TSTP Solution File: RNG076+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG076+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 : n001.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 13:57:43 EDT 2023
% Result : Theorem 100.66s 14.50s
% Output : Proof 108.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG076+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Aug 27 03:03:47 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.64 Running up to 7 provers in parallel.
% 0.17/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.93/1.35 Prover 1: Preprocessing ...
% 3.93/1.35 Prover 4: Preprocessing ...
% 4.22/1.40 Prover 0: Preprocessing ...
% 4.22/1.40 Prover 2: Preprocessing ...
% 4.22/1.40 Prover 3: Preprocessing ...
% 4.22/1.40 Prover 5: Preprocessing ...
% 4.22/1.40 Prover 6: Preprocessing ...
% 11.73/2.47 Prover 3: Constructing countermodel ...
% 11.73/2.51 Prover 1: Constructing countermodel ...
% 12.86/2.68 Prover 6: Proving ...
% 14.25/3.00 Prover 5: Constructing countermodel ...
% 16.05/3.18 Prover 4: Constructing countermodel ...
% 17.23/3.31 Prover 2: Proving ...
% 17.23/3.33 Prover 0: Proving ...
% 68.92/10.40 Prover 2: stopped
% 68.92/10.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 70.04/10.51 Prover 7: Preprocessing ...
% 72.84/10.79 Prover 7: Constructing countermodel ...
% 96.55/13.99 Prover 5: stopped
% 96.55/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 97.93/14.11 Prover 8: Preprocessing ...
% 98.40/14.18 Prover 8: Warning: ignoring some quantifiers
% 98.40/14.18 Prover 8: Constructing countermodel ...
% 100.66/14.50 Prover 3: proved (13835ms)
% 100.66/14.50
% 100.66/14.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.66/14.50
% 100.66/14.51 Prover 6: stopped
% 100.66/14.51 Prover 0: stopped
% 100.66/14.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 100.66/14.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 100.66/14.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 100.66/14.60 Prover 10: Preprocessing ...
% 100.66/14.60 Prover 13: Preprocessing ...
% 100.66/14.63 Prover 11: Preprocessing ...
% 101.69/14.71 Prover 10: Constructing countermodel ...
% 102.92/14.77 Prover 13: Constructing countermodel ...
% 103.56/14.87 Prover 11: Constructing countermodel ...
% 106.75/15.38 Prover 10: Found proof (size 217)
% 106.75/15.38 Prover 10: proved (862ms)
% 106.75/15.38 Prover 13: stopped
% 106.75/15.38 Prover 11: stopped
% 106.75/15.38 Prover 7: stopped
% 107.15/15.38 Prover 1: stopped
% 107.15/15.38 Prover 4: stopped
% 107.15/15.41 Prover 8: stopped
% 107.15/15.41
% 107.15/15.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 107.15/15.41
% 107.85/15.44 % SZS output start Proof for theBenchmark
% 107.85/15.45 Assumptions after simplification:
% 107.85/15.45 ---------------------------------
% 107.85/15.45
% 107.85/15.45 (mArith)
% 107.99/15.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 107.99/15.49 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 107.99/15.49 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5:
% 107.99/15.49 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 &
% 107.99/15.49 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 &
% 107.99/15.49 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 &
% 107.99/15.49 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 107.99/15.49 $i(v3)))
% 107.99/15.49
% 107.99/15.49 (mDefInit)
% 107.99/15.50 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 107.99/15.50 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 107.99/15.50 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 107.99/15.50 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 107.99/15.50 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 107.99/15.50 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 107.99/15.50 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 107.99/15.50 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 107.99/15.50 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 107.99/15.50 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 107.99/15.50 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 107.99/15.50 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 107.99/15.50 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 107.99/15.50
% 107.99/15.50 (mDimNat)
% 107.99/15.50 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 107.99/15.50 aVector0(v0) | aNaturalNumber0(v1))
% 107.99/15.50
% 107.99/15.50 (mDistr)
% 107.99/15.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 107.99/15.50 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 107.99/15.50 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 107.99/15.50 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i]
% 107.99/15.50 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 107.99/15.50 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 &
% 107.99/15.50 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 107.99/15.50
% 107.99/15.50 (mEqInit)
% 107.99/15.51 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 107.99/15.51 (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 107.99/15.51 | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 107.99/15.51 $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = v6 & aDimensionOf0(v2)
% 107.99/15.51 = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & $i(v5) & (v5 = sz00 | ( ~ (v5
% 107.99/15.51 = v4) & aDimensionOf0(v0) = v4 & $i(v4))))))
% 107.99/15.51
% 107.99/15.51 (mIH)
% 107.99/15.51 ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~
% 107.99/15.51 aNaturalNumber0(v0) | iLess0(v0, v1))
% 107.99/15.51
% 107.99/15.51 (mLEMon)
% 107.99/15.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 107.99/15.51 $i] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ $i(v3) |
% 107.99/15.51 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~
% 107.99/15.51 sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) |
% 107.99/15.51 ~ aScalar0(v0) | sdtlseqdt0(v4, v5))
% 107.99/15.51
% 107.99/15.51 (mLETot)
% 107.99/15.51 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~
% 107.99/15.51 aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 107.99/15.51
% 107.99/15.51 (mMulSc)
% 107.99/15.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 107.99/15.51 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 107.99/15.51
% 107.99/15.51 (mNatExtr)
% 107.99/15.51 $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | ?
% 107.99/15.51 [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aNaturalNumber0(v1)))
% 107.99/15.51
% 107.99/15.51 (mSuccEqu)
% 107.99/15.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v1) =
% 107.99/15.51 v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 107.99/15.51 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 107.99/15.51
% 107.99/15.51 (mSumSc)
% 107.99/15.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 107.99/15.51 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 107.99/15.51
% 107.99/15.52 (m__)
% 107.99/15.52 $i(xS) & $i(xP) & $i(xR) & $i(xH) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] :
% 107.99/15.52 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 107.99/15.52 $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH, xH) = v2 & sdtasdt0(xE, xE)
% 107.99/15.52 = v0 & sdtasdt0(xC, xD) = v5 & sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8
% 107.99/15.52 & sdtpldt0(v1, v2) = v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 &
% 107.99/15.52 sdtpldt0(xR, xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 107.99/15.52 & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v4, v8))
% 107.99/15.52
% 107.99/15.52 (m__1652)
% 107.99/15.52 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 107.99/15.52 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 107.99/15.52 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 107.99/15.52 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 107.99/15.52 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 107.99/15.52 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 107.99/15.52 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 107.99/15.52 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 107.99/15.52
% 107.99/15.52 (m__1678)
% 107.99/15.52 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 107.99/15.52
% 107.99/15.52 (m__1678_01)
% 107.99/15.52 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 107.99/15.52 v0 & $i(v0))
% 107.99/15.52
% 107.99/15.52 (m__1692)
% 107.99/15.52 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 107.99/15.52 $i(v0))
% 107.99/15.52
% 107.99/15.52 (m__1709)
% 107.99/15.52 sziznziztdt0(xs) = xp & $i(xp) & $i(xs) & aVector0(xp)
% 107.99/15.52
% 107.99/15.52 (m__1726)
% 107.99/15.52 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq)
% 107.99/15.52
% 107.99/15.52 (m__1746)
% 107.99/15.52 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 107.99/15.53 v0 & $i(v0) & aScalar0(xA))
% 107.99/15.53
% 107.99/15.53 (m__1766)
% 107.99/15.53 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 107.99/15.53 v0 & $i(v0) & aScalar0(xB))
% 107.99/15.53
% 107.99/15.53 (m__1783)
% 107.99/15.53 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC)
% 107.99/15.53
% 107.99/15.53 (m__1800)
% 107.99/15.53 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD)
% 107.99/15.53
% 107.99/15.53 (m__1820)
% 107.99/15.53 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE)
% 107.99/15.53
% 107.99/15.53 (m__1873)
% 107.99/15.53 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH)
% 107.99/15.53
% 107.99/15.53 (m__1892)
% 107.99/15.53 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR)
% 107.99/15.53
% 107.99/15.53 (m__1911)
% 107.99/15.53 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP)
% 107.99/15.53
% 107.99/15.53 (m__1930)
% 107.99/15.53 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS)
% 107.99/15.53
% 107.99/15.53 (m__1967)
% 107.99/15.53 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0
