TSTP Solution File: NUM545+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM545+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 11:48:31 EDT 2023
% Result : Theorem 64.08s 9.13s
% Output : Proof 69.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM545+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.34 % Computer : n014.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 25 17:41:18 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.53/1.14 Prover 1: Preprocessing ...
% 3.53/1.14 Prover 4: Preprocessing ...
% 3.88/1.18 Prover 0: Preprocessing ...
% 3.88/1.18 Prover 6: Preprocessing ...
% 3.88/1.18 Prover 3: Preprocessing ...
% 3.88/1.19 Prover 2: Preprocessing ...
% 3.88/1.19 Prover 5: Preprocessing ...
% 9.24/2.03 Prover 1: Constructing countermodel ...
% 9.24/2.04 Prover 3: Constructing countermodel ...
% 10.11/2.10 Prover 5: Constructing countermodel ...
% 10.65/2.14 Prover 6: Proving ...
% 10.65/2.16 Prover 2: Proving ...
% 12.26/2.43 Prover 4: Constructing countermodel ...
% 13.95/2.64 Prover 0: Proving ...
% 64.08/9.13 Prover 0: proved (8467ms)
% 64.08/9.13
% 64.08/9.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.08/9.13
% 64.08/9.13 Prover 3: stopped
% 64.08/9.13 Prover 5: stopped
% 64.08/9.13 Prover 2: stopped
% 64.08/9.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 64.08/9.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 64.08/9.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 64.08/9.13 Prover 6: stopped
% 64.08/9.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 64.08/9.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 64.85/9.24 Prover 7: Preprocessing ...
% 64.85/9.25 Prover 13: Preprocessing ...
% 64.85/9.26 Prover 8: Preprocessing ...
% 64.85/9.29 Prover 10: Preprocessing ...
% 64.85/9.29 Prover 11: Preprocessing ...
% 65.66/9.39 Prover 7: Constructing countermodel ...
% 66.41/9.41 Prover 8: Warning: ignoring some quantifiers
% 66.41/9.42 Prover 8: Constructing countermodel ...
% 66.41/9.43 Prover 13: Constructing countermodel ...
% 66.41/9.46 Prover 10: Constructing countermodel ...
% 69.07/9.76 Prover 7: Found proof (size 26)
% 69.07/9.76 Prover 7: proved (633ms)
% 69.07/9.76 Prover 13: stopped
% 69.07/9.76 Prover 8: stopped
% 69.07/9.76 Prover 11: Constructing countermodel ...
% 69.07/9.77 Prover 10: stopped
% 69.07/9.78 Prover 11: stopped
% 69.07/9.78 Prover 1: stopped
% 69.07/9.78 Prover 4: stopped
% 69.07/9.78
% 69.07/9.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.07/9.78
% 69.07/9.79 % SZS output start Proof for theBenchmark
% 69.07/9.79 Assumptions after simplification:
% 69.07/9.79 ---------------------------------
% 69.07/9.79
% 69.07/9.79 (mSegZero)
% 69.07/9.81 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 69.07/9.81
% 69.07/9.81 (mSuccNum)
% 69.07/9.81 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 69.07/9.81 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1,
% 69.07/9.81 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~
% 69.07/9.81 aElementOf0(v0, szNzAzT0))
% 69.07/9.81
% 69.07/9.81 (mZeroNum)
% 69.07/9.81 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 69.07/9.81
% 69.07/9.81 (m__)
% 69.07/9.82 $i(xS) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 69.07/9.82 : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v0)
% 69.07/9.82 | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~ aElementOf0(v0,
% 69.07/9.82 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 69.07/9.82 : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~
% 69.07/9.82 $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v0, szNzAzT0) |
% 69.07/9.82 sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 69.07/9.82 : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v0)
