TSTP Solution File: RNG080+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG080+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 : n032.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 13:57:45 EDT 2023
% Result : Theorem 11.75s 2.24s
% Output : Proof 18.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : RNG080+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.07 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Sun Aug 27 02:56:44 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.11/0.47 ________ _____
% 0.11/0.47 ___ __ \_________(_)________________________________
% 0.11/0.47 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.11/0.47 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.11/0.47 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.11/0.47
% 0.11/0.47 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.11/0.47 (2023-06-19)
% 0.11/0.47
% 0.11/0.47 (c) Philipp Rümmer, 2009-2023
% 0.11/0.47 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.11/0.47 Amanda Stjerna.
% 0.11/0.47 Free software under BSD-3-Clause.
% 0.11/0.47
% 0.11/0.47 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.11/0.47
% 0.11/0.47 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.11/0.48 Running up to 7 provers in parallel.
% 0.11/0.49 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.11/0.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.11/0.49 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.11/0.49 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.11/0.49 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.11/0.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.11/0.49 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.74/1.02 Prover 1: Preprocessing ...
% 2.74/1.02 Prover 4: Preprocessing ...
% 3.30/1.05 Prover 0: Preprocessing ...
% 3.30/1.05 Prover 5: Preprocessing ...
% 3.30/1.06 Prover 2: Preprocessing ...
% 3.30/1.06 Prover 6: Preprocessing ...
% 3.30/1.06 Prover 3: Preprocessing ...
% 8.34/1.80 Prover 3: Constructing countermodel ...
% 8.80/1.81 Prover 6: Proving ...
% 8.80/1.81 Prover 1: Constructing countermodel ...
% 9.90/1.97 Prover 5: Constructing countermodel ...
% 10.18/2.11 Prover 2: Proving ...
% 10.18/2.13 Prover 4: Constructing countermodel ...
% 10.18/2.14 Prover 0: Proving ...
% 11.75/2.24 Prover 3: proved (1754ms)
% 11.75/2.24
% 11.75/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.75/2.24
% 11.75/2.25 Prover 5: stopped
% 11.75/2.26 Prover 2: stopped
% 12.23/2.28 Prover 0: stopped
% 12.23/2.28 Prover 6: stopped
% 12.23/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.23/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.23/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.23/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.23/2.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.23/2.35 Prover 7: Preprocessing ...
% 13.10/2.39 Prover 8: Preprocessing ...
% 13.10/2.41 Prover 10: Preprocessing ...
% 13.38/2.43 Prover 11: Preprocessing ...
% 13.44/2.45 Prover 13: Preprocessing ...
% 14.04/2.53 Prover 10: Constructing countermodel ...
% 14.04/2.54 Prover 8: Warning: ignoring some quantifiers
% 14.04/2.56 Prover 8: Constructing countermodel ...
% 14.53/2.59 Prover 7: Constructing countermodel ...
% 14.53/2.63 Prover 13: Constructing countermodel ...
% 15.47/2.81 Prover 11: Constructing countermodel ...