% 107.99/15.53 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 107.99/15.53
% 107.99/15.53 (m__1983)
% 107.99/15.53 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0
% 107.99/15.53 & sdtpldt0(xR, xS) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 107.99/15.53
% 107.99/15.53 (function-axioms)
% 107.99/15.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 107.99/15.54 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 107.99/15.54 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 107.99/15.54 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 107.99/15.54 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 107.99/15.54 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 107.99/15.54 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 107.99/15.54 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 107.99/15.54 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 107.99/15.54 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 107.99/15.54 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 107.99/15.54 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 107.99/15.54 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 107.99/15.54
% 107.99/15.54 Further assumptions not needed in the proof:
% 107.99/15.54 --------------------------------------------
% 108.34/15.54 mDefSPN, mDefSPZ, mDistr2, mElmSc, mIHOrd, mLEASm, mLEMonM, mLERef, mLETrn,
% 108.34/15.54 mLess, mMDNeg, mMNeg, mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort,
% 108.34/15.54 mScSqPos, mScZero, mSqPos, mSqrt, mSuccNat, mVcSort, mZeroNat, m__1837, m__1854,
% 108.34/15.54 m__1949
% 108.34/15.54
% 108.34/15.54 Those formulas are unsatisfiable:
% 108.34/15.54 ---------------------------------
% 108.34/15.54
% 108.34/15.54 Begin of proof
% 108.34/15.54 |
% 108.34/15.54 | ALPHA: (mNatExtr) implies:
% 108.34/15.54 | (1) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | ? [v1:
% 108.34/15.54 | $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aNaturalNumber0(v1)))
% 108.34/15.54 |
% 108.34/15.54 | ALPHA: (mDefInit) implies:
% 108.34/15.55 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 108.34/15.55 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 108.34/15.55 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 108.34/15.55 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 108.34/15.55 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 108.34/15.55 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 108.34/15.55 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 108.34/15.55 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 108.34/15.55 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 108.34/15.55 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 108.34/15.55 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 108.34/15.55 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 108.34/15.55 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 108.34/15.55 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 108.34/15.55 | aVector0(v1))))))
% 108.34/15.55 |
% 108.34/15.55 | ALPHA: (mEqInit) implies:
% 108.34/15.55 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 108.34/15.55 | (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~
% 108.34/15.55 | $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5:
% 108.34/15.55 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) =
% 108.34/15.55 | v6 & aDimensionOf0(v2) = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 &
% 108.34/15.55 | $i(v5) & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4 &
% 108.34/15.55 | $i(v4))))))
% 108.34/15.55 |
% 108.34/15.55 | ALPHA: (m__1678) implies:
% 108.34/15.55 | (4) aVector0(xs)
% 108.34/15.55 | (5) aVector0(xt)
% 108.34/15.55 |
% 108.34/15.55 | ALPHA: (m__1652) implies:
% 108.34/15.55 | (6) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 108.34/15.55 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 108.34/15.55 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 108.34/15.55 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 108.34/15.55 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 108.34/15.55 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 108.34/15.55 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 108.34/15.55 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 108.34/15.55 | $i(v7)))))))
% 108.34/15.55 |
% 108.34/15.55 | ALPHA: (m__1678_01) implies:
% 108.34/15.55 | (7) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 108.34/15.55 | $i(v0))
% 108.34/15.55 |
% 108.34/15.55 | ALPHA: (m__1692) implies:
% 108.34/15.55 | (8) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 108.34/15.55 |
% 108.34/15.55 | ALPHA: (m__1709) implies:
% 108.34/15.56 | (9) aVector0(xp)
% 108.34/15.56 | (10) sziznziztdt0(xs) = xp
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1726) implies:
% 108.34/15.56 | (11) aVector0(xq)
% 108.34/15.56 | (12) sziznziztdt0(xt) = xq
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1746) implies:
% 108.34/15.56 | (13) $i(xs)
% 108.34/15.56 | (14) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 108.34/15.56 | $i(v0) & aScalar0(xA))
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1766) implies:
% 108.34/15.56 | (15) $i(xt)
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1783) implies:
% 108.34/15.56 | (16) aScalar0(xC)
% 108.34/15.56 | (17) sdtasasdt0(xp, xp) = xC
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1800) implies:
% 108.34/15.56 | (18) aScalar0(xD)
% 108.34/15.56 | (19) sdtasasdt0(xq, xq) = xD
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1820) implies:
% 108.34/15.56 | (20) aScalar0(xE)
% 108.34/15.56 | (21) $i(xp)
% 108.34/15.56 | (22) $i(xq)
% 108.34/15.56 | (23) sdtasasdt0(xp, xq) = xE
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1873) implies:
% 108.34/15.56 | (24) aScalar0(xH)
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1892) implies:
% 108.34/15.56 | (25) aScalar0(xR)
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1911) implies:
% 108.34/15.56 | (26) aScalar0(xP)
% 108.34/15.56 | (27) sdtasdt0(xE, xH) = xP
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1930) implies:
% 108.34/15.56 | (28) aScalar0(xS)
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1967) implies:
% 108.34/15.56 | (29) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD)
% 108.34/15.56 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__1983) implies:
% 108.34/15.56 | (30) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xP, xP) = v0 & sdtpldt0(xR, xS)
% 108.34/15.56 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 108.34/15.56 |
% 108.34/15.56 | ALPHA: (m__) implies:
% 108.34/15.56 | (31) $i(xC)
% 108.34/15.56 | (32) $i(xD)
% 108.34/15.56 | (33) $i(xE)
% 108.34/15.56 | (34) $i(xH)
% 108.34/15.56 | (35) $i(xR)
% 108.34/15.56 | (36) $i(xP)
% 108.34/15.56 | (37) $i(xS)
% 108.34/15.56 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 108.34/15.56 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xH,
% 108.34/15.56 | xH) = v2 & sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) = v5 &
% 108.34/15.56 | sdtpldt0(v6, v2) = v7 & sdtpldt0(v5, v7) = v8 & sdtpldt0(v1, v2) =
% 108.34/15.56 | v3 & sdtpldt0(v0, v3) = v4 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xR,
% 108.34/15.56 | xS) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 108.34/15.56 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v4, v8))
% 108.34/15.56 |
% 108.34/15.57 | ALPHA: (function-axioms) implies:
% 108.34/15.57 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 108.34/15.57 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 108.34/15.57 | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 108.34/15.57 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 108.34/15.57 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 108.34/15.57 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 108.34/15.57 | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 108.34/15.57 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0))
% 108.34/15.57 |
% 108.34/15.57 | DELTA: instantiating (8) with fresh symbol all_33_0 gives:
% 108.34/15.57 | (43) ~ (all_33_0 = sz00) & aDimensionOf0(xs) = all_33_0 & $i(all_33_0)
% 108.51/15.57 |
% 108.51/15.57 | ALPHA: (43) implies:
% 108.51/15.57 | (44) ~ (all_33_0 = sz00)
% 108.51/15.57 | (45) aDimensionOf0(xs) = all_33_0
% 108.51/15.57 |
% 108.51/15.57 | DELTA: instantiating (7) with fresh symbol all_35_0 gives:
% 108.51/15.57 | (46) aDimensionOf0(xt) = all_35_0 & aDimensionOf0(xs) = all_35_0 &
% 108.51/15.57 | $i(all_35_0)
% 108.51/15.57 |
% 108.51/15.57 | ALPHA: (46) implies:
% 108.51/15.57 | (47) aDimensionOf0(xs) = all_35_0
% 108.51/15.57 | (48) aDimensionOf0(xt) = all_35_0
% 108.51/15.57 |
% 108.51/15.57 | DELTA: instantiating (14) with fresh symbol all_39_0 gives:
% 108.51/15.57 | (49) sdtlbdtrb0(xs, all_39_0) = xA & aDimensionOf0(xs) = all_39_0 &
% 108.51/15.57 | $i(all_39_0) & aScalar0(xA)
% 108.51/15.57 |
% 108.51/15.57 | ALPHA: (49) implies:
% 108.51/15.57 | (50) aDimensionOf0(xs) = all_39_0
% 108.51/15.57 |
% 108.51/15.57 | DELTA: instantiating (29) with fresh symbols all_41_0, all_41_1 gives:
% 108.51/15.57 | (51) sdtasdt0(xE, xE) = all_41_1 & sdtasdt0(xC, xD) = all_41_0 &
% 108.51/15.57 | $i(all_41_0) & $i(all_41_1) & sdtlseqdt0(all_41_1, all_41_0)
% 108.51/15.57 |
% 108.51/15.57 | ALPHA: (51) implies:
% 108.51/15.57 | (52) sdtasdt0(xC, xD) = all_41_0
% 108.51/15.57 | (53) sdtasdt0(xE, xE) = all_41_1
% 108.51/15.57 |
% 108.51/15.57 | DELTA: instantiating (30) with fresh symbols all_43_0, all_43_1 gives:
% 108.51/15.57 | (54) sdtpldt0(xP, xP) = all_43_1 & sdtpldt0(xR, xS) = all_43_0 &
% 108.51/15.57 | $i(all_43_0) & $i(all_43_1) & sdtlseqdt0(all_43_1, all_43_0)
% 108.51/15.57 |
% 108.51/15.57 | ALPHA: (54) implies:
% 108.51/15.57 | (55) sdtlseqdt0(all_43_1, all_43_0)
% 108.51/15.57 | (56) sdtpldt0(xR, xS) = all_43_0
% 108.51/15.57 | (57) sdtpldt0(xP, xP) = all_43_1
% 108.51/15.57 |
