Added Nitpick manual.
authorblanchet
Thu, 22 Oct 2009 14:45:20 +0200
changeset 33191fe3c65d9c577
parent 33059 d1c9bf0f8ae8
child 33192 08a39a957ed7
Added Nitpick manual.
doc-src/Dirs
doc-src/Makefile.in
doc-src/Nitpick/Makefile
doc-src/Nitpick/nitpick.tex
doc-src/gfx/isabelle_nitpick.eps
doc-src/gfx/isabelle_nitpick.pdf
doc-src/manual.bib
     1.1 --- a/doc-src/Dirs	Thu Oct 22 09:50:29 2009 +0200
     1.2 +++ b/doc-src/Dirs	Thu Oct 22 14:45:20 2009 +0200
     1.3 @@ -1,1 +1,1 @@
     1.4 -Intro Ref System Logics HOL ZF Inductive TutorialI IsarOverview IsarRef IsarImplementation Locales LaTeXsugar Classes Codegen Functions Main
     1.5 +Intro Ref System Logics HOL ZF Inductive TutorialI IsarOverview IsarRef IsarImplementation Locales LaTeXsugar Classes Codegen Functions Nitpick Main
     2.1 --- a/doc-src/Makefile.in	Thu Oct 22 09:50:29 2009 +0200
     2.2 +++ b/doc-src/Makefile.in	Thu Oct 22 14:45:20 2009 +0200
     2.3 @@ -45,6 +45,9 @@
     2.4  isabelle_zf.eps:
     2.5  	test -r isabelle_zf.eps || ln -s ../gfx/isabelle_zf.eps .
     2.6  
     2.7 +isabelle_nitpick.eps:
     2.8 +	test -r isabelle_nitpick.eps || ln -s ../gfx/isabelle_nitpick.eps .
     2.9 +
    2.10  
    2.11  isabelle.pdf:
    2.12  	test -r isabelle.pdf || ln -s ../gfx/isabelle.pdf .
    2.13 @@ -58,6 +61,9 @@
    2.14  isabelle_zf.pdf:
    2.15  	test -r isabelle_zf.pdf || ln -s ../gfx/isabelle_zf.pdf .
    2.16  
    2.17 +isabelle_nitpick.pdf:
    2.18 +	test -r isabelle_nitpick.pdf || ln -s ../gfx/isabelle_nitpick.pdf .
    2.19 +
    2.20  typedef.ps:
    2.21  	test -r typedef.ps || ln -s ../gfx/typedef.ps .
    2.22  
     3.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     3.2 +++ b/doc-src/Nitpick/Makefile	Thu Oct 22 14:45:20 2009 +0200
     3.3 @@ -0,0 +1,36 @@
     3.4 +#
     3.5 +# $Id$
     3.6 +#
     3.7 +
     3.8 +## targets
     3.9 +
    3.10 +default: dvi
    3.11 +
    3.12 +
    3.13 +## dependencies
    3.14 +
    3.15 +include ../Makefile.in
    3.16 +
    3.17 +NAME = nitpick
    3.18 +FILES = nitpick.tex ../iman.sty ../manual.bib
    3.19 +
    3.20 +dvi: $(NAME).dvi
    3.21 +
    3.22 +$(NAME).dvi: $(FILES) isabelle_nitpick.eps
    3.23 +	$(LATEX) $(NAME)
    3.24 +	$(BIBTEX) $(NAME)
    3.25 +	$(LATEX) $(NAME)
    3.26 +	$(LATEX) $(NAME)
    3.27 +	$(SEDINDEX) $(NAME)
    3.28 +	$(LATEX) $(NAME)
    3.29 +
    3.30 +pdf: $(NAME).pdf
    3.31 +
    3.32 +$(NAME).pdf: $(FILES) isabelle_nitpick.pdf
    3.33 +	$(PDFLATEX) $(NAME)
    3.34 +	$(BIBTEX) $(NAME)
    3.35 +	$(PDFLATEX) $(NAME)
    3.36 +	$(PDFLATEX) $(NAME)
    3.37 +	$(SEDINDEX) $(NAME)
    3.38 +	$(FIXBOOKMARKS) $(NAME).out
    3.39 +	$(PDFLATEX) $(NAME)
     4.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     4.2 +++ b/doc-src/Nitpick/nitpick.tex	Thu Oct 22 14:45:20 2009 +0200
     4.3 @@ -0,0 +1,2484 @@
     4.4 +\documentclass[a4paper,12pt]{article}
     4.5 +\usepackage[T1]{fontenc}
     4.6 +\usepackage{amsmath}
     4.7 +\usepackage{amssymb}
     4.8 +\usepackage[french,english]{babel}
     4.9 +\usepackage{color}
    4.10 +\usepackage{graphicx}
    4.11 +%\usepackage{mathpazo}
    4.12 +\usepackage{multicol}
    4.13 +\usepackage{stmaryrd}
    4.14 +%\usepackage[scaled=.85]{beramono}
    4.15 +\usepackage{../iman,../pdfsetup}
    4.16 +
    4.17 +%\oddsidemargin=4.6mm
    4.18 +%\evensidemargin=4.6mm
    4.19 +%\textwidth=150mm
    4.20 +%\topmargin=4.6mm
    4.21 +%\headheight=0mm
    4.22 +%\headsep=0mm
    4.23 +%\textheight=234mm
    4.24 +
    4.25 +\def\Colon{\mathord{:\mkern-1.5mu:}}
    4.26 +%\def\lbrakk{\mathopen{\lbrack\mkern-3.25mu\lbrack}}
    4.27 +%\def\rbrakk{\mathclose{\rbrack\mkern-3.255mu\rbrack}}
    4.28 +\def\lparr{\mathopen{(\mkern-4mu\mid}}
    4.29 +\def\rparr{\mathclose{\mid\mkern-4mu)}}
    4.30 +
    4.31 +\def\undef{\textit{undefined}}
    4.32 +\def\unk{{?}}
    4.33 +%\def\unr{\textit{others}}
    4.34 +\def\unr{\ldots}
    4.35 +\def\Abs#1{\hbox{\rm{\flqq}}{\,#1\,}\hbox{\rm{\frqq}}}
    4.36 +\def\Q{{\smash{\lower.2ex\hbox{$\scriptstyle?$}}}}
    4.37 +
    4.38 +\hyphenation{Mini-Sat size-change First-Steps grand-parent nit-pick
    4.39 +counter-example counter-examples data-type data-types co-data-type 
    4.40 +co-data-types in-duc-tive co-in-duc-tive}
    4.41 +
    4.42 +\urlstyle{tt}
    4.43 +
    4.44 +\begin{document}
    4.45 +
    4.46 +\title{\includegraphics[scale=0.5]{isabelle_nitpick} \\[4ex]
    4.47 +Picking Nits \\[\smallskipamount]
    4.48 +\Large A User's Guide to Nitpick for Isabelle/HOL 2010}
    4.49 +\author{\hbox{} \\
    4.50 +Jasmin Christian Blanchette \\
    4.51 +{\normalsize Fakult\"at f\"ur Informatik, Technische Universit\"at M\"unchen} \\
    4.52 +\hbox{}}
    4.53 +
    4.54 +\maketitle
    4.55 +
    4.56 +\tableofcontents
    4.57 +
    4.58 +\setlength{\parskip}{.7em plus .2em minus .1em}
    4.59 +\setlength{\parindent}{0pt}
    4.60 +\setlength{\abovedisplayskip}{\parskip}
    4.61 +\setlength{\abovedisplayshortskip}{.9\parskip}
    4.62 +\setlength{\belowdisplayskip}{\parskip}
    4.63 +\setlength{\belowdisplayshortskip}{.9\parskip}
    4.64 +
    4.65 +% General-purpose enum environment with correct spacing
    4.66 +\newenvironment{enum}%
    4.67 +    {\begin{list}{}{%
    4.68 +        \setlength{\topsep}{.1\parskip}%
    4.69 +        \setlength{\partopsep}{.1\parskip}%
    4.70 +        \setlength{\itemsep}{\parskip}%
    4.71 +        \advance\itemsep by-\parsep}}
    4.72 +    {\end{list}}
    4.73 +
    4.74 +\def\pre{\begingroup\vskip0pt plus1ex\advance\leftskip by\leftmargin
    4.75 +\advance\rightskip by\leftmargin}
    4.76 +\def\post{\vskip0pt plus1ex\endgroup}
    4.77 +
    4.78 +\def\prew{\pre\advance\rightskip by-\leftmargin}
    4.79 +\def\postw{\post}
    4.80 +
    4.81 +\section{Introduction}
    4.82 +\label{introduction}
    4.83 +
    4.84 +Nitpick \cite{blanchette-nipkow-2009} is a counterexample generator for
    4.85 +Isabelle/HOL \cite{isa-tutorial} that is designed to handle formulas
    4.86 +combining (co)in\-duc\-tive datatypes, (co)in\-duc\-tively defined predicates, and
    4.87 +quantifiers. It builds on Kodkod \cite{torlak-jackson-2007}, a highly optimized
    4.88 +first-order relational model finder developed by the Software Design Group at
    4.89 +MIT. It is conceptually similar to Refute \cite{weber-2008}, from which it
    4.90 +borrows many ideas and code fragments, but it benefits from Kodkod's
    4.91 +optimizations and a new encoding scheme. The name Nitpick is shamelessly
    4.92 +appropriated from a now retired Alloy precursor.
    4.93 +
    4.94 +Nitpick is easy to use---you simply enter \textbf{nitpick} after a putative
    4.95 +theorem and wait a few seconds. Nonetheless, there are situations where knowing
    4.96 +how it works under the hood and how it reacts to various options helps
    4.97 +increase the test coverage. This manual also explains how to install the tool on
    4.98 +your workstation. Should the motivation fail you, think of the many hours of
    4.99 +hard work Nitpick will save you. Proving non-theorems is \textsl{hard work}.
   4.100 +
   4.101 +Another common use of Nitpick is to find out whether the axioms of a locale are
   4.102 +satisfiable, while the locale is being developed. To check this, it suffices to
   4.103 +write
   4.104 +
   4.105 +\prew
   4.106 +\textbf{lemma}~``$\textit{False}$'' \\
   4.107 +\textbf{nitpick}~[\textit{show\_all}]
   4.108 +\postw
   4.109 +
   4.110 +after the locale's \textbf{begin} keyword. To falsify \textit{False}, Nitpick
   4.111 +must find a model for the axioms. If it finds no model, we have an indication
   4.112 +that the axioms might be unsatisfiable.
   4.113 +
   4.114 +\newbox\boxA
   4.115 +\setbox\boxA=\hbox{\texttt{nospam}}
   4.116 +
   4.117 +The known bugs and limitations at the time of writing are listed in
   4.118 +\S\ref{known-bugs-and-limitations}. Comments and bug reports concerning Nitpick
   4.119 +or this manual should be directed to
   4.120 +\texttt{blan{\color{white}nospam}\kern-\wd\boxA{}chette@\allowbreak
   4.121 +in.\allowbreak tum.\allowbreak de}.
   4.122 +
   4.123 +\vskip2.5\smallskipamount
   4.124 +
   4.125 +\textbf{Acknowledgment.} The author would like to thank Mark Summerfield for
   4.126 +suggesting several textual improvements.
   4.127 +% and Perry James for reporting a typo.
   4.128 +
   4.129 +\section{First Steps}
   4.130 +\label{first-steps}
   4.131 +
   4.132 +This section introduces Nitpick by presenting small examples. If possible, you
   4.133 +should try out the examples on your workstation. Your theory file should start
   4.134 +the standard way:
   4.135 +
   4.136 +\prew
   4.137 +\textbf{theory}~\textit{Scratch} \\
   4.138 +\textbf{imports}~\textit{Main} \\
   4.139 +\textbf{begin}
   4.140 +\postw
   4.141 +
   4.142 +The results presented here were obtained using the JNI version of MiniSat and
   4.143 +with multithreading disabled to reduce nondeterminism. This was done by adding
   4.144 +the line
   4.145 +
   4.146 +\prew
   4.147 +\textbf{nitpick\_params} [\textit{sat\_solver}~= \textit{MiniSatJNI}, \,\textit{max\_threads}~= 1]
   4.148 +\postw
   4.149 +
   4.150 +after the \textbf{begin} keyword. The JNI version of MiniSat is bundled with
   4.151 +Kodkodi and is precompiled for the major platforms. Other SAT solvers can also
   4.152 +be installed, as explained in \S\ref{optimizations}. If you have already
   4.153 +configured SAT solvers in Isabelle (e.g., for Refute), these will also be
   4.154 +available to Nitpick.
   4.155 +
   4.156 +Throughout this manual, we will explicitly invoke the \textbf{nitpick} command.
   4.157 +Nitpick also provides an automatic mode that can be enabled by specifying
   4.158 +
   4.159 +\prew
   4.160 +\textbf{nitpick\_params} [\textit{auto}]
   4.161 +\postw
   4.162 +
   4.163 +at the beginning of the theory file. In this mode, Nitpick is run for up to 5
   4.164 +seconds (by default) on every newly entered theorem, much like Auto Quickcheck.
   4.165 +
   4.166 +\subsection{Propositional Logic}
   4.167 +\label{propositional-logic}
   4.168 +
   4.169 +Let's start with a trivial example from propositional logic:
   4.170 +
   4.171 +\prew
   4.172 +\textbf{lemma}~``$P \longleftrightarrow Q$'' \\
   4.173 +\textbf{nitpick}
   4.174 +\postw
   4.175 +
   4.176 +You should get the following output:
   4.177 +
   4.178 +\prew
   4.179 +\slshape
   4.180 +Nitpick found a counterexample: \\[2\smallskipamount]
   4.181 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.182 +\hbox{}\qquad\qquad $P = \textit{True}$ \\
   4.183 +\hbox{}\qquad\qquad $Q = \textit{False}$
   4.184 +\postw
   4.185 +
   4.186 +Nitpick can also be invoked on individual subgoals, as in the example below:
   4.187 +
   4.188 +\prew
   4.189 +\textbf{apply}~\textit{auto} \\[2\smallskipamount]
   4.190 +{\slshape goal (2 subgoals): \\
   4.191 +\ 1. $P\,\Longrightarrow\, Q$ \\
   4.192 +\ 2. $Q\,\Longrightarrow\, P$} \\[2\smallskipamount]
   4.193 +\textbf{nitpick}~1 \\[2\smallskipamount]
   4.194 +{\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.195 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.196 +\hbox{}\qquad\qquad $P = \textit{True}$ \\
   4.197 +\hbox{}\qquad\qquad $Q = \textit{False}$} \\[2\smallskipamount]
   4.198 +\textbf{nitpick}~2 \\[2\smallskipamount]
   4.199 +{\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.200 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.201 +\hbox{}\qquad\qquad $P = \textit{False}$ \\
   4.202 +\hbox{}\qquad\qquad $Q = \textit{True}$} \\[2\smallskipamount]
   4.203 +\textbf{oops}
   4.204 +\postw
   4.205 +
   4.206 +\subsection{Type Variables}
   4.207 +\label{type-variables}
   4.208 +
   4.209 +If you are left unimpressed by the previous example, don't worry. The next
   4.210 +one is more mind- and computer-boggling:
   4.211 +
   4.212 +\prew
   4.213 +\textbf{lemma} ``$P~x\,\Longrightarrow\, P~(\textrm{THE}~y.\;P~y)$''
   4.214 +\postw
   4.215 +\pagebreak[2] %% TYPESETTING
   4.216 +
   4.217 +The putative lemma involves the definite description operator, {THE}, presented
   4.218 +in section 5.10.1 of the Isabelle tutorial \cite{isa-tutorial}. The
   4.219 +operator is defined by the axiom $(\textrm{THE}~x.\; x = a) = a$. The putative
   4.220 +lemma is merely asserting the indefinite description operator axiom with {THE}
   4.221 +substituted for {SOME}.
   4.222 +
   4.223 +The free variable $x$ and the bound variable $y$ have type $'a$. For formulas
   4.224 +containing type variables, Nitpick enumerates the possible domains for each type
   4.225 +variable, up to a given cardinality (8 by default), looking for a finite
   4.226 +countermodel:
   4.227 +
   4.228 +\prew
   4.229 +\textbf{nitpick} [\textit{verbose}] \\[2\smallskipamount]
   4.230 +\slshape
   4.231 +Trying 8 scopes: \nopagebreak \\
   4.232 +\hbox{}\qquad \textit{card}~$'a$~= 1; \\
   4.233 +\hbox{}\qquad \textit{card}~$'a$~= 2; \\
   4.234 +\hbox{}\qquad $\qquad\vdots$ \\[.5\smallskipamount]
   4.235 +\hbox{}\qquad \textit{card}~$'a$~= 8. \\[2\smallskipamount]
   4.236 +Nitpick found a counterexample for \textit{card} $'a$~= 3: \\[2\smallskipamount]
   4.237 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.238 +\hbox{}\qquad\qquad $P = \{a_2,\, a_3\}$ \\
   4.239 +\hbox{}\qquad\qquad $x = a_3$ \\[2\smallskipamount]
   4.240 +Total time: 580 ms.
   4.241 +\postw
   4.242 +
   4.243 +Nitpick found a counterexample in which $'a$ has cardinality 3. (For
   4.244 +cardinalities 1 and 2, the formula holds.) In the counterexample, the three
   4.245 +values of type $'a$ are written $a_1$, $a_2$, and $a_3$.
   4.246 +
   4.247 +The message ``Trying $n$ scopes: {\ldots}''\ is shown only if the option
   4.248 +\textit{verbose} is enabled. You can specify \textit{verbose} each time you
   4.249 +invoke \textbf{nitpick}, or you can set it globally using the command
   4.250 +
   4.251 +\prew
   4.252 +\textbf{nitpick\_params} [\textit{verbose}]
   4.253 +\postw
   4.254 +
   4.255 +This command also displays the current default values for all of the options
   4.256 +supported by Nitpick. The options are listed in \S\ref{option-reference}.
   4.257 +
   4.258 +\subsection{Constants}
   4.259 +\label{constants}
   4.260 +
   4.261 +By just looking at Nitpick's output, it might not be clear why the
   4.262 +counterexample in \S\ref{type-variables} is genuine. Let's invoke Nitpick again,
   4.263 +this time telling it to show the values of the constants that occur in the
   4.264 +formula:
   4.265 +
   4.266 +\prew
   4.267 +\textbf{lemma}~``$P~x\,\Longrightarrow\, P~(\textrm{THE}~y.\;P~y)$'' \\
   4.268 +\textbf{nitpick}~[\textit{show\_consts}] \\[2\smallskipamount]
   4.269 +\slshape
   4.270 +Nitpick found a counterexample for \textit{card} $'a$~= 3: \\[2\smallskipamount]
   4.271 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.272 +\hbox{}\qquad\qquad $P = \{a_2,\, a_3\}$ \\
   4.273 +\hbox{}\qquad\qquad $x = a_3$ \\
   4.274 +\hbox{}\qquad Constant: \nopagebreak \\
   4.275 +\hbox{}\qquad\qquad $\textit{The}~\textsl{fallback} = a_1$
   4.276 +\postw
   4.277 +
   4.278 +We can see more clearly now. Since the predicate $P$ isn't true for a unique
   4.279 +value, $\textrm{THE}~y.\;P~y$ can denote any value of type $'a$, even
   4.280 +$a_1$. Since $P~a_1$ is false, the entire formula is falsified.
   4.281 +
   4.282 +As an optimization, Nitpick's preprocessor introduced the special constant
   4.283 +``\textit{The} fallback'' corresponding to $\textrm{THE}~y.\;P~y$ (i.e.,
   4.284 +$\mathit{The}~(\lambda y.\;P~y)$) when there doesn't exist a unique $y$
   4.285 +satisfying $P~y$. We disable this optimization by passing the
   4.286 +\textit{full\_descrs} option:
   4.287 +
   4.288 +\prew
   4.289 +\textbf{nitpick}~[\textit{full\_descrs},\, \textit{show\_consts}] \\[2\smallskipamount]
   4.290 +\slshape
   4.291 +Nitpick found a counterexample for \textit{card} $'a$~= 3: \\[2\smallskipamount]
   4.292 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.293 +\hbox{}\qquad\qquad $P = \{a_2,\, a_3\}$ \\
   4.294 +\hbox{}\qquad\qquad $x = a_3$ \\
   4.295 +\hbox{}\qquad Constant: \nopagebreak \\
   4.296 +\hbox{}\qquad\qquad $\hbox{\slshape THE}~y.\;P~y = a_1$
   4.297 +\postw
   4.298 +
   4.299 +As the result of another optimization, Nitpick directly assigned a value to the
   4.300 +subterm $\textrm{THE}~y.\;P~y$, rather than to the \textit{The} constant. If we
   4.301 +disable this second optimization by using the command
   4.302 +
   4.303 +\prew
   4.304 +\textbf{nitpick}~[\textit{dont\_specialize},\, \textit{full\_descrs},\,
   4.305 +\textit{show\_consts}]
   4.306 +\postw
   4.307 +
   4.308 +we finally get \textit{The}:
   4.309 +
   4.310 +\prew
   4.311 +\slshape Constant: \nopagebreak \\
   4.312 +\hbox{}\qquad $\mathit{The} = \undef{}
   4.313 +    (\!\begin{aligned}[t]%
   4.314 +    & \{\} := a_3,\> \{a_3\} := a_3,\> \{a_2\} := a_2, \\[-2pt] %% TYPESETTING
   4.315 +    & \{a_2, a_3\} := a_1,\> \{a_1\} := a_1,\> \{a_1, a_3\} := a_3, \\[-2pt]
   4.316 +    & \{a_1, a_2\} := a_3,\> \{a_1, a_2, a_3\} := a_3)\end{aligned}$
   4.317 +\postw
   4.318 +
   4.319 +Notice that $\textit{The}~(\lambda y.\;P~y) = \textit{The}~\{a_2, a_3\} = a_1$,
   4.320 +just like before.\footnote{The \undef{} symbol's presence is explained as
   4.321 +follows: In higher-order logic, any function can be built from the undefined
   4.322 +function using repeated applications of the function update operator $f(x :=
   4.323 +y)$, just like any list can be built from the empty list using $x \mathbin{\#}
   4.324 +xs$.}
   4.325 +
   4.326 +Our misadventures with THE suggest adding `$\exists!x{.}$' (``there exists a
   4.327 +unique $x$ such that'') at the front of our putative lemma's assumption:
   4.328 +
   4.329 +\prew
   4.330 +\textbf{lemma}~``$\exists {!}x.\; P~x\,\Longrightarrow\, P~(\textrm{THE}~y.\;P~y)$''
   4.331 +\postw
   4.332 +
   4.333 +The fix appears to work:
   4.334 +
   4.335 +\prew
   4.336 +\textbf{nitpick} \\[2\smallskipamount]
   4.337 +\slshape Nitpick found no counterexample.
