TSTP Solution File: RNG052+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG052+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 : n018.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 13:57:34 EDT 2023
% Result : Theorem 13.42s 2.61s
% Output : Proof 22.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG052+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:50:00 EDT 2023
% 0.14/0.35 % 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.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.17/1.17 Prover 1: Preprocessing ...
% 3.17/1.17 Prover 4: Preprocessing ...
% 3.17/1.20 Prover 0: Preprocessing ...
% 3.17/1.20 Prover 2: Preprocessing ...
% 3.17/1.20 Prover 6: Preprocessing ...
% 3.17/1.20 Prover 3: Preprocessing ...
% 3.17/1.20 Prover 5: Preprocessing ...
% 9.11/2.03 Prover 1: Constructing countermodel ...
% 9.11/2.04 Prover 3: Constructing countermodel ...
% 9.11/2.08 Prover 6: Proving ...
% 10.41/2.26 Prover 5: Constructing countermodel ...
% 11.47/2.35 Prover 4: Constructing countermodel ...
% 11.47/2.43 Prover 2: Proving ...
% 12.58/2.50 Prover 0: Proving ...
% 13.42/2.61 Prover 3: proved (1972ms)
% 13.42/2.61
% 13.42/2.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.42/2.61
% 13.42/2.61 Prover 5: stopped
% 13.42/2.61 Prover 0: stopped
% 13.42/2.63 Prover 6: stopped
% 13.42/2.64 Prover 2: stopped
% 13.42/2.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.42/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.42/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.42/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.71/2.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.38/2.74 Prover 7: Preprocessing ...
% 14.38/2.75 Prover 11: Preprocessing ...
% 14.38/2.75 Prover 8: Preprocessing ...
% 14.38/2.76 Prover 10: Preprocessing ...
% 14.38/2.77 Prover 13: Preprocessing ...
% 15.26/2.93 Prover 10: Constructing countermodel ...
% 15.26/2.99 Prover 8: Warning: ignoring some quantifiers
% 15.91/3.00 Prover 8: Constructing countermodel ...
% 15.91/3.00 Prover 7: Constructing countermodel ...
% 15.91/3.04 Prover 13: Constructing countermodel ...
% 18.28/3.29 Prover 11: Constructing countermodel ...
% 21.78/3.77 Prover 10: Found proof (size 172)
% 21.78/3.77 Prover 10: proved (1144ms)
% 21.78/3.77 Prover 7: stopped
% 21.78/3.77 Prover 4: stopped
% 21.78/3.77 Prover 13: stopped
% 21.78/3.78 Prover 8: stopped
% 21.78/3.78 Prover 11: stopped
% 21.78/3.78 Prover 1: Found proof (size 287)
% 21.78/3.78 Prover 1: proved (3148ms)
% 21.78/3.78
% 21.78/3.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.78/3.78
% 21.78/3.80 % SZS output start Proof for theBenchmark
% 21.78/3.80 Assumptions after simplification:
% 21.78/3.80 ---------------------------------
% 21.78/3.80
% 21.78/3.80 (mDefInit)
% 22.31/3.83 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 22.31/3.83 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 22.31/3.83 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 22.31/3.83 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 22.31/3.83 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 22.31/3.83 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 22.31/3.83 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 22.31/3.83 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 22.31/3.83 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 22.31/3.83 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 22.31/3.83 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 22.31/3.83 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 22.31/3.83 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 22.31/3.83
% 22.31/3.83 (mDimNat)
% 22.31/3.83 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 22.31/3.83 aVector0(v0) | aNaturalNumber0(v1))
% 22.31/3.83
% 22.31/3.83 (mEqInit)
% 22.31/3.83 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 22.31/3.83 (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 22.31/3.83 | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 22.31/3.83 $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = v6 & aDimensionOf0(v2)
% 22.31/3.83 = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & $i(v5) & (v5 = sz00 | ( ~ (v5
% 22.31/3.83 = v4) & aDimensionOf0(v0) = v4 & $i(v4))))))
% 22.31/3.83
% 22.31/3.83 (mIH)
% 22.31/3.83 ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~
% 22.31/3.83 aNaturalNumber0(v0) | iLess0(v0, v1))
% 22.31/3.83
% 22.31/3.83 (m__)
% 22.31/3.84 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0
% 22.31/3.84 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & ~ sdtlseqdt0(v0, v1))
% 22.31/3.84
% 22.31/3.84 (m__1652)
% 22.31/3.84 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 22.31/3.84 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 22.31/3.84 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 22.31/3.84 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 22.31/3.84 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 22.31/3.84 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 22.31/3.84 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 22.31/3.84 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 22.31/3.84
% 22.31/3.84 (m__1678)
% 22.31/3.84 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 22.31/3.84
% 22.31/3.84 (m__1678_01)
% 22.31/3.84 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 22.31/3.84 v0 & $i(v0))
% 22.31/3.84
% 22.31/3.84 (m__1692)
% 22.31/3.84 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 22.31/3.84 $i(v0))
% 22.31/3.84
% 22.31/3.84 (m__1709)
% 22.31/3.84 sziznziztdt0(xs) = xp & $i(xp) & $i(xs) & aVector0(xp)
% 22.31/3.84
% 22.31/3.84 (m__1726)
% 22.31/3.84 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq)
% 22.31/3.84
% 22.31/3.84 (m__1746)
% 22.31/3.84 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 22.31/3.84 v0 & $i(v0) & aScalar0(xA))
% 22.31/3.84
% 22.31/3.84 (m__1766)
% 22.31/3.84 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 22.31/3.84 v0 & $i(v0) & aScalar0(xB))
% 22.31/3.84
% 22.31/3.84 (m__1783)
% 22.31/3.84 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC)
% 22.31/3.84
% 22.31/3.84 (m__1800)
% 22.31/3.84 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD)
% 22.31/3.84
% 22.31/3.84 (m__1820)
% 22.31/3.84 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE)