% 108.51/15.57 | DELTA: instantiating (38) with fresh symbols all_45_0, all_45_1, all_45_2,
% 108.51/15.57 | all_45_3, all_45_4, all_45_5, all_45_6, all_45_7, all_45_8 gives:
% 108.51/15.57 | (58) sdtasdt0(xH, xH) = all_45_6 & sdtasdt0(xE, xE) = all_45_8 &
% 108.51/15.57 | sdtasdt0(xC, xD) = all_45_3 & sdtpldt0(all_45_2, all_45_6) = all_45_1
% 108.51/15.57 | & sdtpldt0(all_45_3, all_45_1) = all_45_0 & sdtpldt0(all_45_7,
% 108.51/15.57 | all_45_6) = all_45_5 & sdtpldt0(all_45_8, all_45_5) = all_45_4 &
% 108.51/15.57 | sdtpldt0(xP, xP) = all_45_7 & sdtpldt0(xR, xS) = all_45_2 &
% 108.51/15.57 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2) & $i(all_45_3) &
% 108.51/15.57 | $i(all_45_4) & $i(all_45_5) & $i(all_45_6) & $i(all_45_7) &
% 108.51/15.57 | $i(all_45_8) & ~ sdtlseqdt0(all_45_4, all_45_0)
% 108.51/15.57 |
% 108.51/15.57 | ALPHA: (58) implies:
% 108.51/15.58 | (59) ~ sdtlseqdt0(all_45_4, all_45_0)
% 108.51/15.58 | (60) $i(all_45_3)
% 108.51/15.58 | (61) $i(all_45_2)
% 108.51/15.58 | (62) sdtpldt0(xR, xS) = all_45_2
% 108.51/15.58 | (63) sdtpldt0(xP, xP) = all_45_7
% 108.51/15.58 | (64) sdtpldt0(all_45_8, all_45_5) = all_45_4
% 108.51/15.58 | (65) sdtpldt0(all_45_7, all_45_6) = all_45_5
% 108.51/15.58 | (66) sdtpldt0(all_45_3, all_45_1) = all_45_0
% 108.51/15.58 | (67) sdtpldt0(all_45_2, all_45_6) = all_45_1
% 108.51/15.58 | (68) sdtasdt0(xC, xD) = all_45_3
% 108.51/15.58 | (69) sdtasdt0(xE, xE) = all_45_8
% 108.51/15.58 | (70) sdtasdt0(xH, xH) = all_45_6
% 108.51/15.58 |
% 108.51/15.58 | DELTA: instantiating (6) with fresh symbol all_47_0 gives:
% 108.51/15.58 | (71) aDimensionOf0(xs) = all_47_0 & $i(all_47_0) & ! [v0: $i] : ! [v1:
% 108.51/15.58 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 108.51/15.58 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 108.51/15.58 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 108.51/15.58 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 108.51/15.58 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 108.51/15.58 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 108.51/15.58 | iLess0(v5, all_47_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 108.51/15.58 | & $i(v6))))))
% 108.51/15.58 |
% 108.51/15.58 | ALPHA: (71) implies:
% 108.51/15.58 | (72) aDimensionOf0(xs) = all_47_0
% 108.51/15.58 | (73) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 108.51/15.58 | ( ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~
% 108.51/15.58 | (sdtasdt0(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) |
% 108.51/15.58 | ~ aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 108.51/15.58 | $i] : ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) &
% 108.51/15.58 | $i(v7) & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5)
% 108.51/15.58 | & ( ~ iLess0(v5, all_47_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) =
% 108.51/15.58 | v6 & $i(v6))))))
% 108.51/15.58 |
% 108.51/15.58 | GROUND_INST: instantiating (40) with all_43_0, all_45_2, xS, xR, simplifying
% 108.51/15.58 | with (56), (62) gives:
% 108.51/15.58 | (74) all_45_2 = all_43_0
% 108.51/15.58 |
% 108.51/15.58 | GROUND_INST: instantiating (40) with all_43_1, all_45_7, xP, xP, simplifying
% 108.51/15.58 | with (57), (63) gives:
% 108.51/15.58 | (75) all_45_7 = all_43_1
% 108.51/15.58 |
% 108.51/15.58 | GROUND_INST: instantiating (41) with all_41_0, all_45_3, xD, xC, simplifying
% 108.51/15.58 | with (52), (68) gives:
% 108.51/15.58 | (76) all_45_3 = all_41_0
% 108.51/15.58 |
% 108.51/15.58 | GROUND_INST: instantiating (41) with all_41_1, all_45_8, xE, xE, simplifying
% 108.51/15.58 | with (53), (69) gives:
% 108.51/15.58 | (77) all_45_8 = all_41_1
% 108.51/15.58 |
% 108.51/15.58 | GROUND_INST: instantiating (39) with all_35_0, all_39_0, xs, simplifying with
% 108.51/15.58 | (47), (50) gives:
% 108.51/15.58 | (78) all_39_0 = all_35_0
% 108.51/15.58 |
% 108.51/15.58 | GROUND_INST: instantiating (39) with all_39_0, all_47_0, xs, simplifying with
% 108.51/15.58 | (50), (72) gives:
% 108.51/15.58 | (79) all_47_0 = all_39_0
% 108.51/15.58 |
% 108.51/15.58 | GROUND_INST: instantiating (39) with all_33_0, all_47_0, xs, simplifying with
% 108.51/15.58 | (45), (72) gives:
% 108.51/15.59 | (80) all_47_0 = all_33_0
% 108.51/15.59 |
% 108.51/15.59 | COMBINE_EQS: (79), (80) imply:
% 108.51/15.59 | (81) all_39_0 = all_33_0
% 108.51/15.59 |
% 108.51/15.59 | SIMP: (81) implies:
% 108.51/15.59 | (82) all_39_0 = all_33_0
% 108.51/15.59 |
% 108.51/15.59 | COMBINE_EQS: (78), (82) imply:
% 108.51/15.59 | (83) all_35_0 = all_33_0
% 108.51/15.59 |
% 108.51/15.59 | REDUCE: (48), (83) imply:
% 108.51/15.59 | (84) aDimensionOf0(xt) = all_33_0
% 108.51/15.59 |
% 108.51/15.59 | REDUCE: (67), (74) imply:
% 108.51/15.59 | (85) sdtpldt0(all_43_0, all_45_6) = all_45_1
% 108.51/15.59 |
% 108.51/15.59 | REDUCE: (66), (76) imply:
% 108.51/15.59 | (86) sdtpldt0(all_41_0, all_45_1) = all_45_0
% 108.51/15.59 |
% 108.51/15.59 | REDUCE: (65), (75) imply:
% 108.51/15.59 | (87) sdtpldt0(all_43_1, all_45_6) = all_45_5
% 108.51/15.59 |
% 108.51/15.59 | REDUCE: (64), (77) imply:
% 108.51/15.59 | (88) sdtpldt0(all_41_1, all_45_5) = all_45_4
% 108.51/15.59 |
% 108.51/15.59 | REDUCE: (61), (74) imply:
% 108.51/15.59 | (89) $i(all_43_0)
% 108.51/15.59 |
% 108.51/15.59 | REDUCE: (60), (76) imply:
% 108.51/15.59 | (90) $i(all_41_0)
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (mSumSc) with xR, xS, all_43_0, simplifying with
% 108.51/15.59 | (25), (28), (35), (37), (56) gives:
% 108.51/15.59 | (91) aScalar0(all_43_0)
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (mSumSc) with xP, xP, all_43_1, simplifying with
% 108.51/15.59 | (26), (36), (57) gives:
% 108.51/15.59 | (92) aScalar0(all_43_1)
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (mMulSc) with xC, xD, all_41_0, simplifying with
% 108.51/15.59 | (16), (18), (31), (32), (52) gives:
% 108.51/15.59 | (93) aScalar0(all_41_0)
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (mMulSc) with xE, xE, all_41_1, simplifying with
% 108.51/15.59 | (20), (33), (53) gives:
% 108.51/15.59 | (94) aScalar0(all_41_1)
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (mDistr) with xE, xH, xH, xP, xP, all_43_1,
% 108.51/15.59 | simplifying with (20), (24), (27), (33), (34), (57) gives:
% 108.51/15.59 | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1,
% 108.51/15.59 | xH) = v2 & sdtasdt0(xH, xH) = v3 & sdtasdt0(xE, v0) = all_43_1 &
% 108.51/15.59 | sdtpldt0(xP, v3) = v2 & sdtpldt0(xH, xH) = v0 & sdtpldt0(xE, xH) =
% 108.51/15.59 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_43_1))
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (mMulSc) with xH, xH, all_45_6, simplifying with
% 108.51/15.59 | (24), (34), (70) gives:
% 108.51/15.59 | (96) aScalar0(all_45_6)
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (mDimNat) with xt, all_33_0, simplifying with (5),
% 108.51/15.59 | (15), (84) gives:
% 108.51/15.59 | (97) aNaturalNumber0(all_33_0)
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (3) with xs, xs, xp, xp, simplifying with (4),
% 108.51/15.59 | (10), (13) gives:
% 108.51/15.59 | (98) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 108.51/15.59 | aDimensionOf0(xp) = v2 & $i(v2)) | (aDimensionOf0(xs) = v1 &
% 108.51/15.59 | $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & aDimensionOf0(xs) = v0 &
% 108.51/15.59 | $i(v0)))))
% 108.51/15.59 |
% 108.51/15.59 | GROUND_INST: instantiating (2) with xs, xp, simplifying with (4), (10), (13)
% 108.51/15.59 | gives:
% 108.51/15.60 | (99) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1:
% 108.51/15.60 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) =
% 108.51/15.60 | v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp) |
% 108.51/15.60 | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 & $i(v3))) &
% 108.51/15.60 | ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~ (aDimensionOf0(v1) =
% 108.51/15.60 | v2) | ~ $i(v1) | ~ aVector0(v1) | ? [v3: $i] : ? [v4:
% 108.51/15.60 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) &
% 108.51/15.60 | sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs, v4) = v6 &
% 108.51/15.60 | $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( ~ (v3 = v0) &
% 108.51/15.60 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 108.51/15.60 | (aDimensionOf0(xp) = v1) | ~ $i(xp) | szszuzczcdt0(v1) = v0)
% 108.51/15.60 | & ! [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) |
% 108.51/15.60 | aVector0(xp)))))
% 108.51/15.60 |
% 108.51/15.60 | GROUND_INST: instantiating (3) with xt, xt, xq, xq, simplifying with (5),
% 108.51/15.60 | (12), (15) gives:
% 108.51/15.60 | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 108.51/15.60 | aDimensionOf0(xq) = v2 & $i(v2)) | (aDimensionOf0(xt) = v1 &
% 108.51/15.60 | $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & aDimensionOf0(xt) = v0 &
% 108.51/15.60 | $i(v0)))))
% 108.51/15.60 |
% 108.51/15.60 | GROUND_INST: instantiating (3) with xs, xt, xp, xq, simplifying with (4), (5),
% 108.51/15.60 | (10), (12), (13), (15) gives:
% 108.51/15.60 | (101) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 108.51/15.60 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) |
% 108.51/15.60 | (aDimensionOf0(xt) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) &
% 108.51/15.60 | aDimensionOf0(xs) = v0 & $i(v0)))))
% 108.51/15.60 |
% 108.51/15.60 | GROUND_INST: instantiating (3) with xt, xs, xq, xp, simplifying with (4), (5),
% 108.51/15.60 | (10), (12), (13), (15) gives:
% 108.51/15.60 | (102) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 108.51/15.60 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) |
% 108.51/15.60 | (aDimensionOf0(xs) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) &
% 108.51/15.60 | aDimensionOf0(xt) = v0 & $i(v0)))))
% 108.51/15.60 |
% 108.51/15.60 | GROUND_INST: instantiating (2) with xt, xq, simplifying with (5), (12), (15)
% 108.51/15.60 | gives:
% 108.51/15.60 | (103) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( !