   4.338 +\postw
   4.339 +
   4.340 +We can further increase our confidence in the formula by exhausting all
   4.341 +cardinalities up to 50:
   4.342 +
   4.343 +\prew
   4.344 +\textbf{nitpick} [\textit{card} $'a$~= 1--50]\footnote{The symbol `--'
   4.345 +can be entered as \texttt{-} (hyphen) or
   4.346 +\texttt{\char`\\\char`\<midarrow\char`\>}.} \\[2\smallskipamount]
   4.347 +\slshape Nitpick found no counterexample.
   4.348 +\postw
   4.349 +
   4.350 +Let's see if Sledgehammer \cite{sledgehammer-2009} can find a proof:
   4.351 +
   4.352 +\prew
   4.353 +\textbf{sledgehammer} \\[2\smallskipamount]
   4.354 +{\slshape Sledgehammer: external prover ``$e$'' for subgoal 1: \\
   4.355 +$\exists{!}x.\; P~x\,\Longrightarrow\, P~(\hbox{\slshape THE}~y.\; P~y)$ \\
   4.356 +Try this command: \textrm{apply}~(\textit{metis~the\_equality})} \\[2\smallskipamount]
   4.357 +\textbf{apply}~(\textit{metis~the\_equality\/}) \nopagebreak \\[2\smallskipamount]
   4.358 +{\slshape No subgoals!}% \\[2\smallskipamount]
   4.359 +%\textbf{done}
   4.360 +\postw
   4.361 +
   4.362 +This must be our lucky day.
   4.363 +
   4.364 +\subsection{Skolemization}
   4.365 +\label{skolemization}
   4.366 +
   4.367 +Are all invertible functions onto? Let's find out:
   4.368 +
   4.369 +\prew
   4.370 +\textbf{lemma} ``$\exists g.\; \forall x.~g~(f~x) = x
   4.371 + \,\Longrightarrow\, \forall y.\; \exists x.~y = f~x$'' \\
   4.372 +\textbf{nitpick} \\[2\smallskipamount]
   4.373 +\slshape
   4.374 +Nitpick found a counterexample for \textit{card} $'a$~= 2 and \textit{card} $'b$~=~1: \\[2\smallskipamount]
   4.375 +\hbox{}\qquad Free variable: \nopagebreak \\
   4.376 +\hbox{}\qquad\qquad $f = \undef{}(b_1 := a_1)$ \\
   4.377 +\hbox{}\qquad Skolem constants: \nopagebreak \\
   4.378 +\hbox{}\qquad\qquad $g = \undef{}(a_1 := b_1,\> a_2 := b_1)$ \\
   4.379 +\hbox{}\qquad\qquad $y = a_2$
   4.380 +\postw
   4.381 +
   4.382 +Although $f$ is the only free variable occurring in the formula, Nitpick also
   4.383 +displays values for the bound variables $g$ and $y$. These values are available
   4.384 +to Nitpick because it performs skolemization as a preprocessing step.
   4.385 +
   4.386 +In the previous example, skolemization only affected the outermost quantifiers.
   4.387 +This is not always the case, as illustrated below:
   4.388 +
   4.389 +\prew
   4.390 +\textbf{lemma} ``$\exists x.\; \forall f.\; f~x = x$'' \\
   4.391 +\textbf{nitpick} \\[2\smallskipamount]
   4.392 +\slshape
   4.393 +Nitpick found a counterexample for \textit{card} $'a$~= 2: \\[2\smallskipamount]
   4.394 +\hbox{}\qquad Skolem constant: \nopagebreak \\
   4.395 +\hbox{}\qquad\qquad $\lambda x.\; f =
   4.396 +    \undef{}(\!\begin{aligned}[t]
   4.397 +    & a_1 := \undef{}(a_1 := a_2,\> a_2 := a_1), \\[-2pt]
   4.398 +    & a_2 := \undef{}(a_1 := a_1,\> a_2 := a_1))\end{aligned}$
   4.399 +\postw
   4.400 +
   4.401 +The variable $f$ is bound within the scope of $x$; therefore, $f$ depends on
   4.402 +$x$, as suggested by the notation $\lambda x.\,f$. If $x = a_1$, then $f$ is the
   4.403 +function that maps $a_1$ to $a_2$ and vice versa; otherwise, $x = a_2$ and $f$
   4.404 +maps both $a_1$ and $a_2$ to $a_1$. In both cases, $f~x \not= x$.
   4.405 +
   4.406 +The source of the Skolem constants is sometimes more obscure:
   4.407 +
   4.408 +\prew
   4.409 +\textbf{lemma} ``$\mathit{refl}~r\,\Longrightarrow\, \mathit{sym}~r$'' \\
   4.410 +\textbf{nitpick} \\[2\smallskipamount]
   4.411 +\slshape
   4.412 +Nitpick found a counterexample for \textit{card} $'a$~= 2: \\[2\smallskipamount]
   4.413 +\hbox{}\qquad Free variable: \nopagebreak \\
   4.414 +\hbox{}\qquad\qquad $r = \{(a_1, a_1),\, (a_2, a_1),\, (a_2, a_2)\}$ \\
   4.415 +\hbox{}\qquad Skolem constants: \nopagebreak \\
   4.416 +\hbox{}\qquad\qquad $\mathit{sym}.x = a_2$ \\
   4.417 +\hbox{}\qquad\qquad $\mathit{sym}.y = a_1$
   4.418 +\postw
   4.419 +
   4.420 +What happened here is that Nitpick expanded the \textit{sym} constant to its
   4.421 +definition:
   4.422 +
   4.423 +\prew
   4.424 +$\mathit{sym}~r \,\equiv\,
   4.425 + \forall x\> y.\,\> (x, y) \in r \longrightarrow (y, x) \in r.$
   4.426 +\postw
   4.427 +
   4.428 +As their names suggest, the Skolem constants $\mathit{sym}.x$ and
   4.429 +$\mathit{sym}.y$ are simply the bound variables $x$ and $y$
   4.430 +from \textit{sym}'s definition.
   4.431 +
   4.432 +Although skolemization is a useful optimization, you can disable it by invoking
   4.433 +Nitpick with \textit{dont\_skolemize}. See \S\ref{optimizations} for details.
   4.434 +
   4.435 +\subsection{Natural Numbers and Integers}
   4.436 +\label{natural-numbers-and-integers}
   4.437 +
   4.438 +Because of the axiom of infinity, the type \textit{nat} does not admit any
   4.439 +finite models. To deal with this, Nitpick considers prefixes $\{0,\, 1,\,
   4.440 +\ldots,\, K - 1\}$ of \textit{nat} (where $K = \textit{card}~\textit{nat}$) and
   4.441 +maps all other numbers to the undefined value ($\unk$). The type \textit{int} is
   4.442 +handled in a similar way: If $K = \textit{card}~\textit{int}$, the subset of
   4.443 +\textit{int} known to Nitpick is $\{-\lceil K/2 \rceil + 1,\, \ldots,\, +\lfloor
   4.444 +K/2 \rfloor\}$. Undefined values lead to a three-valued logic.
   4.445 +
   4.446 +Here is an example involving \textit{int}:
   4.447 +
   4.448 +\prew
   4.449 +\textbf{lemma} ``$\lbrakk i \le j;\> n \le (m{\Colon}\mathit{int})\rbrakk \,\Longrightarrow\, i * n + j * m \le i * m + j * n$'' \\
   4.450 +\textbf{nitpick} \\[2\smallskipamount]
   4.451 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.452 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.453 +\hbox{}\qquad\qquad $i = 0$ \\
   4.454 +\hbox{}\qquad\qquad $j = 1$ \\
   4.455 +\hbox{}\qquad\qquad $m = 1$ \\
   4.456 +\hbox{}\qquad\qquad $n = 0$
   4.457 +\postw
   4.458 +
   4.459 +With infinite types, we don't always have the luxury of a genuine counterexample
   4.460 +and must often content ourselves with a potential one. The tedious task of
   4.461 +finding out whether the potential counterexample is in fact genuine can be
   4.462 +outsourced to \textit{auto} by passing the option \textit{check\_potential}. For
   4.463 +example:
   4.464 +
   4.465 +\prew
   4.466 +\textbf{lemma} ``$\forall n.\; \textit{Suc}~n \mathbin{\not=} n \,\Longrightarrow\, P$'' \\
   4.467 +\textbf{nitpick} [\textit{card~nat}~= 100,\, \textit{check\_potential}] \\[2\smallskipamount]
   4.468 +\slshape Nitpick found a potential counterexample: \\[2\smallskipamount]
   4.469 +\hbox{}\qquad Free variable: \nopagebreak \\
   4.470 +\hbox{}\qquad\qquad $P = \textit{False}$ \\[2\smallskipamount]
   4.471 +Confirmation by ``\textit{auto}'': The above counterexample is genuine.
   4.472 +\postw
   4.473 +
   4.474 +You might wonder why the counterexample is first reported as potential. The root
   4.475 +of the problem is that the bound variable in $\forall n.\; \textit{Suc}~n
   4.476 +\mathbin{\not=} n$ ranges over an infinite type. If Nitpick finds an $n$ such
   4.477 +that $\textit{Suc}~n \mathbin{=} n$, it evaluates the assumption to
   4.478 +\textit{False}; but otherwise, it does not know anything about values of $n \ge
   4.479 +\textit{card~nat}$ and must therefore evaluate the assumption to $\unk$, not
   4.480 +\textit{True}. Since the assumption can never be satisfied, the putative lemma
   4.481 +can never be falsified.
   4.482 +
   4.483 +Incidentally, if you distrust the so-called genuine counterexamples, you can
   4.484 +enable \textit{check\_\allowbreak genuine} to verify them as well. However, be
   4.485 +aware that \textit{auto} will often fail to prove that the counterexample is
   4.486 +genuine or spurious.
   4.487 +
   4.488 +Some conjectures involving elementary number theory make Nitpick look like a
   4.489 +giant with feet of clay:
   4.490 +
   4.491 +\prew
   4.492 +\textbf{lemma} ``$P~\textit{Suc}$'' \\
   4.493 +\textbf{nitpick} [\textit{card} = 1--6] \\[2\smallskipamount]
   4.494 +\slshape
   4.495 +Nitpick found no counterexample.
   4.496 +\postw
   4.497 +
   4.498 +For any cardinality $k$, \textit{Suc} is the partial function $\{0 \mapsto 1,\,
   4.499 +1 \mapsto 2,\, \ldots,\, k - 1 \mapsto \unk\}$, which evaluates to $\unk$ when
   4.500 +it is passed as argument to $P$. As a result, $P~\textit{Suc}$ is always $\unk$.
   4.501 +The next example is similar:
   4.502 +
   4.503 +\prew
   4.504 +\textbf{lemma} ``$P~(\textit{op}~{+}\Colon
   4.505 +\textit{nat}\mathbin{\Rightarrow}\textit{nat}\mathbin{\Rightarrow}\textit{nat})$'' \\
   4.506 +\textbf{nitpick} [\textit{card nat} = 1] \\[2\smallskipamount]
   4.507 +{\slshape Nitpick found a counterexample:} \\[2\smallskipamount]
   4.508 +\hbox{}\qquad Free variable: \nopagebreak \\
   4.509 +\hbox{}\qquad\qquad $P = \{\}$ \\[2\smallskipamount]
   4.510 +\textbf{nitpick} [\textit{card nat} = 2] \\[2\smallskipamount]
   4.511 +{\slshape Nitpick found no counterexample.}
   4.512 +\postw
   4.513 +
   4.514 +The problem here is that \textit{op}~+ is total when \textit{nat} is taken to be
   4.515 +$\{0\}$ but becomes partial as soon as we add $1$, because $1 + 1 \notin \{0,
   4.516 +1\}$.
   4.517 +
   4.518 +Because numbers are infinite and are approximated using a three-valued logic,
   4.519 +there is usually no need to systematically enumerate domain sizes. If Nitpick
   4.520 +cannot find a genuine counterexample for \textit{card~nat}~= $k$, it is very
   4.521 +unlikely that one could be found for smaller domains. (The $P~(\textit{op}~{+})$
   4.522 +example above is an exception to this principle.) Nitpick nonetheless enumerates
   4.523 +all cardinalities from 1 to 8 for \textit{nat}, mainly because smaller
   4.524 +cardinalities are fast to handle and give rise to simpler counterexamples. This
   4.525 +is explained in more detail in \S\ref{scope-monotonicity}.
   4.526 +
   4.527 +\subsection{Inductive Datatypes}
   4.528 +\label{inductive-datatypes}
   4.529 +
   4.530 +Like natural numbers and integers, inductive datatypes with recursive
   4.531 +constructors admit no finite models and must be approximated by a subterm-closed
   4.532 +subset. For example, using a cardinality of 10 for ${'}a~\textit{list}$,
   4.533 +Nitpick looks for all counterexamples that can be built using at most 10
   4.534 +different lists.
   4.535 +
   4.536 +Let's see with an example involving \textit{hd} (which returns the first element
   4.537 +of a list) and $@$ (which concatenates two lists):
   4.538 +
   4.539 +\prew
   4.540 +\textbf{lemma} ``$\textit{hd}~(\textit{xs} \mathbin{@} [y, y]) = \textit{hd}~\textit{xs}$'' \\
   4.541 +\textbf{nitpick} \\[2\smallskipamount]
   4.542 +\slshape Nitpick found a counterexample for \textit{card} $'a$~= 3: \\[2\smallskipamount]
   4.543 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.544 +\hbox{}\qquad\qquad $\textit{xs} = []$ \\
   4.545 +\hbox{}\qquad\qquad $\textit{y} = a_3$
   4.546 +\postw
   4.547 +
   4.548 +To see why the counterexample is genuine, we enable \textit{show\_consts}
   4.549 +and \textit{show\_\allowbreak datatypes}:
   4.550 +
   4.551 +\prew
   4.552 +{\slshape Datatype:} \\
   4.553 +\hbox{}\qquad $'a$~\textit{list}~= $\{[],\, [a_3, a_3],\, [a_3],\, \unr\}$ \\
   4.554 +{\slshape Constants:} \\
   4.555 +\hbox{}\qquad $\lambda x_1.\; x_1 \mathbin{@} [y, y] = \undef([] := [a_3, a_3],\> [a_3, a_3] := \unk,\> [a_3] := \unk)$ \\
   4.556 +\hbox{}\qquad $\textit{hd} = \undef([] := a_2,\> [a_3, a_3] := a_3,\> [a_3] := a_3)$
   4.557 +\postw
   4.558 +
   4.559 +Since $\mathit{hd}~[]$ is undefined in the logic, it may be given any value,
   4.560 +including $a_2$.
   4.561 +
   4.562 +The second constant, $\lambda x_1.\; x_1 \mathbin{@} [y, y]$, is simply the
   4.563 +append operator whose second argument is fixed to be $[y, y]$. Appending $[a_3,
   4.564 +a_3]$ to $[a_3]$ would normally give $[a_3, a_3, a_3]$, but this value is not
   4.565 +representable in the subset of $'a$~\textit{list} considered by Nitpick, which
   4.566 +is shown under the ``Datatype'' heading; hence the result is $\unk$. Similarly,
   4.567 +appending $[a_3, a_3]$ to itself gives $\unk$.
   4.568 +
   4.569 +Given \textit{card}~$'a = 3$ and \textit{card}~$'a~\textit{list} = 3$, Nitpick
   4.570 +considers the following subsets:
   4.571 +
   4.572 +\kern-.5\smallskipamount %% TYPESETTING
   4.573 +
   4.574 +\prew
   4.575 +\begin{multicols}{3}
   4.576 +$\{[],\, [a_1],\, [a_2]\}$; \\
   4.577 +$\{[],\, [a_1],\, [a_3]\}$; \\
   4.578 +$\{[],\, [a_2],\, [a_3]\}$; \\
   4.579 +$\{[],\, [a_1],\, [a_1, a_1]\}$; \\
   4.580 +$\{[],\, [a_1],\, [a_2, a_1]\}$; \\
   4.581 +$\{[],\, [a_1],\, [a_3, a_1]\}$; \\
   4.582 +$\{[],\, [a_2],\, [a_1, a_2]\}$; \\
   4.583 +$\{[],\, [a_2],\, [a_2, a_2]\}$; \\
   4.584 +$\{[],\, [a_2],\, [a_3, a_2]\}$; \\
   4.585 +$\{[],\, [a_3],\, [a_1, a_3]\}$; \\
   4.586 +$\{[],\, [a_3],\, [a_2, a_3]\}$; \\
   4.587 +$\{[],\, [a_3],\, [a_3, a_3]\}$.
   4.588 +\end{multicols}
   4.589 +\postw
   4.590 +
   4.591 +\kern-2\smallskipamount %% TYPESETTING
   4.592 +
   4.593 +All subterm-closed subsets of $'a~\textit{list}$ consisting of three values
   4.594 +are listed and only those. As an example of a non-subterm-closed subset,
   4.595 +consider $\mathcal{S} = \{[],\, [a_1],\,\allowbreak [a_1, a_3]\}$, and observe
   4.596 +that $[a_1, a_3]$ (i.e., $a_1 \mathbin{\#} [a_3]$) has $[a_3] \notin
   4.597 +\mathcal{S}$ as a subterm.
   4.598 +
   4.599 +Here's another m\"ochtegern-lemma that Nitpick can refute without a blink:
   4.600 +
   4.601 +\prew
   4.602 +\textbf{lemma} ``$\lbrakk \textit{length}~\textit{xs} = 1;\> \textit{length}~\textit{ys} = 1
   4.603 +\rbrakk \,\Longrightarrow\, \textit{xs} = \textit{ys}$''
   4.604 +\\
   4.605 +\textbf{nitpick} [\textit{show\_datatypes}] \\[2\smallskipamount]
   4.606 +\slshape Nitpick found a counterexample for \textit{card} $'a$~= 3: \\[2\smallskipamount]
   4.607 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.608 +\hbox{}\qquad\qquad $\textit{xs} = [a_2]$ \\
   4.609 +\hbox{}\qquad\qquad $\textit{ys} = [a_3]$ \\
   4.610 +\hbox{}\qquad Datatypes: \\
   4.611 +\hbox{}\qquad\qquad $\textit{nat} = \{0,\, 1,\, 2,\, \unr\}$ \\
   4.612 +\hbox{}\qquad\qquad $'a$~\textit{list} = $\{[],\, [a_3],\, [a_2],\, \unr\}$
   4.613 +\postw
   4.614 +
   4.615 +Because datatypes are approximated using a three-valued logic, there is usually
   4.616 +no need to systematically enumerate cardinalities: If Nitpick cannot find a
   4.617 +genuine counterexample for \textit{card}~$'a~\textit{list}$~= 10, it is very
   4.618 +unlikely that one could be found for smaller cardinalities.
   4.619 +
   4.620 +\subsection{Typedefs, Records, Rationals, and Reals}
   4.621 +\label{typedefs-records-rationals-and-reals}
   4.622 +
   4.623 +Nitpick generally treats types declared using \textbf{typedef} as datatypes
   4.624 +whose single constructor is the corresponding \textit{Abs\_\kern.1ex} function.
   4.625 +For example:
   4.626 +
   4.627 +\prew
   4.628 +\textbf{typedef}~\textit{three} = ``$\{0\Colon\textit{nat},\, 1,\, 2\}$'' \\
   4.629 +\textbf{by}~\textit{blast} \\[2\smallskipamount]
   4.630 +\textbf{definition}~$A \mathbin{\Colon} \textit{three}$ \textbf{where} ``\kern-.1em$A \,\equiv\, \textit{Abs\_\allowbreak three}~0$'' \\
   4.631 +\textbf{definition}~$B \mathbin{\Colon} \textit{three}$ \textbf{where} ``$B \,\equiv\, \textit{Abs\_three}~1$'' \\
   4.632 +\textbf{definition}~$C \mathbin{\Colon} \textit{three}$ \textbf{where} ``$C \,\equiv\, \textit{Abs\_three}~2$'' \\[2\smallskipamount]
   4.633 +\textbf{lemma} ``$\lbrakk P~A;\> P~B\rbrakk \,\Longrightarrow\, P~x$'' \\
   4.634 +\textbf{nitpick} [\textit{show\_datatypes}] \\[2\smallskipamount]
   4.635 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.636 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.637 +\hbox{}\qquad\qquad $P = \{\Abs{1},\, \Abs{0}\}$ \\
   4.638 +\hbox{}\qquad\qquad $x = \Abs{2}$ \\
   4.639 +\hbox{}\qquad Datatypes: \\
   4.640 +\hbox{}\qquad\qquad $\textit{nat} = \{0,\, 1,\, 2,\, \unr\}$ \\
   4.641 +\hbox{}\qquad\qquad $\textit{three} = \{\Abs{2},\, \Abs{1},\, \Abs{0},\, \unr\}$
   4.642 +\postw
   4.643 +
   4.644 +%% MARK
   4.645 +In the output above, $\Abs{n}$ abbreviates $\textit{Abs\_three}~n$.
