TSTP Solution File: NUM632+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM632+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 : n008.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 11:49:06 EDT 2023
% Result : Theorem 14.16s 2.74s
% Output : Proof 19.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM632+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n008.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 16:40:02 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.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.55/1.39 Prover 1: Preprocessing ...
% 4.55/1.39 Prover 4: Preprocessing ...
% 4.55/1.43 Prover 6: Preprocessing ...
% 4.55/1.43 Prover 3: Preprocessing ...
% 4.55/1.43 Prover 0: Preprocessing ...
% 4.55/1.43 Prover 2: Preprocessing ...
% 4.55/1.43 Prover 5: Preprocessing ...
% 13.84/2.58 Prover 1: Constructing countermodel ...
% 13.84/2.60 Prover 3: Constructing countermodel ...
% 14.16/2.70 Prover 6: Proving ...
% 14.16/2.74 Prover 3: proved (2081ms)
% 14.16/2.74
% 14.16/2.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.16/2.74
% 14.16/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.70/2.75 Prover 6: stopped
% 14.70/2.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.70/2.80 Prover 5: Proving ...
% 14.70/2.80 Prover 5: stopped
% 14.70/2.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.05/2.90 Prover 8: Preprocessing ...
% 16.05/2.91 Prover 7: Preprocessing ...
% 16.05/2.92 Prover 2: Proving ...
% 16.05/2.92 Prover 1: Found proof (size 39)
% 16.05/2.92 Prover 2: stopped
% 16.05/2.93 Prover 1: proved (2267ms)
% 16.05/2.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.57/2.95 Prover 10: Preprocessing ...
% 16.66/3.01 Prover 7: stopped
% 16.96/3.04 Prover 10: stopped
% 17.20/3.10 Prover 11: Preprocessing ...
% 18.36/3.22 Prover 8: Warning: ignoring some quantifiers
% 18.36/3.24 Prover 8: Constructing countermodel ...
% 18.36/3.25 Prover 11: stopped
% 18.91/3.26 Prover 4: Constructing countermodel ...
% 18.91/3.26 Prover 8: stopped
% 18.98/3.29 Prover 4: stopped
% 18.98/3.35 Prover 0: Proving ...
% 18.98/3.36 Prover 0: stopped
% 18.98/3.36
% 18.98/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.98/3.36
% 18.98/3.37 % SZS output start Proof for theBenchmark
% 18.98/3.37 Assumptions after simplification:
% 18.98/3.37 ---------------------------------
% 18.98/3.37
% 18.98/3.37 (m__)
% 18.98/3.39 $i(xQ) & $i(xd) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 18.98/3.39 szDzizrdt0(xd) = v1 & sdtlpdtrp0(xc, xQ) = v0 & $i(v1) & $i(v0))
% 18.98/3.39
% 18.98/3.39 (m__4854)
% 18.98/3.40 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 18.98/3.40 sdtlbdtrb0(xd, v0) = v1 & isCountable0(v1) = 0 & aElementOf0(v0, xT) = 0 &
% 18.98/3.40 $i(v1) & $i(v0))
% 18.98/3.40
% 18.98/3.40 (m__4891)
% 18.98/3.40 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 18.98/3.40 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & aSet0(xO) = 0 & $i(v1) &
% 18.98/3.40 $i(v0))
% 18.98/3.40
% 18.98/3.40 (m__4982)
% 18.98/3.40 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 18.98/3.40 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 18.98/3.40 : ( ~ (aElementOf0(v2, xO) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtlpdtrp0(xe,
% 18.98/3.40 v3) = v2 & aElementOf0(v3, v1) = 0 & aElementOf0(v3, szNzAzT0) = 0 &
% 18.98/3.40 $i(v3))))
% 18.98/3.40
% 18.98/3.40 (m__5309)
% 18.98/3.40 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 18.98/3.40 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, xn) = xp &
% 18.98/3.40 aElementOf0(xn, v1) = 0 & aElementOf0(xn, szNzAzT0) = 0 & $i(v1) & $i(v0))
% 18.98/3.40
% 18.98/3.40 (m__5321)
% 18.98/3.40 $i(xn) & $i(xd) & ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0
% 18.98/3.40 & $i(v0))
% 18.98/3.40