% 108.51/15.60 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2)
% 108.51/15.60 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq)
% 108.51/15.60 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 &
% 108.51/15.60 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~
% 108.51/15.60 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ?
% 108.51/15.60 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4)
% 108.51/15.60 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt,
% 108.51/15.60 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | (
% 108.51/15.60 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & !
% 108.51/15.60 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) |
% 108.51/15.60 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq)
% 108.51/15.60 | = v1) | ~ $i(xq) | aVector0(xq)))))
% 108.51/15.60 |
% 108.51/15.60 | GROUND_INST: instantiating (73) with xp, xq, xC, xD, all_41_0, simplifying
% 108.51/15.60 | with (9), (11), (17), (19), (21), (22), (52) gives:
% 108.51/15.60 | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 108.51/15.60 | ((sdtasasdt0(xp, xq) = v2 & sdtasdt0(v2, v2) = v3 & $i(v3) & $i(v2) &
% 108.51/15.60 | sdtlseqdt0(v3, all_41_0)) | (aDimensionOf0(xp) = v0 & $i(v0) & (
% 108.51/15.60 | ~ iLess0(v0, all_47_0) | ( ~ (v1 = v0) & aDimensionOf0(xq) = v1
% 108.51/15.60 | & $i(v1)))))
% 108.51/15.60 |
% 108.51/15.60 | DELTA: instantiating (98) with fresh symbols all_63_0, all_63_1, all_63_2,
% 108.51/15.60 | all_63_3 gives:
% 108.51/15.61 | (105) (all_63_0 = all_63_1 & aDimensionOf0(xp) = all_63_1 & $i(all_63_1)) |
% 108.51/15.61 | (aDimensionOf0(xs) = all_63_2 & $i(all_63_2) & (all_63_2 = sz00 | ( ~
% 108.51/15.61 | (all_63_2 = all_63_3) & aDimensionOf0(xs) = all_63_3 &
% 108.51/15.61 | $i(all_63_3))))
% 108.51/15.61 |
% 108.51/15.61 | DELTA: instantiating (100) with fresh symbols all_64_0, all_64_1, all_64_2,
% 108.51/15.61 | all_64_3 gives:
% 108.51/15.61 | (106) (all_64_0 = all_64_1 & aDimensionOf0(xq) = all_64_1 & $i(all_64_1)) |
% 108.51/15.61 | (aDimensionOf0(xt) = all_64_2 & $i(all_64_2) & (all_64_2 = sz00 | ( ~
% 108.51/15.61 | (all_64_2 = all_64_3) & aDimensionOf0(xt) = all_64_3 &
% 108.51/15.61 | $i(all_64_3))))
% 108.51/15.61 |
% 108.51/15.61 | DELTA: instantiating (102) with fresh symbols all_65_0, all_65_1, all_65_2,
% 108.51/15.61 | all_65_3 gives:
% 108.51/15.61 | (107) (all_65_0 = all_65_1 & aDimensionOf0(xq) = all_65_1 &
% 108.51/15.61 | aDimensionOf0(xp) = all_65_1 & $i(all_65_1)) | (aDimensionOf0(xs) =
% 108.51/15.61 | all_65_2 & $i(all_65_2) & (all_65_2 = sz00 | ( ~ (all_65_2 =
% 108.51/15.61 | all_65_3) & aDimensionOf0(xt) = all_65_3 & $i(all_65_3))))
% 108.51/15.61 |
% 108.51/15.61 | DELTA: instantiating (101) with fresh symbols all_66_0, all_66_1, all_66_2,
% 108.51/15.61 | all_66_3 gives:
% 108.51/15.61 | (108) (all_66_0 = all_66_1 & aDimensionOf0(xq) = all_66_1 &
% 108.51/15.61 | aDimensionOf0(xp) = all_66_1 & $i(all_66_1)) | (aDimensionOf0(xt) =
% 108.51/15.61 | all_66_2 & $i(all_66_2) & (all_66_2 = sz00 | ( ~ (all_66_2 =
% 108.51/15.61 | all_66_3) & aDimensionOf0(xs) = all_66_3 & $i(all_66_3))))
% 108.51/15.61 |
% 108.51/15.61 | DELTA: instantiating (104) with fresh symbols all_67_0, all_67_1, all_67_2,
% 108.51/15.61 | all_67_3 gives:
% 108.51/15.61 | (109) (sdtasasdt0(xp, xq) = all_67_1 & sdtasdt0(all_67_1, all_67_1) =
% 108.51/15.61 | all_67_0 & $i(all_67_0) & $i(all_67_1) & sdtlseqdt0(all_67_0,
% 108.51/15.61 | all_41_0)) | (aDimensionOf0(xp) = all_67_3 & $i(all_67_3) & ( ~
% 108.51/15.61 | iLess0(all_67_3, all_47_0) | ( ~ (all_67_2 = all_67_3) &
% 108.51/15.61 | aDimensionOf0(xq) = all_67_2 & $i(all_67_2))))
% 108.51/15.61 |
% 108.51/15.61 | DELTA: instantiating (95) with fresh symbols all_68_0, all_68_1, all_68_2,
% 108.51/15.61 | all_68_3 gives:
% 108.51/15.61 | (110) sdtasdt0(all_68_2, xH) = all_68_1 & sdtasdt0(xH, xH) = all_68_0 &
% 108.51/15.61 | sdtasdt0(xE, all_68_3) = all_43_1 & sdtpldt0(xP, all_68_0) = all_68_1
% 108.51/15.61 | & sdtpldt0(xH, xH) = all_68_3 & sdtpldt0(xE, xH) = all_68_2 &
% 108.51/15.61 | $i(all_68_0) & $i(all_68_1) & $i(all_68_2) & $i(all_68_3) &
% 108.51/15.61 | $i(all_43_1)
% 108.51/15.61 |
% 108.51/15.61 | ALPHA: (110) implies:
% 108.51/15.61 | (111) $i(all_43_1)
% 108.51/15.61 | (112) $i(all_68_0)
% 108.51/15.61 | (113) sdtasdt0(xH, xH) = all_68_0
% 108.51/15.61 |
% 108.51/15.61 | DELTA: instantiating (99) with fresh symbol all_70_0 gives:
% 108.51/15.61 | (114) aDimensionOf0(xs) = all_70_0 & $i(all_70_0) & (all_70_0 = sz00 | ( !
% 108.51/15.61 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) =
% 108.51/15.61 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) |
% 108.51/15.61 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) &
% 108.51/15.61 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1)
% 108.51/15.61 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 108.51/15.61 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 108.51/15.61 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 &
% 108.51/15.61 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 108.51/15.61 | all_70_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 108.51/15.61 | [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) |
% 108.51/15.61 | szszuzczcdt0(v0) = all_70_0) & ! [v0: $i] : ( ~
% 108.51/15.61 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | aVector0(xp))))
% 108.51/15.61 |
% 108.51/15.61 | ALPHA: (114) implies:
% 108.51/15.61 | (115) $i(all_70_0)
% 108.51/15.61 | (116) aDimensionOf0(xs) = all_70_0
% 108.51/15.62 | (117) all_70_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 108.51/15.62 | (sdtlbdtrb0(xs, v1) = v2) | ~ (aDimensionOf0(xp) = v0) | ~
% 108.51/15.62 | $i(v1) | ~ $i(xp) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1)
% 108.51/15.62 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~
% 108.51/15.62 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 108.51/15.62 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 108.51/15.62 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) =
% 108.51/15.62 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 108.51/15.62 | all_70_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 108.51/15.62 | $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) | szszuzczcdt0(v0)
% 108.51/15.62 | = all_70_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~
% 108.51/15.62 | $i(xp) | aVector0(xp)))
% 108.51/15.62 |
% 108.51/15.62 | DELTA: instantiating (103) with fresh symbol all_72_0 gives:
% 108.51/15.62 | (118) aDimensionOf0(xt) = all_72_0 & $i(all_72_0) & (all_72_0 = sz00 | ( !