   4.646 +
   4.647 +%% MARK
   4.648 +Records, which are implemented as \textbf{typedef}s behind the scenes, are
   4.649 +handled in much the same way:
   4.650 +
   4.651 +\prew
   4.652 +\textbf{record} \textit{point} = \\
   4.653 +\hbox{}\quad $\textit{Xcoord} \mathbin{\Colon} \textit{int}$ \\
   4.654 +\hbox{}\quad $\textit{Ycoord} \mathbin{\Colon} \textit{int}$ \\[2\smallskipamount]
   4.655 +\textbf{lemma} ``$\textit{Xcoord}~(p\Colon\textit{point}) = \textit{Xcoord}~(q\Colon\textit{point})$'' \\
   4.656 +\textbf{nitpick} [\textit{show\_datatypes}] \\[2\smallskipamount]
   4.657 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.658 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.659 +\hbox{}\qquad\qquad $p = \lparr\textit{Xcoord} = 0,\> \textit{Ycoord} = 0\rparr$ \\
   4.660 +\hbox{}\qquad\qquad $q = \lparr\textit{Xcoord} = 1,\> \textit{Ycoord} = 1\rparr$ \\
   4.661 +\hbox{}\qquad Datatypes: \\
   4.662 +\hbox{}\qquad\qquad $\textit{int} = \{0,\, 1,\, \unr\}$ \\
   4.663 +\hbox{}\qquad\qquad $\textit{point} = \{\lparr\textit{Xcoord} = 1,\>
   4.664 +\textit{Ycoord} = 1\rparr,\> \lparr\textit{Xcoord} = 0,\> \textit{Ycoord} = 0\rparr,\, \unr\}$\kern-1pt %% QUIET
   4.665 +\postw
   4.666 +
   4.667 +Finally, Nitpick provides rudimentary support for rationals and reals using a
   4.668 +similar approach:
   4.669 +
   4.670 +\prew
   4.671 +\textbf{lemma} ``$4 * x + 3 * (y\Colon\textit{real}) \not= 1/2$'' \\
   4.672 +\textbf{nitpick} [\textit{show\_datatypes}] \\[2\smallskipamount]
   4.673 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.674 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.675 +\hbox{}\qquad\qquad $x = 1/2$ \\
   4.676 +\hbox{}\qquad\qquad $y = -1/2$ \\
   4.677 +\hbox{}\qquad Datatypes: \\
   4.678 +\hbox{}\qquad\qquad $\textit{nat} = \{0,\, 1,\, 2,\, 3,\, 4,\, 5,\, 6,\, 7,\, \unr\}$ \\
   4.679 +\hbox{}\qquad\qquad $\textit{int} = \{0,\, 1,\, 2,\, 3,\, 4,\, -3,\, -2,\, -1,\, \unr\}$ \\
   4.680 +\hbox{}\qquad\qquad $\textit{real} = \{1,\, 0,\, 4,\, -3/2,\, 3,\, 2,\, 1/2,\, -1/2,\, \unr\}$
   4.681 +\postw
   4.682 +
   4.683 +\subsection{Inductive and Coinductive Predicates}
   4.684 +\label{inductive-and-coinductive-predicates}
   4.685 +
   4.686 +Inductively defined predicates (and sets) are particularly problematic for
   4.687 +counterexample generators. They can make Quickcheck~\cite{berghofer-nipkow-2004}
   4.688 +loop forever and Refute~\cite{weber-2008} run out of resources. The crux of
   4.689 +the problem is that they are defined using a least fixed point construction.
   4.690 +
   4.691 +Nitpick's philosophy is that not all inductive predicates are equal. Consider
   4.692 +the \textit{even} predicate below:
   4.693 +
   4.694 +\prew
   4.695 +\textbf{inductive}~\textit{even}~\textbf{where} \\
   4.696 +``\textit{even}~0'' $\,\mid$ \\
   4.697 +``\textit{even}~$n\,\Longrightarrow\, \textit{even}~(\textit{Suc}~(\textit{Suc}~n))$''
   4.698 +\postw
   4.699 +
   4.700 +This predicate enjoys the desirable property of being well-founded, which means
   4.701 +that the introduction rules don't give rise to infinite chains of the form
   4.702 +
   4.703 +\prew
   4.704 +$\cdots\,\Longrightarrow\, \textit{even}~k''
   4.705 +       \,\Longrightarrow\, \textit{even}~k'
   4.706 +       \,\Longrightarrow\, \textit{even}~k.$
   4.707 +\postw
   4.708 +
   4.709 +For \textit{even}, this is obvious: Any chain ending at $k$ will be of length
   4.710 +$k/2 + 1$:
   4.711 +
   4.712 +\prew
   4.713 +$\textit{even}~0\,\Longrightarrow\, \textit{even}~2\,\Longrightarrow\, \cdots
   4.714 +       \,\Longrightarrow\, \textit{even}~(k - 2)
   4.715 +       \,\Longrightarrow\, \textit{even}~k.$
   4.716 +\postw
   4.717 +
   4.718 +Wellfoundedness is desirable because it enables Nitpick to use a very efficient
   4.719 +fixed point computation.%
   4.720 +\footnote{If an inductive predicate is
   4.721 +well-founded, then it has exactly one fixed point, which is simultaneously the
   4.722 +least and the greatest fixed point. In these circumstances, the computation of
   4.723 +the least fixed point amounts to the computation of an arbitrary fixed point,
   4.724 +which can be performed using a straightforward recursive equation.}
   4.725 +Moreover, Nitpick can prove wellfoundedness of most well-founded predicates,
   4.726 +just as Isabelle's \textbf{function} package usually discharges termination
   4.727 +proof obligations automatically.
   4.728 +
   4.729 +Let's try an example:
   4.730 +
   4.731 +\prew
   4.732 +\textbf{lemma} ``$\exists n.\; \textit{even}~n \mathrel{\land} \textit{even}~(\textit{Suc}~n)$'' \\
   4.733 +\textbf{nitpick}~[\textit{card nat}~= 100,\, \textit{verbose}] \\[2\smallskipamount]
   4.734 +\slshape The inductive predicate ``\textit{even}'' was proved well-founded.
   4.735 +Nitpick can compute it efficiently. \\[2\smallskipamount]
   4.736 +Trying 1 scope: \\
   4.737 +\hbox{}\qquad \textit{card nat}~= 100. \\[2\smallskipamount]
   4.738 +Nitpick found a potential counterexample for \textit{card nat}~= 100: \\[2\smallskipamount]
   4.739 +\hbox{}\qquad Empty assignment \\[2\smallskipamount]
   4.740 +Nitpick could not find a better counterexample. \\[2\smallskipamount]
   4.741 +Total time: 2274 ms.
   4.742 +\postw
   4.743 +
   4.744 +No genuine counterexample is possible because Nitpick cannot rule out the
   4.745 +existence of a natural number $n \ge 100$ such that both $\textit{even}~n$ and
   4.746 +$\textit{even}~(\textit{Suc}~n)$ are true. To help Nitpick, we can bound the
   4.747 +existential quantifier:
   4.748 +
   4.749 +\prew
   4.750 +\textbf{lemma} ``$\exists n \mathbin{\le} 99.\; \textit{even}~n \mathrel{\land} \textit{even}~(\textit{Suc}~n)$'' \\
   4.751 +\textbf{nitpick}~[\textit{card nat}~= 100] \\[2\smallskipamount]
   4.752 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.753 +\hbox{}\qquad Empty assignment
   4.754 +\postw
   4.755 +
   4.756 +So far we were blessed by the wellfoundedness of \textit{even}. What happens if
   4.757 +we use the following definition instead?
   4.758 +
   4.759 +\prew
   4.760 +\textbf{inductive} $\textit{even}'$ \textbf{where} \\
   4.761 +``$\textit{even}'~(0{\Colon}\textit{nat})$'' $\,\mid$ \\
   4.762 +``$\textit{even}'~2$'' $\,\mid$ \\
   4.763 +``$\lbrakk\textit{even}'~m;\> \textit{even}'~n\rbrakk \,\Longrightarrow\, \textit{even}'~(m + n)$''
   4.764 +\postw
   4.765 +
   4.766 +This definition is not well-founded: From $\textit{even}'~0$ and
   4.767 +$\textit{even}'~0$, we can derive that $\textit{even}'~0$. Nonetheless, the
   4.768 +predicates $\textit{even}$ and $\textit{even}'$ are equivalent.
   4.769 +
   4.770 +Let's check a property involving $\textit{even}'$. To make up for the
   4.771 +foreseeable computational hurdles entailed by non-wellfoundedness, we decrease
   4.772 +\textit{nat}'s cardinality to a mere 10:
   4.773 +
   4.774 +\prew
   4.775 +\textbf{lemma}~``$\exists n \in \{0, 2, 4, 6, 8\}.\;
   4.776 +\lnot\;\textit{even}'~n$'' \\
   4.777 +\textbf{nitpick}~[\textit{card nat}~= 10,\, \textit{verbose},\, \textit{show\_consts}] \\[2\smallskipamount]
   4.778 +\slshape
   4.779 +The inductive predicate ``$\textit{even}'\!$'' could not be proved well-founded.
   4.780 +Nitpick might need to unroll it. \\[2\smallskipamount]
   4.781 +Trying 6 scopes: \\
   4.782 +\hbox{}\qquad \textit{card nat}~= 10 and \textit{iter} $\textit{even}'$~= 0; \\
   4.783 +\hbox{}\qquad \textit{card nat}~= 10 and \textit{iter} $\textit{even}'$~= 1; \\
   4.784 +\hbox{}\qquad \textit{card nat}~= 10 and \textit{iter} $\textit{even}'$~= 2; \\
   4.785 +\hbox{}\qquad \textit{card nat}~= 10 and \textit{iter} $\textit{even}'$~= 4; \\
   4.786 +\hbox{}\qquad \textit{card nat}~= 10 and \textit{iter} $\textit{even}'$~= 8; \\
   4.787 +\hbox{}\qquad \textit{card nat}~= 10 and \textit{iter} $\textit{even}'$~= 9. \\[2\smallskipamount]
   4.788 +Nitpick found a counterexample for \textit{card nat}~= 10 and \textit{iter} $\textit{even}'$~= 2: \\[2\smallskipamount]
   4.789 +\hbox{}\qquad Constant: \nopagebreak \\
   4.790 +\hbox{}\qquad\qquad $\lambda i.\; \textit{even}'$ = $\undef(\!\begin{aligned}[t]
   4.791 +& 2 := \{0, 2, 4, 6, 8, 1^\Q, 3^\Q, 5^\Q, 7^\Q, 9^\Q\}, \\[-2pt]
   4.792 +& 1 := \{0, 2, 4, 1^\Q, 3^\Q, 5^\Q, 6^\Q, 7^\Q, 8^\Q, 9^\Q\}, \\[-2pt]
   4.793 +& 0 := \{0, 2, 1^\Q, 3^\Q, 4^\Q, 5^\Q, 6^\Q, 7^\Q, 8^\Q, 9^\Q\})\end{aligned}$ \\[2\smallskipamount]
   4.794 +Total time: 1140 ms.
   4.795 +\postw
   4.796 +
   4.797 +Nitpick's output is very instructive. First, it tells us that the predicate is
   4.798 +unrolled, meaning that it is computed iteratively from the empty set. Then it
   4.799 +lists six scopes specifying different bounds on the numbers of iterations:\ 0,
   4.800 +1, 2, 4, 8, and~9.
   4.801 +
   4.802 +The output also shows how each iteration contributes to $\textit{even}'$. The
   4.803 +notation $\lambda i.\; \textit{even}'$ indicates that the value of the
   4.804 +predicate depends on an iteration counter. Iteration 0 provides the basis
   4.805 +elements, $0$ and $2$. Iteration 1 contributes $4$ ($= 2 + 2$). Iteration 2
   4.806 +throws $6$ ($= 2 + 4 = 4 + 2$) and $8$ ($= 4 + 4$) into the mix. Further
   4.807 +iterations would not contribute any new elements.
   4.808 +
   4.809 +Some values are marked with superscripted question
   4.810 +marks~(`\lower.2ex\hbox{$^\Q$}'). These are the elements for which the
   4.811 +predicate evaluates to $\unk$. Thus, $\textit{even}'$ evaluates to either
   4.812 +\textit{True} or $\unk$, never \textit{False}.
   4.813 +
   4.814 +When unrolling a predicate, Nitpick tries 0, 1, 2, 4, 8, 12, 16, and 24
   4.815 +iterations. However, these numbers are bounded by the cardinality of the
   4.816 +predicate's domain. With \textit{card~nat}~= 10, no more than 9 iterations are
   4.817 +ever needed to compute the value of a \textit{nat} predicate. You can specify
   4.818 +the number of iterations using the \textit{iter} option, as explained in
   4.819 +\S\ref{scope-of-search}.
   4.820 +
   4.821 +In the next formula, $\textit{even}'$ occurs both positively and negatively:
   4.822 +
   4.823 +\prew
   4.824 +\textbf{lemma} ``$\textit{even}'~(n - 2) \,\Longrightarrow\, \textit{even}'~n$'' \\
   4.825 +\textbf{nitpick} [\textit{card nat} = 10,\, \textit{show\_consts}] \\[2\smallskipamount]
   4.826 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
   4.827 +\hbox{}\qquad Free variable: \nopagebreak \\
   4.828 +\hbox{}\qquad\qquad $n = 1$ \\
   4.829 +\hbox{}\qquad Constants: \nopagebreak \\
   4.830 +\hbox{}\qquad\qquad $\lambda i.\; \textit{even}'$ = $\undef(\!\begin{aligned}[t]
   4.831 +& 0 := \{0, 2, 1^\Q, 3^\Q, 4^\Q, 5^\Q, 6^\Q, 7^\Q, 8^\Q, 9^\Q\})\end{aligned}$  \\
   4.832 +\hbox{}\qquad\qquad $\textit{even}' \subseteq \{0, 2, 4, 6, 8, \unr\}$
   4.833 +\postw
   4.834 +
   4.835 +Notice the special constraint $\textit{even}' \subseteq \{0,\, 2,\, 4,\, 6,\,
   4.836 +8,\, \unr\}$ in the output, whose right-hand side represents an arbitrary
   4.837 +fixed point (not necessarily the least one). It is used to falsify
   4.838 +$\textit{even}'~n$. In contrast, the unrolled predicate is used to satisfy
   4.839 +$\textit{even}'~(n - 2)$.
   4.840 +
   4.841 +Coinductive predicates are handled dually. For example:
   4.842 +
   4.843 +\prew
   4.844 +\textbf{coinductive} \textit{nats} \textbf{where} \\
   4.845 +``$\textit{nats}~(x\Colon\textit{nat}) \,\Longrightarrow\, \textit{nats}~x$'' \\[2\smallskipamount]
   4.846 +\textbf{lemma} ``$\textit{nats} = \{0, 1, 2, 3, 4\}$'' \\
   4.847 +\textbf{nitpick}~[\textit{card nat} = 10,\, \textit{show\_consts}] \\[2\smallskipamount]
   4.848 +\slshape Nitpick found a counterexample:
   4.849 +\\[2\smallskipamount]
   4.850 +\hbox{}\qquad Constants: \nopagebreak \\
   4.851 +\hbox{}\qquad\qquad $\lambda i.\; \textit{nats} = \undef(0 := \{\!\begin{aligned}[t]
   4.852 +& 0^\Q, 1^\Q, 2^\Q, 3^\Q, 4^\Q, 5^\Q, 6^\Q, 7^\Q, 8^\Q, 9^\Q, \\[-2pt]
   4.853 +& \unr\})\end{aligned}$ \\
   4.854 +\hbox{}\qquad\qquad $nats \supseteq \{9, 5^\Q, 6^\Q, 7^\Q, 8^\Q, \unr\}$
   4.855 +\postw
   4.856 +
   4.857 +As a special case, Nitpick uses Kodkod's transitive closure operator to encode
   4.858 +negative occurrences of non-well-founded ``linear inductive predicates,'' i.e.,
   4.859 +inductive predicates for which each the predicate occurs in at most one
   4.860 +assumption of each introduction rule. For example:
   4.861 +
   4.862 +\prew
   4.863 +\textbf{inductive} \textit{odd} \textbf{where} \\
   4.864 +``$\textit{odd}~1$'' $\,\mid$ \\
   4.865 +``$\lbrakk \textit{odd}~m;\>\, \textit{even}~n\rbrakk \,\Longrightarrow\, \textit{odd}~(m + n)$'' \\[2\smallskipamount]
   4.866 +\textbf{lemma}~``$\textit{odd}~n \,\Longrightarrow\, \textit{odd}~(n - 2)$'' \\
   4.867 +\textbf{nitpick}~[\textit{card nat} = 10,\, \textit{show\_consts}] \\[2\smallskipamount]
   4.868 +\slshape Nitpick found a counterexample:
   4.869 +\\[2\smallskipamount]
   4.870 +\hbox{}\qquad Free variable: \nopagebreak \\
   4.871 +\hbox{}\qquad\qquad $n = 1$ \\
   4.872 +\hbox{}\qquad Constants: \nopagebreak \\
   4.873 +\hbox{}\qquad\qquad $\textit{even} = \{0, 2, 4, 6, 8, \unr\}$ \\
   4.874 +\hbox{}\qquad\qquad $\textit{odd}_{\textsl{base}} = \{1, \unr\}$ \\
   4.875 +\hbox{}\qquad\qquad $\textit{odd}_{\textsl{step}} = \!
   4.876 +\!\begin{aligned}[t]
   4.877 +  & \{(0, 0), (0, 2), (0, 4), (0, 6), (0, 8), (1, 1), (1, 3), (1, 5), \\[-2pt]
   4.878 +  & \phantom{\{} (1, 7), (1, 9), (2, 2), (2, 4), (2, 6), (2, 8), (3, 3),
   4.879 +       (3, 5), \\[-2pt]
   4.880 +  & \phantom{\{} (3, 7), (3, 9), (4, 4), (4, 6), (4, 8), (5, 5), (5, 7), (5, 9), \\[-2pt]
   4.881 +  & \phantom{\{} (6, 6), (6, 8), (7, 7), (7, 9), (8, 8), (9, 9), \unr\}\end{aligned}$ \\
   4.882 +\hbox{}\qquad\qquad $\textit{odd} \subseteq \{1, 3, 5, 7, 9, 8^\Q, \unr\}$
   4.883 +\postw
   4.884 +
   4.885 +\noindent
   4.886 +In the output, $\textit{odd}_{\textrm{base}}$ represents the base elements and
   4.887 +$\textit{odd}_{\textrm{step}}$ is a transition relation that computes new
   4.888 +elements from known ones. The set $\textit{odd}$ consists of all the values
   4.889 +reachable through the reflexive transitive closure of
   4.890 +$\textit{odd}_{\textrm{step}}$ starting with any element from
   4.891 +$\textit{odd}_{\textrm{base}}$, namely 1, 3, 5, 7, and 9. Using Kodkod's
   4.892 +transitive closure to encode linear predicates is normally either more thorough
   4.893 +or more efficient than unrolling (depending on the value of \textit{iter}), but
   4.894 +for those cases where it isn't you can disable it by passing the
   4.895 +\textit{dont\_star\_linear\_preds} option.
   4.896 +
   4.897 +\subsection{Coinductive Datatypes}
   4.898 +\label{coinductive-datatypes}
   4.899 +
   4.900 +While Isabelle regrettably lacks a high-level mechanism for defining coinductive
   4.901 +datatypes, the \textit{Coinductive\_List} theory provides a coinductive ``lazy
   4.902 +list'' datatype, $'a~\textit{llist}$, defined the hard way. Nitpick supports
   4.903 +these lazy lists seamlessly and provides a hook, described in
   4.904 +\S\ref{registration-of-coinductive-datatypes}, to register custom coinductive
   4.905 +datatypes.
   4.906 +
   4.907 +(Co)intuitively, a coinductive datatype is similar to an inductive datatype but
   4.908 +allows infinite objects. Thus, the infinite lists $\textit{ps}$ $=$ $[a, a, a,
   4.909 +\ldots]$, $\textit{qs}$ $=$ $[a, b, a, b, \ldots]$, and $\textit{rs}$ $=$ $[0,
   4.910 +1, 2, 3, \ldots]$ can be defined as lazy lists using the
   4.911 +$\textit{LNil}\mathbin{\Colon}{'}a~\textit{llist}$ and
   4.912 +$\textit{LCons}\mathbin{\Colon}{'}a \mathbin{\Rightarrow} {'}a~\textit{llist}
   4.913 +\mathbin{\Rightarrow} {'}a~\textit{llist}$ constructors.
   4.914 +
   4.915 +Although it is otherwise no friend of infinity, Nitpick can find counterexamples
   4.916 +involving cyclic lists such as \textit{ps} and \textit{qs} above as well as
   4.917 +finite lists:
   4.918 +
   4.919 +\prew
   4.920 +\textbf{lemma} ``$\textit{xs} \not= \textit{LCons}~a~\textit{xs}$'' \\
   4.921 +\textbf{nitpick} \\[2\smallskipamount]
   4.922 +\slshape Nitpick found a counterexample for {\itshape card}~$'a$ = 1: \\[2\smallskipamount]
   4.923 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.924 +\hbox{}\qquad\qquad $\textit{a} = a_1$ \\
   4.925 +\hbox{}\qquad\qquad $\textit{xs} = \textsl{THE}~\omega.\; \omega = \textit{LCons}~a_1~\omega$
   4.926 +\postw
   4.927 +
   4.928 +The notation $\textrm{THE}~\omega.\; \omega = t(\omega)$ stands
   4.929 +for the infinite term $t(t(t(\ldots)))$. Hence, \textit{xs} is simply the
   4.930 +infinite list $[a_1, a_1, a_1, \ldots]$.