% 17.97/3.06 Prover 10: Found proof (size 82)
% 17.97/3.06 Prover 10: proved (779ms)
% 17.97/3.06 Prover 7: stopped
% 17.97/3.06 Prover 13: stopped
% 17.97/3.06 Prover 8: stopped
% 17.97/3.06 Prover 4: stopped
% 17.97/3.06 Prover 11: stopped
% 17.97/3.06 Prover 1: stopped
% 17.97/3.06
% 17.97/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.97/3.06
% 17.97/3.08 % SZS output start Proof for theBenchmark
% 17.97/3.08 Assumptions after simplification:
% 17.97/3.08 ---------------------------------
% 17.97/3.08
% 17.97/3.09 (mDefSPN)
% 17.97/3.11 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.97/3.11 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v2 =
% 17.97/3.11 sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) | ~
% 17.97/3.11 (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ (sdtlbdtrb0(v0,
% 17.97/3.11 v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) |
% 17.97/3.11 ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~
% 17.97/3.11 $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 &
% 17.97/3.11 $i(v9)))
% 17.97/3.11
% 17.97/3.11 (m__)
% 17.97/3.11 $i(xt) & $i(xs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 17.97/3.11 [v4: $i] : (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs,
% 17.97/3.11 xs) = v2 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & $i(v4) & $i(v3)
% 17.97/3.11 & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4))
% 17.97/3.11
% 17.97/3.11 (m__1652)
% 17.97/3.11 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 17.97/3.11 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 17.97/3.11 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 17.97/3.11 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 17.97/3.11 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 17.97/3.11 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 17.97/3.11 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 17.97/3.11 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 17.97/3.11
% 17.97/3.11 (m__1678)
% 17.97/3.11 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 17.97/3.11
% 17.97/3.11 (m__1678_01)
% 17.97/3.12 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 17.97/3.12 v0 & $i(v0))
% 17.97/3.12
% 17.97/3.12 (m__1692)
% 17.97/3.12 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 17.97/3.12 $i(v0))
% 17.97/3.12
% 17.97/3.12 (m__1709)
% 17.97/3.12 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp &
% 17.97/3.12 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 &
% 17.97/3.12 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 17.97/3.12 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 17.97/3.12 (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 17.97/3.12
% 17.97/3.12 (m__1726)
% 17.97/3.12 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq &
% 17.97/3.12 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 &
% 17.97/3.12 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 17.97/3.12 (sdtlbdtrb0(xq, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 17.97/3.12 (sdtlbdtrb0(xt, v2) = v3 & $i(v3))))
% 17.97/3.12
% 17.97/3.12 (m__1746)
% 17.97/3.12 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 17.97/3.12 v0 & $i(v0) & aScalar0(xA))
% 17.97/3.12
% 17.97/3.12 (m__1766)
% 17.97/3.12 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 17.97/3.12 v0 & $i(v0) & aScalar0(xB))
% 17.97/3.12
% 17.97/3.12 (m__1783)
% 17.97/3.12 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC)
% 17.97/3.12
% 17.97/3.12 (m__1800)
% 17.97/3.12 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD)
% 17.97/3.12
% 17.97/3.12 (m__1820)
% 17.97/3.12 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE)
% 17.97/3.12
% 17.97/3.12 (m__1837)
% 17.97/3.12 sdtasdt0(xA, xA) = xF & $i(xF) & $i(xA) & aScalar0(xF)
% 17.97/3.12
% 17.97/3.12 (m__1854)
% 18.54/3.12 sdtasdt0(xB, xB) = xG & $i(xG) & $i(xB) & aScalar0(xG)
% 18.54/3.12
% 18.54/3.12 (m__1873)