% 108.51/15.62 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 108.51/15.62 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) |
% 108.51/15.62 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) &
% 108.51/15.62 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1)
% 108.51/15.62 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 108.51/15.62 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 108.51/15.62 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 &
% 108.51/15.62 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 108.51/15.62 | all_72_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 108.51/15.62 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) |
% 108.51/15.62 | szszuzczcdt0(v0) = all_72_0) & ! [v0: $i] : ( ~
% 108.51/15.62 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq))))
% 108.51/15.62 |
% 108.51/15.62 | ALPHA: (118) implies:
% 108.51/15.62 | (119) aDimensionOf0(xt) = all_72_0
% 108.51/15.62 |
% 108.51/15.62 | GROUND_INST: instantiating (41) with all_45_6, all_68_0, xH, xH, simplifying
% 108.51/15.62 | with (70), (113) gives:
% 108.51/15.62 | (120) all_68_0 = all_45_6
% 108.51/15.62 |
% 108.51/15.62 | GROUND_INST: instantiating (39) with all_33_0, all_70_0, xs, simplifying with
% 108.51/15.62 | (45), (116) gives:
% 108.51/15.62 | (121) all_70_0 = all_33_0
% 108.51/15.62 |
% 108.51/15.62 | GROUND_INST: instantiating (39) with all_33_0, all_72_0, xt, simplifying with
% 108.51/15.62 | (84), (119) gives:
% 108.51/15.62 | (122) all_72_0 = all_33_0
% 108.51/15.62 |
% 108.51/15.62 | REDUCE: (115), (121) imply:
% 108.51/15.62 | (123) $i(all_33_0)
% 108.51/15.62 |
% 108.51/15.62 | REDUCE: (112), (120) imply:
% 108.51/15.62 | (124) $i(all_45_6)
% 108.51/15.62 |
% 108.51/15.62 | BETA: splitting (106) gives:
% 108.51/15.62 |
% 108.51/15.62 | Case 1:
% 108.51/15.62 | |
% 108.51/15.62 | | (125) all_64_0 = all_64_1 & aDimensionOf0(xq) = all_64_1 & $i(all_64_1)
% 108.51/15.62 | |
% 108.51/15.62 | | ALPHA: (125) implies:
% 108.51/15.62 | | (126) $i(all_64_1)
% 108.51/15.62 | | (127) aDimensionOf0(xq) = all_64_1
% 108.51/15.62 | |
% 108.51/15.62 | | BETA: splitting (105) gives:
% 108.51/15.62 | |
% 108.51/15.62 | | Case 1:
% 108.51/15.62 | | |
% 108.51/15.62 | | | (128) all_63_0 = all_63_1 & aDimensionOf0(xp) = all_63_1 & $i(all_63_1)
% 108.51/15.62 | | |
% 108.51/15.62 | | | ALPHA: (128) implies:
% 108.51/15.62 | | | (129) aDimensionOf0(xp) = all_63_1
% 108.51/15.62 | | |
% 108.51/15.62 | | | BETA: splitting (117) gives:
% 108.51/15.62 | | |
% 108.51/15.62 | | | Case 1:
% 108.51/15.62 | | | |
% 108.51/15.62 | | | | (130) all_70_0 = sz00
% 108.51/15.62 | | | |
% 108.51/15.62 | | | | COMBINE_EQS: (121), (130) imply:
% 108.51/15.62 | | | | (131) all_33_0 = sz00
% 108.51/15.62 | | | |
% 108.51/15.62 | | | | REDUCE: (44), (131) imply:
% 108.51/15.62 | | | | (132) $false
% 108.51/15.62 | | | |
% 108.51/15.62 | | | | CLOSE: (132) is inconsistent.
% 108.51/15.62 | | | |
% 108.51/15.62 | | | Case 2:
% 108.51/15.62 | | | |
% 108.51/15.62 | | | | (133) ~ (all_70_0 = sz00)
% 108.51/15.63 | | | | (134) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs,
% 108.51/15.63 | | | | v1) = v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~
% 108.51/15.63 | | | | $i(xp) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 &
% 108.51/15.63 | | | | $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~
% 108.51/15.63 | | | | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ?
% 108.51/15.63 | | | | [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3)
% 108.51/15.63 | | | | & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs,
% 108.51/15.63 | | | | v3) = v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | (
% 108.51/15.63 | | | | ~ (v2 = all_70_0) & szszuzczcdt0(v1) = v2 & $i(v2)))))
% 108.51/15.63 | | | | & ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) |
% 108.51/15.63 | | | | szszuzczcdt0(v0) = all_70_0) & ! [v0: $i] : ( ~
% 108.51/15.63 | | | | (aDimensionOf0(xp) = v0) | ~ $i(xp) | aVector0(xp))
% 108.51/15.63 | | | |
% 108.51/15.63 | | | | ALPHA: (134) implies:
% 108.51/15.63 | | | | (135) ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) |
% 108.51/15.63 | | | | szszuzczcdt0(v0) = all_70_0)
% 108.51/15.63 | | | |
% 108.51/15.63 | | | | BETA: splitting (108) gives:
% 108.51/15.63 | | | |
% 108.51/15.63 | | | | Case 1:
% 108.51/15.63 | | | | |
% 108.51/15.63 | | | | | (136) all_66_0 = all_66_1 & aDimensionOf0(xq) = all_66_1 &
% 108.51/15.63 | | | | | aDimensionOf0(xp) = all_66_1 & $i(all_66_1)
% 108.51/15.63 | | | | |
% 108.51/15.63 | | | | | ALPHA: (136) implies:
% 108.51/15.63 | | | | | (137) aDimensionOf0(xq) = all_66_1
% 108.51/15.63 | | | | |
% 108.51/15.63 | | | | | BETA: splitting (107) gives:
% 108.51/15.63 | | | | |
% 108.51/15.63 | | | | | Case 1:
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | (138) all_65_0 = all_65_1 & aDimensionOf0(xq) = all_65_1 &
% 108.51/15.63 | | | | | | aDimensionOf0(xp) = all_65_1 & $i(all_65_1)
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | ALPHA: (138) implies:
% 108.51/15.63 | | | | | | (139) aDimensionOf0(xp) = all_65_1
% 108.51/15.63 | | | | | | (140) aDimensionOf0(xq) = all_65_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | GROUND_INST: instantiating (39) with all_63_1, all_65_1, xp,
% 108.51/15.63 | | | | | | simplifying with (129), (139) gives:
% 108.51/15.63 | | | | | | (141) all_65_1 = all_63_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | GROUND_INST: instantiating (39) with all_65_1, all_66_1, xq,
% 108.51/15.63 | | | | | | simplifying with (137), (140) gives:
% 108.51/15.63 | | | | | | (142) all_66_1 = all_65_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | GROUND_INST: instantiating (39) with all_64_1, all_66_1, xq,
% 108.51/15.63 | | | | | | simplifying with (127), (137) gives:
% 108.51/15.63 | | | | | | (143) all_66_1 = all_64_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | COMBINE_EQS: (142), (143) imply:
% 108.51/15.63 | | | | | | (144) all_65_1 = all_64_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | SIMP: (144) implies:
% 108.51/15.63 | | | | | | (145) all_65_1 = all_64_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | COMBINE_EQS: (141), (145) imply:
% 108.51/15.63 | | | | | | (146) all_64_1 = all_63_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | SIMP: (146) implies:
% 108.51/15.63 | | | | | | (147) all_64_1 = all_63_1
% 108.51/15.63 | | | | | |
% 108.51/15.63 | | | | | | REDUCE: (127), (147) imply:
% 108.79/15.63 | | | | | | (148) aDimensionOf0(xq) = all_63_1
% 108.79/15.63 | | | | | |
% 108.79/15.63 | | | | | | REDUCE: (126), (147) imply:
% 108.79/15.63 | | | | | | (149) $i(all_63_1)
% 108.79/15.63 | | | | | |
% 108.79/15.63 | | | | | | GROUND_INST: instantiating (1) with all_33_0, simplifying with (97),
% 108.79/15.63 | | | | | | (123) gives:
% 108.79/15.63 | | | | | | (150) all_33_0 = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) =
% 108.79/15.63 | | | | | | all_33_0 & $i(v0) & aNaturalNumber0(v0))
% 108.79/15.63 | | | | | |
% 108.79/15.63 | | | | | | GROUND_INST: instantiating (mArith) with xR, xS, all_45_6, all_43_0,
% 108.79/15.63 | | | | | | all_45_1, simplifying with (25), (28), (35), (37),
% 108.79/15.63 | | | | | | (56), (85), (96), (124) gives:
% 108.79/15.63 | | | | | | (151) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 108.79/15.63 | | | | | | (sdtasdt0(v1, all_45_6) = v2 & sdtasdt0(xS, all_45_6) = v3
% 108.79/15.63 | | | | | | & sdtasdt0(xS, xR) = v1 & sdtasdt0(xR, v3) = v2 &
% 108.79/15.63 | | | | | | sdtasdt0(xR, xS) = v1 & sdtpldt0(xS, all_45_6) = v0 &
% 108.79/15.63 | | | | | | sdtpldt0(xS, xR) = all_43_0 & sdtpldt0(xR, v0) = all_45_1
% 108.79/15.63 | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_45_1) &
% 108.79/15.63 | | | | | | $i(all_43_0))
% 108.79/15.63 | | | | | |
% 108.79/15.63 | | | | | | GROUND_INST: instantiating (mSumSc) with all_43_0, all_45_6,
% 108.79/15.63 | | | | | | all_45_1, simplifying with (85), (89), (91), (96),
% 108.79/15.63 | | | | | | (124) gives:
% 108.79/15.63 | | | | | | (152) aScalar0(all_45_1)
% 108.79/15.63 | | | | | |
% 108.79/15.63 | | | | | | GROUND_INST: instantiating (mArith) with xP, xP, all_45_6, all_43_1,
% 108.79/15.63 | | | | | | all_45_5, simplifying with (26), (36), (57), (87),
% 108.79/15.63 | | | | | | (96), (124) gives:
% 108.79/15.64 | | | | | | (153) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 108.79/15.64 | | | | | | (sdtasdt0(v1, all_45_6) = v2 & sdtasdt0(xP, v3) = v2 &
% 108.79/15.64 | | | | | | sdtasdt0(xP, all_45_6) = v3 & sdtasdt0(xP, xP) = v1 &
% 108.79/15.64 | | | | | | sdtpldt0(xP, v0) = all_45_5 & sdtpldt0(xP, all_45_6) = v0
% 108.79/15.64 | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_45_5) &
% 108.79/15.64 | | | | | | $i(all_43_1))
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | GROUND_INST: instantiating (mSumSc) with all_43_1, all_45_6,