% 69.07/9.82 | ~ aElementOf0(v2, v1) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2,
% 69.07/9.82 szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~
% 69.07/9.82 $i(v0) | ~ aSubsetOf0(xS, v1) | ~ aElementOf0(v0, szNzAzT0)) & ! [v0: $i]
% 69.07/9.82 : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 69.07/9.82 szNzAzT0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) =
% 69.07/9.82 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ($i(v2) &
% 69.07/9.82 aElementOf0(v2, xS) & ~ aElementOf0(v2, v1)))
% 69.07/9.82
% 69.07/9.82 (m__1986)
% 69.07/9.82 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isFinite0(xS) & aSet0(xS) &
% 69.07/9.82 ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | aElementOf0(v0, szNzAzT0))
% 69.07/9.82
% 69.07/9.82 (m__2035)
% 69.07/9.82 $i(xS) & $i(szNzAzT0) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 69.07/9.82 ((xS = slcrc0 & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, slcrc0))) |
% 69.07/9.82 (slbdtrb0(v1) = v2 & szmzazxdt0(xS) = v0 & szszuzczcdt0(v0) = v1 & $i(v2) &
% 69.07/9.82 $i(v1) & $i(v0) & aSubsetOf0(xS, v2) & aElementOf0(v0, xS) & aSet0(v2) &
% 69.07/9.82 ! [v3: $i] : ! [v4: $i] : ( ~ (szszuzczcdt0(v3) = v4) | ~ $i(v3) | ~
% 69.07/9.82 sdtlseqdt0(v4, v1) | ~ aElementOf0(v3, szNzAzT0) | aElementOf0(v3, v2))
% 69.07/9.82 & ! [v3: $i] : ! [v4: $i] : ( ~ (szszuzczcdt0(v3) = v4) | ~ $i(v3) | ~
% 69.07/9.82 aElementOf0(v3, v2) | sdtlseqdt0(v4, v1)) & ! [v3: $i] : ! [v4: $i] :
% 69.07/9.82 ( ~ (szszuzczcdt0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 69.07/9.82 aElementOf0(v3, szNzAzT0)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 69.07/9.82 aElementOf0(v3, xS) | sdtlseqdt0(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) |
% 69.07/9.82 ~ aElementOf0(v3, xS) | aElementOf0(v3, v2))))
% 69.07/9.82
% 69.07/9.82 Further assumptions not needed in the proof:
% 69.07/9.82 --------------------------------------------
% 69.07/9.82 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 69.07/9.82 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons,
% 69.07/9.82 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSub, mDiffCons, mEOfElem,
% 69.07/9.82 mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mIH, mIHSort, mLessASymm,
% 69.07/9.82 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet,
% 69.07/9.82 mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSetSort,
% 69.07/9.82 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mZeroLess
% 69.07/9.82
% 69.07/9.82 Those formulas are unsatisfiable:
% 69.07/9.82 ---------------------------------
% 69.07/9.82
% 69.07/9.82 Begin of proof
% 69.07/9.82 |
% 69.07/9.82 | ALPHA: (mZeroNum) implies:
% 69.07/9.82 | (1) aElementOf0(sz00, szNzAzT0)
% 69.07/9.82 |
% 69.07/9.82 | ALPHA: (mSuccNum) implies:
% 69.07/9.82 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 69.07/9.82 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0))
% 69.07/9.82 |
% 69.07/9.82 | ALPHA: (mSegZero) implies:
% 69.07/9.83 | (3) $i(sz00)
% 69.07/9.83 | (4) slbdtrb0(sz00) = slcrc0
% 69.07/9.83 |
% 69.07/9.83 | ALPHA: (m__1986) implies:
% 69.07/9.83 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | aElementOf0(v0,
% 69.07/9.83 | szNzAzT0))
% 69.07/9.83 |
% 69.07/9.83 | ALPHA: (m__2035) implies:
% 69.07/9.83 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((xS = slcrc0 & ! [v3: $i] :
% 69.07/9.83 | ( ~ $i(v3) | ~ aElementOf0(v3, slcrc0))) | (slbdtrb0(v1) = v2 &
% 69.07/9.83 | szmzazxdt0(xS) = v0 & szszuzczcdt0(v0) = v1 & $i(v2) & $i(v1) &
% 69.07/9.83 | $i(v0) & aSubsetOf0(xS, v2) & aElementOf0(v0, xS) & aSet0(v2) & !