% 22.31/3.84
% 22.31/3.84 (function-axioms)
% 22.31/3.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.31/3.84 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 22.31/3.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 22.31/3.84 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 22.31/3.84 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 22.31/3.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 22.31/3.84 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 22.31/3.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 22.31/3.84 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 22.31/3.84 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 22.31/3.84 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 22.31/3.84 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.31/3.84 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 22.31/3.84
% 22.31/3.84 Further assumptions not needed in the proof:
% 22.31/3.84 --------------------------------------------
% 22.31/3.85 mArith, mDefSPN, mDefSPZ, mDistr, mDistr2, mElmSc, mIHOrd, mLEASm, mLEMon,
% 22.31/3.85 mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, mNatExtr,
% 22.31/3.85 mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos,
% 22.31/3.85 mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1837, m__1854, m__1873,
% 22.31/3.85 m__1892, m__1911, m__1930, m__1949
% 22.31/3.85
% 22.31/3.85 Those formulas are unsatisfiable:
% 22.31/3.85 ---------------------------------
% 22.31/3.85
% 22.31/3.85 Begin of proof
% 22.31/3.85 |
% 22.31/3.85 | ALPHA: (mDefInit) implies:
% 22.31/3.85 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 22.31/3.85 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 22.31/3.85 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 22.31/3.85 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 22.31/3.85 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 22.31/3.85 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 22.31/3.85 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 22.31/3.85 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 22.31/3.85 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 22.31/3.85 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 22.31/3.85 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 22.31/3.85 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 22.31/3.85 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 22.31/3.85 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 22.31/3.85 | aVector0(v1))))))
% 22.31/3.85 |
% 22.31/3.85 | ALPHA: (mEqInit) implies:
% 22.31/3.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 22.31/3.85 | (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~
% 22.31/3.85 | $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5:
% 22.31/3.85 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) =
% 22.31/3.85 | v6 & aDimensionOf0(v2) = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 &
% 22.31/3.85 | $i(v5) & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4 &
% 22.31/3.85 | $i(v4))))))
% 22.31/3.85 |
% 22.31/3.85 | ALPHA: (m__1678) implies:
% 22.31/3.85 | (3) aVector0(xs)
% 22.31/3.85 | (4) aVector0(xt)
% 22.31/3.85 |
% 22.31/3.85 | ALPHA: (m__1652) implies:
% 22.31/3.85 | (5) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 22.31/3.85 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 22.31/3.85 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 22.31/3.85 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 22.31/3.85 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 22.31/3.85 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 22.31/3.85 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 22.31/3.85 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 22.31/3.85 | $i(v7)))))))
% 22.31/3.85 |
% 22.31/3.85 | ALPHA: (m__1678_01) implies:
% 22.31/3.85 | (6) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 22.31/3.85 | $i(v0))
% 22.31/3.85 |
% 22.31/3.85 | ALPHA: (m__1692) implies:
% 22.31/3.86 | (7) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__1709) implies:
% 22.31/3.86 | (8) aVector0(xp)
% 22.31/3.86 | (9) sziznziztdt0(xs) = xp
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__1726) implies:
% 22.31/3.86 | (10) aVector0(xq)
% 22.31/3.86 | (11) sziznziztdt0(xt) = xq
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__1746) implies:
% 22.31/3.86 | (12) $i(xs)
% 22.31/3.86 | (13) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 22.31/3.86 | $i(v0) & aScalar0(xA))
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__1766) implies:
% 22.31/3.86 | (14) $i(xt)
% 22.31/3.86 | (15) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 &
% 22.31/3.86 | $i(v0) & aScalar0(xB))
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__1783) implies:
% 22.31/3.86 | (16) sdtasasdt0(xp, xp) = xC
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__1800) implies:
% 22.31/3.86 | (17) sdtasasdt0(xq, xq) = xD
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__1820) implies:
% 22.31/3.86 | (18) $i(xp)
% 22.31/3.86 | (19) $i(xq)
% 22.31/3.86 | (20) sdtasasdt0(xp, xq) = xE
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (m__) implies:
% 22.31/3.86 | (21) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD)
% 22.31/3.86 | = v1 & $i(v1) & $i(v0) & ~ sdtlseqdt0(v0, v1))
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (function-axioms) implies:
% 22.31/3.86 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.31/3.86 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 22.31/3.86 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.31/3.86 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 22.31/3.86 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.31/3.86 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0))
% 22.31/3.86 |
% 22.31/3.86 | DELTA: instantiating (6) with fresh symbol all_33_0 gives:
% 22.31/3.86 | (25) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 22.31/3.86 | $i(all_33_0)
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (25) implies:
% 22.31/3.86 | (26) aDimensionOf0(xs) = all_33_0
% 22.31/3.86 | (27) aDimensionOf0(xt) = all_33_0
% 22.31/3.86 |
% 22.31/3.86 | DELTA: instantiating (7) with fresh symbol all_35_0 gives:
% 22.31/3.86 | (28) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0)