   4.931 +
   4.932 +The next example is more interesting:
   4.933 +
   4.934 +\prew
   4.935 +\textbf{lemma}~``$\lbrakk\textit{xs} = \textit{LCons}~a~\textit{xs};\>\,
   4.936 +\textit{ys} = \textit{iterates}~(\lambda b.\> a)~b\rbrakk \,\Longrightarrow\, \textit{xs} = \textit{ys}$'' \\
   4.937 +\textbf{nitpick} [\textit{verbose}] \\[2\smallskipamount]
   4.938 +\slshape The type ``\kern1pt$'a$'' passed the monotonicity test. Nitpick might be able to skip
   4.939 +some scopes. \\[2\smallskipamount]
   4.940 +Trying 8 scopes: \\
   4.941 +\hbox{}\qquad \textit{card} $'a$~= 1, \textit{card} ``\kern1pt$'a~\textit{list}$''~= 1,
   4.942 +and \textit{bisim\_depth}~= 0. \\
   4.943 +\hbox{}\qquad $\qquad\vdots$ \\[.5\smallskipamount]
   4.944 +\hbox{}\qquad \textit{card} $'a$~= 8, \textit{card} ``\kern1pt$'a~\textit{list}$''~= 8,
   4.945 +and \textit{bisim\_depth}~= 7. \\[2\smallskipamount]
   4.946 +Nitpick found a counterexample for {\itshape card}~$'a$ = 2,
   4.947 +\textit{card}~``\kern1pt$'a~\textit{list}$''~= 2, and \textit{bisim\_\allowbreak
   4.948 +depth}~= 1:
   4.949 +\\[2\smallskipamount]
   4.950 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.951 +\hbox{}\qquad\qquad $\textit{a} = a_2$ \\
   4.952 +\hbox{}\qquad\qquad $\textit{b} = a_1$ \\
   4.953 +\hbox{}\qquad\qquad $\textit{xs} = \textsl{THE}~\omega.\; \omega = \textit{LCons}~a_2~\omega$ \\
   4.954 +\hbox{}\qquad\qquad $\textit{ys} = \textit{LCons}~a_1~(\textsl{THE}~\omega.\; \omega = \textit{LCons}~a_2~\omega)$ \\[2\smallskipamount]
   4.955 +Total time: 726 ms.
   4.956 +\postw
   4.957 +
   4.958 +The lazy list $\textit{xs}$ is simply $[a_2, a_2, a_2, \ldots]$, whereas
   4.959 +$\textit{ys}$ is $[a_1, a_2, a_2, a_2, \ldots]$, i.e., a lasso-shaped list with
   4.960 +$[a_1]$ as its stem and $[a_2]$ as its cycle. In general, the list segment
   4.961 +within the scope of the {THE} binder corresponds to the lasso's cycle, whereas
   4.962 +the segment leading to the binder is the stem.
   4.963 +
   4.964 +A salient property of coinductive datatypes is that two objects are considered
   4.965 +equal if and only if they lead to the same observations. For example, the lazy
   4.966 +lists $\textrm{THE}~\omega.\; \omega =
   4.967 +\textit{LCons}~a~(\textit{LCons}~b~\omega)$ and
   4.968 +$\textit{LCons}~a~(\textrm{THE}~\omega.\; \omega =
   4.969 +\textit{LCons}~b~(\textit{LCons}~a~\omega))$ are identical, because both lead
   4.970 +to the sequence of observations $a$, $b$, $a$, $b$, \hbox{\ldots} (or,
   4.971 +equivalently, both encode the infinite list $[a, b, a, b, \ldots]$). This
   4.972 +concept of equality for coinductive datatypes is called bisimulation and is
   4.973 +defined coinductively.
   4.974 +
   4.975 +Internally, Nitpick encodes the coinductive bisimilarity predicate as part of
   4.976 +the Kodkod problem to ensure that distinct objects lead to different
   4.977 +observations. This precaution is somewhat expensive and often unnecessary, so it
   4.978 +can be disabled by setting the \textit{bisim\_depth} option to $-1$. The
   4.979 +bisimilarity check is then performed \textsl{after} the counterexample has been
   4.980 +found to ensure correctness. If this after-the-fact check fails, the
   4.981 +counterexample is tagged as ``likely genuine'' and Nitpick recommends to try
   4.982 +again with \textit{bisim\_depth} set to a nonnegative integer. Disabling the
   4.983 +check for the previous example saves approximately 150~milli\-seconds; the speed
   4.984 +gains can be more significant for larger scopes.
   4.985 +
   4.986 +The next formula illustrates the need for bisimilarity (either as a Kodkod
   4.987 +predicate or as an after-the-fact check) to prevent spurious counterexamples:
   4.988 +
   4.989 +\prew
   4.990 +\textbf{lemma} ``$\lbrakk xs = \textit{LCons}~a~\textit{xs};\>\, \textit{ys} = \textit{LCons}~a~\textit{ys}\rbrakk
   4.991 +\,\Longrightarrow\, \textit{xs} = \textit{ys}$'' \\
   4.992 +\textbf{nitpick} [\textit{bisim\_depth} = $-1$,\, \textit{show\_datatypes}] \\[2\smallskipamount]
   4.993 +\slshape Nitpick found a likely genuine counterexample for $\textit{card}~'a$ = 2: \\[2\smallskipamount]
   4.994 +\hbox{}\qquad Free variables: \nopagebreak \\
   4.995 +\hbox{}\qquad\qquad $a = a_2$ \\
   4.996 +\hbox{}\qquad\qquad $\textit{xs} = \textsl{THE}~\omega.\; \omega =
   4.997 +\textit{LCons}~a_2~\omega$ \\
   4.998 +\hbox{}\qquad\qquad $\textit{ys} = \textsl{THE}~\omega.\; \omega = \textit{LCons}~a_2~\omega$ \\
   4.999 +\hbox{}\qquad Codatatype:\strut \nopagebreak \\
  4.1000 +\hbox{}\qquad\qquad $'a~\textit{llist} =
  4.1001 +\{\!\begin{aligned}[t]
  4.1002 +  & \textsl{THE}~\omega.\; \omega = \textit{LCons}~a_2~\omega, \\[-2pt]
  4.1003 +  & \textsl{THE}~\omega.\; \omega = \textit{LCons}~a_2~\omega,\> \unr\}\end{aligned}$
  4.1004 +\\[2\smallskipamount]
  4.1005 +Try again with ``\textit{bisim\_depth}'' set to a nonnegative value to confirm
  4.1006 +that the counterexample is genuine. \\[2\smallskipamount]
  4.1007 +{\upshape\textbf{nitpick}} \\[2\smallskipamount]
  4.1008 +\slshape Nitpick found no counterexample.
  4.1009 +\postw
  4.1010 +
  4.1011 +In the first \textbf{nitpick} invocation, the after-the-fact check discovered 
  4.1012 +that the two known elements of type $'a~\textit{llist}$ are bisimilar.
  4.1013 +
  4.1014 +A compromise between leaving out the bisimilarity predicate from the Kodkod
  4.1015 +problem and performing the after-the-fact check is to specify a lower
  4.1016 +nonnegative \textit{bisim\_depth} value than the default one provided by
  4.1017 +Nitpick. In general, a value of $K$ means that Nitpick will require all lists to
  4.1018 +be distinguished from each other by their prefixes of length $K$. Be aware that
  4.1019 +setting $K$ to a too low value can overconstrain Nitpick, preventing it from
  4.1020 +finding any counterexamples.
  4.1021 +
  4.1022 +\subsection{Boxing}
  4.1023 +\label{boxing}
  4.1024 +
  4.1025 +Nitpick normally maps function and product types directly to the corresponding
  4.1026 +Kodkod concepts. As a consequence, if $'a$ has cardinality 3 and $'b$ has
  4.1027 +cardinality 4, then $'a \times {'}b$ has cardinality 12 ($= 4 \times 3$) and $'a
  4.1028 +\Rightarrow {'}b$ has cardinality 64 ($= 4^3$). In some circumstances, it pays
  4.1029 +off to treat these types in the same way as plain datatypes, by approximating
  4.1030 +them by a subset of a given cardinality. This technique is called ``boxing'' and
  4.1031 +is particularly useful for functions passed as arguments to other functions, for
  4.1032 +high-arity functions, and for large tuples. Under the hood, boxing involves
  4.1033 +wrapping occurrences of the types $'a \times {'}b$ and $'a \Rightarrow {'}b$ in
  4.1034 +isomorphic datatypes, as can be seen by enabling the \textit{debug} option.
  4.1035 +
  4.1036 +To illustrate boxing, we consider a formalization of $\lambda$-terms represented
  4.1037 +using de Bruijn's notation:
  4.1038 +
  4.1039 +\prew
  4.1040 +\textbf{datatype} \textit{tm} = \textit{Var}~\textit{nat}~$\mid$~\textit{Lam}~\textit{tm} $\mid$ \textit{App~tm~tm}
  4.1041 +\postw
  4.1042 +
  4.1043 +The $\textit{lift}~t~k$ function increments all variables with indices greater
  4.1044 +than or equal to $k$ by one:
  4.1045 +
  4.1046 +\prew
  4.1047 +\textbf{primrec} \textit{lift} \textbf{where} \\
  4.1048 +``$\textit{lift}~(\textit{Var}~j)~k = \textit{Var}~(\textrm{if}~j < k~\textrm{then}~j~\textrm{else}~j + 1)$'' $\mid$ \\
  4.1049 +``$\textit{lift}~(\textit{Lam}~t)~k = \textit{Lam}~(\textit{lift}~t~(k + 1))$'' $\mid$ \\
  4.1050 +``$\textit{lift}~(\textit{App}~t~u)~k = \textit{App}~(\textit{lift}~t~k)~(\textit{lift}~u~k)$''
  4.1051 +\postw
  4.1052 +
  4.1053 +The $\textit{loose}~t~k$ predicate returns \textit{True} if and only if
  4.1054 +term $t$ has a loose variable with index $k$ or more:
  4.1055 +
  4.1056 +\prew
  4.1057 +\textbf{primrec}~\textit{loose} \textbf{where} \\
  4.1058 +``$\textit{loose}~(\textit{Var}~j)~k = (j \ge k)$'' $\mid$ \\
  4.1059 +``$\textit{loose}~(\textit{Lam}~t)~k = \textit{loose}~t~(\textit{Suc}~k)$'' $\mid$ \\
  4.1060 +``$\textit{loose}~(\textit{App}~t~u)~k = (\textit{loose}~t~k \mathrel{\lor} \textit{loose}~u~k)$''
  4.1061 +\postw
  4.1062 +
  4.1063 +Next, the $\textit{subst}~\sigma~t$ function applies the substitution $\sigma$
  4.1064 +on $t$:
  4.1065 +
  4.1066 +\prew
  4.1067 +\textbf{primrec}~\textit{subst} \textbf{where} \\
  4.1068 +``$\textit{subst}~\sigma~(\textit{Var}~j) = \sigma~j$'' $\mid$ \\
  4.1069 +``$\textit{subst}~\sigma~(\textit{Lam}~t) = {}$\phantom{''} \\
  4.1070 +\phantom{``}$\textit{Lam}~(\textit{subst}~(\lambda n.\> \textrm{case}~n~\textrm{of}~0 \Rightarrow \textit{Var}~0 \mid \textit{Suc}~m \Rightarrow \textit{lift}~(\sigma~m)~1)~t)$'' $\mid$ \\
  4.1071 +``$\textit{subst}~\sigma~(\textit{App}~t~u) = \textit{App}~(\textit{subst}~\sigma~t)~(\textit{subst}~\sigma~u)$''
  4.1072 +\postw
  4.1073 +
  4.1074 +A substitution is a function that maps variable indices to terms. Observe that
  4.1075 +$\sigma$ is a function passed as argument and that Nitpick can't optimize it
  4.1076 +away, because the recursive call for the \textit{Lam} case involves an altered
  4.1077 +version. Also notice the \textit{lift} call, which increments the variable
  4.1078 +indices when moving under a \textit{Lam}.
  4.1079 +
  4.1080 +A reasonable property to expect of substitution is that it should leave closed
  4.1081 +terms unchanged. Alas, even this simple property does not hold:
  4.1082 +
  4.1083 +\pre
  4.1084 +\textbf{lemma}~``$\lnot\,\textit{loose}~t~0 \,\Longrightarrow\, \textit{subst}~\sigma~t = t$'' \\
  4.1085 +\textbf{nitpick} [\textit{verbose}] \\[2\smallskipamount]
  4.1086 +\slshape
  4.1087 +Trying 8 scopes: \nopagebreak \\
  4.1088 +\hbox{}\qquad \textit{card~nat}~= 1, \textit{card tm}~= 1, and \textit{card} ``$\textit{nat} \Rightarrow \textit{tm}$'' = 1; \\
  4.1089 +\hbox{}\qquad \textit{card~nat}~= 2, \textit{card tm}~= 2, and \textit{card} ``$\textit{nat} \Rightarrow \textit{tm}$'' = 2; \\
  4.1090 +\hbox{}\qquad $\qquad\vdots$ \\[.5\smallskipamount]
  4.1091 +\hbox{}\qquad \textit{card~nat}~= 8, \textit{card tm}~= 8, and \textit{card} ``$\textit{nat} \Rightarrow \textit{tm}$'' = 8. \\[2\smallskipamount]
  4.1092 +Nitpick found a counterexample for \textit{card~nat}~= 6, \textit{card~tm}~= 6,
  4.1093 +and \textit{card}~``$\textit{nat} \Rightarrow \textit{tm}$''~= 6: \\[2\smallskipamount]
  4.1094 +\hbox{}\qquad Free variables: \nopagebreak \\
  4.1095 +\hbox{}\qquad\qquad $\sigma = \undef(\!\begin{aligned}[t]
  4.1096 +& 0 := \textit{Var}~0,\>
  4.1097 +  1 := \textit{Var}~0,\>
  4.1098 +  2 := \textit{Var}~0, \\[-2pt]
  4.1099 +& 3 := \textit{Var}~0,\>
  4.1100 +  4 := \textit{Var}~0,\>
  4.1101 +  5 := \textit{Var}~0)\end{aligned}$ \\
  4.1102 +\hbox{}\qquad\qquad $t = \textit{Lam}~(\textit{Lam}~(\textit{Var}~1))$ \\[2\smallskipamount]
  4.1103 +Total time: $4679$ ms.
  4.1104 +\postw
  4.1105 +
  4.1106 +Using \textit{eval}, we find out that $\textit{subst}~\sigma~t =
  4.1107 +\textit{Lam}~(\textit{Lam}~(\textit{Var}~0))$. Using the traditional
  4.1108 +$\lambda$-term notation, $t$~is
  4.1109 +$\lambda x\, y.\> x$ whereas $\textit{subst}~\sigma~t$ is $\lambda x\, y.\> y$.
  4.1110 +The bug is in \textit{subst}: The $\textit{lift}~(\sigma~m)~1$ call should be
  4.1111 +replaced with $\textit{lift}~(\sigma~m)~0$.
  4.1112 +
  4.1113 +An interesting aspect of Nitpick's verbose output is that it assigned inceasing
  4.1114 +cardinalities from 1 to 8 to the type $\textit{nat} \Rightarrow \textit{tm}$.
  4.1115 +For the formula of interest, knowing 6 values of that type was enough to find
  4.1116 +the counterexample. Without boxing, $46\,656$ ($= 6^6$) values must be
  4.1117 +considered, a hopeless undertaking:
  4.1118 +
  4.1119 +\prew
  4.1120 +\textbf{nitpick} [\textit{dont\_box}] \\[2\smallskipamount]
  4.1121 +{\slshape Nitpick ran out of time after checking 4 of 8 scopes.}
  4.1122 +\postw
  4.1123 +
  4.1124 +{\looseness=-1
  4.1125 +Boxing can be enabled or disabled globally or on a per-type basis using the
  4.1126 +\textit{box} option. Moreover, setting the cardinality of a function or
  4.1127 +product type implicitly enables boxing for that type. Nitpick usually performs
  4.1128 +reasonable choices about which types should be boxed, but option tweaking
  4.1129 +sometimes helps.
  4.1130 +
  4.1131 +}
  4.1132 +
  4.1133 +\subsection{Scope Monotonicity}
  4.1134 +\label{scope-monotonicity}
  4.1135 +
  4.1136 +The \textit{card} option (together with \textit{iter}, \textit{bisim\_depth},
  4.1137 +and \textit{max}) controls which scopes are actually tested. In general, to
  4.1138 +exhaust all models below a certain cardinality bound, the number of scopes that
  4.1139 +Nitpick must consider increases exponentially with the number of type variables
  4.1140 +(and \textbf{typedecl}'d types) occurring in the formula. Given the default
  4.1141 +cardinality specification of 1--8, no fewer than $8^4 = 4096$ scopes must be
  4.1142 +considered for a formula involving $'a$, $'b$, $'c$, and $'d$.
  4.1143 +
  4.1144 +Fortunately, many formulas exhibit a property called \textsl{scope
  4.1145 +monotonicity}, meaning that if the formula is falsifiable for a given scope,
  4.1146 +it is also falsifiable for all larger scopes \cite[p.~165]{jackson-2006}.
  4.1147 +
  4.1148 +Consider the formula
  4.1149 +
  4.1150 +\prew
  4.1151 +\textbf{lemma}~``$\textit{length~xs} = \textit{length~ys} \,\Longrightarrow\, \textit{rev}~(\textit{zip~xs~ys}) = \textit{zip~xs}~(\textit{rev~ys})$''
  4.1152 +\postw
  4.1153 +
  4.1154 +where \textit{xs} is of type $'a~\textit{list}$ and \textit{ys} is of type
  4.1155 +$'b~\textit{list}$. A priori, Nitpick would need to consider 512 scopes to
  4.1156 +exhaust the specification \textit{card}~= 1--8. However, our intuition tells us
  4.1157 +that any counterexample found with a small scope would still be a counterexample
  4.1158 +in a larger scope---by simply ignoring the fresh $'a$ and $'b$ values provided
  4.1159 +by the larger scope. Nitpick comes to the same conclusion after a careful
  4.1160 +inspection of the formula and the relevant definitions:
  4.1161 +
  4.1162 +\prew
  4.1163 +\textbf{nitpick}~[\textit{verbose}] \\[2\smallskipamount]
  4.1164 +\slshape
  4.1165 +The types ``\kern1pt$'a$'' and ``\kern1pt$'b$'' passed the monotonicity test.
  4.1166 +Nitpick might be able to skip some scopes.
  4.1167 + \\[2\smallskipamount]
  4.1168 +Trying 8 scopes: \\
  4.1169 +\hbox{}\qquad \textit{card} $'a$~= 1, \textit{card} $'b$~= 1,
  4.1170 +\textit{card} \textit{nat}~= 1, \textit{card} ``$('a \times {'}b)$
  4.1171 +\textit{list}''~= 1, \\
  4.1172 +\hbox{}\qquad\quad \textit{card} ``\kern1pt$'a$ \textit{list}''~= 1, and
  4.1173 +\textit{card} ``\kern1pt$'b$ \textit{list}''~= 1. \\
  4.1174 +\hbox{}\qquad \textit{card} $'a$~= 2, \textit{card} $'b$~= 2,
  4.1175 +\textit{card} \textit{nat}~= 2, \textit{card} ``$('a \times {'}b)$
  4.1176 +\textit{list}''~= 2, \\
  4.1177 +\hbox{}\qquad\quad \textit{card} ``\kern1pt$'a$ \textit{list}''~= 2, and
  4.1178 +\textit{card} ``\kern1pt$'b$ \textit{list}''~= 2. \\
  4.1179 +\hbox{}\qquad $\qquad\vdots$ \\[.5\smallskipamount]
  4.1180 +\hbox{}\qquad \textit{card} $'a$~= 8, \textit{card} $'b$~= 8,
  4.1181 +\textit{card} \textit{nat}~= 8, \textit{card} ``$('a \times {'}b)$
  4.1182 +\textit{list}''~= 8, \\
  4.1183 +\hbox{}\qquad\quad \textit{card} ``\kern1pt$'a$ \textit{list}''~= 8, and
  4.1184 +\textit{card} ``\kern1pt$'b$ \textit{list}''~= 8.
  4.1185 +\\[2\smallskipamount]
  4.1186 +Nitpick found a counterexample for
  4.1187 +\textit{card} $'a$~= 5, \textit{card} $'b$~= 5,
  4.1188 +\textit{card} \textit{nat}~= 5, \textit{card} ``$('a \times {'}b)$
  4.1189 +\textit{list}''~= 5, \textit{card} ``\kern1pt$'a$ \textit{list}''~= 5, and
  4.1190 +\textit{card} ``\kern1pt$'b$ \textit{list}''~= 5:
  4.1191 +\\[2\smallskipamount]
  4.1192 +\hbox{}\qquad Free variables: \nopagebreak \\
  4.1193 +\hbox{}\qquad\qquad $\textit{xs} = [a_4, a_5]$ \\
  4.1194 +\hbox{}\qquad\qquad $\textit{ys} = [b_3, b_3]$ \\[2\smallskipamount]
  4.1195 +Total time: 1636 ms.
  4.1196 +\postw
  4.1197 +
  4.1198 +In theory, it should be sufficient to test a single scope:
  4.1199 +
  4.1200 +\prew
  4.1201 +\textbf{nitpick}~[\textit{card}~= 8]
  4.1202 +\postw
  4.1203 +
  4.1204 +However, this is often less efficient in practice and may lead to overly complex
  4.1205 +counterexamples.
  4.1206 +
  4.1207 +If the monotonicity check fails but we believe that the formula is monotonic (or
  4.1208 +we don't mind missing some counterexamples), we can pass the
  4.1209 +\textit{mono} option. To convince yourself that this option is risky,
  4.1210 +simply consider this example from \S\ref{skolemization}:
  4.1211 +
  4.1212 +\prew
  4.1213 +\textbf{lemma} ``$\exists g.\; \forall x\Colon 'b.~g~(f~x) = x
  4.1214 + \,\Longrightarrow\, \forall y\Colon {'}a.\; \exists x.~y = f~x$'' \\
  4.1215 +\textbf{nitpick} [\textit{mono}] \\[2\smallskipamount]
  4.1216 +{\slshape Nitpick found no counterexample.} \\[2\smallskipamount]
  4.1217 +\textbf{nitpick} \\[2\smallskipamount]
  4.1218 +\slshape
  4.1219 +Nitpick found a counterexample for \textit{card} $'a$~= 2 and \textit{card} $'b$~=~1: \\
  4.1220 +\hbox{}\qquad $\vdots$
  4.1221 +\postw
  4.1222 +
  4.1223 +(It turns out the formula holds if and only if $\textit{card}~'a \le
  4.1224 +\textit{card}~'b$.) Although this is rarely advisable, the automatic
  4.1225 +monotonicity checks can be disabled by passing \textit{non\_mono}
  4.1226 +(\S\ref{optimizations}).