% 18.54/3.12 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH)
% 18.54/3.12
% 18.54/3.12 (m__2733)
% 18.54/3.13 $i(xH) & $i(xG) & $i(xF) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1:
% 18.54/3.13 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v2, v3) = v4 &
% 18.54/3.13 sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 & sdtpldt0(xD, xG) = v3 &
% 18.54/3.13 sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 18.54/3.13 sdtlseqdt0(v1, v4))
% 18.54/3.13
% 18.54/3.13 (function-axioms)
% 18.54/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.54/3.13 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 18.54/3.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 18.54/3.13 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 18.54/3.13 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 18.54/3.13 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 18.54/3.13 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 18.54/3.13 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 18.54/3.13 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 18.54/3.13 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 18.54/3.13 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 18.54/3.13 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.54/3.13 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 18.54/3.13
% 18.54/3.13 Further assumptions not needed in the proof:
% 18.54/3.13 --------------------------------------------
% 18.54/3.13 mArith, mDefInit, mDefSPZ, mDimNat, mDistr, mDistr2, mElmSc, mEqInit, mIH,
% 18.54/3.13 mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg,
% 18.54/3.13 mMulSc, mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos,
% 18.54/3.13 mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1892,
% 18.54/3.13 m__1911, m__1930, m__1949, m__1967, m__1983
% 18.54/3.13
% 18.54/3.13 Those formulas are unsatisfiable:
% 18.54/3.13 ---------------------------------
% 18.54/3.13
% 18.54/3.13 Begin of proof
% 18.54/3.13 |
% 18.54/3.13 | ALPHA: (mDefSPN) implies:
% 18.54/3.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.54/3.13 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 18.54/3.13 | (v2 = sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4)
% 18.54/3.13 | | ~ (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~
% 18.54/3.13 | (sdtlbdtrb0(v0, v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~
% 18.54/3.13 | (aDimensionOf0(v0) = v2) | ~ (sdtasdt0(v6, v7) = v8) | ~
% 18.54/3.13 | (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) |
% 18.54/3.13 | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & $i(v9)))
% 18.54/3.13 |
% 18.54/3.13 | ALPHA: (m__1678) implies:
% 18.54/3.13 | (2) aVector0(xs)
% 18.54/3.13 | (3) aVector0(xt)
% 18.54/3.13 |
% 18.54/3.13 | ALPHA: (m__1652) implies:
% 18.54/3.14 | (4) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 18.54/3.14 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 18.54/3.14 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 18.54/3.14 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 18.54/3.14 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 18.54/3.14 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 18.54/3.14 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 18.54/3.14 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 18.54/3.14 | $i(v7)))))))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1678_01) implies:
% 18.54/3.14 | (5) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 18.54/3.14 | $i(v0))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1692) implies:
% 18.54/3.14 | (6) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1709) implies:
% 18.54/3.14 | (7) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp)
% 18.54/3.14 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 18.54/3.14 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 18.54/3.14 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 18.54/3.14 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1726) implies:
% 18.54/3.14 | (8) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq)
% 18.54/3.14 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 18.54/3.14 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 18.54/3.14 | (sdtlbdtrb0(xq, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 18.54/3.14 | (sdtlbdtrb0(xt, v2) = v3 & $i(v3))))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1746) implies:
% 18.54/3.14 | (9) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 18.54/3.14 | $i(v0) & aScalar0(xA))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1766) implies:
% 18.54/3.14 | (10) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 &
% 18.54/3.14 | $i(v0) & aScalar0(xB))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1783) implies:
% 18.54/3.14 | (11) sdtasasdt0(xp, xp) = xC
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1800) implies:
% 18.54/3.14 | (12) sdtasasdt0(xq, xq) = xD
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1820) implies:
% 18.54/3.14 | (13) sdtasasdt0(xp, xq) = xE
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1837) implies:
% 18.54/3.14 | (14) sdtasdt0(xA, xA) = xF
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1854) implies:
% 18.54/3.14 | (15) sdtasdt0(xB, xB) = xG
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__1873) implies:
% 18.54/3.14 | (16) sdtasdt0(xA, xB) = xH
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__2733) implies:
% 18.54/3.14 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 18.54/3.14 | (sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0
% 18.54/3.14 | & sdtpldt0(xD, xG) = v3 & sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) &
% 18.54/3.14 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (m__) implies:
% 18.54/3.14 | (18) $i(xs)
% 18.54/3.14 | (19) $i(xt)
% 18.54/3.14 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 18.54/3.14 | (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs,
% 18.54/3.14 | xs) = v2 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & $i(v4)
% 18.54/3.14 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4))
% 18.54/3.14 |
% 18.54/3.14 | ALPHA: (function-axioms) implies:
% 18.54/3.15 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.54/3.15 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 18.54/3.15 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.54/3.15 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 18.54/3.15 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.54/3.15 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0))
% 18.54/3.15 |
% 18.54/3.15 | DELTA: instantiating (5) with fresh symbol all_33_0 gives:
% 18.54/3.15 | (24) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 18.54/3.15 | $i(all_33_0)
% 18.54/3.15 |
% 18.54/3.15 | ALPHA: (24) implies:
% 18.54/3.15 | (25) aDimensionOf0(xs) = all_33_0
% 18.54/3.15 | (26) aDimensionOf0(xt) = all_33_0
% 18.54/3.15 |
% 18.54/3.15 | DELTA: instantiating (6) with fresh symbol all_35_0 gives:
% 18.54/3.15 | (27) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0)
% 18.54/3.15 |
% 18.54/3.15 | ALPHA: (27) implies:
% 18.54/3.15 | (28) ~ (all_35_0 = sz00)
% 18.54/3.15 | (29) aDimensionOf0(xs) = all_35_0
% 18.54/3.15 |
% 18.54/3.15 | DELTA: instantiating (9) with fresh symbol all_37_0 gives:
% 18.54/3.15 | (30) sdtlbdtrb0(xs, all_37_0) = xA & aDimensionOf0(xs) = all_37_0 &
% 18.54/3.15 | $i(all_37_0) & aScalar0(xA)
% 18.54/3.15 |
% 18.54/3.15 | ALPHA: (30) implies:
% 18.54/3.15 | (31) aDimensionOf0(xs) = all_37_0
% 18.54/3.15 | (32) sdtlbdtrb0(xs, all_37_0) = xA
% 18.54/3.15 |
% 18.54/3.15 | DELTA: instantiating (10) with fresh symbol all_39_0 gives:
% 18.54/3.15 | (33) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 &
% 18.54/3.15 | $i(all_39_0) & aScalar0(xB)
% 18.54/3.15 |
% 18.54/3.15 | ALPHA: (33) implies:
% 18.54/3.15 | (34) aDimensionOf0(xt) = all_39_0
% 18.54/3.15 | (35) sdtlbdtrb0(xt, all_39_0) = xB
% 18.54/3.15 |
% 18.54/3.15 | DELTA: instantiating (17) with fresh symbols all_45_0, all_45_1, all_45_2,
% 18.54/3.15 | all_45_3, all_45_4 gives:
% 18.54/3.15 | (36) sdtasdt0(all_45_2, all_45_1) = all_45_0 & sdtasdt0(all_45_4, all_45_4)
% 18.54/3.15 | = all_45_3 & sdtpldt0(xE, xH) = all_45_4 & sdtpldt0(xD, xG) = all_45_1
% 18.54/3.15 | & sdtpldt0(xC, xF) = all_45_2 & $i(all_45_0) & $i(all_45_1) &
% 18.54/3.15 | $i(all_45_2) & $i(all_45_3) & $i(all_45_4) & sdtlseqdt0(all_45_3,
% 18.54/3.15 | all_45_0)
% 18.54/3.15 |
% 18.54/3.15 | ALPHA: (36) implies:
% 18.54/3.15 | (37) sdtlseqdt0(all_45_3, all_45_0)
% 18.54/3.15 | (38) sdtpldt0(xC, xF) = all_45_2
% 18.54/3.15 | (39) sdtpldt0(xD, xG) = all_45_1
% 18.54/3.15 | (40) sdtpldt0(xE, xH) = all_45_4
% 18.54/3.15 | (41) sdtasdt0(all_45_4, all_45_4) = all_45_3
% 18.54/3.15 | (42) sdtasdt0(all_45_2, all_45_1) = all_45_0
% 18.54/3.15 |
% 18.54/3.15 | DELTA: instantiating (20) with fresh symbols all_47_0, all_47_1, all_47_2,
% 18.54/3.15 | all_47_3, all_47_4 gives:
% 18.54/3.15 | (43) sdtasasdt0(xt, xt) = all_47_1 & sdtasasdt0(xs, xt) = all_47_4 &
% 18.54/3.15 | sdtasasdt0(xs, xs) = all_47_2 & sdtasdt0(all_47_2, all_47_1) =
% 18.54/3.15 | all_47_0 & sdtasdt0(all_47_4, all_47_4) = all_47_3 & $i(all_47_0) &
% 18.54/3.15 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & ~
% 18.54/3.15 | sdtlseqdt0(all_47_3, all_47_0)
% 18.54/3.15 |
% 18.54/3.15 | ALPHA: (43) implies:
% 18.54/3.15 | (44) ~ sdtlseqdt0(all_47_3, all_47_0)
% 18.54/3.15 | (45) sdtasdt0(all_47_4, all_47_4) = all_47_3
% 18.54/3.15 | (46) sdtasdt0(all_47_2, all_47_1) = all_47_0
% 18.54/3.15 | (47) sdtasasdt0(xs, xs) = all_47_2
% 18.54/3.15 | (48) sdtasasdt0(xs, xt) = all_47_4
% 18.54/3.15 | (49) sdtasasdt0(xt, xt) = all_47_1
% 18.54/3.15 |
% 18.54/3.15 | DELTA: instantiating (7) with fresh symbols all_49_0, all_49_1 gives:
% 18.54/3.16 | (50) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_49_1 &
% 18.54/3.16 | aDimensionOf0(xs) = all_49_0 & szszuzczcdt0(all_49_1) = all_49_0 &
% 18.54/3.16 | $i(all_49_0) & $i(all_49_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i]
% 18.54/3.16 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 18.54/3.16 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1)))
% 18.54/3.16 |
% 18.54/3.16 | ALPHA: (50) implies:
% 18.54/3.16 | (51) aDimensionOf0(xs) = all_49_0
% 18.54/3.16 | (52) sziznziztdt0(xs) = xp
% 18.54/3.16 |
% 18.54/3.16 | DELTA: instantiating (8) with fresh symbols all_52_0, all_52_1 gives:
% 18.54/3.16 | (53) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_52_1 &
% 18.54/3.16 | aDimensionOf0(xt) = all_52_0 & szszuzczcdt0(all_52_1) = all_52_0 &
% 18.54/3.16 | $i(all_52_0) & $i(all_52_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i]
% 18.54/3.16 | : ( ~ (sdtlbdtrb0(xq, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 18.54/3.16 | (sdtlbdtrb0(xt, v0) = v1 & $i(v1)))
% 18.54/3.16 |
% 18.54/3.16 | ALPHA: (53) implies:
% 18.54/3.16 | (54) aDimensionOf0(xt) = all_52_0
% 18.54/3.16 | (55) sziznziztdt0(xt) = xq
% 18.54/3.16 |
% 18.54/3.16 | DELTA: instantiating (4) with fresh symbol all_55_0 gives:
% 18.54/3.16 | (56) aDimensionOf0(xs) = all_55_0 & $i(all_55_0) & ! [v0: $i] : ! [v1:
% 18.54/3.16 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 18.54/3.16 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 18.54/3.16 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 18.54/3.16 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 18.54/3.16 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 18.54/3.16 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 18.54/3.16 | iLess0(v5, all_55_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 18.54/3.16 | & $i(v6))))))
% 18.54/3.16 |
% 18.54/3.16 | ALPHA: (56) implies:
% 18.54/3.16 | (57) aDimensionOf0(xs) = all_55_0
% 18.54/3.16 |