% 18.98/3.40 (m__5568)
% 18.98/3.40 $i(xn) & $i(xQ) & $i(xd) & $i(xc) & ? [v0: $i] : (sdtlpdtrp0(xd, xn) = v0 &
% 18.98/3.40 sdtlpdtrp0(xc, xQ) = v0 & $i(v0))
% 18.98/3.40
% 18.98/3.40 (function-axioms)
% 18.98/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.98/3.41 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 18.98/3.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 18.98/3.41 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 18.98/3.41 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 18.98/3.41 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 18.98/3.41 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 18.98/3.41 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 18.98/3.41 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 18.98/3.41 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.98/3.41 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0:
% 18.98/3.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.98/3.41 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 18.98/3.41 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.98/3.41 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 18.98/3.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 18.98/3.41 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.98/3.41 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.98/3.41 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 18.98/3.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.98/3.41 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 18.98/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 18.98/3.41 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.98/3.41 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~
% 18.98/3.41 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 18.98/3.41 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 18.98/3.41 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 18.98/3.41 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.98/3.41 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 18.98/3.41 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 18.98/3.41 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.98/3.41 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 18.98/3.41 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 18.98/3.41 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 18.98/3.41 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) &
% 18.98/3.41 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 18.98/3.41 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 18.98/3.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 18.98/3.41 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.98/3.41 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 18.98/3.41 ~ (aElement0(v2) = v0))
% 18.98/3.41
% 18.98/3.41 Further assumptions not needed in the proof:
% 18.98/3.41 --------------------------------------------
% 18.98/3.41 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 18.98/3.41 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 18.98/3.41 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 18.98/3.41 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort,
% 18.98/3.41 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort,
% 18.98/3.41 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 18.98/3.41 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 18.98/3.41 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet,
% 18.98/3.41 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 18.98/3.41 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398,
% 18.98/3.41 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754,
% 18.98/3.41 m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730,
% 18.98/3.41 m__4758, m__4908, m__4998, m__5078, m__5093, m__5106, m__5116, m__5147, m__5164,