  4.1227 +
  4.1228 +As insinuated in \S\ref{natural-numbers-and-integers} and
  4.1229 +\S\ref{inductive-datatypes}, \textit{nat}, \textit{int}, and inductive datatypes
  4.1230 +are normally monotonic and treated as such. The same is true for record types,
  4.1231 +\textit{rat}, \textit{real}, and some \textbf{typedef}'d types. Thus, given the
  4.1232 +cardinality specification 1--8, a formula involving \textit{nat}, \textit{int},
  4.1233 +\textit{int~list}, \textit{rat}, and \textit{rat~list} will lead Nitpick to
  4.1234 +consider only 8~scopes instead of $32\,768$.
  4.1235 +
  4.1236 +\section{Case Studies}
  4.1237 +\label{case-studies}
  4.1238 +
  4.1239 +As a didactic device, the previous section focused mostly on toy formulas whose
  4.1240 +validity can easily be assessed just by looking at the formula. We will now
  4.1241 +review two somewhat more realistic case studies that are within Nitpick's
  4.1242 +reach:\ a context-free grammar modeled by mutually inductive sets and a
  4.1243 +functional implementation of AA trees. The results presented in this
  4.1244 +section were produced with the following settings:
  4.1245 +
  4.1246 +\prew
  4.1247 +\textbf{nitpick\_params} [\textit{max\_potential}~= 0,\, \textit{max\_threads} = 2]
  4.1248 +\postw
  4.1249 +
  4.1250 +\subsection{A Context-Free Grammar}
  4.1251 +\label{a-context-free-grammar}
  4.1252 +
  4.1253 +Our first case study is taken from section 7.4 in the Isabelle tutorial
  4.1254 +\cite{isa-tutorial}. The following grammar, originally due to Hopcroft and
  4.1255 +Ullman, produces all strings with an equal number of $a$'s and $b$'s:
  4.1256 +
  4.1257 +\prew
  4.1258 +\begin{tabular}{@{}r@{$\;\,$}c@{$\;\,$}l@{}}
  4.1259 +$S$ & $::=$ & $\epsilon \mid bA \mid aB$ \\
  4.1260 +$A$ & $::=$ & $aS \mid bAA$ \\
  4.1261 +$B$ & $::=$ & $bS \mid aBB$
  4.1262 +\end{tabular}
  4.1263 +\postw
  4.1264 +
  4.1265 +The intuition behind the grammar is that $A$ generates all string with one more
  4.1266 +$a$ than $b$'s and $B$ generates all strings with one more $b$ than $a$'s.
  4.1267 +
  4.1268 +The alphabet consists exclusively of $a$'s and $b$'s:
  4.1269 +
  4.1270 +\prew
  4.1271 +\textbf{datatype} \textit{alphabet}~= $a$ $\mid$ $b$
  4.1272 +\postw
  4.1273 +
  4.1274 +Strings over the alphabet are represented by \textit{alphabet list}s.
  4.1275 +Nonterminals in the grammar become sets of strings. The production rules
  4.1276 +presented above can be expressed as a mutually inductive definition:
  4.1277 +
  4.1278 +\prew
  4.1279 +\textbf{inductive\_set} $S$ \textbf{and} $A$ \textbf{and} $B$ \textbf{where} \\
  4.1280 +\textit{R1}:\kern.4em ``$[] \in S$'' $\,\mid$ \\
  4.1281 +\textit{R2}:\kern.4em ``$w \in A\,\Longrightarrow\, b \mathbin{\#} w \in S$'' $\,\mid$ \\
  4.1282 +\textit{R3}:\kern.4em ``$w \in B\,\Longrightarrow\, a \mathbin{\#} w \in S$'' $\,\mid$ \\
  4.1283 +\textit{R4}:\kern.4em ``$w \in S\,\Longrightarrow\, a \mathbin{\#} w \in A$'' $\,\mid$ \\
  4.1284 +\textit{R5}:\kern.4em ``$w \in S\,\Longrightarrow\, b \mathbin{\#} w \in S$'' $\,\mid$ \\
  4.1285 +\textit{R6}:\kern.4em ``$\lbrakk v \in B;\> v \in B\rbrakk \,\Longrightarrow\, a \mathbin{\#} v \mathbin{@} w \in B$''
  4.1286 +\postw
  4.1287 +
  4.1288 +The conversion of the grammar into the inductive definition was done manually by
  4.1289 +Joe Blow, an underpaid undergraduate student. As a result, some errors might
  4.1290 +have sneaked in.
  4.1291 +
  4.1292 +Debugging faulty specifications is at the heart of Nitpick's \textsl{raison
  4.1293 +d'\^etre}. A good approach is to state desirable properties of the specification
  4.1294 +(here, that $S$ is exactly the set of strings over $\{a, b\}$ with as many $a$'s
  4.1295 +as $b$'s) and check them with Nitpick. If the properties are correctly stated,
  4.1296 +counterexamples will point to bugs in the specification. For our grammar
  4.1297 +example, we will proceed in two steps, separating the soundness and the
  4.1298 +completeness of the set $S$. First, soundness:
  4.1299 +
  4.1300 +\prew
  4.1301 +\textbf{theorem}~\textit{S\_sound}: \\
  4.1302 +``$w \in S \longrightarrow \textit{length}~[x\mathbin{\leftarrow} w.\; x = a] =
  4.1303 +  \textit{length}~[x\mathbin{\leftarrow} w.\; x = b]$'' \\
  4.1304 +\textbf{nitpick} \\[2\smallskipamount]
  4.1305 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
  4.1306 +\hbox{}\qquad Free variable: \nopagebreak \\
  4.1307 +\hbox{}\qquad\qquad $w = [b]$
  4.1308 +\postw
  4.1309 +
  4.1310 +It would seem that $[b] \in S$. How could this be? An inspection of the
  4.1311 +introduction rules reveals that the only rule with a right-hand side of the form
  4.1312 +$b \mathbin{\#} {\ldots} \in S$ that could have introduced $[b]$ into $S$ is
  4.1313 +\textit{R5}:
  4.1314 +
  4.1315 +\prew
  4.1316 +``$w \in S\,\Longrightarrow\, b \mathbin{\#} w \in S$''
  4.1317 +\postw
  4.1318 +
  4.1319 +On closer inspection, we can see that this rule is wrong. To match the
  4.1320 +production $B ::= bS$, the second $S$ should be a $B$. We fix the typo and try
  4.1321 +again:
  4.1322 +
  4.1323 +\prew
  4.1324 +\textbf{nitpick} \\[2\smallskipamount]
  4.1325 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
  4.1326 +\hbox{}\qquad Free variable: \nopagebreak \\
  4.1327 +\hbox{}\qquad\qquad $w = [a, a, b]$
  4.1328 +\postw
  4.1329 +
  4.1330 +Some detective work is necessary to find out what went wrong here. To get $[a,
  4.1331 +a, b] \in S$, we need $[a, b] \in B$ by \textit{R3}, which in turn can only come
  4.1332 +from \textit{R6}:
  4.1333 +
  4.1334 +\prew
  4.1335 +``$\lbrakk v \in B;\> v \in B\rbrakk \,\Longrightarrow\, a \mathbin{\#} v \mathbin{@} w \in B$''
  4.1336 +\postw
  4.1337 +
  4.1338 +Now, this formula must be wrong: The same assumption occurs twice, and the
  4.1339 +variable $w$ is unconstrained. Clearly, one of the two occurrences of $v$ in
  4.1340 +the assumptions should have been a $w$.
  4.1341 +
  4.1342 +With the correction made, we don't get any counterexample from Nitpick. Let's
  4.1343 +move on and check completeness:
  4.1344 +
  4.1345 +\prew
  4.1346 +\textbf{theorem}~\textit{S\_complete}: \\
  4.1347 +``$\textit{length}~[x\mathbin{\leftarrow} w.\; x = a] =
  4.1348 +   \textit{length}~[x\mathbin{\leftarrow} w.\; x = b]
  4.1349 +  \longrightarrow w \in S$'' \\
  4.1350 +\textbf{nitpick} \\[2\smallskipamount]
  4.1351 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
  4.1352 +\hbox{}\qquad Free variable: \nopagebreak \\
  4.1353 +\hbox{}\qquad\qquad $w = [b, b, a, a]$
  4.1354 +\postw
  4.1355 +
  4.1356 +Apparently, $[b, b, a, a] \notin S$, even though it has the same numbers of
  4.1357 +$a$'s and $b$'s. But since our inductive definition passed the soundness check,
  4.1358 +the introduction rules we have are probably correct. Perhaps we simply lack an
  4.1359 +introduction rule. Comparing the grammar with the inductive definition, our
  4.1360 +suspicion is confirmed: Joe Blow simply forgot the production $A ::= bAA$,
  4.1361 +without which the grammar cannot generate two or more $b$'s in a row. So we add
  4.1362 +the rule
  4.1363 +
  4.1364 +\prew
  4.1365 +``$\lbrakk v \in A;\> w \in A\rbrakk \,\Longrightarrow\, b \mathbin{\#} v \mathbin{@} w \in A$''
  4.1366 +\postw
  4.1367 +
  4.1368 +With this last change, we don't get any counterexamples from Nitpick for either
  4.1369 +soundness or completeness. We can even generalize our result to cover $A$ and
  4.1370 +$B$ as well:
  4.1371 +
  4.1372 +\prew
  4.1373 +\textbf{theorem} \textit{S\_A\_B\_sound\_and\_complete}: \\
  4.1374 +``$w \in S \longleftrightarrow \textit{length}~[x \mathbin{\leftarrow} w.\; x = a] = \textit{length}~[x \mathbin{\leftarrow} w.\; x = b]$'' \\
  4.1375 +``$w \in A \longleftrightarrow \textit{length}~[x \mathbin{\leftarrow} w.\; x = a] = \textit{length}~[x \mathbin{\leftarrow} w.\; x = b] + 1$'' \\
  4.1376 +``$w \in B \longleftrightarrow \textit{length}~[x \mathbin{\leftarrow} w.\; x = b] = \textit{length}~[x \mathbin{\leftarrow} w.\; x = a] + 1$'' \\
  4.1377 +\textbf{nitpick} \\[2\smallskipamount]
  4.1378 +\slshape Nitpick found no counterexample.
  4.1379 +\postw
  4.1380 +
  4.1381 +\subsection{AA Trees}
  4.1382 +\label{aa-trees}
  4.1383 +
  4.1384 +AA trees are a kind of balanced trees discovered by Arne Andersson that provide
  4.1385 +similar performance to red-black trees, but with a simpler implementation
  4.1386 +\cite{andersson-1993}. They can be used to store sets of elements equipped with
  4.1387 +a total order $<$. We start by defining the datatype and some basic extractor
  4.1388 +functions:
  4.1389 +
  4.1390 +\prew
  4.1391 +\textbf{datatype} $'a$~\textit{tree} = $\Lambda$ $\mid$ $N$ ``\kern1pt$'a\Colon \textit{linorder}$'' \textit{nat} ``\kern1pt$'a$ \textit{tree}'' ``\kern1pt$'a$ \textit{tree}''  \\[2\smallskipamount]
  4.1392 +\textbf{primrec} \textit{data} \textbf{where} \\
  4.1393 +``$\textit{data}~\Lambda = \undef$'' $\,\mid$ \\
  4.1394 +``$\textit{data}~(N~x~\_~\_~\_) = x$'' \\[2\smallskipamount]
  4.1395 +\textbf{primrec} \textit{dataset} \textbf{where} \\
  4.1396 +``$\textit{dataset}~\Lambda = \{\}$'' $\,\mid$ \\
  4.1397 +``$\textit{dataset}~(N~x~\_~t~u) = \{x\} \cup \textit{dataset}~t \mathrel{\cup} \textit{dataset}~u$'' \\[2\smallskipamount]
  4.1398 +\textbf{primrec} \textit{level} \textbf{where} \\
  4.1399 +``$\textit{level}~\Lambda = 0$'' $\,\mid$ \\
  4.1400 +``$\textit{level}~(N~\_~k~\_~\_) = k$'' \\[2\smallskipamount]
  4.1401 +\textbf{primrec} \textit{left} \textbf{where} \\
  4.1402 +``$\textit{left}~\Lambda = \Lambda$'' $\,\mid$ \\
  4.1403 +``$\textit{left}~(N~\_~\_~t~\_) = t$'' \\[2\smallskipamount]
  4.1404 +\textbf{primrec} \textit{right} \textbf{where} \\
  4.1405 +``$\textit{right}~\Lambda = \Lambda$'' $\,\mid$ \\
  4.1406 +``$\textit{right}~(N~\_~\_~\_~u) = u$''
  4.1407 +\postw
  4.1408 +
  4.1409 +The wellformedness criterion for AA trees is fairly complex. Wikipedia states it
  4.1410 +as follows \cite{wikipedia-2009-aa-trees}:
  4.1411 +
  4.1412 +\kern.2\parskip %% TYPESETTING
  4.1413 +
  4.1414 +\pre
  4.1415 +Each node has a level field, and the following invariants must remain true for
  4.1416 +the tree to be valid:
  4.1417 +
  4.1418 +\raggedright
  4.1419 +
  4.1420 +\kern-.4\parskip %% TYPESETTING
  4.1421 +
  4.1422 +\begin{enum}
  4.1423 +\item[]
  4.1424 +\begin{enum}
  4.1425 +\item[1.] The level of a leaf node is one.
  4.1426 +\item[2.] The level of a left child is strictly less than that of its parent.
  4.1427 +\item[3.] The level of a right child is less than or equal to that of its parent.
  4.1428 +\item[4.] The level of a right grandchild is strictly less than that of its grandparent.
  4.1429 +\item[5.] Every node of level greater than one must have two children.
  4.1430 +\end{enum}
  4.1431 +\end{enum}
  4.1432 +\post
  4.1433 +
  4.1434 +\kern.4\parskip %% TYPESETTING
  4.1435 +
  4.1436 +The \textit{wf} predicate formalizes this description:
  4.1437 +
  4.1438 +\prew
  4.1439 +\textbf{primrec} \textit{wf} \textbf{where} \\
  4.1440 +``$\textit{wf}~\Lambda = \textit{True}$'' $\,\mid$ \\
  4.1441 +``$\textit{wf}~(N~\_~k~t~u) =$ \\
  4.1442 +\phantom{``}$(\textrm{if}~t = \Lambda~\textrm{then}$ \\
  4.1443 +\phantom{``$(\quad$}$k = 1 \mathrel{\land} (u = \Lambda \mathrel{\lor} (\textit{level}~u = 1 \mathrel{\land} \textit{left}~u = \Lambda \mathrel{\land} \textit{right}~u = \Lambda))$ \\
  4.1444 +\phantom{``$($}$\textrm{else}$ \\
  4.1445 +\hbox{\phantom{``$(\quad$}$\textit{wf}~t \mathrel{\land} \textit{wf}~u
  4.1446 +\mathrel{\land} u \not= \Lambda \mathrel{\land} \textit{level}~t < k
  4.1447 +\mathrel{\land} \textit{level}~u \le k \mathrel{\land}
  4.1448 +\textit{level}~(\textit{right}~u) < k)$''}\kern-200mm
  4.1449 +\postw
  4.1450 +
  4.1451 +Rebalancing the tree upon insertion and removal of elements is performed by two
  4.1452 +auxiliary functions called \textit{skew} and \textit{split}, defined below:
  4.1453 +
  4.1454 +\prew
  4.1455 +\textbf{primrec} \textit{skew} \textbf{where} \\
  4.1456 +``$\textit{skew}~\Lambda = \Lambda$'' $\,\mid$ \\
  4.1457 +``$\textit{skew}~(N~x~k~t~u) = {}$ \\
  4.1458 +\phantom{``}$(\textrm{if}~t \not= \Lambda \mathrel{\land} k =
  4.1459 +\textit{level}~t~\textrm{then}$ \\
  4.1460 +\phantom{``(\quad}$N~(\textit{data}~t)~k~(\textit{left}~t)~(N~x~k~
  4.1461 +(\textit{right}~t)~u)$ \\
  4.1462 +\phantom{``(}$\textrm{else}$ \\
  4.1463 +\phantom{``(\quad}$N~x~k~t~u)$''
  4.1464 +\postw
  4.1465 +
  4.1466 +\prew
  4.1467 +\textbf{primrec} \textit{split} \textbf{where} \\
  4.1468 +``$\textit{split}~\Lambda = \Lambda$'' $\,\mid$ \\
  4.1469 +``$\textit{split}~(N~x~k~t~u) = {}$ \\
  4.1470 +\phantom{``}$(\textrm{if}~u \not= \Lambda \mathrel{\land} k =
  4.1471 +\textit{level}~(\textit{right}~u)~\textrm{then}$ \\
  4.1472 +\phantom{``(\quad}$N~(\textit{data}~u)~(\textit{Suc}~k)~
  4.1473 +(N~x~k~t~(\textit{left}~u))~(\textit{right}~u)$ \\
  4.1474 +\phantom{``(}$\textrm{else}$ \\
  4.1475 +\phantom{``(\quad}$N~x~k~t~u)$''
  4.1476 +\postw
  4.1477 +
  4.1478 +Performing a \textit{skew} or a \textit{split} should have no impact on the set
  4.1479 +of elements stored in the tree:
  4.1480 +
  4.1481 +\prew
  4.1482 +\textbf{theorem}~\textit{dataset\_skew\_split}:\\
  4.1483 +``$\textit{dataset}~(\textit{skew}~t) = \textit{dataset}~t$'' \\
  4.1484 +``$\textit{dataset}~(\textit{split}~t) = \textit{dataset}~t$'' \\
  4.1485 +\textbf{nitpick} \\[2\smallskipamount]
  4.1486 +{\slshape Nitpick ran out of time after checking 7 of 8 scopes.}
  4.1487 +\postw
  4.1488 +
  4.1489 +Furthermore, applying \textit{skew} or \textit{split} to a well-formed tree
  4.1490 +should not alter the tree:
  4.1491 +
  4.1492 +\prew
  4.1493 +\textbf{theorem}~\textit{wf\_skew\_split}:\\
  4.1494 +``$\textit{wf}~t\,\Longrightarrow\, \textit{skew}~t = t$'' \\
  4.1495 +``$\textit{wf}~t\,\Longrightarrow\, \textit{split}~t = t$'' \\
  4.1496 +\textbf{nitpick} \\[2\smallskipamount]
  4.1497 +{\slshape Nitpick found no counterexample.}
  4.1498 +\postw
  4.1499 +
  4.1500 +Insertion is implemented recursively. It preserves the sort order:
  4.1501 +
  4.1502 +\prew
  4.1503 +\textbf{primrec}~\textit{insort} \textbf{where} \\
  4.1504 +``$\textit{insort}~\Lambda~x = N~x~1~\Lambda~\Lambda$'' $\,\mid$ \\
  4.1505 +``$\textit{insort}~(N~y~k~t~u)~x =$ \\
  4.1506 +\phantom{``}$({*}~(\textit{split} \circ \textit{skew})~{*})~(N~y~k~(\textrm{if}~x < y~\textrm{then}~\textit{insort}~t~x~\textrm{else}~t)$ \\
  4.1507 +\phantom{``$({*}~(\textit{split} \circ \textit{skew})~{*})~(N~y~k~$}$(\textrm{if}~x > y~\textrm{then}~\textit{insort}~u~x~\textrm{else}~u))$''
  4.1508 +\postw
  4.1509 +
  4.1510 +Notice that we deliberately commented out the application of \textit{skew} and
  4.1511 +\textit{split}. Let's see if this causes any problems:
  4.1512 +
  4.1513 +\prew
  4.1514 +\textbf{theorem}~\textit{wf\_insort}:\kern.4em ``$\textit{wf}~t\,\Longrightarrow\, \textit{wf}~(\textit{insort}~t~x)$'' \\
  4.1515 +\textbf{nitpick} \\[2\smallskipamount]
  4.1516 +\slshape Nitpick found a counterexample for \textit{card} $'a$ = 4: \\[2\smallskipamount]
  4.1517 +\hbox{}\qquad Free variables: \nopagebreak \\
  4.1518 +\hbox{}\qquad\qquad $t = N~a_3~1~\Lambda~\Lambda$ \\
  4.1519 +\hbox{}\qquad\qquad $x = a_4$ \\[2\smallskipamount]
  4.1520 +Hint: Maybe you forgot a type constraint?
  4.1521 +\postw
  4.1522 +
  4.1523 +It's hard to see why this is a counterexample. The hint is of no help here. To
  4.1524 +improve readability, we will restrict the theorem to \textit{nat}, so that we
  4.1525 +don't need to look up the value of the $\textit{op}~{<}$ constant to find out
  4.1526 +which element is smaller than the other. In addition, we will tell Nitpick to
  4.1527 +display the value of $\textit{insort}~t~x$ using the \textit{eval} option. This
  4.1528 +gives
  4.1529 +
  4.1530 +\prew
  4.1531 +\textbf{theorem} \textit{wf\_insort\_nat}:\kern.4em ``$\textit{wf}~t\,\Longrightarrow\, \textit{wf}~(\textit{insort}~t~(x\Colon\textit{nat}))$'' \\
  4.1532 +\textbf{nitpick} [\textit{eval} = ``$\textit{insort}~t~x$''] \\[2\smallskipamount]
  4.1533 +\slshape Nitpick found a counterexample: \\[2\smallskipamount]
  4.1534 +\hbox{}\qquad Free variables: \nopagebreak \\
  4.1535 +\hbox{}\qquad\qquad $t = N~1~1~\Lambda~\Lambda$ \\
  4.1536 +\hbox{}\qquad\qquad $x = 0$ \\
  4.1537 +\hbox{}\qquad Evaluated term: \\
  4.1538 +\hbox{}\qquad\qquad $\textit{insort}~t~x = N~1~1~(N~0~1~\Lambda~\Lambda)~\Lambda$
  4.1539 +\postw
  4.1540 +
  4.1541 +Nitpick's output reveals that the element $0$ was added as a left child of $1$,
  4.1542 +where both have a level of 1. This violates the second AA tree invariant, which
  4.1543 +states that a left child's level must be less than its parent's. This shouldn't
  4.1544 +come as a surprise, considering that we commented out the tree rebalancing code.