% 69.07/9.83 | [v3: $i] : ! [v4: $i] : ( ~ (szszuzczcdt0(v3) = v4) | ~ $i(v3) |
% 69.07/9.83 | ~ sdtlseqdt0(v4, v1) | ~ aElementOf0(v3, szNzAzT0) |
% 69.07/9.83 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 69.07/9.83 | (szszuzczcdt0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 69.07/9.83 | sdtlseqdt0(v4, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 69.07/9.83 | (szszuzczcdt0(v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 69.07/9.83 | aElementOf0(v3, szNzAzT0)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 69.07/9.83 | aElementOf0(v3, xS) | sdtlseqdt0(v3, v0)) & ! [v3: $i] : ( ~
% 69.07/9.83 | $i(v3) | ~ aElementOf0(v3, xS) | aElementOf0(v3, v2))))
% 69.07/9.83 |
% 69.07/9.83 | ALPHA: (m__) implies:
% 69.07/9.83 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~
% 69.07/9.83 | aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ($i(v2) & aElementOf0(v2,
% 69.07/9.83 | xS) & ~ aElementOf0(v2, v1)))
% 69.07/9.83 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~
% 69.07/9.83 | aSubsetOf0(xS, v1) | ~ aElementOf0(v0, szNzAzT0))
% 69.07/9.83 |
% 69.07/9.83 | DELTA: instantiating (6) with fresh symbols all_49_0, all_49_1, all_49_2
% 69.07/9.83 | gives:
% 69.07/9.83 | (9) (xS = slcrc0 & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)))
% 69.07/9.83 | | (slbdtrb0(all_49_1) = all_49_0 & szmzazxdt0(xS) = all_49_2 &
% 69.07/9.83 | szszuzczcdt0(all_49_2) = all_49_1 & $i(all_49_0) & $i(all_49_1) &
% 69.07/9.83 | $i(all_49_2) & aSubsetOf0(xS, all_49_0) & aElementOf0(all_49_2, xS) &
% 69.07/9.83 | aSet0(all_49_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 69.07/9.83 | v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, all_49_1) | ~
% 69.07/9.83 | aElementOf0(v0, szNzAzT0) | aElementOf0(v0, all_49_0)) & ! [v0:
% 69.07/9.83 | $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~
% 69.07/9.83 | aElementOf0(v0, all_49_0) | sdtlseqdt0(v1, all_49_1)) & ! [v0: $i]
% 69.07/9.83 | : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~
% 69.07/9.83 | aElementOf0(v0, all_49_0) | aElementOf0(v0, szNzAzT0)) & ! [v0:
% 69.07/9.83 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | sdtlseqdt0(v0,
% 69.07/9.83 | all_49_2)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) |
% 69.07/9.83 | aElementOf0(v0, all_49_0)))
% 69.07/9.83 |
% 69.07/9.83 | GROUND_INST: instantiating (7) with sz00, slcrc0, simplifying with (1), (3),
% 69.07/9.83 | (4) gives:
% 69.07/9.83 | (10) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & ~ aElementOf0(v0,
% 69.07/9.83 | slcrc0))
% 69.07/9.83 |
% 69.07/9.83 | DELTA: instantiating (10) with fresh symbol all_64_0 gives:
% 69.07/9.83 | (11) $i(all_64_0) & aElementOf0(all_64_0, xS) & ~ aElementOf0(all_64_0,
% 69.07/9.83 | slcrc0)
% 69.07/9.83 |
% 69.07/9.83 | ALPHA: (11) implies:
% 69.07/9.83 | (12) ~ aElementOf0(all_64_0, slcrc0)
% 69.07/9.83 | (13) aElementOf0(all_64_0, xS)
% 69.07/9.83 |
% 69.07/9.83 | PRED_UNIFY: (12), (13) imply:
% 69.07/9.83 | (14) ~ (xS = slcrc0)
% 69.07/9.83 |
% 69.07/9.83 | BETA: splitting (9) gives:
% 69.07/9.83 |
% 69.07/9.83 | Case 1:
% 69.07/9.83 | |
% 69.07/9.83 | | (15) xS = slcrc0 & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 69.07/9.83 | |
% 69.07/9.83 | | ALPHA: (15) implies:
% 69.07/9.83 | | (16) xS = slcrc0
% 69.07/9.83 | |
% 69.07/9.83 | | REDUCE: (14), (16) imply:
% 69.07/9.83 | | (17) $false
% 69.07/9.84 | |
% 69.07/9.84 | | CLOSE: (17) is inconsistent.