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (28) implies:
% 22.31/3.86 | (29) ~ (all_35_0 = sz00)
% 22.31/3.86 | (30) aDimensionOf0(xs) = all_35_0
% 22.31/3.86 |
% 22.31/3.86 | DELTA: instantiating (13) with fresh symbol all_37_0 gives:
% 22.31/3.86 | (31) sdtlbdtrb0(xs, all_37_0) = xA & aDimensionOf0(xs) = all_37_0 &
% 22.31/3.86 | $i(all_37_0) & aScalar0(xA)
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (31) implies:
% 22.31/3.86 | (32) aDimensionOf0(xs) = all_37_0
% 22.31/3.86 |
% 22.31/3.86 | DELTA: instantiating (15) with fresh symbol all_39_0 gives:
% 22.31/3.86 | (33) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 &
% 22.31/3.86 | $i(all_39_0) & aScalar0(xB)
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (33) implies:
% 22.31/3.86 | (34) aDimensionOf0(xt) = all_39_0
% 22.31/3.86 |
% 22.31/3.86 | DELTA: instantiating (21) with fresh symbols all_41_0, all_41_1 gives:
% 22.31/3.86 | (35) sdtasdt0(xE, xE) = all_41_1 & sdtasdt0(xC, xD) = all_41_0 &
% 22.31/3.86 | $i(all_41_0) & $i(all_41_1) & ~ sdtlseqdt0(all_41_1, all_41_0)
% 22.31/3.86 |
% 22.31/3.86 | ALPHA: (35) implies:
% 22.31/3.86 | (36) ~ sdtlseqdt0(all_41_1, all_41_0)
% 22.31/3.86 | (37) sdtasdt0(xC, xD) = all_41_0
% 22.31/3.86 | (38) sdtasdt0(xE, xE) = all_41_1
% 22.31/3.86 |
% 22.31/3.86 | DELTA: instantiating (5) with fresh symbol all_43_0 gives:
% 22.31/3.87 | (39) aDimensionOf0(xs) = all_43_0 & $i(all_43_0) & ! [v0: $i] : ! [v1:
% 22.31/3.87 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 22.31/3.87 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 22.31/3.87 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 22.31/3.87 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 22.31/3.87 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 22.31/3.87 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 22.31/3.87 | iLess0(v5, all_43_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 22.31/3.87 | & $i(v6))))))
% 22.31/3.87 |
% 22.31/3.87 | ALPHA: (39) implies:
% 22.31/3.87 | (40) aDimensionOf0(xs) = all_43_0
% 22.31/3.87 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 22.31/3.87 | ( ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~
% 22.31/3.87 | (sdtasdt0(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) |
% 22.31/3.87 | ~ aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 22.31/3.87 | $i] : ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) &
% 22.31/3.87 | $i(v7) & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5)
% 22.31/3.87 | & ( ~ iLess0(v5, all_43_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) =
% 22.31/3.87 | v6 & $i(v6))))))
% 22.31/3.87 |
% 22.31/3.87 | GROUND_INST: instantiating (22) with all_35_0, all_37_0, xs, simplifying with
% 22.31/3.87 | (30), (32) gives:
% 22.31/3.87 | (42) all_37_0 = all_35_0
% 22.31/3.87 |
% 22.31/3.87 | GROUND_INST: instantiating (22) with all_37_0, all_43_0, xs, simplifying with
% 22.31/3.87 | (32), (40) gives:
% 22.31/3.87 | (43) all_43_0 = all_37_0
% 22.31/3.87 |
% 22.31/3.87 | GROUND_INST: instantiating (22) with all_33_0, all_43_0, xs, simplifying with
% 22.31/3.87 | (26), (40) gives:
% 22.31/3.87 | (44) all_43_0 = all_33_0
% 22.31/3.87 |
% 22.31/3.87 | GROUND_INST: instantiating (22) with all_33_0, all_39_0, xt, simplifying with
% 22.31/3.87 | (27), (34) gives:
% 22.31/3.87 | (45) all_39_0 = all_33_0
% 22.31/3.87 |
% 22.31/3.87 | COMBINE_EQS: (43), (44) imply:
% 22.31/3.87 | (46) all_37_0 = all_33_0
% 22.31/3.87 |
% 22.31/3.87 | SIMP: (46) implies:
% 22.31/3.87 | (47) all_37_0 = all_33_0
% 22.31/3.87 |
% 22.31/3.87 | COMBINE_EQS: (42), (47) imply:
% 22.31/3.87 | (48) all_35_0 = all_33_0
% 22.31/3.87 |
% 22.31/3.87 | REDUCE: (29), (48) imply:
% 22.31/3.87 | (49) ~ (all_33_0 = sz00)
% 22.31/3.87 |
% 22.31/3.87 | GROUND_INST: instantiating (2) with xs, xs, xp, xp, simplifying with (3), (9),
% 22.31/3.87 | (12) gives:
% 22.31/3.87 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 22.31/3.87 | aDimensionOf0(xp) = v2 & $i(v2)) | (aDimensionOf0(xs) = v1 &
% 22.31/3.87 | $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & aDimensionOf0(xs) = v0 &
% 22.31/3.87 | $i(v0)))))
% 22.31/3.87 |
% 22.31/3.87 | GROUND_INST: instantiating (1) with xs, xp, simplifying with (3), (9), (12)
% 22.31/3.87 | gives:
% 22.31/3.87 | (51) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1:
% 22.31/3.87 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) =
% 22.31/3.87 | v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp) |
% 22.31/3.87 | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 & $i(v3))) &
% 22.31/3.87 | ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~ (aDimensionOf0(v1) =
% 22.31/3.87 | v2) | ~ $i(v1) | ~ aVector0(v1) | ? [v3: $i] : ? [v4:
% 22.31/3.87 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) &
% 22.31/3.87 | sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs, v4) = v6 &
% 22.31/3.87 | $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( ~ (v3 = v0) &
% 22.31/3.87 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 22.31/3.87 | (aDimensionOf0(xp) = v1) | ~ $i(xp) | szszuzczcdt0(v1) = v0)
% 22.31/3.87 | & ! [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) |
% 22.31/3.87 | aVector0(xp)))))
% 22.31/3.87 |
% 22.31/3.87 | GROUND_INST: instantiating (2) with xt, xt, xq, xq, simplifying with (4),
% 22.31/3.87 | (11), (14) gives:
% 22.31/3.88 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 22.31/3.88 | aDimensionOf0(xq) = v2 & $i(v2)) | (aDimensionOf0(xt) = v1 &
% 22.31/3.88 | $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & aDimensionOf0(xt) = v0 &
% 22.31/3.88 | $i(v0)))))
% 22.31/3.88 |
% 22.31/3.88 | GROUND_INST: instantiating (2) with xs, xt, xp, xq, simplifying with (3), (4),
% 22.31/3.88 | (9), (11), (12), (14) gives:
% 22.31/3.88 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 22.31/3.88 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) |
% 22.31/3.88 | (aDimensionOf0(xt) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) &
% 22.31/3.88 | aDimensionOf0(xs) = v0 & $i(v0)))))
% 22.31/3.88 |
% 22.31/3.88 | GROUND_INST: instantiating (2) with xt, xs, xq, xp, simplifying with (3), (4),
% 22.31/3.88 | (9), (11), (12), (14) gives:
% 22.31/3.88 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 22.31/3.88 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) |