% 18.54/3.16 | GROUND_INST: instantiating (21) with all_37_0, all_49_0, xs, simplifying with
% 18.54/3.16 | (31), (51) gives:
% 18.54/3.16 | (58) all_49_0 = all_37_0
% 18.54/3.16 |
% 18.54/3.16 | GROUND_INST: instantiating (21) with all_35_0, all_49_0, xs, simplifying with
% 18.54/3.16 | (29), (51) gives:
% 18.54/3.16 | (59) all_49_0 = all_35_0
% 18.54/3.16 |
% 18.54/3.16 | GROUND_INST: instantiating (21) with all_49_0, all_55_0, xs, simplifying with
% 18.54/3.16 | (51), (57) gives:
% 18.54/3.16 | (60) all_55_0 = all_49_0
% 18.54/3.16 |
% 18.54/3.16 | GROUND_INST: instantiating (21) with all_33_0, all_55_0, xs, simplifying with
% 18.54/3.16 | (25), (57) gives:
% 18.54/3.16 | (61) all_55_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | GROUND_INST: instantiating (21) with all_39_0, all_52_0, xt, simplifying with
% 18.54/3.16 | (34), (54) gives:
% 18.54/3.16 | (62) all_52_0 = all_39_0
% 18.54/3.16 |
% 18.54/3.16 | GROUND_INST: instantiating (21) with all_33_0, all_52_0, xt, simplifying with
% 18.54/3.16 | (26), (54) gives:
% 18.54/3.16 | (63) all_52_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | COMBINE_EQS: (60), (61) imply:
% 18.54/3.16 | (64) all_49_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | SIMP: (64) implies:
% 18.54/3.16 | (65) all_49_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | COMBINE_EQS: (62), (63) imply:
% 18.54/3.16 | (66) all_39_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | COMBINE_EQS: (58), (65) imply:
% 18.54/3.16 | (67) all_37_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | COMBINE_EQS: (58), (59) imply:
% 18.54/3.16 | (68) all_37_0 = all_35_0
% 18.54/3.16 |
% 18.54/3.16 | COMBINE_EQS: (67), (68) imply:
% 18.54/3.16 | (69) all_35_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | SIMP: (69) implies:
% 18.54/3.16 | (70) all_35_0 = all_33_0
% 18.54/3.16 |
% 18.54/3.16 | REDUCE: (28), (70) imply:
% 18.54/3.16 | (71) ~ (all_33_0 = sz00)
% 18.54/3.16 |
% 18.54/3.16 | REDUCE: (35), (66) imply:
% 18.54/3.17 | (72) sdtlbdtrb0(xt, all_33_0) = xB
% 18.54/3.17 |
% 18.54/3.17 | REDUCE: (32), (67) imply:
% 18.54/3.17 | (73) sdtlbdtrb0(xs, all_33_0) = xA
% 18.54/3.17 |
% 18.54/3.17 | GROUND_INST: instantiating (1) with xs, xs, all_33_0, xp, xp, xC, xA, xA, xF,
% 18.54/3.17 | all_45_2, simplifying with (2), (11), (14), (18), (25), (38),
% 18.54/3.17 | (52), (73) gives:
% 18.54/3.17 | (74) all_33_0 = sz00 | (sdtasasdt0(xs, xs) = all_45_2 & $i(all_45_2))
% 18.54/3.17 |
% 18.54/3.17 | GROUND_INST: instantiating (1) with xs, xt, all_33_0, xp, xq, xE, xA, xB, xH,
% 18.54/3.17 | all_45_4, simplifying with (2), (3), (13), (16), (18), (19),
% 18.54/3.17 | (25), (26), (40), (52), (55), (72), (73) gives:
% 18.54/3.17 | (75) all_33_0 = sz00 | (sdtasasdt0(xs, xt) = all_45_4 & $i(all_45_4))
% 18.54/3.17 |
% 18.54/3.17 | GROUND_INST: instantiating (1) with xt, xt, all_33_0, xq, xq, xD, xB, xB, xG,
% 18.54/3.17 | all_45_1, simplifying with (3), (12), (15), (19), (26), (39),
% 18.54/3.17 | (55), (72) gives:
% 18.54/3.17 | (76) all_33_0 = sz00 | (sdtasasdt0(xt, xt) = all_45_1 & $i(all_45_1))
% 18.54/3.17 |
% 18.54/3.17 | BETA: splitting (76) gives:
% 18.54/3.17 |
% 18.54/3.17 | Case 1:
% 18.54/3.17 | |
% 18.54/3.17 | | (77) all_33_0 = sz00
% 18.54/3.17 | |
% 18.54/3.17 | | REDUCE: (71), (77) imply:
% 18.54/3.17 | | (78) $false
% 18.54/3.17 | |
% 18.54/3.17 | | CLOSE: (78) is inconsistent.
% 18.54/3.17 | |
% 18.54/3.17 | Case 2:
% 18.54/3.17 | |
% 18.54/3.17 | | (79) sdtasasdt0(xt, xt) = all_45_1 & $i(all_45_1)
% 18.54/3.17 | |
% 18.54/3.17 | | ALPHA: (79) implies:
% 18.54/3.17 | | (80) sdtasasdt0(xt, xt) = all_45_1
% 18.54/3.17 | |
% 18.54/3.17 | | BETA: splitting (74) gives:
% 18.54/3.17 | |
% 18.54/3.17 | | Case 1:
% 18.54/3.17 | | |
% 18.54/3.17 | | | (81) all_33_0 = sz00
% 18.54/3.17 | | |
% 18.54/3.17 | | | REDUCE: (71), (81) imply:
% 18.54/3.17 | | | (82) $false
% 18.54/3.17 | | |
% 18.54/3.17 | | | CLOSE: (82) is inconsistent.