% 18.98/3.41 m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5334
% 18.98/3.41
% 18.98/3.41 Those formulas are unsatisfiable:
% 18.98/3.41 ---------------------------------
% 18.98/3.41
% 18.98/3.41 Begin of proof
% 18.98/3.42 |
% 19.47/3.42 | ALPHA: (m__4854) implies:
% 19.47/3.42 | (1) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 19.47/3.42 | v1 & isCountable0(v1) = 0 & aElementOf0(v0, xT) = 0 & $i(v1) &
% 19.47/3.42 | $i(v0))
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (m__4891) implies:
% 19.47/3.42 | (2) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) =
% 19.47/3.42 | xO & sdtlbdtrb0(xd, v0) = v1 & aSet0(xO) = 0 & $i(v1) & $i(v0))
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (m__4982) implies:
% 19.47/3.42 | (3) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 19.47/3.42 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (aElementOf0(v2, xO) = 0) |
% 19.47/3.42 | ~ $i(v2) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 & aElementOf0(v3,
% 19.47/3.42 | v1) = 0 & aElementOf0(v3, szNzAzT0) = 0 & $i(v3))))
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (m__5309) implies:
% 19.47/3.42 | (4) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 19.47/3.42 | v1 & sdtlpdtrp0(xe, xn) = xp & aElementOf0(xn, v1) = 0 &
% 19.47/3.42 | aElementOf0(xn, szNzAzT0) = 0 & $i(v1) & $i(v0))
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (m__5321) implies:
% 19.47/3.42 | (5) ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0 & $i(v0))
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (m__5568) implies:
% 19.47/3.42 | (6) ? [v0: $i] : (sdtlpdtrp0(xd, xn) = v0 & sdtlpdtrp0(xc, xQ) = v0 &
% 19.47/3.42 | $i(v0))
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (m__) implies:
% 19.47/3.42 | (7) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & szDzizrdt0(xd) = v1 &
% 19.47/3.42 | sdtlpdtrp0(xc, xQ) = v0 & $i(v1) & $i(v0))
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (function-axioms) implies:
% 19.47/3.42 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2)
% 19.47/3.42 | = v1) | ~ (szDzizrdt0(v2) = v0))
% 19.47/3.42 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.47/3.42 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 19.47/3.42 |
% 19.47/3.42 | DELTA: instantiating (6) with fresh symbol all_78_0 gives:
% 19.47/3.42 | (10) sdtlpdtrp0(xd, xn) = all_78_0 & sdtlpdtrp0(xc, xQ) = all_78_0 &
% 19.47/3.42 | $i(all_78_0)
% 19.47/3.42 |
% 19.47/3.42 | ALPHA: (10) implies:
% 19.47/3.43 | (11) sdtlpdtrp0(xc, xQ) = all_78_0
% 19.47/3.43 | (12) sdtlpdtrp0(xd, xn) = all_78_0
% 19.47/3.43 |
% 19.47/3.43 | DELTA: instantiating (5) with fresh symbol all_80_0 gives:
% 19.47/3.43 | (13) szDzizrdt0(xd) = all_80_0 & sdtlpdtrp0(xd, xn) = all_80_0 &
% 19.47/3.43 | $i(all_80_0)
% 19.47/3.43 |
% 19.47/3.43 | ALPHA: (13) implies:
% 19.47/3.43 | (14) sdtlpdtrp0(xd, xn) = all_80_0
% 19.47/3.43 | (15) szDzizrdt0(xd) = all_80_0
% 19.47/3.43 |
% 19.47/3.43 | DELTA: instantiating (7) with fresh symbols all_90_0, all_90_1 gives:
% 19.47/3.43 | (16) ~ (all_90_0 = all_90_1) & szDzizrdt0(xd) = all_90_0 & sdtlpdtrp0(xc,
% 19.47/3.43 | xQ) = all_90_1 & $i(all_90_0) & $i(all_90_1)
% 19.47/3.43 |
% 19.47/3.43 | ALPHA: (16) implies:
% 19.47/3.43 | (17) ~ (all_90_0 = all_90_1)
% 19.47/3.43 | (18) sdtlpdtrp0(xc, xQ) = all_90_1
% 19.47/3.43 | (19) szDzizrdt0(xd) = all_90_0
% 19.47/3.43 |
% 19.47/3.43 | DELTA: instantiating (2) with fresh symbols all_94_0, all_94_1 gives:
% 19.47/3.43 | (20) szDzizrdt0(xd) = all_94_1 & sdtlcdtrc0(xe, all_94_0) = xO &
% 19.47/3.43 | sdtlbdtrb0(xd, all_94_1) = all_94_0 & aSet0(xO) = 0 & $i(all_94_0) &
% 19.47/3.43 | $i(all_94_1)
% 19.47/3.43 |
% 19.47/3.43 | ALPHA: (20) implies:
% 19.47/3.43 | (21) szDzizrdt0(xd) = all_94_1
% 19.47/3.43 |