% 22.31/3.88 | (aDimensionOf0(xs) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) &
% 22.62/3.88 | aDimensionOf0(xt) = v0 & $i(v0)))))
% 22.62/3.88 |
% 22.62/3.88 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (4), (11), (14)
% 22.62/3.88 | gives:
% 22.62/3.88 | (55) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1:
% 22.62/3.88 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) =
% 22.62/3.88 | v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq) |
% 22.62/3.88 | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 & $i(v3))) &
% 22.62/3.88 | ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~ (aDimensionOf0(v1) =
% 22.62/3.88 | v2) | ~ $i(v1) | ~ aVector0(v1) | ? [v3: $i] : ? [v4:
% 22.62/3.88 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) &
% 22.62/3.88 | sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt, v4) = v6 &
% 22.62/3.88 | $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( ~ (v3 = v0) &
% 22.62/3.88 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 22.62/3.88 | (aDimensionOf0(xq) = v1) | ~ $i(xq) | szszuzczcdt0(v1) = v0)
% 22.62/3.88 | & ! [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) |
% 22.62/3.88 | aVector0(xq)))))
% 22.62/3.88 |
% 22.62/3.88 | GROUND_INST: instantiating (41) with xp, xq, xC, xD, all_41_0, simplifying
% 22.62/3.88 | with (8), (10), (16), (17), (18), (19), (37) gives:
% 22.62/3.88 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 22.62/3.88 | ((sdtasasdt0(xp, xq) = v2 & sdtasdt0(v2, v2) = v3 & $i(v3) & $i(v2) &
% 22.62/3.88 | sdtlseqdt0(v3, all_41_0)) | (aDimensionOf0(xp) = v0 & $i(v0) & ( ~
% 22.62/3.88 | iLess0(v0, all_43_0) | ( ~ (v1 = v0) & aDimensionOf0(xq) = v1 &
% 22.62/3.88 | $i(v1)))))
% 22.62/3.88 |
% 22.62/3.88 | DELTA: instantiating (50) with fresh symbols all_59_0, all_59_1, all_59_2,
% 22.62/3.88 | all_59_3 gives:
% 22.62/3.88 | (57) (all_59_0 = all_59_1 & aDimensionOf0(xp) = all_59_1 & $i(all_59_1)) |
% 22.62/3.88 | (aDimensionOf0(xs) = all_59_2 & $i(all_59_2) & (all_59_2 = sz00 | ( ~
% 22.62/3.88 | (all_59_2 = all_59_3) & aDimensionOf0(xs) = all_59_3 &
% 22.62/3.88 | $i(all_59_3))))
% 22.62/3.88 |
% 22.62/3.88 | DELTA: instantiating (52) with fresh symbols all_60_0, all_60_1, all_60_2,
% 22.62/3.88 | all_60_3 gives:
% 22.62/3.88 | (58) (all_60_0 = all_60_1 & aDimensionOf0(xq) = all_60_1 & $i(all_60_1)) |
% 22.62/3.88 | (aDimensionOf0(xt) = all_60_2 & $i(all_60_2) & (all_60_2 = sz00 | ( ~
% 22.62/3.88 | (all_60_2 = all_60_3) & aDimensionOf0(xt) = all_60_3 &
% 22.62/3.89 | $i(all_60_3))))
% 22.62/3.89 |
% 22.62/3.89 | DELTA: instantiating (54) with fresh symbols all_61_0, all_61_1, all_61_2,
% 22.62/3.89 | all_61_3 gives:
% 22.62/3.89 | (59) (all_61_0 = all_61_1 & aDimensionOf0(xq) = all_61_1 &
% 22.62/3.89 | aDimensionOf0(xp) = all_61_1 & $i(all_61_1)) | (aDimensionOf0(xs) =
% 22.62/3.89 | all_61_2 & $i(all_61_2) & (all_61_2 = sz00 | ( ~ (all_61_2 =
% 22.62/3.89 | all_61_3) & aDimensionOf0(xt) = all_61_3 & $i(all_61_3))))
% 22.62/3.89 |
% 22.62/3.89 | DELTA: instantiating (53) with fresh symbols all_62_0, all_62_1, all_62_2,
% 22.62/3.89 | all_62_3 gives:
% 22.62/3.89 | (60) (all_62_0 = all_62_1 & aDimensionOf0(xq) = all_62_1 &
% 22.62/3.89 | aDimensionOf0(xp) = all_62_1 & $i(all_62_1)) | (aDimensionOf0(xt) =
% 22.62/3.89 | all_62_2 & $i(all_62_2) & (all_62_2 = sz00 | ( ~ (all_62_2 =
% 22.62/3.89 | all_62_3) & aDimensionOf0(xs) = all_62_3 & $i(all_62_3))))
% 22.62/3.89 |
% 22.62/3.89 | DELTA: instantiating (56) with fresh symbols all_63_0, all_63_1, all_63_2,
% 22.62/3.89 | all_63_3 gives:
% 22.62/3.89 | (61) (sdtasasdt0(xp, xq) = all_63_1 & sdtasdt0(all_63_1, all_63_1) =
% 22.62/3.89 | all_63_0 & $i(all_63_0) & $i(all_63_1) & sdtlseqdt0(all_63_0,
% 22.62/3.89 | all_41_0)) | (aDimensionOf0(xp) = all_63_3 & $i(all_63_3) & ( ~
% 22.62/3.89 | iLess0(all_63_3, all_43_0) | ( ~ (all_63_2 = all_63_3) &
% 22.62/3.89 | aDimensionOf0(xq) = all_63_2 & $i(all_63_2))))
% 22.62/3.89 |
% 22.62/3.89 | DELTA: instantiating (51) with fresh symbol all_64_0 gives:
% 22.62/3.89 | (62) aDimensionOf0(xs) = all_64_0 & $i(all_64_0) & (all_64_0 = sz00 | ( !
% 22.62/3.89 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) =
% 22.62/3.89 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) | ~
% 22.62/3.89 | aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) & !
% 22.62/3.89 | [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1) |
% 22.62/3.89 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 22.62/3.89 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 22.62/3.89 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 & $i(v5)
% 22.62/3.89 | & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = all_64_0) &
% 22.62/3.89 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 22.62/3.89 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | szszuzczcdt0(v0) =
% 22.62/3.89 | all_64_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~
% 22.62/3.89 | $i(xp) | aVector0(xp))))
% 22.62/3.89 |
% 22.62/3.89 | ALPHA: (62) implies:
% 22.62/3.89 | (63) aDimensionOf0(xs) = all_64_0
% 22.62/3.89 | (64) all_64_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 22.62/3.89 | (sdtlbdtrb0(xs, v1) = v2) | ~ (aDimensionOf0(xp) = v0) | ~
% 22.62/3.89 | $i(v1) | ~ $i(xp) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1)
% 22.62/3.89 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~
% 22.62/3.89 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 22.62/3.89 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 22.62/3.89 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) =
% 22.62/3.89 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 22.62/3.89 | all_64_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 22.62/3.89 | $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) | szszuzczcdt0(v0)
% 22.62/3.89 | = all_64_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~
% 22.62/3.89 | $i(xp) | aVector0(xp)))
% 22.62/3.89 |
% 22.62/3.89 | DELTA: instantiating (55) with fresh symbol all_66_0 gives:
% 22.62/3.89 | (65) aDimensionOf0(xt) = all_66_0 & $i(all_66_0) & (all_66_0 = sz00 | ( !
% 22.62/3.89 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 22.62/3.89 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) | ~
% 22.62/3.89 | aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) & !