% 69.07/9.84 | |
% 69.07/9.84 | Case 2:
% 69.07/9.84 | |
% 69.07/9.84 | | (18) slbdtrb0(all_49_1) = all_49_0 & szmzazxdt0(xS) = all_49_2 &
% 69.07/9.84 | | szszuzczcdt0(all_49_2) = all_49_1 & $i(all_49_0) & $i(all_49_1) &
% 69.07/9.84 | | $i(all_49_2) & aSubsetOf0(xS, all_49_0) & aElementOf0(all_49_2, xS)
% 69.07/9.84 | | & aSet0(all_49_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 69.07/9.84 | | (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, all_49_1)
% 69.07/9.84 | | | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v0, all_49_0)) & !
% 69.07/9.84 | | [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 69.07/9.84 | | ~ aElementOf0(v0, all_49_0) | sdtlseqdt0(v1, all_49_1)) & ! [v0:
% 69.07/9.84 | | $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~
% 69.07/9.84 | | aElementOf0(v0, all_49_0) | aElementOf0(v0, szNzAzT0)) & ! [v0:
% 69.07/9.84 | | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | sdtlseqdt0(v0,
% 69.07/9.84 | | all_49_2)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) |
% 69.07/9.84 | | aElementOf0(v0, all_49_0))
% 69.07/9.84 | |
% 69.07/9.84 | | ALPHA: (18) implies:
% 69.07/9.84 | | (19) aElementOf0(all_49_2, xS)
% 69.07/9.84 | | (20) aSubsetOf0(xS, all_49_0)
% 69.07/9.84 | | (21) $i(all_49_2)
% 69.07/9.84 | | (22) $i(all_49_1)
% 69.07/9.84 | | (23) szszuzczcdt0(all_49_2) = all_49_1
% 69.07/9.84 | | (24) slbdtrb0(all_49_1) = all_49_0
% 69.07/9.84 | |
% 69.07/9.84 | | GROUND_INST: instantiating (5) with all_49_2, simplifying with (19), (21)
% 69.07/9.84 | | gives:
% 69.07/9.84 | | (25) aElementOf0(all_49_2, szNzAzT0)
% 69.07/9.84 | |
% 69.07/9.84 | | GROUND_INST: instantiating (2) with all_49_2, all_49_1, simplifying with
% 69.07/9.84 | | (21), (23) gives:
% 69.07/9.84 | | (26) ~ aElementOf0(all_49_2, szNzAzT0) | aElementOf0(all_49_1, szNzAzT0)
% 69.07/9.84 | |
% 69.07/9.84 | | GROUND_INST: instantiating (8) with all_49_1, all_49_0, simplifying with
% 69.07/9.84 | | (20), (22), (24) gives:
% 69.07/9.84 | | (27) ~ aElementOf0(all_49_1, szNzAzT0)
% 69.07/9.84 | |
% 69.07/9.84 | | BETA: splitting (26) gives:
% 69.07/9.84 | |
% 69.07/9.84 | | Case 1:
% 69.07/9.84 | | |
% 69.07/9.84 | | | (28) ~ aElementOf0(all_49_2, szNzAzT0)
% 69.07/9.84 | | |
% 69.07/9.84 | | | PRED_UNIFY: (25), (28) imply:
% 69.07/9.84 | | | (29) $false
% 69.07/9.84 | | |
% 69.07/9.84 | | | CLOSE: (29) is inconsistent.
% 69.07/9.84 | | |
% 69.07/9.84 | | Case 2:
% 69.07/9.84 | | |
% 69.07/9.84 | | | (30) aElementOf0(all_49_1, szNzAzT0)
% 69.07/9.84 | | |
% 69.07/9.84 | | | PRED_UNIFY: (27), (30) imply:
% 69.07/9.84 | | | (31) $false
% 69.07/9.84 | | |
% 69.07/9.84 | | | CLOSE: (31) is inconsistent.
% 69.07/9.84 | | |
% 69.07/9.84 | | End of split
% 69.07/9.84 | |
% 69.07/9.84 | End of split
% 69.07/9.84 |
% 69.07/9.84 End of proof
% 69.07/9.84 % SZS output end Proof for theBenchmark
% 69.07/9.84
% 69.07/9.84 9232ms
%------------------------------------------------------------------------------