% 108.79/15.64 | | | | | | all_45_5, simplifying with (87), (92), (96), (111),
% 108.79/15.64 | | | | | | (124) gives:
% 108.79/15.64 | | | | | | (154) aScalar0(all_45_5)
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | GROUND_INST: instantiating (mLETot) with all_45_6, all_45_6,
% 108.79/15.64 | | | | | | simplifying with (96), (124) gives:
% 108.79/15.64 | | | | | | (155) sdtlseqdt0(all_45_6, all_45_6)
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | GROUND_INST: instantiating (135) with all_63_1, simplifying with
% 108.79/15.64 | | | | | | (21), (129) gives:
% 108.79/15.64 | | | | | | (156) szszuzczcdt0(all_63_1) = all_70_0
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | GROUND_INST: instantiating (mDimNat) with xq, all_63_1, simplifying
% 108.79/15.64 | | | | | | with (11), (22), (148) gives:
% 108.79/15.64 | | | | | | (157) aNaturalNumber0(all_63_1)
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | DELTA: instantiating (153) with fresh symbols all_116_0, all_116_1,
% 108.79/15.64 | | | | | | all_116_2, all_116_3 gives:
% 108.79/15.64 | | | | | | (158) sdtasdt0(all_116_2, all_45_6) = all_116_1 & sdtasdt0(xP,
% 108.79/15.64 | | | | | | all_116_0) = all_116_1 & sdtasdt0(xP, all_45_6) =
% 108.79/15.64 | | | | | | all_116_0 & sdtasdt0(xP, xP) = all_116_2 & sdtpldt0(xP,
% 108.79/15.64 | | | | | | all_116_3) = all_45_5 & sdtpldt0(xP, all_45_6) =
% 108.79/15.64 | | | | | | all_116_3 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) &
% 108.79/15.64 | | | | | | $i(all_116_3) & $i(all_45_5) & $i(all_43_1)
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | ALPHA: (158) implies:
% 108.79/15.64 | | | | | | (159) $i(all_45_5)
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | DELTA: instantiating (151) with fresh symbols all_118_0, all_118_1,
% 108.79/15.64 | | | | | | all_118_2, all_118_3 gives:
% 108.79/15.64 | | | | | | (160) sdtasdt0(all_118_2, all_45_6) = all_118_1 & sdtasdt0(xS,
% 108.79/15.64 | | | | | | all_45_6) = all_118_0 & sdtasdt0(xS, xR) = all_118_2 &
% 108.79/15.64 | | | | | | sdtasdt0(xR, all_118_0) = all_118_1 & sdtasdt0(xR, xS) =
% 108.79/15.64 | | | | | | all_118_2 & sdtpldt0(xS, all_45_6) = all_118_3 &
% 108.79/15.64 | | | | | | sdtpldt0(xS, xR) = all_43_0 & sdtpldt0(xR, all_118_3) =
% 108.79/15.64 | | | | | | all_45_1 & $i(all_118_0) & $i(all_118_1) & $i(all_118_2) &
% 108.79/15.64 | | | | | | $i(all_118_3) & $i(all_45_1) & $i(all_43_0)
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | ALPHA: (160) implies:
% 108.79/15.64 | | | | | | (161) sdtpldt0(xS, xR) = all_43_0
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | REDUCE: (121), (156) imply:
% 108.79/15.64 | | | | | | (162) szszuzczcdt0(all_63_1) = all_33_0
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | BETA: splitting (150) gives:
% 108.79/15.64 | | | | | |
% 108.79/15.64 | | | | | | Case 1:
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | (163) all_33_0 = sz00
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | REDUCE: (44), (163) imply:
% 108.79/15.64 | | | | | | | (164) $false
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | CLOSE: (164) is inconsistent.
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | Case 2:
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | (165) ? [v0: $i] : (szszuzczcdt0(v0) = all_33_0 & $i(v0) &
% 108.79/15.64 | | | | | | | aNaturalNumber0(v0))
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | DELTA: instantiating (165) with fresh symbol all_127_0 gives:
% 108.79/15.64 | | | | | | | (166) szszuzczcdt0(all_127_0) = all_33_0 & $i(all_127_0) &
% 108.79/15.64 | | | | | | | aNaturalNumber0(all_127_0)
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | ALPHA: (166) implies:
% 108.79/15.64 | | | | | | | (167) aNaturalNumber0(all_127_0)
% 108.79/15.64 | | | | | | | (168) $i(all_127_0)
% 108.79/15.64 | | | | | | | (169) szszuzczcdt0(all_127_0) = all_33_0
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | GROUND_INST: instantiating (mLEMon) with all_43_1, all_43_0,
% 108.79/15.64 | | | | | | | all_45_6, all_45_6, all_45_5, all_45_1, simplifying
% 108.79/15.64 | | | | | | | with (55), (85), (87), (89), (91), (92), (96), (111),
% 108.79/15.64 | | | | | | | (124), (155) gives:
% 108.79/15.64 | | | | | | | (170) sdtlseqdt0(all_45_5, all_45_1)
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | GROUND_INST: instantiating (mSuccEqu) with all_63_1, all_127_0,
% 108.79/15.64 | | | | | | | all_33_0, simplifying with (149), (157), (162),
% 108.79/15.64 | | | | | | | (167), (168), (169) gives:
% 108.79/15.64 | | | | | | | (171) all_127_0 = all_63_1
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | GROUND_INST: instantiating (mIH) with all_127_0, all_33_0,
% 108.79/15.64 | | | | | | | simplifying with (167), (168), (169) gives:
% 108.79/15.64 | | | | | | | (172) iLess0(all_127_0, all_33_0)
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | GROUND_INST: instantiating (mArith) with xS, xR, all_45_6,
% 108.79/15.64 | | | | | | | all_43_0, all_45_1, simplifying with (25), (28),
% 108.79/15.64 | | | | | | | (35), (37), (85), (96), (124), (161) gives:
% 108.79/15.64 | | | | | | | (173) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 108.79/15.64 | | | | | | | (sdtasdt0(v1, all_45_6) = v2 & sdtasdt0(xS, v3) = v2 &
% 108.79/15.64 | | | | | | | sdtasdt0(xS, xR) = v1 & sdtasdt0(xR, all_45_6) = v3 &
% 108.79/15.64 | | | | | | | sdtasdt0(xR, xS) = v1 & sdtpldt0(xS, v0) = all_45_1 &
% 108.79/15.64 | | | | | | | sdtpldt0(xR, all_45_6) = v0 & sdtpldt0(xR, xS) =
% 108.79/15.64 | | | | | | | all_43_0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 108.79/15.64 | | | | | | | $i(all_45_1) & $i(all_43_0))
% 108.79/15.64 | | | | | | |
% 108.79/15.64 | | | | | | | DELTA: instantiating (173) with fresh symbols all_139_0,
% 108.79/15.64 | | | | | | | all_139_1, all_139_2, all_139_3 gives:
% 108.79/15.65 | | | | | | | (174) sdtasdt0(all_139_2, all_45_6) = all_139_1 & sdtasdt0(xS,
% 108.79/15.65 | | | | | | | all_139_0) = all_139_1 & sdtasdt0(xS, xR) = all_139_2 &
% 108.79/15.65 | | | | | | | sdtasdt0(xR, all_45_6) = all_139_0 & sdtasdt0(xR, xS) =
% 108.79/15.65 | | | | | | | all_139_2 & sdtpldt0(xS, all_139_3) = all_45_1 &
% 108.79/15.65 | | | | | | | sdtpldt0(xR, all_45_6) = all_139_3 & sdtpldt0(xR, xS) =
% 108.79/15.65 | | | | | | | all_43_0 & $i(all_139_0) & $i(all_139_1) & $i(all_139_2)
% 108.79/15.65 | | | | | | | & $i(all_139_3) & $i(all_45_1) & $i(all_43_0)
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | ALPHA: (174) implies:
% 108.79/15.65 | | | | | | | (175) $i(all_45_1)
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | REDUCE: (171), (172) imply:
% 108.79/15.65 | | | | | | | (176) iLess0(all_63_1, all_33_0)
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | BETA: splitting (109) gives:
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | Case 1:
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | (177) sdtasasdt0(xp, xq) = all_67_1 & sdtasdt0(all_67_1,
% 108.79/15.65 | | | | | | | | all_67_1) = all_67_0 & $i(all_67_0) & $i(all_67_1) &
% 108.79/15.65 | | | | | | | | sdtlseqdt0(all_67_0, all_41_0)
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | ALPHA: (177) implies:
% 108.79/15.65 | | | | | | | | (178) sdtlseqdt0(all_67_0, all_41_0)
% 108.79/15.65 | | | | | | | | (179) $i(all_67_0)
% 108.79/15.65 | | | | | | | | (180) sdtasdt0(all_67_1, all_67_1) = all_67_0
% 108.79/15.65 | | | | | | | | (181) sdtasasdt0(xp, xq) = all_67_1
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | GROUND_INST: instantiating (42) with xE, all_67_1, xq, xp,
% 108.79/15.65 | | | | | | | | simplifying with (23), (181) gives:
% 108.79/15.65 | | | | | | | | (182) all_67_1 = xE
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | REDUCE: (180), (182) imply:
% 108.79/15.65 | | | | | | | | (183) sdtasdt0(xE, xE) = all_67_0
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | GROUND_INST: instantiating (41) with all_41_1, all_67_0, xE, xE,
% 108.79/15.65 | | | | | | | | simplifying with (53), (183) gives:
% 108.79/15.65 | | | | | | | | (184) all_67_0 = all_41_1
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | REDUCE: (179), (184) imply:
% 108.79/15.65 | | | | | | | | (185) $i(all_41_1)
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | REDUCE: (178), (184) imply:
% 108.79/15.65 | | | | | | | | (186) sdtlseqdt0(all_41_1, all_41_0)
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | GROUND_INST: instantiating (mLEMon) with all_41_1, all_41_0,
% 108.79/15.65 | | | | | | | | all_45_5, all_45_1, all_45_4, all_45_0, simplifying
% 108.79/15.65 | | | | | | | | with (59), (86), (88), (90), (93), (94), (152),
% 108.79/15.65 | | | | | | | | (154), (159), (170), (175), (185), (186) gives:
% 108.79/15.65 | | | | | | | | (187) $false
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | CLOSE: (187) is inconsistent.