% 22.62/3.89 | [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1) |
% 22.62/3.89 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 22.62/3.89 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 22.62/3.89 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 & $i(v5)
% 22.62/3.89 | & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = all_66_0) &
% 22.62/3.89 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 22.62/3.89 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0) =
% 22.62/3.89 | all_66_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~
% 22.62/3.89 | $i(xq) | aVector0(xq))))
% 22.62/3.89 |
% 22.62/3.89 | ALPHA: (65) implies:
% 22.62/3.89 | (66) aDimensionOf0(xt) = all_66_0
% 22.62/3.90 | (67) all_66_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 22.62/3.90 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(xq) = v0) | ~
% 22.62/3.90 | $i(v1) | ~ $i(xq) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1)
% 22.62/3.90 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~
% 22.62/3.90 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 22.62/3.90 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 22.62/3.90 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) =
% 22.62/3.90 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 22.62/3.90 | all_66_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 22.62/3.90 | $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0)
% 22.62/3.90 | = all_66_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~
% 22.62/3.90 | $i(xq) | aVector0(xq)))
% 22.62/3.90 |
% 22.62/3.90 | BETA: splitting (61) gives:
% 22.62/3.90 |
% 22.62/3.90 | Case 1:
% 22.62/3.90 | |
% 22.62/3.90 | | (68) sdtasasdt0(xp, xq) = all_63_1 & sdtasdt0(all_63_1, all_63_1) =
% 22.62/3.90 | | all_63_0 & $i(all_63_0) & $i(all_63_1) & sdtlseqdt0(all_63_0,
% 22.62/3.90 | | all_41_0)
% 22.62/3.90 | |
% 22.62/3.90 | | ALPHA: (68) implies:
% 22.62/3.90 | | (69) sdtlseqdt0(all_63_0, all_41_0)
% 22.62/3.90 | | (70) sdtasdt0(all_63_1, all_63_1) = all_63_0
% 22.62/3.90 | | (71) sdtasasdt0(xp, xq) = all_63_1
% 22.62/3.90 | |
% 22.62/3.90 | | GROUND_INST: instantiating (24) with xE, all_63_1, xq, xp, simplifying with
% 22.62/3.90 | | (20), (71) gives:
% 22.62/3.90 | | (72) all_63_1 = xE
% 22.62/3.90 | |
% 22.62/3.90 | | REDUCE: (70), (72) imply:
% 22.62/3.90 | | (73) sdtasdt0(xE, xE) = all_63_0
% 22.62/3.90 | |
% 22.62/3.90 | | GROUND_INST: instantiating (23) with all_41_1, all_63_0, xE, xE, simplifying
% 22.62/3.90 | | with (38), (73) gives:
% 22.62/3.90 | | (74) all_63_0 = all_41_1
% 22.62/3.90 | |
% 22.62/3.90 | | REDUCE: (69), (74) imply:
% 22.62/3.90 | | (75) sdtlseqdt0(all_41_1, all_41_0)
% 22.62/3.90 | |
% 22.62/3.90 | | PRED_UNIFY: (36), (75) imply:
% 22.62/3.90 | | (76) $false
% 22.62/3.90 | |
% 22.62/3.90 | | CLOSE: (76) is inconsistent.
% 22.62/3.90 | |
% 22.62/3.90 | Case 2:
% 22.62/3.90 | |
% 22.62/3.90 | | (77) aDimensionOf0(xp) = all_63_3 & $i(all_63_3) & ( ~ iLess0(all_63_3,
% 22.62/3.90 | | all_43_0) | ( ~ (all_63_2 = all_63_3) & aDimensionOf0(xq) =
% 22.62/3.90 | | all_63_2 & $i(all_63_2)))
% 22.62/3.90 | |
% 22.62/3.90 | | ALPHA: (77) implies:
% 22.62/3.90 | | (78) aDimensionOf0(xp) = all_63_3
% 22.62/3.90 | | (79) ~ iLess0(all_63_3, all_43_0) | ( ~ (all_63_2 = all_63_3) &
% 22.62/3.90 | | aDimensionOf0(xq) = all_63_2 & $i(all_63_2))
% 22.62/3.90 | |
% 22.62/3.90 | | GROUND_INST: instantiating (22) with all_33_0, all_64_0, xs, simplifying
% 22.62/3.90 | | with (26), (63) gives:
% 22.62/3.90 | | (80) all_64_0 = all_33_0
% 22.62/3.90 | |
% 22.62/3.90 | | GROUND_INST: instantiating (22) with all_33_0, all_66_0, xt, simplifying
% 22.62/3.90 | | with (27), (66) gives:
% 22.62/3.90 | | (81) all_66_0 = all_33_0
% 22.62/3.90 | |
% 22.62/3.90 | | BETA: splitting (57) gives:
% 22.62/3.90 | |
% 22.62/3.90 | | Case 1:
% 22.62/3.90 | | |
% 22.62/3.90 | | | (82) all_59_0 = all_59_1 & aDimensionOf0(xp) = all_59_1 & $i(all_59_1)
% 22.62/3.90 | | |
% 22.62/3.90 | | | ALPHA: (82) implies:
% 22.62/3.90 | | | (83) aDimensionOf0(xp) = all_59_1
% 22.62/3.90 | | |
% 22.62/3.90 | | | BETA: splitting (64) gives:
% 22.62/3.90 | | |
% 22.62/3.90 | | | Case 1:
% 22.62/3.90 | | | |
% 22.62/3.90 | | | | (84) all_64_0 = sz00
% 22.62/3.90 | | | |
% 22.62/3.90 | | | | COMBINE_EQS: (80), (84) imply:
% 22.62/3.90 | | | | (85) all_33_0 = sz00
% 22.62/3.90 | | | |
% 22.62/3.90 | | | | SIMP: (85) implies:
% 22.62/3.90 | | | | (86) all_33_0 = sz00
% 22.62/3.90 | | | |
% 22.62/3.90 | | | | REDUCE: (49), (86) imply:
% 22.62/3.90 | | | | (87) $false
% 22.62/3.90 | | | |
% 22.62/3.90 | | | | CLOSE: (87) is inconsistent.
% 22.62/3.90 | | | |
% 22.62/3.90 | | | Case 2:
% 22.62/3.90 | | | |
% 22.62/3.90 | | | | (88) ~ (all_64_0 = sz00)
% 22.62/3.90 | | | | (89) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs,
% 22.62/3.90 | | | | v1) = v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~
% 22.62/3.90 | | | | $i(xp) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 &
% 22.62/3.90 | | | | $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~
% 22.62/3.90 | | | | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ?