  4.1545 +Reintroducing the code seems to solve the problem:
  4.1546 +
  4.1547 +\prew
  4.1548 +\textbf{theorem}~\textit{wf\_insort}:\kern.4em ``$\textit{wf}~t\,\Longrightarrow\, \textit{wf}~(\textit{insort}~t~x)$'' \\
  4.1549 +\textbf{nitpick} \\[2\smallskipamount]
  4.1550 +{\slshape Nitpick ran out of time after checking 6 of 8 scopes.}
  4.1551 +\postw
  4.1552 +
  4.1553 +Insertion should transform the set of elements represented by the tree in the
  4.1554 +obvious way:
  4.1555 +
  4.1556 +\prew
  4.1557 +\textbf{theorem} \textit{dataset\_insort}:\kern.4em
  4.1558 +``$\textit{dataset}~(\textit{insort}~t~x) = \{x\} \cup \textit{dataset}~t$'' \\
  4.1559 +\textbf{nitpick} \\[2\smallskipamount]
  4.1560 +{\slshape Nitpick ran out of time after checking 5 of 8 scopes.}
  4.1561 +\postw
  4.1562 +
  4.1563 +We could continue like this and sketch a complete theory of AA trees without
  4.1564 +performing a single proof. Once the definitions and main theorems are in place
  4.1565 +and have been thoroughly tested using Nitpick, we could start working on the
  4.1566 +proofs. Developing theories this way usually saves time, because faulty theorems
  4.1567 +and definitions are discovered much earlier in the process.
  4.1568 +
  4.1569 +\section{Option Reference}
  4.1570 +\label{option-reference}
  4.1571 +
  4.1572 +\def\flushitem#1{\item[]\noindent\kern-\leftmargin \textbf{#1}}
  4.1573 +\def\qty#1{$\left<\textit{#1}\right>$}
  4.1574 +\def\qtybf#1{$\mathbf{\left<\textbf{\textit{#1}}\right>}$}
  4.1575 +\def\optrue#1#2{\flushitem{\textit{#1} $\bigl[$= \qtybf{bool}$\bigr]$\quad [\textit{true}]\hfill (neg.: \textit{#2})}\nopagebreak\\[\parskip]}
  4.1576 +\def\opfalse#1#2{\flushitem{\textit{#1} $\bigl[$= \qtybf{bool}$\bigr]$\quad [\textit{false}]\hfill (neg.: \textit{#2})}\nopagebreak\\[\parskip]}
  4.1577 +\def\opsmart#1#2{\flushitem{\textit{#1} $\bigl[$= \qtybf{bool\_or\_smart}$\bigr]$\quad [\textit{smart}]\hfill (neg.: \textit{#2})}\nopagebreak\\[\parskip]}
  4.1578 +\def\ops#1#2{\flushitem{\textit{#1} = \qtybf{#2}} \nopagebreak\\[\parskip]}
  4.1579 +\def\opt#1#2#3{\flushitem{\textit{#1} = \qtybf{#2}\quad [\textit{#3}]} \nopagebreak\\[\parskip]}
  4.1580 +\def\opu#1#2#3{\flushitem{\textit{#1} \qtybf{#2} = \qtybf{#3}} \nopagebreak\\[\parskip]}
  4.1581 +\def\opusmart#1#2#3{\flushitem{\textit{#1} \qtybf{#2} $\bigl[$= \qtybf{bool\_or\_smart}$\bigr]$\hfill (neg.: \textit{#3})}\nopagebreak\\[\parskip]}
  4.1582 +
  4.1583 +Nitpick's behavior can be influenced by various options, which can be specified
  4.1584 +in brackets after the \textbf{nitpick} command. Default values can be set
  4.1585 +using \textbf{nitpick\_\allowbreak params}. For example:
  4.1586 +
  4.1587 +\prew
  4.1588 +\textbf{nitpick\_params} [\textit{verbose}, \,\textit{timeout} = 60$\,s$]
  4.1589 +\postw
  4.1590 +
  4.1591 +The options are categorized as follows:\ mode of operation
  4.1592 +(\S\ref{mode-of-operation}), scope of search (\S\ref{scope-of-search}), output
  4.1593 +format (\S\ref{output-format}), automatic counterexample checks
  4.1594 +(\S\ref{authentication}), optimizations
  4.1595 +(\S\ref{optimizations}), and timeouts (\S\ref{timeouts}).
  4.1596 +
  4.1597 +The number of options can be overwhelming at first glance. Do not let that worry
  4.1598 +you: Nitpick's defaults have been chosen so that it almost always does the right
  4.1599 +thing, and the most important options have been covered in context in
  4.1600 +\S\ref{first-steps}.
  4.1601 +
  4.1602 +The descriptions below refer to the following syntactic quantities:
  4.1603 +
  4.1604 +\begin{enum}
  4.1605 +\item[$\bullet$] \qtybf{string}: A string.
  4.1606 +\item[$\bullet$] \qtybf{bool}: \textit{true} or \textit{false}.
  4.1607 +\item[$\bullet$] \qtybf{bool\_or\_smart}: \textit{true}, \textit{false}, or \textit{smart}.
  4.1608 +\item[$\bullet$] \qtybf{int}: An integer. Negative integers are prefixed with a hyphen.
  4.1609 +\item[$\bullet$] \qtybf{int\_or\_smart}: An integer or \textit{smart}.
  4.1610 +\item[$\bullet$] \qtybf{int\_range}: An integer (e.g., 3) or a range
  4.1611 +of nonnegative integers (e.g., $1$--$4$). The range symbol `--' can be entered as \texttt{-} (hyphen) or \texttt{\char`\\\char`\<midarrow\char`\>}.
  4.1612 +
  4.1613 +\item[$\bullet$] \qtybf{int\_seq}: A comma-separated sequence of ranges of integers (e.g.,~1{,}3{,}\allowbreak6--8).
  4.1614 +\item[$\bullet$] \qtybf{time}: An integer followed by $\textit{min}$ (minutes), $s$ (seconds), or \textit{ms}
  4.1615 +(milliseconds), or the keyword \textit{none} ($\infty$ years).
  4.1616 +\item[$\bullet$] \qtybf{const}: The name of a HOL constant.
  4.1617 +\item[$\bullet$] \qtybf{term}: A HOL term (e.g., ``$f~x$'').
  4.1618 +\item[$\bullet$] \qtybf{term\_list}: A space-separated list of HOL terms (e.g.,
  4.1619 +``$f~x$''~``$g~y$'').
  4.1620 +\item[$\bullet$] \qtybf{type}: A HOL type.
  4.1621 +\end{enum}
  4.1622 +
  4.1623 +Default values are indicated in square brackets. Boolean options have a negated
  4.1624 +counterpart (e.g., \textit{auto} vs.\ \textit{no\_auto}). When setting Boolean
  4.1625 +options, ``= \textit{true}'' may be omitted.
  4.1626 +
  4.1627 +\subsection{Mode of Operation}
  4.1628 +\label{mode-of-operation}
  4.1629 +
  4.1630 +\begin{enum}
  4.1631 +\opfalse{auto}{no\_auto}
  4.1632 +Specifies whether Nitpick should be run automatically on newly entered theorems.
  4.1633 +For automatic runs, \textit{user\_axioms} (\S\ref{mode-of-operation}) and
  4.1634 +\textit{assms} (\S\ref{mode-of-operation}) are implicitly enabled,
  4.1635 +\textit{blocking} (\S\ref{mode-of-operation}), \textit{verbose}
  4.1636 +(\S\ref{output-format}), and \textit{debug} (\S\ref{output-format}) are
  4.1637 +disabled, \textit{max\_potential} (\S\ref{output-format}) is taken to be 0, and
  4.1638 +\textit{auto\_timeout} (\S\ref{timeouts}) is used as the time limit instead of
  4.1639 +\textit{timeout} (\S\ref{timeouts}). The output is also more concise.
  4.1640 +
  4.1641 +\nopagebreak
  4.1642 +{\small See also \textit{auto\_timeout} (\S\ref{timeouts}).}
  4.1643 +
  4.1644 +\optrue{blocking}{non\_blocking}
  4.1645 +Specifies whether the \textbf{nitpick} command should operate synchronously.
  4.1646 +The asynchronous (non-blocking) mode lets the user start proving the putative
  4.1647 +theorem while Nitpick looks for a counterexample, but it can also be more
  4.1648 +confusing. For technical reasons, automatic runs currently always block.
  4.1649 +
  4.1650 +\nopagebreak
  4.1651 +{\small See also \textit{auto} (\S\ref{mode-of-operation}).}
  4.1652 +
  4.1653 +\optrue{falsify}{satisfy}
  4.1654 +Specifies whether Nitpick should look for falsifying examples (countermodels) or
  4.1655 +satisfying examples (models). This manual assumes throughout that
  4.1656 +\textit{falsify} is enabled.
  4.1657 +
  4.1658 +\opsmart{user\_axioms}{no\_user\_axioms}
  4.1659 +Specifies whether the user-defined axioms (specified using 
  4.1660 +\textbf{axiomatization} and \textbf{axioms}) should be considered. If the option
  4.1661 +is set to \textit{smart}, Nitpick performs an ad hoc axiom selection based on
  4.1662 +the constants that occur in the formula to falsify. The option is implicitly set
  4.1663 +to \textit{true} for automatic runs.
  4.1664 +
  4.1665 +\textbf{Warning:} If the option is set to \textit{true}, Nitpick might
  4.1666 +nonetheless ignore some polymorphic axioms. Counterexamples generated under
  4.1667 +these conditions are tagged as ``likely genuine.'' The \textit{debug}
  4.1668 +(\S\ref{output-format}) option can be used to find out which axioms were
  4.1669 +considered.
  4.1670 +
  4.1671 +\nopagebreak
  4.1672 +{\small See also \textit{auto} (\S\ref{mode-of-operation}), \textit{assms}
  4.1673 +(\S\ref{mode-of-operation}), and \textit{debug} (\S\ref{output-format}).}
  4.1674 +
  4.1675 +\optrue{assms}{no\_assms}
  4.1676 +Specifies whether the relevant assumptions in structured proof should be
  4.1677 +considered. The option is implicitly enabled for automatic runs.
  4.1678 +
  4.1679 +\nopagebreak
  4.1680 +{\small See also \textit{auto} (\S\ref{mode-of-operation})
  4.1681 +and \textit{user\_axioms} (\S\ref{mode-of-operation}).}
  4.1682 +
  4.1683 +\opfalse{overlord}{no\_overlord}
  4.1684 +Specifies whether Nitpick should put its temporary files in
  4.1685 +\texttt{\$ISABELLE\_\allowbreak HOME\_\allowbreak USER}, which is useful for
  4.1686 +debugging Nitpick but also unsafe if several instances of the tool are run
  4.1687 +simultaneously. This option is disabled by default unless your home directory
  4.1688 +ends with \texttt{blanchet} or \texttt{blanchette}.
  4.1689 +%``I thought there was only one overlord.'' --- Tobias Nipkow
  4.1690 +
  4.1691 +\nopagebreak
  4.1692 +{\small See also \textit{debug} (\S\ref{output-format}).}
  4.1693 +\end{enum}
  4.1694 +
  4.1695 +\subsection{Scope of Search}
  4.1696 +\label{scope-of-search}
  4.1697 +
  4.1698 +\begin{enum}
  4.1699 +\opu{card}{type}{int\_seq}
  4.1700 +Specifies the sequence of cardinalities to use for a given type. For
  4.1701 +\textit{nat} and \textit{int}, the cardinality fully specifies the subset used
  4.1702 +to approximate the type. For example:
  4.1703 +%
  4.1704 +$$\hbox{\begin{tabular}{@{}rll@{}}%
  4.1705 +\textit{card nat} = 4 & induces & $\{0,\, 1,\, 2,\, 3\}$ \\
  4.1706 +\textit{card int} = 4 & induces & $\{-1,\, 0,\, +1,\, +2\}$ \\
  4.1707 +\textit{card int} = 5 & induces & $\{-2,\, -1,\, 0,\, +1,\, +2\}.$%
  4.1708 +\end{tabular}}$$
  4.1709 +%
  4.1710 +In general:
  4.1711 +%
  4.1712 +$$\hbox{\begin{tabular}{@{}rll@{}}%
  4.1713 +\textit{card nat} = $K$ & induces & $\{0,\, \ldots,\, K - 1\}$ \\
  4.1714 +\textit{card int} = $K$ & induces & $\{-\lceil K/2 \rceil + 1,\, \ldots,\, +\lfloor K/2 \rfloor\}.$%
  4.1715 +\end{tabular}}$$
  4.1716 +%
  4.1717 +For free types, and often also for \textbf{typedecl}'d types, it usually makes
  4.1718 +sense to specify cardinalities as a range of the form \textit{$1$--$n$}.
  4.1719 +Although function and product types are normally mapped directly to the
  4.1720 +corresponding Kodkod concepts, setting
  4.1721 +the cardinality of such types is also allowed and implicitly enables ``boxing''
  4.1722 +for them, as explained in the description of the \textit{box}~\qty{type}
  4.1723 +and \textit{box} (\S\ref{scope-of-search}) options.
  4.1724 +
  4.1725 +\nopagebreak
  4.1726 +{\small See also \textit{mono} (\S\ref{scope-of-search}).}
  4.1727 +
  4.1728 +\opt{card}{int\_seq}{$\mathbf{1}$--$\mathbf{8}$}
  4.1729 +Specifies the default sequence of cardinalities to use. This can be overridden
  4.1730 +on a per-type basis using the \textit{card}~\qty{type} option described above.
  4.1731 +
  4.1732 +\opu{max}{const}{int\_seq}
  4.1733 +Specifies the sequence of maximum multiplicities to use for a given
  4.1734 +(co)in\-duc\-tive datatype constructor. A constructor's multiplicity is the
  4.1735 +number of distinct values that it can construct. Nonsensical values (e.g.,
  4.1736 +\textit{max}~[]~$=$~2) are silently repaired. This option is only available for
  4.1737 +datatypes equipped with several constructors.
  4.1738 +
  4.1739 +\ops{max}{int\_seq}
  4.1740 +Specifies the default sequence of maximum multiplicities to use for
  4.1741 +(co)in\-duc\-tive datatype constructors. This can be overridden on a per-constructor
  4.1742 +basis using the \textit{max}~\qty{const} option described above.
  4.1743 +
  4.1744 +\opusmart{wf}{const}{non\_wf}
  4.1745 +Specifies whether the specified (co)in\-duc\-tively defined predicate is
  4.1746 +well-founded. The option can take the following values:
  4.1747 +
  4.1748 +\begin{enum}
  4.1749 +\item[$\bullet$] \textbf{\textit{true}}: Tentatively treat the (co)in\-duc\-tive
  4.1750 +predicate as if it were well-founded. Since this is generally not sound when the
  4.1751 +predicate is not well-founded, the counterexamples are tagged as ``likely
  4.1752 +genuine.''
  4.1753 +
  4.1754 +\item[$\bullet$] \textbf{\textit{false}}: Treat the (co)in\-duc\-tive predicate
  4.1755 +as if it were not well-founded. The predicate is then unrolled as prescribed by
  4.1756 +the \textit{star\_linear\_preds}, \textit{iter}~\qty{const}, and \textit{iter}
  4.1757 +options.
  4.1758 +
  4.1759 +\item[$\bullet$] \textbf{\textit{smart}}: Try to prove that the inductive
  4.1760 +predicate is well-founded using Isabelle's \textit{lexicographic\_order} and
  4.1761 +\textit{sizechange} tactics. If this succeeds (or the predicate occurs with an
  4.1762 +appropriate polarity in the formula to falsify), use an efficient fixed point
  4.1763 +equation as specification of the predicate; otherwise, unroll the predicates
  4.1764 +according to the \textit{iter}~\qty{const} and \textit{iter} options.
  4.1765 +\end{enum}
  4.1766 +
  4.1767 +\nopagebreak
  4.1768 +{\small See also \textit{iter} (\S\ref{scope-of-search}),
  4.1769 +\textit{star\_linear\_preds} (\S\ref{optimizations}), and \textit{tac\_timeout}
  4.1770 +(\S\ref{timeouts}).}
  4.1771 +
  4.1772 +\opsmart{wf}{non\_wf}
  4.1773 +Specifies the default wellfoundedness setting to use. This can be overridden on
  4.1774 +a per-predicate basis using the \textit{wf}~\qty{const} option above.
  4.1775 +
  4.1776 +\opu{iter}{const}{int\_seq}
  4.1777 +Specifies the sequence of iteration counts to use when unrolling a given
  4.1778 +(co)in\-duc\-tive predicate. By default, unrolling is applied for inductive
  4.1779 +predicates that occur negatively and coinductive predicates that occur
  4.1780 +positively in the formula to falsify and that cannot be proved to be
  4.1781 +well-founded, but this behavior is influenced by the \textit{wf} option. The
  4.1782 +iteration counts are automatically bounded by the cardinality of the predicate's
  4.1783 +domain.
  4.1784 +
  4.1785 +{\small See also \textit{wf} (\S\ref{scope-of-search}) and
  4.1786 +\textit{star\_linear\_preds} (\S\ref{optimizations}).}
  4.1787 +
  4.1788 +\opt{iter}{int\_seq}{$\mathbf{1{,}2{,}4{,}8{,}12{,}16{,}24{,}32}$}
  4.1789 +Specifies the sequence of iteration counts to use when unrolling (co)in\-duc\-tive
  4.1790 +predicates. This can be overridden on a per-predicate basis using the
  4.1791 +\textit{iter} \qty{const} option above.
  4.1792 +
  4.1793 +\opt{bisim\_depth}{int\_seq}{$\mathbf{7}$}
  4.1794 +Specifies the sequence of iteration counts to use when unrolling the
  4.1795 +bisimilarity predicate generated by Nitpick for coinductive datatypes. A value
  4.1796 +of $-1$ means that no predicate is generated, in which case Nitpick performs an
  4.1797 +after-the-fact check to see if the known coinductive datatype values are
  4.1798 +bidissimilar. If two values are found to be bisimilar, the counterexample is
  4.1799 +tagged as ``likely genuine.'' The iteration counts are automatically bounded by
  4.1800 +the sum of the cardinalities of the coinductive datatypes occurring in the
  4.1801 +formula to falsify.
  4.1802 +
  4.1803 +\opusmart{box}{type}{dont\_box}
  4.1804 +Specifies whether Nitpick should attempt to wrap (``box'') a given function or
  4.1805 +product type in an isomorphic datatype internally. Boxing is an effective mean
  4.1806 +to reduce the search space and speed up Nitpick, because the isomorphic datatype
  4.1807 +is approximated by a subset of the possible function or pair values;
  4.1808 +like other drastic optimizations, it can also prevent the discovery of
  4.1809 +counterexamples. The option can take the following values:
  4.1810 +
  4.1811 +\begin{enum}
  4.1812 +\item[$\bullet$] \textbf{\textit{true}}: Box the specified type whenever
  4.1813 +practicable.
  4.1814 +\item[$\bullet$] \textbf{\textit{false}}: Never box the type.
  4.1815 +\item[$\bullet$] \textbf{\textit{smart}}: Box the type only in contexts where it
  4.1816 +is likely to help. For example, $n$-tuples where $n > 2$ and arguments to
  4.1817 +higher-order functions are good candidates for boxing.
  4.1818 +\end{enum}
  4.1819 +
  4.1820 +Setting the \textit{card}~\qty{type} option for a function or product type
  4.1821 +implicitly enables boxing for that type.
  4.1822 +
  4.1823 +\nopagebreak
  4.1824 +{\small See also \textit{verbose} (\S\ref{output-format})
  4.1825 +and \textit{debug} (\S\ref{output-format}).}
  4.1826 +
  4.1827 +\opsmart{box}{dont\_box}
  4.1828 +Specifies the default boxing setting to use. This can be overridden on a
  4.1829 +per-type basis using the \textit{box}~\qty{type} option described above.
  4.1830 +
  4.1831 +\opusmart{mono}{type}{non\_mono}
  4.1832 +Specifies whether the specified type should be considered monotonic when
  4.1833 +enumerating scopes. If the option is set to \textit{smart}, Nitpick performs a
  4.1834 +monotonicity check on the type. Setting this option to \textit{true} can reduce
  4.1835 +the number of scopes tried, but it also diminishes the theoretical chance of
  4.1836 +finding a counterexample, as demonstrated in \S\ref{scope-monotonicity}.
  4.1837 +
  4.1838 +\nopagebreak
  4.1839 +{\small See also \textit{card} (\S\ref{scope-of-search}),
  4.1840 +\textit{coalesce\_type\_vars} (\S\ref{scope-of-search}), and \textit{verbose}
  4.1841 +(\S\ref{output-format}).}
  4.1842 +
  4.1843 +\opsmart{mono}{non\_box}
  4.1844 +Specifies the default monotonicity setting to use. This can be overridden on a
  4.1845 +per-type basis using the \textit{mono}~\qty{type} option described above.
  4.1846 +
  4.1847 +\opfalse{coalesce\_type\_vars}{dont\_coalesce\_type\_vars}
  4.1848 +Specifies whether type variables with the same sort constraints should be
  4.1849 +merged. Setting this option to \textit{true} can reduce the number of scopes
  4.1850 +tried and the size of the generated Kodkod formulas, but it also diminishes the
  4.1851 +theoretical chance of finding a counterexample.