% 19.47/3.43 | DELTA: instantiating (1) with fresh symbols all_96_0, all_96_1 gives:
% 19.47/3.43 | (22) szDzizrdt0(xd) = all_96_1 & sdtlbdtrb0(xd, all_96_1) = all_96_0 &
% 19.47/3.43 | isCountable0(all_96_0) = 0 & aElementOf0(all_96_1, xT) = 0 &
% 19.47/3.43 | $i(all_96_0) & $i(all_96_1)
% 19.47/3.43 |
% 19.47/3.43 | ALPHA: (22) implies:
% 19.47/3.43 | (23) szDzizrdt0(xd) = all_96_1
% 19.47/3.43 |
% 19.47/3.43 | DELTA: instantiating (4) with fresh symbols all_100_0, all_100_1 gives:
% 19.47/3.43 | (24) szDzizrdt0(xd) = all_100_1 & sdtlbdtrb0(xd, all_100_1) = all_100_0 &
% 19.47/3.43 | sdtlpdtrp0(xe, xn) = xp & aElementOf0(xn, all_100_0) = 0 &
% 19.47/3.43 | aElementOf0(xn, szNzAzT0) = 0 & $i(all_100_0) & $i(all_100_1)
% 19.47/3.43 |
% 19.47/3.43 | ALPHA: (24) implies:
% 19.47/3.43 | (25) szDzizrdt0(xd) = all_100_1
% 19.47/3.43 |
% 19.47/3.43 | DELTA: instantiating (3) with fresh symbols all_102_0, all_102_1 gives:
% 19.47/3.43 | (26) szDzizrdt0(xd) = all_102_1 & sdtlbdtrb0(xd, all_102_1) = all_102_0 &
% 19.47/3.43 | $i(all_102_0) & $i(all_102_1) & ! [v0: $i] : ( ~ (aElementOf0(v0, xO)
% 19.47/3.43 | = 0) | ~ $i(v0) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 19.47/3.43 | aElementOf0(v1, all_102_0) = 0 & aElementOf0(v1, szNzAzT0) = 0 &
% 19.47/3.43 | $i(v1)))
% 19.47/3.43 |
% 19.47/3.43 | ALPHA: (26) implies:
% 19.47/3.43 | (27) szDzizrdt0(xd) = all_102_1
% 19.47/3.43 |
% 19.47/3.43 | GROUND_INST: instantiating (9) with all_78_0, all_90_1, xQ, xc, simplifying
% 19.47/3.43 | with (11), (18) gives:
% 19.47/3.43 | (28) all_90_1 = all_78_0
% 19.47/3.43 |
% 19.47/3.43 | GROUND_INST: instantiating (9) with all_78_0, all_80_0, xn, xd, simplifying
% 19.47/3.43 | with (12), (14) gives:
% 19.47/3.43 | (29) all_80_0 = all_78_0
% 19.47/3.43 |
% 19.47/3.43 | GROUND_INST: instantiating (8) with all_96_1, all_100_1, xd, simplifying with
% 19.47/3.43 | (23), (25) gives:
% 19.47/3.43 | (30) all_100_1 = all_96_1
% 19.47/3.43 |
% 19.47/3.43 | GROUND_INST: instantiating (8) with all_94_1, all_100_1, xd, simplifying with
% 19.47/3.43 | (21), (25) gives:
% 19.47/3.43 | (31) all_100_1 = all_94_1
% 19.47/3.43 |
% 19.47/3.43 | GROUND_INST: instantiating (8) with all_80_0, all_100_1, xd, simplifying with
% 19.47/3.43 | (15), (25) gives:
% 19.47/3.43 | (32) all_100_1 = all_80_0
% 19.47/3.43 |
% 19.47/3.43 | GROUND_INST: instantiating (8) with all_94_1, all_102_1, xd, simplifying with
% 19.47/3.43 | (21), (27) gives:
% 19.47/3.43 | (33) all_102_1 = all_94_1
% 19.47/3.43 |
% 19.47/3.43 | GROUND_INST: instantiating (8) with all_90_0, all_102_1, xd, simplifying with
% 19.47/3.43 | (19), (27) gives:
% 19.47/3.43 | (34) all_102_1 = all_90_0
% 19.47/3.43 |
% 19.47/3.43 | COMBINE_EQS: (33), (34) imply:
% 19.47/3.43 | (35) all_94_1 = all_90_0
% 19.47/3.43 |
% 19.47/3.43 | SIMP: (35) implies:
% 19.47/3.44 | (36) all_94_1 = all_90_0
% 19.47/3.44 |
% 19.47/3.44 | COMBINE_EQS: (30), (31) imply:
% 19.47/3.44 | (37) all_96_1 = all_94_1
% 19.47/3.44 |
% 19.47/3.44 | COMBINE_EQS: (30), (32) imply:
% 19.47/3.44 | (38) all_96_1 = all_80_0
% 19.47/3.44 |
% 19.47/3.44 | COMBINE_EQS: (37), (38) imply:
% 19.47/3.44 | (39) all_94_1 = all_80_0
% 19.47/3.44 |
% 19.47/3.44 | SIMP: (39) implies:
% 19.47/3.44 | (40) all_94_1 = all_80_0
% 19.47/3.44 |
% 19.47/3.44 | COMBINE_EQS: (36), (40) imply:
% 19.47/3.44 | (41) all_90_0 = all_80_0
% 19.47/3.44 |
% 19.47/3.44 | COMBINE_EQS: (29), (41) imply:
% 19.47/3.44 | (42) all_90_0 = all_78_0
% 19.47/3.44 |
% 19.47/3.44 | REDUCE: (17), (28), (42) imply:
% 19.47/3.44 | (43) $false
% 19.47/3.44 |
% 19.47/3.44 | CLOSE: (43) is inconsistent.
% 19.47/3.44 |
% 19.47/3.44 End of proof
% 19.47/3.44 % SZS output end Proof for theBenchmark
% 19.47/3.44
% 19.47/3.44 2802ms
%------------------------------------------------------------------------------