% 22.62/3.90 | | | | [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3)
% 22.62/3.90 | | | | & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs,
% 22.62/3.90 | | | | v3) = v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | (
% 22.62/3.90 | | | | ~ (v2 = all_64_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) &
% 22.62/3.90 | | | | ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) |
% 22.62/3.90 | | | | szszuzczcdt0(v0) = all_64_0) & ! [v0: $i] : ( ~
% 22.62/3.90 | | | | (aDimensionOf0(xp) = v0) | ~ $i(xp) | aVector0(xp))
% 22.62/3.90 | | | |
% 22.62/3.90 | | | | ALPHA: (89) implies:
% 22.62/3.91 | | | | (90) ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) |
% 22.62/3.91 | | | | szszuzczcdt0(v0) = all_64_0)
% 22.62/3.91 | | | |
% 22.62/3.91 | | | | BETA: splitting (59) gives:
% 22.62/3.91 | | | |
% 22.62/3.91 | | | | Case 1:
% 22.62/3.91 | | | | |
% 22.62/3.91 | | | | | (91) all_61_0 = all_61_1 & aDimensionOf0(xq) = all_61_1 &
% 22.62/3.91 | | | | | aDimensionOf0(xp) = all_61_1 & $i(all_61_1)
% 22.62/3.91 | | | | |
% 22.62/3.91 | | | | | ALPHA: (91) implies:
% 22.62/3.91 | | | | | (92) aDimensionOf0(xp) = all_61_1
% 22.62/3.91 | | | | | (93) aDimensionOf0(xq) = all_61_1
% 22.62/3.91 | | | | |
% 22.62/3.91 | | | | | BETA: splitting (60) gives:
% 22.62/3.91 | | | | |
% 22.62/3.91 | | | | | Case 1:
% 22.62/3.91 | | | | | |
% 22.62/3.91 | | | | | | (94) all_62_0 = all_62_1 & aDimensionOf0(xq) = all_62_1 &
% 22.62/3.91 | | | | | | aDimensionOf0(xp) = all_62_1 & $i(all_62_1)
% 22.62/3.91 | | | | | |
% 22.62/3.91 | | | | | | ALPHA: (94) implies:
% 22.62/3.91 | | | | | | (95) aDimensionOf0(xq) = all_62_1
% 22.62/3.91 | | | | | |
% 22.62/3.91 | | | | | | BETA: splitting (58) gives:
% 22.62/3.91 | | | | | |
% 22.62/3.91 | | | | | | Case 1:
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | (96) all_60_0 = all_60_1 & aDimensionOf0(xq) = all_60_1 &
% 22.62/3.91 | | | | | | | $i(all_60_1)
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | ALPHA: (96) implies:
% 22.62/3.91 | | | | | | | (97) $i(all_60_1)
% 22.62/3.91 | | | | | | | (98) aDimensionOf0(xq) = all_60_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | GROUND_INST: instantiating (22) with all_63_3, all_59_1, xp,
% 22.62/3.91 | | | | | | | simplifying with (78), (83) gives:
% 22.62/3.91 | | | | | | | (99) all_63_3 = all_59_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | GROUND_INST: instantiating (22) with all_63_3, all_61_1, xp,
% 22.62/3.91 | | | | | | | simplifying with (78), (92) gives:
% 22.62/3.91 | | | | | | | (100) all_63_3 = all_61_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | GROUND_INST: instantiating (22) with all_61_1, all_62_1, xq,
% 22.62/3.91 | | | | | | | simplifying with (93), (95) gives:
% 22.62/3.91 | | | | | | | (101) all_62_1 = all_61_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | GROUND_INST: instantiating (22) with all_60_1, all_62_1, xq,
% 22.62/3.91 | | | | | | | simplifying with (95), (98) gives:
% 22.62/3.91 | | | | | | | (102) all_62_1 = all_60_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | COMBINE_EQS: (99), (100) imply:
% 22.62/3.91 | | | | | | | (103) all_61_1 = all_59_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | SIMP: (103) implies:
% 22.62/3.91 | | | | | | | (104) all_61_1 = all_59_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | COMBINE_EQS: (101), (102) imply:
% 22.62/3.91 | | | | | | | (105) all_61_1 = all_60_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | SIMP: (105) implies:
% 22.62/3.91 | | | | | | | (106) all_61_1 = all_60_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | COMBINE_EQS: (104), (106) imply:
% 22.62/3.91 | | | | | | | (107) all_60_1 = all_59_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | REDUCE: (98), (107) imply:
% 22.62/3.91 | | | | | | | (108) aDimensionOf0(xq) = all_59_1
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | REDUCE: (97), (107) imply:
% 22.62/3.91 | | | | | | | (109) $i(all_59_1)
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | BETA: splitting (79) gives:
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | Case 1:
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | (110) ~ iLess0(all_63_3, all_43_0)
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | REDUCE: (44), (99), (110) imply:
% 22.62/3.91 | | | | | | | | (111) ~ iLess0(all_59_1, all_33_0)
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | GROUND_INST: instantiating (90) with all_59_1, simplifying with
% 22.62/3.91 | | | | | | | | (18), (83) gives:
% 22.62/3.91 | | | | | | | | (112) szszuzczcdt0(all_59_1) = all_64_0
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | GROUND_INST: instantiating (mDimNat) with xq, all_59_1,
% 22.62/3.91 | | | | | | | | simplifying with (10), (19), (108) gives:
% 22.62/3.91 | | | | | | | | (113) aNaturalNumber0(all_59_1)
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | REDUCE: (80), (112) imply:
% 22.62/3.91 | | | | | | | | (114) szszuzczcdt0(all_59_1) = all_33_0
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | GROUND_INST: instantiating (mIH) with all_59_1, all_33_0,
% 22.62/3.91 | | | | | | | | simplifying with (109), (111), (113), (114) gives:
% 22.62/3.91 | | | | | | | | (115) $false
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | CLOSE: (115) is inconsistent.
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | Case 2:
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | (116) ~ (all_63_2 = all_63_3) & aDimensionOf0(xq) = all_63_2
% 22.62/3.91 | | | | | | | | & $i(all_63_2)
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | ALPHA: (116) implies:
% 22.62/3.91 | | | | | | | | (117) ~ (all_63_2 = all_63_3)
% 22.62/3.91 | | | | | | | | (118) aDimensionOf0(xq) = all_63_2
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | REDUCE: (99), (117) imply:
% 22.62/3.91 | | | | | | | | (119) ~ (all_63_2 = all_59_1)
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | GROUND_INST: instantiating (22) with all_59_1, all_63_2, xq,
% 22.62/3.91 | | | | | | | | simplifying with (108), (118) gives:
% 22.62/3.91 | | | | | | | | (120) all_63_2 = all_59_1
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | REDUCE: (119), (120) imply:
% 22.62/3.91 | | | | | | | | (121) $false
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | CLOSE: (121) is inconsistent.