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | Case 2:
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | (188) aDimensionOf0(xp) = all_67_3 & $i(all_67_3) & ( ~
% 108.79/15.65 | | | | | | | | iLess0(all_67_3, all_47_0) | ( ~ (all_67_2 =
% 108.79/15.65 | | | | | | | | all_67_3) & aDimensionOf0(xq) = all_67_2 &
% 108.79/15.65 | | | | | | | | $i(all_67_2)))
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | ALPHA: (188) implies:
% 108.79/15.65 | | | | | | | | (189) aDimensionOf0(xp) = all_67_3
% 108.79/15.65 | | | | | | | | (190) ~ iLess0(all_67_3, all_47_0) | ( ~ (all_67_2 =
% 108.79/15.65 | | | | | | | | all_67_3) & aDimensionOf0(xq) = all_67_2 &
% 108.79/15.65 | | | | | | | | $i(all_67_2))
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | GROUND_INST: instantiating (39) with all_63_1, all_67_3, xp,
% 108.79/15.65 | | | | | | | | simplifying with (129), (189) gives:
% 108.79/15.65 | | | | | | | | (191) all_67_3 = all_63_1
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | BETA: splitting (190) gives:
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | | Case 1:
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | (192) ~ iLess0(all_67_3, all_47_0)
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | REDUCE: (80), (191), (192) imply:
% 108.79/15.65 | | | | | | | | | (193) ~ iLess0(all_63_1, all_33_0)
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | PRED_UNIFY: (176), (193) imply:
% 108.79/15.65 | | | | | | | | | (194) $false
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | CLOSE: (194) is inconsistent.
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | Case 2:
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | (195) ~ (all_67_2 = all_67_3) & aDimensionOf0(xq) =
% 108.79/15.65 | | | | | | | | | all_67_2 & $i(all_67_2)
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | ALPHA: (195) implies:
% 108.79/15.65 | | | | | | | | | (196) ~ (all_67_2 = all_67_3)
% 108.79/15.65 | | | | | | | | | (197) aDimensionOf0(xq) = all_67_2
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | REDUCE: (191), (196) imply:
% 108.79/15.65 | | | | | | | | | (198) ~ (all_67_2 = all_63_1)
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | GROUND_INST: instantiating (39) with all_63_1, all_67_2, xq,
% 108.79/15.65 | | | | | | | | | simplifying with (148), (197) gives:
% 108.79/15.65 | | | | | | | | | (199) all_67_2 = all_63_1
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | REDUCE: (198), (199) imply:
% 108.79/15.65 | | | | | | | | | (200) $false
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | | CLOSE: (200) is inconsistent.
% 108.79/15.65 | | | | | | | | |
% 108.79/15.65 | | | | | | | | End of split
% 108.79/15.65 | | | | | | | |
% 108.79/15.65 | | | | | | | End of split
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | End of split
% 108.79/15.65 | | | | | |
% 108.79/15.65 | | | | | Case 2:
% 108.79/15.65 | | | | | |
% 108.79/15.65 | | | | | | (201) aDimensionOf0(xs) = all_65_2 & $i(all_65_2) & (all_65_2 =
% 108.79/15.65 | | | | | | sz00 | ( ~ (all_65_2 = all_65_3) & aDimensionOf0(xt) =
% 108.79/15.65 | | | | | | all_65_3 & $i(all_65_3)))
% 108.79/15.65 | | | | | |
% 108.79/15.65 | | | | | | ALPHA: (201) implies:
% 108.79/15.65 | | | | | | (202) aDimensionOf0(xs) = all_65_2
% 108.79/15.65 | | | | | | (203) all_65_2 = sz00 | ( ~ (all_65_2 = all_65_3) &
% 108.79/15.65 | | | | | | aDimensionOf0(xt) = all_65_3 & $i(all_65_3))
% 108.79/15.65 | | | | | |
% 108.79/15.65 | | | | | | GROUND_INST: instantiating (39) with all_33_0, all_65_2, xs,
% 108.79/15.65 | | | | | | simplifying with (45), (202) gives:
% 108.79/15.65 | | | | | | (204) all_65_2 = all_33_0
% 108.79/15.65 | | | | | |
% 108.79/15.65 | | | | | | BETA: splitting (203) gives:
% 108.79/15.65 | | | | | |
% 108.79/15.65 | | | | | | Case 1:
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | (205) all_65_2 = sz00
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | COMBINE_EQS: (204), (205) imply:
% 108.79/15.65 | | | | | | | (206) all_33_0 = sz00
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | SIMP: (206) implies:
% 108.79/15.65 | | | | | | | (207) all_33_0 = sz00
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | REDUCE: (44), (207) imply:
% 108.79/15.65 | | | | | | | (208) $false
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | | CLOSE: (208) is inconsistent.
% 108.79/15.65 | | | | | | |
% 108.79/15.65 | | | | | | Case 2:
% 108.79/15.65 | | | | | | |
% 108.79/15.66 | | | | | | | (209) ~ (all_65_2 = all_65_3) & aDimensionOf0(xt) = all_65_3 &
% 108.79/15.66 | | | | | | | $i(all_65_3)
% 108.79/15.66 | | | | | | |
% 108.79/15.66 | | | | | | | ALPHA: (209) implies:
% 108.79/15.66 | | | | | | | (210) ~ (all_65_2 = all_65_3)
% 108.79/15.66 | | | | | | | (211) aDimensionOf0(xt) = all_65_3
% 108.79/15.66 | | | | | | |
% 108.79/15.66 | | | | | | | REDUCE: (204), (210) imply:
% 108.79/15.66 | | | | | | | (212) ~ (all_65_3 = all_33_0)
% 108.79/15.66 | | | | | | |
% 108.79/15.66 | | | | | | | SIMP: (212) implies:
% 108.79/15.66 | | | | | | | (213) ~ (all_65_3 = all_33_0)
% 108.79/15.66 | | | | | | |
% 108.79/15.66 | | | | | | | GROUND_INST: instantiating (39) with all_33_0, all_65_3, xt,
% 108.79/15.66 | | | | | | | simplifying with (84), (211) gives:
% 108.79/15.66 | | | | | | | (214) all_65_3 = all_33_0
% 108.79/15.66 | | | | | | |
% 108.79/15.66 | | | | | | | REDUCE: (213), (214) imply:
% 108.79/15.66 | | | | | | | (215) $false
% 108.79/15.66 | | | | | | |
% 108.79/15.66 | | | | | | | CLOSE: (215) is inconsistent.
% 108.79/15.66 | | | | | | |
% 108.79/15.66 | | | | | | End of split
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | End of split
% 108.79/15.66 | | | | |
% 108.79/15.66 | | | | Case 2:
% 108.79/15.66 | | | | |
% 108.79/15.66 | | | | | (216) aDimensionOf0(xt) = all_66_2 & $i(all_66_2) & (all_66_2 =
% 108.79/15.66 | | | | | sz00 | ( ~ (all_66_2 = all_66_3) & aDimensionOf0(xs) =
% 108.79/15.66 | | | | | all_66_3 & $i(all_66_3)))
% 108.79/15.66 | | | | |
% 108.79/15.66 | | | | | ALPHA: (216) implies:
% 108.79/15.66 | | | | | (217) aDimensionOf0(xt) = all_66_2
% 108.79/15.66 | | | | | (218) all_66_2 = sz00 | ( ~ (all_66_2 = all_66_3) &
% 108.79/15.66 | | | | | aDimensionOf0(xs) = all_66_3 & $i(all_66_3))
% 108.79/15.66 | | | | |
% 108.79/15.66 | | | | | GROUND_INST: instantiating (39) with all_33_0, all_66_2, xt,
% 108.79/15.66 | | | | | simplifying with (84), (217) gives:
% 108.79/15.66 | | | | | (219) all_66_2 = all_33_0
% 108.79/15.66 | | | | |
% 108.79/15.66 | | | | | BETA: splitting (218) gives:
% 108.79/15.66 | | | | |
% 108.79/15.66 | | | | | Case 1:
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | (220) all_66_2 = sz00
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | COMBINE_EQS: (219), (220) imply:
% 108.79/15.66 | | | | | | (221) all_33_0 = sz00
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | REDUCE: (44), (221) imply:
% 108.79/15.66 | | | | | | (222) $false
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | CLOSE: (222) is inconsistent.