% 18.54/3.17 | | |
% 18.54/3.17 | | Case 2:
% 18.54/3.17 | | |
% 18.54/3.17 | | | (83) sdtasasdt0(xs, xs) = all_45_2 & $i(all_45_2)
% 18.54/3.17 | | |
% 18.54/3.17 | | | ALPHA: (83) implies:
% 18.54/3.17 | | | (84) sdtasasdt0(xs, xs) = all_45_2
% 18.54/3.17 | | |
% 18.54/3.17 | | | BETA: splitting (75) gives:
% 18.54/3.17 | | |
% 18.54/3.17 | | | Case 1:
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | (85) all_33_0 = sz00
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | REDUCE: (71), (85) imply:
% 18.54/3.17 | | | | (86) $false
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | CLOSE: (86) is inconsistent.
% 18.54/3.17 | | | |
% 18.54/3.17 | | | Case 2:
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | (87) sdtasasdt0(xs, xt) = all_45_4 & $i(all_45_4)
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | ALPHA: (87) implies:
% 18.54/3.17 | | | | (88) sdtasasdt0(xs, xt) = all_45_4
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | GROUND_INST: instantiating (23) with all_47_2, all_45_2, xs, xs,
% 18.54/3.17 | | | | simplifying with (47), (84) gives:
% 18.54/3.17 | | | | (89) all_47_2 = all_45_2
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | GROUND_INST: instantiating (23) with all_47_4, all_45_4, xt, xs,
% 18.54/3.17 | | | | simplifying with (48), (88) gives:
% 18.54/3.17 | | | | (90) all_47_4 = all_45_4
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | GROUND_INST: instantiating (23) with all_47_1, all_45_1, xt, xt,
% 18.54/3.17 | | | | simplifying with (49), (80) gives:
% 18.54/3.17 | | | | (91) all_47_1 = all_45_1
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | REDUCE: (46), (89), (91) imply:
% 18.54/3.17 | | | | (92) sdtasdt0(all_45_2, all_45_1) = all_47_0
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | REDUCE: (45), (90) imply:
% 18.54/3.17 | | | | (93) sdtasdt0(all_45_4, all_45_4) = all_47_3
% 18.54/3.17 | | | |
% 18.54/3.17 | | | | GROUND_INST: instantiating (22) with all_45_3, all_47_3, all_45_4,
% 18.54/3.17 | | | | all_45_4, simplifying with (41), (93) gives:
% 18.54/3.18 | | | | (94) all_47_3 = all_45_3
% 18.54/3.18 | | | |
% 18.54/3.18 | | | | GROUND_INST: instantiating (22) with all_45_0, all_47_0, all_45_1,
% 18.54/3.18 | | | | all_45_2, simplifying with (42), (92) gives:
% 18.54/3.18 | | | | (95) all_47_0 = all_45_0
% 18.54/3.18 | | | |
% 18.54/3.18 | | | | REDUCE: (44), (94), (95) imply:
% 18.54/3.18 | | | | (96) ~ sdtlseqdt0(all_45_3, all_45_0)
% 18.54/3.18 | | | |
% 18.54/3.18 | | | | PRED_UNIFY: (37), (96) imply:
% 18.54/3.18 | | | | (97) $false
% 18.54/3.18 | | | |
% 18.54/3.18 | | | | CLOSE: (97) is inconsistent.
% 18.54/3.18 | | | |
% 18.54/3.18 | | | End of split
% 18.54/3.18 | | |
% 18.54/3.18 | | End of split
% 18.54/3.18 | |
% 18.54/3.18 | End of split
% 18.54/3.18 |
% 18.54/3.18 End of proof
% 18.54/3.18 % SZS output end Proof for theBenchmark
% 18.54/3.18
% 18.54/3.18 2706ms
%------------------------------------------------------------------------------