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | End of split
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | Case 2:
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | (122) aDimensionOf0(xt) = all_60_2 & $i(all_60_2) & (all_60_2 =
% 22.62/3.91 | | | | | | | sz00 | ( ~ (all_60_2 = all_60_3) & aDimensionOf0(xt) =
% 22.62/3.91 | | | | | | | all_60_3 & $i(all_60_3)))
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | ALPHA: (122) implies:
% 22.62/3.91 | | | | | | | (123) aDimensionOf0(xt) = all_60_2
% 22.62/3.91 | | | | | | | (124) all_60_2 = sz00 | ( ~ (all_60_2 = all_60_3) &
% 22.62/3.91 | | | | | | | aDimensionOf0(xt) = all_60_3 & $i(all_60_3))
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | BETA: splitting (124) gives:
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | | Case 1:
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | (125) all_60_2 = sz00
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | REDUCE: (123), (125) imply:
% 22.62/3.91 | | | | | | | | (126) aDimensionOf0(xt) = sz00
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | GROUND_INST: instantiating (22) with all_33_0, sz00, xt,
% 22.62/3.91 | | | | | | | | simplifying with (27), (126) gives:
% 22.62/3.91 | | | | | | | | (127) all_33_0 = sz00
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | REDUCE: (49), (127) imply:
% 22.62/3.91 | | | | | | | | (128) $false
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | CLOSE: (128) is inconsistent.
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | Case 2:
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | (129) ~ (all_60_2 = all_60_3) & aDimensionOf0(xt) = all_60_3
% 22.62/3.91 | | | | | | | | & $i(all_60_3)
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | ALPHA: (129) implies:
% 22.62/3.91 | | | | | | | | (130) ~ (all_60_2 = all_60_3)
% 22.62/3.91 | | | | | | | | (131) aDimensionOf0(xt) = all_60_3
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | GROUND_INST: instantiating (22) with all_33_0, all_60_2, xt,
% 22.62/3.91 | | | | | | | | simplifying with (27), (123) gives:
% 22.62/3.91 | | | | | | | | (132) all_60_2 = all_33_0
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | GROUND_INST: instantiating (22) with all_60_3, all_60_2, xt,
% 22.62/3.91 | | | | | | | | simplifying with (123), (131) gives:
% 22.62/3.91 | | | | | | | | (133) all_60_2 = all_60_3
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | COMBINE_EQS: (132), (133) imply:
% 22.62/3.91 | | | | | | | | (134) all_60_3 = all_33_0
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | REDUCE: (130), (132), (134) imply:
% 22.62/3.91 | | | | | | | | (135) $false
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | | CLOSE: (135) is inconsistent.
% 22.62/3.91 | | | | | | | |
% 22.62/3.91 | | | | | | | End of split
% 22.62/3.91 | | | | | | |
% 22.62/3.91 | | | | | | End of split
% 22.62/3.91 | | | | | |
% 22.62/3.91 | | | | | Case 2:
% 22.62/3.91 | | | | | |
% 22.62/3.91 | | | | | | (136) aDimensionOf0(xt) = all_62_2 & $i(all_62_2) & (all_62_2 =
% 22.62/3.91 | | | | | | sz00 | ( ~ (all_62_2 = all_62_3) & aDimensionOf0(xs) =
% 22.62/3.91 | | | | | | all_62_3 & $i(all_62_3)))
% 22.62/3.91 | | | | | |
% 22.62/3.91 | | | | | | ALPHA: (136) implies:
% 22.62/3.92 | | | | | | (137) aDimensionOf0(xt) = all_62_2
% 22.62/3.92 | | | | | | (138) all_62_2 = sz00 | ( ~ (all_62_2 = all_62_3) &
% 22.62/3.92 | | | | | | aDimensionOf0(xs) = all_62_3 & $i(all_62_3))
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | GROUND_INST: instantiating (22) with all_33_0, all_62_2, xt,
% 22.62/3.92 | | | | | | simplifying with (27), (137) gives:
% 22.62/3.92 | | | | | | (139) all_62_2 = all_33_0
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | BETA: splitting (138) gives:
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | Case 1:
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | (140) all_62_2 = sz00
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | COMBINE_EQS: (139), (140) imply:
% 22.62/3.92 | | | | | | | (141) all_33_0 = sz00
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | REDUCE: (49), (141) imply:
% 22.62/3.92 | | | | | | | (142) $false
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | CLOSE: (142) is inconsistent.
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | Case 2:
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | (143) ~ (all_62_2 = all_62_3) & aDimensionOf0(xs) = all_62_3 &
% 22.62/3.92 | | | | | | | $i(all_62_3)
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | ALPHA: (143) implies:
% 22.62/3.92 | | | | | | | (144) ~ (all_62_2 = all_62_3)
% 22.62/3.92 | | | | | | | (145) aDimensionOf0(xs) = all_62_3
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | REDUCE: (139), (144) imply:
% 22.62/3.92 | | | | | | | (146) ~ (all_62_3 = all_33_0)
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | SIMP: (146) implies:
% 22.62/3.92 | | | | | | | (147) ~ (all_62_3 = all_33_0)
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | GROUND_INST: instantiating (22) with all_33_0, all_62_3, xs,
% 22.62/3.92 | | | | | | | simplifying with (26), (145) gives:
% 22.62/3.92 | | | | | | | (148) all_62_3 = all_33_0
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | REDUCE: (147), (148) imply:
% 22.62/3.92 | | | | | | | (149) $false
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | CLOSE: (149) is inconsistent.