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | Case 2:
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | (223) ~ (all_66_2 = all_66_3) & aDimensionOf0(xs) = all_66_3 &
% 108.79/15.66 | | | | | | $i(all_66_3)
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | ALPHA: (223) implies:
% 108.79/15.66 | | | | | | (224) ~ (all_66_2 = all_66_3)
% 108.79/15.66 | | | | | | (225) aDimensionOf0(xs) = all_66_3
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | REDUCE: (219), (224) imply:
% 108.79/15.66 | | | | | | (226) ~ (all_66_3 = all_33_0)
% 108.79/15.66 | | | | | |
% 108.79/15.66 | | | | | | SIMP: (226) implies:
% 108.79/15.66 | | | | | | (227) ~ (all_66_3 = all_33_0)
% 108.79/15.66 | | | | | |
% 108.92/15.66 | | | | | | GROUND_INST: instantiating (39) with all_33_0, all_66_3, xs,
% 108.92/15.66 | | | | | | simplifying with (45), (225) gives:
% 108.92/15.66 | | | | | | (228) all_66_3 = all_33_0
% 108.92/15.66 | | | | | |
% 108.92/15.66 | | | | | | REDUCE: (227), (228) imply:
% 108.92/15.66 | | | | | | (229) $false
% 108.92/15.66 | | | | | |
% 108.92/15.66 | | | | | | CLOSE: (229) is inconsistent.
% 108.92/15.66 | | | | | |
% 108.92/15.66 | | | | | End of split
% 108.92/15.66 | | | | |
% 108.92/15.66 | | | | End of split
% 108.92/15.66 | | | |
% 108.92/15.66 | | | End of split
% 108.92/15.66 | | |
% 108.92/15.66 | | Case 2:
% 108.92/15.66 | | |
% 108.92/15.66 | | | (230) aDimensionOf0(xs) = all_63_2 & $i(all_63_2) & (all_63_2 = sz00 |
% 108.92/15.66 | | | ( ~ (all_63_2 = all_63_3) & aDimensionOf0(xs) = all_63_3 &
% 108.92/15.66 | | | $i(all_63_3)))
% 108.92/15.66 | | |
% 108.92/15.66 | | | ALPHA: (230) implies:
% 108.92/15.66 | | | (231) aDimensionOf0(xs) = all_63_2
% 108.92/15.66 | | | (232) all_63_2 = sz00 | ( ~ (all_63_2 = all_63_3) & aDimensionOf0(xs) =
% 108.92/15.66 | | | all_63_3 & $i(all_63_3))
% 108.92/15.66 | | |
% 108.92/15.66 | | | BETA: splitting (232) gives:
% 108.92/15.66 | | |
% 108.92/15.66 | | | Case 1:
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | (233) all_63_2 = sz00
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | REDUCE: (231), (233) imply:
% 108.92/15.66 | | | | (234) aDimensionOf0(xs) = sz00
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | GROUND_INST: instantiating (39) with all_33_0, sz00, xs, simplifying
% 108.92/15.66 | | | | with (45), (234) gives:
% 108.92/15.66 | | | | (235) all_33_0 = sz00
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | REDUCE: (44), (235) imply:
% 108.92/15.66 | | | | (236) $false
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | CLOSE: (236) is inconsistent.
% 108.92/15.66 | | | |
% 108.92/15.66 | | | Case 2:
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | (237) ~ (all_63_2 = all_63_3) & aDimensionOf0(xs) = all_63_3 &
% 108.92/15.66 | | | | $i(all_63_3)
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | ALPHA: (237) implies:
% 108.92/15.66 | | | | (238) ~ (all_63_2 = all_63_3)
% 108.92/15.66 | | | | (239) aDimensionOf0(xs) = all_63_3
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | GROUND_INST: instantiating (39) with all_33_0, all_63_2, xs, simplifying
% 108.92/15.66 | | | | with (45), (231) gives:
% 108.92/15.66 | | | | (240) all_63_2 = all_33_0
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | GROUND_INST: instantiating (39) with all_63_3, all_63_2, xs, simplifying
% 108.92/15.66 | | | | with (231), (239) gives:
% 108.92/15.66 | | | | (241) all_63_2 = all_63_3
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | COMBINE_EQS: (240), (241) imply:
% 108.92/15.66 | | | | (242) all_63_3 = all_33_0
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | SIMP: (242) implies:
% 108.92/15.66 | | | | (243) all_63_3 = all_33_0
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | REDUCE: (238), (240), (243) imply:
% 108.92/15.66 | | | | (244) $false
% 108.92/15.66 | | | |
% 108.92/15.66 | | | | CLOSE: (244) is inconsistent.
% 108.92/15.66 | | | |
% 108.92/15.66 | | | End of split
% 108.92/15.66 | | |
% 108.92/15.66 | | End of split
% 108.92/15.66 | |
% 108.92/15.66 | Case 2:
% 108.92/15.66 | |
% 108.92/15.66 | | (245) aDimensionOf0(xt) = all_64_2 & $i(all_64_2) & (all_64_2 = sz00 | (
% 108.92/15.66 | | ~ (all_64_2 = all_64_3) & aDimensionOf0(xt) = all_64_3 &
% 108.92/15.66 | | $i(all_64_3)))
% 108.92/15.66 | |
% 108.92/15.66 | | ALPHA: (245) implies:
% 108.92/15.66 | | (246) aDimensionOf0(xt) = all_64_2
% 108.92/15.66 | | (247) all_64_2 = sz00 | ( ~ (all_64_2 = all_64_3) & aDimensionOf0(xt) =
% 108.92/15.66 | | all_64_3 & $i(all_64_3))
% 108.92/15.66 | |
% 108.92/15.66 | | BETA: splitting (247) gives:
% 108.92/15.66 | |
% 108.92/15.66 | | Case 1:
% 108.92/15.66 | | |
% 108.92/15.66 | | | (248) all_64_2 = sz00
% 108.92/15.66 | | |
% 108.92/15.66 | | | REDUCE: (246), (248) imply:
% 108.92/15.66 | | | (249) aDimensionOf0(xt) = sz00
% 108.92/15.66 | | |
% 108.92/15.66 | | | GROUND_INST: instantiating (39) with all_33_0, sz00, xt, simplifying with
% 108.92/15.66 | | | (84), (249) gives:
% 108.92/15.67 | | | (250) all_33_0 = sz00
% 108.92/15.67 | | |
% 108.92/15.67 | | | REDUCE: (44), (250) imply:
% 108.92/15.67 | | | (251) $false
% 108.92/15.67 | | |
% 108.92/15.67 | | | CLOSE: (251) is inconsistent.
% 108.92/15.67 | | |
% 108.92/15.67 | | Case 2:
% 108.92/15.67 | | |
% 108.92/15.67 | | | (252) ~ (all_64_2 = all_64_3) & aDimensionOf0(xt) = all_64_3 &
% 108.92/15.67 | | | $i(all_64_3)
% 108.92/15.67 | | |
% 108.92/15.67 | | | ALPHA: (252) implies:
% 108.92/15.67 | | | (253) ~ (all_64_2 = all_64_3)
% 108.92/15.67 | | | (254) aDimensionOf0(xt) = all_64_3
% 108.92/15.67 | | |
% 108.92/15.67 | | | GROUND_INST: instantiating (39) with all_33_0, all_64_2, xt, simplifying
% 108.92/15.67 | | | with (84), (246) gives:
% 108.92/15.67 | | | (255) all_64_2 = all_33_0
% 108.92/15.67 | | |
% 108.92/15.67 | | | GROUND_INST: instantiating (39) with all_64_3, all_64_2, xt, simplifying
% 108.92/15.67 | | | with (246), (254) gives:
% 108.92/15.67 | | | (256) all_64_2 = all_64_3
% 108.92/15.67 | | |
% 108.92/15.67 | | | COMBINE_EQS: (255), (256) imply:
% 108.92/15.67 | | | (257) all_64_3 = all_33_0
% 108.92/15.67 | | |
% 108.92/15.67 | | | REDUCE: (253), (255), (257) imply:
% 108.92/15.67 | | | (258) $false
% 108.92/15.67 | | |
% 108.92/15.67 | | | CLOSE: (258) is inconsistent.
% 108.92/15.67 | | |
% 108.92/15.67 | | End of split
% 108.92/15.67 | |
% 108.92/15.67 | End of split
% 108.92/15.67 |
% 108.92/15.67 End of proof
% 108.92/15.67 % SZS output end Proof for theBenchmark
% 108.92/15.67
% 108.92/15.67 15043ms
%------------------------------------------------------------------------------