  4.1852 +
  4.1853 +{\small See also \textit{mono} (\S\ref{scope-of-search}).}
  4.1854 +\end{enum}
  4.1855 +
  4.1856 +\subsection{Output Format}
  4.1857 +\label{output-format}
  4.1858 +
  4.1859 +\begin{enum}
  4.1860 +\opfalse{verbose}{quiet}
  4.1861 +Specifies whether the \textbf{nitpick} command should explain what it does. This
  4.1862 +option is useful to determine which scopes are tried or which SAT solver is
  4.1863 +used. This option is implicitly disabled for automatic runs.
  4.1864 +
  4.1865 +\nopagebreak
  4.1866 +{\small See also \textit{auto} (\S\ref{mode-of-operation}).}
  4.1867 +
  4.1868 +\opfalse{debug}{no\_debug}
  4.1869 +Specifies whether Nitpick should display additional debugging information beyond
  4.1870 +what \textit{verbose} already displays. Enabling \textit{debug} also enables
  4.1871 +\textit{verbose} and \textit{show\_all} behind the scenes. The \textit{debug}
  4.1872 +option is implicitly disabled for automatic runs.
  4.1873 +
  4.1874 +\nopagebreak
  4.1875 +{\small See also \textit{auto} (\S\ref{mode-of-operation}), \textit{overlord}
  4.1876 +(\S\ref{mode-of-operation}), and \textit{batch\_size} (\S\ref{optimizations}).}
  4.1877 +
  4.1878 +\optrue{show\_skolems}{hide\_skolem}
  4.1879 +Specifies whether the values of Skolem constants should be displayed as part of
  4.1880 +counterexamples. Skolem constants correspond to bound variables in the original
  4.1881 +formula and usually help us to understand why the counterexample falsifies the
  4.1882 +formula.
  4.1883 +
  4.1884 +\nopagebreak
  4.1885 +{\small See also \textit{skolemize} (\S\ref{optimizations}).}
  4.1886 +
  4.1887 +\opfalse{show\_datatypes}{hide\_datatypes}
  4.1888 +Specifies whether the subsets used to approximate (co)in\-duc\-tive datatypes should
  4.1889 +be displayed as part of counterexamples. Such subsets are sometimes helpful when
  4.1890 +investigating whether a potential counterexample is genuine or spurious, but
  4.1891 +their potential for clutter is real.
  4.1892 +
  4.1893 +\opfalse{show\_consts}{hide\_consts}
  4.1894 +Specifies whether the values of constants occurring in the formula (including
  4.1895 +its axioms) should be displayed along with any counterexample. These values are
  4.1896 +sometimes helpful when investigating why a counterexample is
  4.1897 +genuine, but they can clutter the output.
  4.1898 +
  4.1899 +\opfalse{show\_all}{dont\_show\_all}
  4.1900 +Enabling this option effectively enables \textit{show\_skolems},
  4.1901 +\textit{show\_datatypes}, and \textit{show\_consts}.
  4.1902 +
  4.1903 +\opt{max\_potential}{int}{$\mathbf{1}$}
  4.1904 +Specifies the maximum number of potential counterexamples to display. Setting
  4.1905 +this option to 0 speeds up the search for a genuine counterexample. This option
  4.1906 +is implicitly set to 0 for automatic runs. If you set this option to a value
  4.1907 +greater than 1, you will need an incremental SAT solver: For efficiency, it is
  4.1908 +recommended to install the JNI version of MiniSat and set \textit{sat\_solver} =
  4.1909 +\textit{MiniSatJNI}. Also be aware that many of the counterexamples may look
  4.1910 +identical, unless the \textit{show\_all} (\S\ref{output-format}) option is
  4.1911 +enabled.
  4.1912 +
  4.1913 +\nopagebreak
  4.1914 +{\small See also \textit{auto} (\S\ref{mode-of-operation}),
  4.1915 +\textit{check\_potential} (\S\ref{authentication}), and
  4.1916 +\textit{sat\_solver} (\S\ref{optimizations}).}
  4.1917 +
  4.1918 +\opt{max\_genuine}{int}{$\mathbf{1}$}
  4.1919 +Specifies the maximum number of genuine counterexamples to display. If you set
  4.1920 +this option to a value greater than 1, you will need an incremental SAT solver:
  4.1921 +For efficiency, it is recommended to install the JNI version of MiniSat and set
  4.1922 +\textit{sat\_solver} = \textit{MiniSatJNI}. Also be aware that many of the
  4.1923 +counterexamples may look identical, unless the \textit{show\_all}
  4.1924 +(\S\ref{output-format}) option is enabled.
  4.1925 +
  4.1926 +\nopagebreak
  4.1927 +{\small See also \textit{check\_genuine} (\S\ref{authentication}) and
  4.1928 +\textit{sat\_solver} (\S\ref{optimizations}).}
  4.1929 +
  4.1930 +\ops{eval}{term\_list}
  4.1931 +Specifies the list of terms whose values should be displayed along with
  4.1932 +counterexamples. This option suffers from an ``observer effect'': Nitpick might
  4.1933 +find different counterexamples for different values of this option.
  4.1934 +
  4.1935 +\opu{format}{term}{int\_seq}
  4.1936 +Specifies how to uncurry the value displayed for a variable or constant.
  4.1937 +Uncurrying sometimes increases the readability of the output for high-arity
  4.1938 +functions. For example, given the variable $y \mathbin{\Colon} {'a}\Rightarrow
  4.1939 +{'b}\Rightarrow {'c}\Rightarrow {'d}\Rightarrow {'e}\Rightarrow {'f}\Rightarrow
  4.1940 +{'g}$, setting \textit{format}~$y$ = 3 tells Nitpick to group the last three
  4.1941 +arguments, as if the type had been ${'a}\Rightarrow {'b}\Rightarrow
  4.1942 +{'c}\Rightarrow {'d}\times {'e}\times {'f}\Rightarrow {'g}$. In general, a list
  4.1943 +of values $n_1,\ldots,n_k$ tells Nitpick to show the last $n_k$ arguments as an
  4.1944 +$n_k$-tuple, the previous $n_{k-1}$ arguments as an $n_{k-1}$-tuple, and so on;
  4.1945 +arguments that are not accounted for are left alone, as if the specification had
  4.1946 +been $1,\ldots,1,n_1,\ldots,n_k$.
  4.1947 +
  4.1948 +\nopagebreak
  4.1949 +{\small See also \textit{uncurry} (\S\ref{optimizations}).}
  4.1950 +
  4.1951 +\opt{format}{int\_seq}{$\mathbf{1}$}
  4.1952 +Specifies the default format to use. Irrespective of the default format, the
  4.1953 +extra arguments to a Skolem constant corresponding to the outer bound variables
  4.1954 +are kept separated from the remaining arguments, the \textbf{for} arguments of
  4.1955 +an inductive definitions are kept separated from the remaining arguments, and
  4.1956 +the iteration counter of an unrolled inductive definition is shown alone. The
  4.1957 +default format can be overridden on a per-variable or per-constant basis using
  4.1958 +the \textit{format}~\qty{term} option described above.
  4.1959 +\end{enum}
  4.1960 +
  4.1961 +%% MARK: Authentication
  4.1962 +\subsection{Authentication}
  4.1963 +\label{authentication}
  4.1964 +
  4.1965 +\begin{enum}
  4.1966 +\opfalse{check\_potential}{trust\_potential}
  4.1967 +Specifies whether potential counterexamples should be given to Isabelle's
  4.1968 +\textit{auto} tactic to assess their validity. If a potential counterexample is
  4.1969 +shown to be genuine, Nitpick displays a message to this effect and terminates.
  4.1970 +
  4.1971 +\nopagebreak
  4.1972 +{\small See also \textit{max\_potential} (\S\ref{output-format}) and
  4.1973 +\textit{auto\_timeout} (\S\ref{timeouts}).}
  4.1974 +
  4.1975 +\opfalse{check\_genuine}{trust\_genuine}
  4.1976 +Specifies whether genuine and likely genuine counterexamples should be given to
  4.1977 +Isabelle's \textit{auto} tactic to assess their validity. If a ``genuine''
  4.1978 +counterexample is shown to be spurious, the user is kindly asked to send a bug
  4.1979 +report to the author at
  4.1980 +\texttt{blan{\color{white}nospam}\kern-\wd\boxA{}chette@in.tum.de}.
  4.1981 +
  4.1982 +\nopagebreak
  4.1983 +{\small See also \textit{max\_genuine} (\S\ref{output-format}) and
  4.1984 +\textit{auto\_timeout} (\S\ref{timeouts}).}
  4.1985 +
  4.1986 +\ops{expect}{string}
  4.1987 +Specifies the expected outcome, which must be one of the following:
  4.1988 +
  4.1989 +\begin{enum}
  4.1990 +\item[$\bullet$] \textbf{\textit{genuine}}: Nitpick found a genuine counterexample.
  4.1991 +\item[$\bullet$] \textbf{\textit{likely\_genuine}}: Nitpick found a ``likely
  4.1992 +genuine'' counterexample (i.e., a counterexample that is genuine unless
  4.1993 +it contradicts a missing axiom or a dangerous option was used inappropriately).
  4.1994 +\item[$\bullet$] \textbf{\textit{potential}}: Nitpick found a potential counterexample.
  4.1995 +\item[$\bullet$] \textbf{\textit{none}}: Nitpick found no counterexample.
  4.1996 +\item[$\bullet$] \textbf{\textit{unknown}}: Nitpick encountered some problem (e.g.,
  4.1997 +Kodkod ran out of memory).
  4.1998 +\end{enum}
  4.1999 +
  4.2000 +Nitpick emits an error if the actual outcome differs from the expected outcome.
  4.2001 +This option is useful for regression testing.
  4.2002 +\end{enum}
  4.2003 +
  4.2004 +\subsection{Optimizations}
  4.2005 +\label{optimizations}
  4.2006 +
  4.2007 +\def\cpp{C\nobreak\raisebox{.1ex}{+}\nobreak\raisebox{.1ex}{+}}
  4.2008 +
  4.2009 +\sloppy
  4.2010 +
  4.2011 +\begin{enum}
  4.2012 +\opt{sat\_solver}{string}{smart}
  4.2013 +Specifies which SAT solver to use. SAT solvers implemented in C or \cpp{} tend
  4.2014 +to be faster than their Java counterparts, but they can be more difficult to
  4.2015 +install. Also, if you set the \textit{max\_potential} (\S\ref{output-format}) or
  4.2016 +\textit{max\_genuine} (\S\ref{output-format}) option to a value greater than 1,
  4.2017 +you will need an incremental SAT solver, such as \textit{MiniSatJNI}
  4.2018 +(recommended) or \textit{SAT4J}.
  4.2019 +
  4.2020 +The supported solvers are listed below:
  4.2021 +
  4.2022 +\begin{enum}
  4.2023 +
  4.2024 +\item[$\bullet$] \textbf{\textit{MiniSat}}: MiniSat is an efficient solver
  4.2025 +written in \cpp{}. To use MiniSat, set the environment variable
  4.2026 +\texttt{MINISAT\_HOME} to the directory that contains the \texttt{minisat}
  4.2027 +executable. The \cpp{} sources and executables for MiniSat are available at
  4.2028 +\url{http://minisat.se/MiniSat.html}. Nitpick has been tested with versions 1.14
  4.2029 +and 2.0 beta (2007-07-21).
  4.2030 +
  4.2031 +\item[$\bullet$] \textbf{\textit{MiniSatJNI}}: The JNI (Java Native Interface)
  4.2032 +version of MiniSat is bundled in \texttt{nativesolver.\allowbreak tgz}, which
  4.2033 +you will find on Kodkod's web site \cite{kodkod-2009}. Unlike the standard
  4.2034 +version of MiniSat, the JNI version can be used incrementally.
  4.2035 +
  4.2036 +\item[$\bullet$] \textbf{\textit{PicoSAT}}: PicoSAT is an efficient solver
  4.2037 +written in C. It is bundled with Kodkodi and requires no further installation or
  4.2038 +configuration steps. Alternatively, you can install a standard version of
  4.2039 +PicoSAT and set the environment variable \texttt{PICOSAT\_HOME} to the directory
  4.2040 +that contains the \texttt{picosat} executable. The C sources for PicoSAT are
  4.2041 +available at \url{http://fmv.jku.at/picosat/} and are also bundled with Kodkodi.
  4.2042 +Nitpick has been tested with version 913.
  4.2043 +
  4.2044 +\item[$\bullet$] \textbf{\textit{zChaff}}: zChaff is an efficient solver written
  4.2045 +in \cpp{}. To use zChaff, set the environment variable \texttt{ZCHAFF\_HOME} to
  4.2046 +the directory that contains the \texttt{zchaff} executable. The \cpp{} sources
  4.2047 +and executables for zChaff are available at
  4.2048 +\url{http://www.princeton.edu/~chaff/zchaff.html}. Nitpick has been tested with
  4.2049 +versions 2004-05-13, 2004-11-15, and 2007-03-12.
  4.2050 +
  4.2051 +\item[$\bullet$] \textbf{\textit{zChaffJNI}}: The JNI version of zChaff is
  4.2052 +bundled in \texttt{native\-solver.\allowbreak tgz}, which you will find on
  4.2053 +Kodkod's web site \cite{kodkod-2009}.
  4.2054 +
  4.2055 +\item[$\bullet$] \textbf{\textit{RSat}}: RSat is an efficient solver written in
  4.2056 +\cpp{}. To use RSat, set the environment variable \texttt{RSAT\_HOME} to the
  4.2057 +directory that contains the \texttt{rsat} executable. The \cpp{} sources for
  4.2058 +RSat are available at \url{http://reasoning.cs.ucla.edu/rsat/}. Nitpick has been
  4.2059 +tested with version 2.01.
  4.2060 +
  4.2061 +\item[$\bullet$] \textbf{\textit{BerkMin}}: BerkMin561 is an efficient solver
  4.2062 +written in C. To use BerkMin, set the environment variable
  4.2063 +\texttt{BERKMIN\_HOME} to the directory that contains the \texttt{BerkMin561}
  4.2064 +executable. The BerkMin executables are available at
  4.2065 +\url{http://eigold.tripod.com/BerkMin.html}.
  4.2066 +
  4.2067 +\item[$\bullet$] \textbf{\textit{BerkMinAlloy}}: Variant of BerkMin that is
  4.2068 +included with Alloy 4 and calls itself ``sat56'' in its banner text. To use this
  4.2069 +version of BerkMin, set the environment variable
  4.2070 +\texttt{BERKMINALLOY\_HOME} to the directory that contains the \texttt{berkmin}
  4.2071 +executable.
  4.2072 +
  4.2073 +\item[$\bullet$] \textbf{\textit{Jerusat}}: Jerusat 1.3 is an efficient solver
  4.2074 +written in C. To use Jerusat, set the environment variable
  4.2075 +\texttt{JERUSAT\_HOME} to the directory that contains the \texttt{Jerusat1.3}
  4.2076 +executable. The C sources for Jerusat are available at
  4.2077 +\url{http://www.cs.tau.ac.il/~ale1/Jerusat1.3.tgz}.
  4.2078 +
  4.2079 +\item[$\bullet$] \textbf{\textit{SAT4J}}: SAT4J is a reasonably efficient solver
  4.2080 +written in Java that can be used incrementally. It is bundled with Kodkodi and
  4.2081 +requires no further installation or configuration steps. Do not attempt to
  4.2082 +install the official SAT4J packages, because their API is incompatible with
  4.2083 +Kodkod.
  4.2084 +
  4.2085 +\item[$\bullet$] \textbf{\textit{SAT4JLight}}: Variant of SAT4J that is
  4.2086 +optimized for small problems. It can also be used incrementally.
  4.2087 +
  4.2088 +\item[$\bullet$] \textbf{\textit{HaifaSat}}: HaifaSat 1.0 beta is an
  4.2089 +experimental solver written in \cpp. To use HaifaSat, set the environment
  4.2090 +variable \texttt{HAIFASAT\_\allowbreak HOME} to the directory that contains the
  4.2091 +\texttt{HaifaSat} executable. The \cpp{} sources for HaifaSat are available at
  4.2092 +\url{http://cs.technion.ac.il/~gershman/HaifaSat.htm}.
  4.2093 +
  4.2094 +\item[$\bullet$] \textbf{\textit{smart}}: If \textit{sat\_solver} is set to
  4.2095 +\textit{smart}, Nitpick selects the first solver among MiniSat, PicoSAT, zChaff,
  4.2096 +RSat, BerkMin, BerkMinAlloy, and Jerusat that is recognized by Isabelle. If none
  4.2097 +is found, it falls back on SAT4J, which should always be available. If
  4.2098 +\textit{verbose} is enabled, Nitpick displays which SAT solver was chosen.
  4.2099 +
  4.2100 +\end{enum}
  4.2101 +\fussy
  4.2102 +
  4.2103 +\opt{batch\_size}{int\_or\_smart}{smart}
  4.2104 +Specifies the maximum number of Kodkod problems that should be lumped together
  4.2105 +when invoking Kodkodi. Each problem corresponds to one scope. Lumping problems
  4.2106 +together ensures that Kodkodi is launched less often, but it makes the verbose
  4.2107 +output less readable and is sometimes detrimental to performance. If
  4.2108 +\textit{batch\_size} is set to \textit{smart}, the actual value used is 1 if
  4.2109 +\textit{debug} (\S\ref{output-format}) is set and 64 otherwise.
  4.2110 +
  4.2111 +\optrue{destroy\_constrs}{dont\_destroy\_constrs}
  4.2112 +Specifies whether formulas involving (co)in\-duc\-tive datatype constructors should
  4.2113 +be rewritten to use (automatically generated) discriminators and destructors.
  4.2114 +This optimization can drastically reduce the size of the Boolean formulas given
  4.2115 +to the SAT solver.
  4.2116 +
  4.2117 +\nopagebreak
  4.2118 +{\small See also \textit{debug} (\S\ref{output-format}).}
  4.2119 +
  4.2120 +\optrue{specialize}{dont\_specialize}
  4.2121 +Specifies whether functions invoked with static arguments should be specialized.
  4.2122 +This optimization can drastically reduce the search space, especially for
  4.2123 +higher-order functions.
  4.2124 +
  4.2125 +\nopagebreak
  4.2126 +{\small See also \textit{debug} (\S\ref{output-format}) and
  4.2127 +\textit{show\_consts} (\S\ref{output-format}).}
  4.2128 +
  4.2129 +\optrue{skolemize}{dont\_skolemize}
  4.2130 +Specifies whether the formula should be skolemized. For performance reasons,
  4.2131 +(positive) $\forall$-quanti\-fiers that occur in the scope of a higher-order
  4.2132 +(positive) $\exists$-quanti\-fier are left unchanged.
  4.2133 +
  4.2134 +\nopagebreak
  4.2135 +{\small See also \textit{debug} (\S\ref{output-format}) and
  4.2136 +\textit{show\_skolems} (\S\ref{output-format}).}
  4.2137 +
  4.2138 +\optrue{star\_linear\_preds}{dont\_star\_linear\_preds}
  4.2139 +Specifies whether Nitpick should use Kodkod's transitive closure operator to
  4.2140 +encode non-well-founded ``linear inductive predicates,'' i.e., inductive
  4.2141 +predicates for which each the predicate occurs in at most one assumption of each
  4.2142 +introduction rule. Using the reflexive transitive closure is in principle
  4.2143 +equivalent to setting \textit{iter} to the cardinality of the predicate's
  4.2144 +domain, but it is usually more efficient.
  4.2145 +
  4.2146 +{\small See also \textit{wf} (\S\ref{scope-of-search}), \textit{debug}
  4.2147 +(\S\ref{output-format}), and \textit{iter} (\S\ref{scope-of-search}).}
  4.2148 +
  4.2149 +\optrue{uncurry}{dont\_uncurry}
  4.2150 +Specifies whether Nitpick should uncurry functions. Uncurrying has on its own no
  4.2151 +tangible effect on efficiency, but it creates opportunities for the boxing 
  4.2152 +optimization.
  4.2153 +
  4.2154 +\nopagebreak
  4.2155 +{\small See also \textit{box} (\S\ref{scope-of-search}), \textit{debug}
  4.2156 +(\S\ref{output-format}), and \textit{format} (\S\ref{output-format}).}
  4.2157 +
  4.2158 +\optrue{fast\_descrs}{full\_descrs}
  4.2159 +Specifies whether Nitpick should optimize the definite and indefinite
  4.2160 +description operators (THE and SOME). The optimized versions usually help
  4.2161 +Nitpick generate more counterexamples or at least find them faster, but only the
  4.2162 +unoptimized versions are complete when all types occurring in the formula are
  4.2163 +finite.
  4.2164 +
  4.2165 +{\small See also \textit{debug} (\S\ref{output-format}).}
  4.2166 +
  4.2167 +\optrue{peephole\_optim}{no\_peephole\_optim}
  4.2168 +Specifies whether Nitpick should simplify the generated Kodkod formulas using a
  4.2169 +peephole optimizer. These optimizations can make a significant difference.
  4.2170 +Unless you are tracking down a bug in Nitpick or distrust the peephole
  4.2171 +optimizer, you should leave this option enabled.
  4.2172 +
  4.2173 +\opt{sym\_break}{int}{20}
  4.2174 +Specifies an upper bound on the number of relations for which Kodkod generates
  4.2175 +symmetry breaking predicates. According to the Kodkod documentation
  4.2176 +\cite{kodkod-2009-options}, ``in general, the higher this value, the more
  4.2177 +symmetries will be broken, and the faster the formula will be solved. But,
  4.2178 +setting the value too high may have the opposite effect and slow down the
  4.2179 +solving.''
  4.2180 +
  4.2181 +\opt{sharing\_depth}{int}{3}
  4.2182 +Specifies the depth to which Kodkod should check circuits for equivalence during
  4.2183 +the translation to SAT. The default of 3 is the same as in Alloy. The minimum
  4.2184 +allowed depth is 1. Increasing the sharing may result in a smaller SAT problem,
  4.2185 +but can also slow down Kodkod.