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | End of split
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | End of split
% 22.62/3.92 | | | | |
% 22.62/3.92 | | | | Case 2:
% 22.62/3.92 | | | | |
% 22.62/3.92 | | | | | (150) aDimensionOf0(xs) = all_61_2 & $i(all_61_2) & (all_61_2 =
% 22.62/3.92 | | | | | sz00 | ( ~ (all_61_2 = all_61_3) & aDimensionOf0(xt) =
% 22.62/3.92 | | | | | all_61_3 & $i(all_61_3)))
% 22.62/3.92 | | | | |
% 22.62/3.92 | | | | | ALPHA: (150) implies:
% 22.62/3.92 | | | | | (151) aDimensionOf0(xs) = all_61_2
% 22.62/3.92 | | | | | (152) all_61_2 = sz00 | ( ~ (all_61_2 = all_61_3) &
% 22.62/3.92 | | | | | aDimensionOf0(xt) = all_61_3 & $i(all_61_3))
% 22.62/3.92 | | | | |
% 22.62/3.92 | | | | | BETA: splitting (67) gives:
% 22.62/3.92 | | | | |
% 22.62/3.92 | | | | | Case 1:
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | (153) all_66_0 = sz00
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | COMBINE_EQS: (81), (153) imply:
% 22.62/3.92 | | | | | | (154) all_33_0 = sz00
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | REDUCE: (49), (154) imply:
% 22.62/3.92 | | | | | | (155) $false
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | CLOSE: (155) is inconsistent.
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | Case 2:
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | (156) ~ (all_66_0 = sz00)
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | GROUND_INST: instantiating (22) with all_33_0, all_61_2, xs,
% 22.62/3.92 | | | | | | simplifying with (26), (151) gives:
% 22.62/3.92 | | | | | | (157) all_61_2 = all_33_0
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | BETA: splitting (152) gives:
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | | Case 1:
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | (158) all_61_2 = sz00
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | COMBINE_EQS: (157), (158) imply:
% 22.62/3.92 | | | | | | | (159) all_33_0 = sz00
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | SIMP: (159) implies:
% 22.62/3.92 | | | | | | | (160) all_33_0 = sz00
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | REDUCE: (49), (160) imply:
% 22.62/3.92 | | | | | | | (161) $false
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | CLOSE: (161) is inconsistent.
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | Case 2:
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | (162) ~ (all_61_2 = all_61_3) & aDimensionOf0(xt) = all_61_3 &
% 22.62/3.92 | | | | | | | $i(all_61_3)
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | ALPHA: (162) implies:
% 22.62/3.92 | | | | | | | (163) ~ (all_61_2 = all_61_3)
% 22.62/3.92 | | | | | | | (164) aDimensionOf0(xt) = all_61_3
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | REDUCE: (157), (163) imply:
% 22.62/3.92 | | | | | | | (165) ~ (all_61_3 = all_33_0)
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | SIMP: (165) implies:
% 22.62/3.92 | | | | | | | (166) ~ (all_61_3 = all_33_0)
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | GROUND_INST: instantiating (22) with all_33_0, all_61_3, xt,
% 22.62/3.92 | | | | | | | simplifying with (27), (164) gives:
% 22.62/3.92 | | | | | | | (167) all_61_3 = all_33_0
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | REDUCE: (166), (167) imply:
% 22.62/3.92 | | | | | | | (168) $false
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | | CLOSE: (168) is inconsistent.
% 22.62/3.92 | | | | | | |
% 22.62/3.92 | | | | | | End of split
% 22.62/3.92 | | | | | |
% 22.62/3.92 | | | | | End of split
% 22.62/3.92 | | | | |
% 22.62/3.92 | | | | End of split
% 22.62/3.92 | | | |
% 22.62/3.92 | | | End of split
% 22.62/3.92 | | |
% 22.62/3.92 | | Case 2:
% 22.62/3.92 | | |
% 22.62/3.92 | | | (169) aDimensionOf0(xs) = all_59_2 & $i(all_59_2) & (all_59_2 = sz00 |
% 22.62/3.92 | | | ( ~ (all_59_2 = all_59_3) & aDimensionOf0(xs) = all_59_3 &
% 22.62/3.92 | | | $i(all_59_3)))
% 22.62/3.92 | | |
% 22.62/3.92 | | | ALPHA: (169) implies:
% 22.62/3.92 | | | (170) aDimensionOf0(xs) = all_59_2
% 22.62/3.92 | | | (171) all_59_2 = sz00 | ( ~ (all_59_2 = all_59_3) & aDimensionOf0(xs) =
% 22.62/3.92 | | | all_59_3 & $i(all_59_3))
% 22.62/3.92 | | |
% 22.62/3.92 | | | BETA: splitting (171) gives:
% 22.62/3.92 | | |
% 22.62/3.92 | | | Case 1:
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | (172) all_59_2 = sz00
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | REDUCE: (170), (172) imply:
% 22.62/3.92 | | | | (173) aDimensionOf0(xs) = sz00
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | GROUND_INST: instantiating (22) with all_33_0, sz00, xs, simplifying
% 22.62/3.92 | | | | with (26), (173) gives:
% 22.62/3.92 | | | | (174) all_33_0 = sz00
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | REDUCE: (49), (174) imply:
% 22.62/3.92 | | | | (175) $false
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | CLOSE: (175) is inconsistent.
% 22.62/3.92 | | | |
% 22.62/3.92 | | | Case 2:
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | (176) ~ (all_59_2 = all_59_3) & aDimensionOf0(xs) = all_59_3 &
% 22.62/3.92 | | | | $i(all_59_3)
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | ALPHA: (176) implies:
% 22.62/3.92 | | | | (177) ~ (all_59_2 = all_59_3)
% 22.62/3.92 | | | | (178) aDimensionOf0(xs) = all_59_3
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | GROUND_INST: instantiating (22) with all_33_0, all_59_2, xs, simplifying
% 22.62/3.92 | | | | with (26), (170) gives:
% 22.62/3.92 | | | | (179) all_59_2 = all_33_0
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | GROUND_INST: instantiating (22) with all_59_3, all_59_2, xs, simplifying
% 22.62/3.92 | | | | with (170), (178) gives:
% 22.62/3.92 | | | | (180) all_59_2 = all_59_3
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | COMBINE_EQS: (179), (180) imply:
% 22.62/3.92 | | | | (181) all_59_3 = all_33_0
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | REDUCE: (177), (179), (181) imply:
% 22.62/3.92 | | | | (182) $false
% 22.62/3.92 | | | |
% 22.62/3.92 | | | | CLOSE: (182) is inconsistent.
% 22.62/3.92 | | | |
% 22.62/3.92 | | | End of split
% 22.62/3.92 | | |
% 22.62/3.92 | | End of split
% 22.62/3.92 | |
% 22.62/3.92 | End of split
% 22.62/3.92 |
% 22.62/3.92 End of proof
% 22.62/3.92 % SZS output end Proof for theBenchmark
% 22.62/3.92
% 22.62/3.92 3313ms
%------------------------------------------------------------------------------