOf0(xm, szNzAzT0)
% 50.30/7.43 | (15) $i(xe)
% 50.30/7.43 | (16) sdtlpdtrp0(xe, xm) = xx
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (m__5461) implies:
% 50.30/7.43 | (17) $i(xn)
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (m__5481) implies:
% 50.30/7.43 | (18) $i(xQ)
% 50.30/7.43 | (19) $i(xm)
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (m__5496) implies:
% 50.30/7.43 | (20) xx = xp
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (function-axioms) implies:
% 50.30/7.43 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 50.30/7.43 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 50.30/7.43 |
% 50.30/7.43 | DELTA: instantiating (9) with fresh symbol all_88_0 gives:
% 50.30/7.43 | (22) szmzizndt0(xQ) = all_88_0 & sdtmndt0(xQ, all_88_0) = xP & $i(all_88_0)
% 50.30/7.43 | & aSet0(xP)
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (22) implies:
% 50.30/7.43 | (23) sdtmndt0(xQ, all_88_0) = xP
% 50.30/7.43 | (24) szmzizndt0(xQ) = all_88_0
% 50.30/7.43 |
% 50.30/7.43 | DELTA: instantiating (6) with fresh symbols all_94_0, all_94_1 gives:
% 50.30/7.43 | (25) szDzizrdt0(xd) = all_94_1 & sdtlcdtrc0(xe, all_94_0) = xO &
% 50.30/7.43 | sdtlbdtrb0(xd, all_94_1) = all_94_0 & $i(all_94_0) & $i(all_94_1) &
% 50.30/7.43 | aSet0(xO)
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (25) implies:
% 50.30/7.43 | (26) aSet0(xO)
% 50.30/7.43 |
% 50.30/7.43 | DELTA: instantiating (10) with fresh symbols all_100_0, all_100_1 gives:
% 50.30/7.43 | (27) szDzizrdt0(xd) = all_100_1 & sdtlbdtrb0(xd, all_100_1) = all_100_0 &
% 50.30/7.43 | sdtlpdtrp0(xe, xn) = xp & $i(all_100_0) & $i(all_100_1) &
% 50.30/7.43 | aElementOf0(xn, all_100_0) & aElementOf0(xn, szNzAzT0)
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (27) implies:
% 50.30/7.43 | (28) aElementOf0(xn, szNzAzT0)
% 50.30/7.43 | (29) sdtlpdtrp0(xe, xn) = xp
% 50.30/7.43 |
% 50.30/7.43 | REDUCE: (16), (20) imply:
% 50.30/7.43 | (30) sdtlpdtrp0(xe, xm) = xp
% 50.30/7.43 |
% 50.30/7.43 | REDUCE: (11), (20) imply:
% 50.30/7.43 | (31) aElementOf0(xp, xP)
% 50.30/7.43 |
% 50.30/7.43 | GROUND_INST: instantiating (21) with xp, all_88_0, xQ, simplifying with (8),
% 50.30/7.43 | (24) gives:
% 50.30/7.43 | (32) all_88_0 = xp
% 50.30/7.43 |
% 50.30/7.43 | REDUCE: (23), (32) imply:
% 50.30/7.43 | (33) sdtmndt0(xQ, xp) = xP
% 50.30/7.43 |
% 50.30/7.43 | GROUND_INST: instantiating (1) with xO, xQ, simplifying with (7), (13), (18),
% 50.30/7.43 | (26) gives:
% 50.30/7.43 | (34) aSet0(xQ)
% 50.30/7.43 |
% 50.30/7.43 | GROUND_INST: instantiating (5) with xn, xp, simplifying with (17), (28), (29)
% 50.30/7.43 | gives:
% 50.30/7.43 | (35) ? [v0: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) = xp & $i(v0)
% 50.30/7.43 | & $i(xp))
% 50.30/7.43 |
% 50.30/7.43 | GROUND_INST: instantiating (mImgElm) with xe, szNzAzT0, xm, xp, simplifying
% 50.30/7.43 | with (3), (4), (14), (15), (19), (30) gives:
% 50.30/7.43 | (36) aElement0(xp)
% 50.30/7.43 |
% 50.30/7.43 | DELTA: instantiating (35) with fresh symbol all_128_0 gives:
% 50.30/7.43 | (37) sdtlpdtrp0(xN, xn) = all_128_0 & szmzizndt0(all_128_0) = xp &
% 50.30/7.43 | $i(all_128_0) & $i(xp)
% 50.30/7.43 |
% 50.30/7.43 | ALPHA: (37) implies:
% 50.30/7.43 | (38) $i(xp)
% 50.30/7.43 |
% 50.30/7.44 | GROUND_INST: instantiating (2) with xQ, xp, xP, simplifying with (12), (18),
% 50.30/7.44 | (31), (33), (34), (36), (38) gives:
% 50.30/7.44 | (39) $false
% 50.30/7.44 |
% 50.30/7.44 | CLOSE: (39) is inconsistent.
% 50.30/7.44 |
% 50.30/7.44 End of proof
% 50.30/7.44 % SZS output end Proof for theBenchmark
% 50.30/7.44
% 50.30/7.44 6834ms
%------------------------------------------------------------------------------