  4.2186 +
  4.2187 +\opfalse{flatten\_props}{dont\_flatten\_props}
  4.2188 +Specifies whether Kodkod should try to eliminate intermediate Boolean variables.
  4.2189 +Although this might sound like a good idea, in practice it can drastically slow
  4.2190 +down Kodkod.
  4.2191 +
  4.2192 +\opt{max\_threads}{int}{0}
  4.2193 +Specifies the maximum number of threads to use in Kodkod. If this option is set
  4.2194 +to 0, Kodkod will compute an appropriate value based on the number of processor
  4.2195 +cores available.
  4.2196 +
  4.2197 +\nopagebreak
  4.2198 +{\small See also \textit{batch\_size} (\S\ref{optimizations}) and
  4.2199 +\textit{timeout} (\S\ref{timeouts}).}
  4.2200 +\end{enum}
  4.2201 +
  4.2202 +\subsection{Timeouts}
  4.2203 +\label{timeouts}
  4.2204 +
  4.2205 +\begin{enum}
  4.2206 +\opt{timeout}{time}{$\mathbf{30}$ s}
  4.2207 +Specifies the maximum amount of time that the \textbf{nitpick} command should
  4.2208 +spend looking for a counterexample. Nitpick tries to honor this constraint as
  4.2209 +well as it can but offers no guarantees. For automatic runs,
  4.2210 +\textit{auto\_timeout} is used instead.
  4.2211 +
  4.2212 +\nopagebreak
  4.2213 +{\small See also \textit{auto} (\S\ref{mode-of-operation})
  4.2214 +and \textit{max\_threads} (\S\ref{optimizations}).}
  4.2215 +
  4.2216 +\opt{auto\_timeout}{time}{$\mathbf{5}$ s}
  4.2217 +Specifies the maximum amount of time that Nitpick should use to find a
  4.2218 +counterexample when running automatically. Nitpick tries to honor this
  4.2219 +constraint as well as it can but offers no guarantees.
  4.2220 +
  4.2221 +\nopagebreak
  4.2222 +{\small See also \textit{auto} (\S\ref{mode-of-operation}).}
  4.2223 +
  4.2224 +\opt{tac\_timeout}{time}{$\mathbf{500}$ ms}
  4.2225 +Specifies the maximum amount of time that the \textit{auto} tactic should use
  4.2226 +when checking a counterexample, and similarly that \textit{lexicographic\_order}
  4.2227 +and \textit{sizechange} should use when checking whether a (co)in\-duc\-tive
  4.2228 +predicate is well-founded. Nitpick tries to honor this constraint as well as it
  4.2229 +can but offers no guarantees.
  4.2230 +
  4.2231 +\nopagebreak
  4.2232 +{\small See also \textit{wf} (\S\ref{scope-of-search}),
  4.2233 +\textit{check\_potential} (\S\ref{authentication}),
  4.2234 +and \textit{check\_genuine} (\S\ref{authentication}).}
  4.2235 +\end{enum}
  4.2236 +
  4.2237 +\section{Attribute Reference}
  4.2238 +\label{attribute-reference}
  4.2239 +
  4.2240 +Nitpick needs to consider the definitions of all constants occurring in a
  4.2241 +formula in order to falsify it. For constants introduced using the
  4.2242 +\textbf{definition} command, the definition is simply the associated
  4.2243 +\textit{\_def} axiom. In contrast, instead of using the internal representation
  4.2244 +of functions synthesized by Isabelle's \textbf{primrec}, \textbf{function}, and
  4.2245 +\textbf{nominal\_primrec} packages, Nitpick relies on the more natural
  4.2246 +equational specification entered by the user.
  4.2247 +
  4.2248 +Behind the scenes, Isabelle's built-in packages and theories rely on the
  4.2249 +following attributes to affect Nitpick's behavior:
  4.2250 +
  4.2251 +\begin{itemize}
  4.2252 +\flushitem{\textit{nitpick\_def}}
  4.2253 +
  4.2254 +\nopagebreak
  4.2255 +This attribute specifies an alternative definition of a constant. The
  4.2256 +alternative definition should be logically equivalent to the constant's actual
  4.2257 +axiomatic definition and should be of the form
  4.2258 +
  4.2259 +\qquad $c~{?}x_1~\ldots~{?}x_n \,\equiv\, t$,
  4.2260 +
  4.2261 +where ${?}x_1, \ldots, {?}x_n$ are distinct variables and $c$ does not occur in
  4.2262 +$t$.
  4.2263 +
  4.2264 +\flushitem{\textit{nitpick\_simp}}
  4.2265 +
  4.2266 +\nopagebreak
  4.2267 +This attribute specifies the equations that constitute the specification of a
  4.2268 +constant. For functions defined using the \textbf{primrec}, \textbf{function},
  4.2269 +and \textbf{nominal\_\allowbreak primrec} packages, this corresponds to the
  4.2270 +\textit{simps} rules. The equations must be of the form
  4.2271 +
  4.2272 +\qquad $c~t_1~\ldots\ t_n \,=\, u.$
  4.2273 +
  4.2274 +\flushitem{\textit{nitpick\_psimp}}
  4.2275 +
  4.2276 +\nopagebreak
  4.2277 +This attribute specifies the equations that constitute the partial specification
  4.2278 +of a constant. For functions defined using the \textbf{function} package, this
  4.2279 +corresponds to the \textit{psimps} rules. The conditional equations must be of
  4.2280 +the form
  4.2281 +
  4.2282 +\qquad $\lbrakk P_1;\> \ldots;\> P_m\rbrakk \,\Longrightarrow\, c\ t_1\ \ldots\ t_n \,=\, u$.
  4.2283 +
  4.2284 +\flushitem{\textit{nitpick\_intro}}
  4.2285 +
  4.2286 +\nopagebreak
  4.2287 +This attribute specifies the introduction rules of a (co)in\-duc\-tive predicate.
  4.2288 +For predicates defined using the \textbf{inductive} or \textbf{coinductive}
  4.2289 +command, this corresponds to the \textit{intros} rules. The introduction rules
  4.2290 +must be of the form
  4.2291 +
  4.2292 +\qquad $\lbrakk P_1;\> \ldots;\> P_m;\> M~(c\ t_{11}\ \ldots\ t_{1n});\>
  4.2293 +\ldots;\> M~(c\ t_{k1}\ \ldots\ t_{kn})\rbrakk \,\Longrightarrow\, c\ u_1\
  4.2294 +\ldots\ u_n$,
  4.2295 +
  4.2296 +where the $P_i$'s are side conditions that do not involve $c$ and $M$ is an
  4.2297 +optional monotonic operator. The order of the assumptions is irrelevant.
  4.2298 +
  4.2299 +\end{itemize}
  4.2300 +
  4.2301 +When faced with a constant, Nitpick proceeds as follows:
  4.2302 +
  4.2303 +\begin{enum}
  4.2304 +\item[1.] If the \textit{nitpick\_simp} set associated with the constant
  4.2305 +is not empty, Nitpick uses these rules as the specification of the constant.
  4.2306 +
  4.2307 +\item[2.] Otherwise, if the \textit{nitpick\_psimp} set associated with
  4.2308 +the constant is not empty, it uses these rules as the specification of the
  4.2309 +constant.
  4.2310 +
  4.2311 +\item[3.] Otherwise, it looks up the definition of the constant:
  4.2312 +
  4.2313 +\begin{enum}
  4.2314 +\item[1.] If the \textit{nitpick\_def} set associated with the constant
  4.2315 +is not empty, it uses the latest rule added to the set as the definition of the
  4.2316 +constant; otherwise it uses the actual definition axiom.
  4.2317 +\item[2.] If the definition is of the form
  4.2318 +
  4.2319 +\qquad $c~{?}x_1~\ldots~{?}x_m \,\equiv\, \lambda y_1~\ldots~y_n.\; \textit{lfp}~(\lambda f.\; t)$,
  4.2320 +
  4.2321 +then Nitpick assumes that the definition was made using an inductive package and
  4.2322 +based on the introduction rules marked with \textit{nitpick\_\allowbreak
  4.2323 +ind\_\allowbreak intros} tries to determine whether the definition is
  4.2324 +well-founded.
  4.2325 +\end{enum}
  4.2326 +\end{enum}
  4.2327 +
  4.2328 +As an illustration, consider the inductive definition
  4.2329 +
  4.2330 +\prew
  4.2331 +\textbf{inductive}~\textit{odd}~\textbf{where} \\
  4.2332 +``\textit{odd}~1'' $\,\mid$ \\
  4.2333 +``\textit{odd}~$n\,\Longrightarrow\, \textit{odd}~(\textit{Suc}~(\textit{Suc}~n))$''
  4.2334 +\postw
  4.2335 +
  4.2336 +Isabelle automatically attaches the \textit{nitpick\_intro} attribute to
  4.2337 +the above rules. Nitpick then uses the \textit{lfp}-based definition in
  4.2338 +conjunction with these rules. To override this, we can specify an alternative
  4.2339 +definition as follows:
  4.2340 +
  4.2341 +\prew
  4.2342 +\textbf{lemma} $\mathit{odd\_def}'$ [\textit{nitpick\_def}]: ``$\textit{odd}~n \,\equiv\, n~\textrm{mod}~2 = 1$''
  4.2343 +\postw
  4.2344 +
  4.2345 +Nitpick then expands all occurrences of $\mathit{odd}~n$ to $n~\textrm{mod}~2
  4.2346 += 1$. Alternatively, we can specify an equational specification of the constant:
  4.2347 +
  4.2348 +\prew
  4.2349 +\textbf{lemma} $\mathit{odd\_simp}'$ [\textit{nitpick\_simp}]: ``$\textit{odd}~n = (n~\textrm{mod}~2 = 1)$''
  4.2350 +\postw
  4.2351 +
  4.2352 +Such tweaks should be done with great care, because Nitpick will assume that the
  4.2353 +constant is completely defined by its equational specification. For example, if
  4.2354 +you make ``$\textit{odd}~(2 * k + 1)$'' a \textit{nitpick\_simp} rule and neglect to provide rules to handle the $2 * k$ case, Nitpick will define
  4.2355 +$\textit{odd}~n$ arbitrarily for even values of $n$. The \textit{debug}
  4.2356 +(\S\ref{output-format}) option is extremely useful to understand what is going
  4.2357 +on when experimenting with \textit{nitpick\_} attributes.
  4.2358 +
  4.2359 +\section{Standard ML Interface}
  4.2360 +\label{standard-ml-interface}
  4.2361 +
  4.2362 +Nitpick provides a rich Standard ML interface used mainly for internal purposes
  4.2363 +and debugging. Among the most interesting functions exported by Nitpick are
  4.2364 +those that let you invoke the tool programmatically and those that let you
  4.2365 +register and unregister custom coinductive datatypes.
  4.2366 +
  4.2367 +\subsection{Invocation of Nitpick}
  4.2368 +\label{invocation-of-nitpick}
  4.2369 +
  4.2370 +The \textit{Nitpick} structure offers the following functions for invoking your
  4.2371 +favorite counterexample generator:
  4.2372 +
  4.2373 +\prew
  4.2374 +$\textbf{val}\,~\textit{pick\_nits\_in\_term} : \\
  4.2375 +\hbox{}\quad\textit{Proof.state} \rightarrow \textit{params} \rightarrow \textit{bool} \rightarrow \textit{term~list} \rightarrow \textit{term} \\
  4.2376 +\hbox{}\quad{\rightarrow}\; \textit{string} * \textit{Proof.state}$ \\
  4.2377 +$\textbf{val}\,~\textit{pick\_nits\_in\_subgoal} : \\
  4.2378 +\hbox{}\quad\textit{Proof.state} \rightarrow \textit{params} \rightarrow \textit{bool} \rightarrow \textit{int} \rightarrow \textit{string} * \textit{Proof.state}$
  4.2379 +\postw
  4.2380 +
  4.2381 +The return value is a new proof state paired with an outcome string
  4.2382 +(``genuine'', ``likely\_genuine'', ``potential'', ``none'', or ``unknown''). The
  4.2383 +\textit{params} type is a large record that lets you set Nitpick's options. The
  4.2384 +current default options can be retrieved by calling the following function
  4.2385 +defined in the \textit{NitpickIsar} structure:
  4.2386 +
  4.2387 +\prew
  4.2388 +$\textbf{val}\,~\textit{default\_params} :\,
  4.2389 +\textit{theory} \rightarrow (\textit{string} * \textit{string})~\textit{list} \rightarrow \textit{params}$
  4.2390 +\postw
  4.2391 +
  4.2392 +The second argument lets you override option values before they are parsed and
  4.2393 +put into a \textit{params} record. Here is an example:
  4.2394 +
  4.2395 +\prew
  4.2396 +$\textbf{val}\,~\textit{params} = \textit{NitpickIsar.default\_params}~\textit{thy}~[(\textrm{``}\textrm{timeout}\textrm{''},\, \textrm{``}\textrm{none}\textrm{''})]$ \\
  4.2397 +$\textbf{val}\,~(\textit{outcome},\, \textit{state}') = \textit{Nitpick.pick\_nits\_in\_subgoal}~\begin{aligned}[t]
  4.2398 +& \textit{state}~\textit{params}~\textit{false} \\[-2pt]
  4.2399 +& \textit{subgoal}\end{aligned}$
  4.2400 +\postw
  4.2401 +
  4.2402 +\subsection{Registration of Coinductive Datatypes}
  4.2403 +\label{registration-of-coinductive-datatypes}
  4.2404 +
  4.2405 +\let\antiq=\textrm
  4.2406 +
  4.2407 +If you have defined a custom coinductive datatype, you can tell Nitpick about
  4.2408 +it, so that it can use an efficient Kodkod axiomatization similar to the one it
  4.2409 +uses for lazy lists. The interface for registering and unregistering coinductive
  4.2410 +datatypes consists of the following pair of functions defined in the
  4.2411 +\textit{Nitpick} structure:
  4.2412 +
  4.2413 +\prew
  4.2414 +$\textbf{val}\,~\textit{register\_codatatype} :\,
  4.2415 +\textit{typ} \rightarrow \textit{string} \rightarrow \textit{styp~list} \rightarrow \textit{theory} \rightarrow \textit{theory}$ \\
  4.2416 +$\textbf{val}\,~\textit{unregister\_codatatype} :\,
  4.2417 +\textit{typ} \rightarrow \textit{theory} \rightarrow \textit{theory}$
  4.2418 +\postw
  4.2419 +
  4.2420 +The type $'a~\textit{llist}$ of lazy lists is already registered; had it
  4.2421 +not been, you could have told Nitpick about it by adding the following line
  4.2422 +to your theory file:
  4.2423 +
  4.2424 +\prew
  4.2425 +$\textbf{setup}~\,\{{*}\,~\!\begin{aligned}[t]
  4.2426 +& \textit{Nitpick.register\_codatatype} \\[-2pt]
  4.2427 +& \qquad @\{\antiq{typ}~``\kern1pt'a~\textit{llist}\textrm{''}\}~@\{\antiq{const\_name}~ \textit{llist\_case}\} \\[-2pt] %% TYPESETTING
  4.2428 +& \qquad (\textit{map}~\textit{dest\_Const}~[@\{\antiq{term}~\textit{LNil}\},\, @\{\antiq{term}~\textit{LCons}\}])\,\ {*}\}\end{aligned}$
  4.2429 +\postw
  4.2430 +
  4.2431 +The \textit{register\_codatatype} function takes a coinductive type, its case
  4.2432 +function, and the list of its constructors. The case function must take its
  4.2433 +arguments in the order that the constructors are listed. If no case function
  4.2434 +with the correct signature is available, simply pass the empty string.
  4.2435 +
  4.2436 +On the other hand, if your goal is to cripple Nitpick, add the following line to
  4.2437 +your theory file and try to check a few conjectures about lazy lists:
  4.2438 +
  4.2439 +\prew
  4.2440 +$\textbf{setup}~\,\{{*}\,~\textit{Nitpick.unregister\_codatatype}~@\{\antiq{typ}~``
  4.2441 +\kern1pt'a~\textit{list}\textrm{''}\}\ \,{*}\}$
  4.2442 +\postw
  4.2443 +
  4.2444 +\section{Known Bugs and Limitations}
  4.2445 +\label{known-bugs-and-limitations}
  4.2446 +
  4.2447 +Here are the known bugs and limitations in Nitpick at the time of writing:
  4.2448 +
  4.2449 +\begin{enum}
  4.2450 +\item[$\bullet$] Underspecified functions defined using the \textbf{primrec},
  4.2451 +\textbf{function}, or \textbf{nominal\_\allowbreak primrec} packages can lead
  4.2452 +Nitpick to generate spurious counterexamples for theorems that refer to values
  4.2453 +for which the function is not defined. For example:
  4.2454 +
  4.2455 +\prew
  4.2456 +\textbf{primrec} \textit{prec} \textbf{where} \\
  4.2457 +``$\textit{prec}~(\textit{Suc}~n) = n$'' \\[2\smallskipamount]
  4.2458 +\textbf{lemma} ``$\textit{prec}~0 = \undef$'' \\
  4.2459 +\textbf{nitpick} \\[2\smallskipamount]
  4.2460 +\quad{\slshape Nitpick found a counterexample for \textit{card nat}~= 2: 
  4.2461 +\nopagebreak
  4.2462 +\\[2\smallskipamount]
  4.2463 +\hbox{}\qquad Empty assignment} \nopagebreak\\[2\smallskipamount]
  4.2464 +\textbf{by}~(\textit{auto simp}: \textit{prec\_def})
  4.2465 +\postw
  4.2466 +
  4.2467 +Such theorems are considered bad style because they rely on the internal
  4.2468 +representation of functions synthesized by Isabelle, which is an implementation
  4.2469 +detail.
  4.2470 +
  4.2471 +\item[$\bullet$] Nitpick produces spurious counterexamples when invoked after a
  4.2472 +\textbf{guess} command in a structured proof.
  4.2473 +
  4.2474 +\item[$\bullet$] The \textit{nitpick\_} attributes and the
  4.2475 +\textit{Nitpick.register\_} functions can cause havoc if used improperly.
  4.2476 +
  4.2477 +\item[$\bullet$] Local definitions are not supported and result in an error.
  4.2478 +
  4.2479 +\item[$\bullet$] All constants and types whose names start with
  4.2480 +\textit{Nitpick}{.} or \textit{NitpickDefs}{.} are reserved for internal use.
  4.2481 +\end{enum}
  4.2482 +
  4.2483 +\let\em=\sl
  4.2484 +\bibliography{../manual}{}
  4.2485 +\bibliographystyle{abbrv}
  4.2486 +
  4.2487 +\end{document}
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  5.1736 + add add add 1 min neg 1 add
  5.1737 +}bdf
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  5.1739 +/maxcolor { 
  5.1740 + max max max  
  5.1741 +} ndf
  5.1742 +/maxspot {
  5.1743 + pop
  5.1744 +} ndf
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  5.1746 +/findcmykcustomcolor{5 packedarray}ndf
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  5.1748 +/setseparationgray{setgray}ndf
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  5.1753 + { 
  5.1754 +4 index 1 index get 0.3 mul 
  5.1755 +4 index 2 index get 0.59 mul 
  5.1756 +4 index 3 index get 0.11 mul 
  5.1757 +4 index 4 index get 
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  5.1759 +255 exch sub
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  5.1761 + }for
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  5.1763 +}bdf
  5.1764 +/colorimage{
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  5.1766 + [
  5.1767 +5 -1 roll/exec cvx 
  5.1768 +6 -1 roll/exec cvx 
  5.1769 +7 -1 roll/exec cvx 
  5.1770 +8 -1 roll/exec cvx
  5.1771 +/cmykbufs2gray cvx
  5.1772 + ]cvx 
  5.1773 + image
  5.1774 +}
  5.1775 +%. version 47.1 on Linotronic of Postscript defines colorimage incorrectly (rgb model only)
  5.1776 +version cvr 47.1 le 
  5.1777 +statusdict /product get (Lino) anchorsearch{pop pop true}{pop false}ifelse
  5.1778 +and{userdict begin bdf end}{ndf}ifelse
  5.1779 +fhnumcolors 1 ne {/yt save def} if
  5.1780 +/customcolorimage{
  5.1781 + aload pop
  5.1782 + (_vc_Registration) eq 
  5.1783 + {
  5.1784 +pop pop pop pop separationimage
  5.1785 + }
  5.1786 + {
  5.1787 +/ik xdf /iy xdf /im xdf /ic xdf
  5.1788 +ic im iy ik cmyk2gray /xt xdf
  5.1789 +currenttransfer
  5.1790 +{dup 1.0 exch sub xt mul add}concatprocs
  5.1791 +st 
  5.1792 +image
  5.1793 + }
  5.1794 + ifelse
  5.1795 +}ndf
  5.1796 +fhnumcolors 1 ne {yt restore} if
  5.1797 +fhnumcolors 3 ne {/yt save def} if
  5.1798 +/customcolorimage{
  5.1799 + aload pop 
  5.1800 + (_vc_Registration) eq 
  5.1801 + {
  5.1802 +pop pop pop pop separationimage
  5.1803 + }
  5.1804 + {
  5.1805 +/ik xdf /iy xdf /im xdf /ic xdf
  5.1806 +1.0 dup ic ik add min sub 
  5.1807 +1.0 dup im ik add min sub 
  5.1808 +1.0 dup iy ik add min sub 
  5.1809 +/ic xdf /iy xdf /im xdf
  5.1810 +currentcolortransfer
  5.1811 +4 1 roll 
  5.1812 +{dup 1.0 exch sub ic mul add}concatprocs 4 1 roll 
  5.1813 +{dup 1.0 exch sub iy mul add}concatprocs 4 1 roll 
  5.1814 +{dup 1.0 exch sub im mul add}concatprocs 4 1 roll 
  5.1815 +setcolortransfer
  5.1816 +{/dummy xdf dummy}concatprocs{dummy}{dummy}true 3 colorimage
  5.1817 + }
  5.1818 + ifelse
  5.1819 +}ndf
  5.1820 +fhnumcolors 3 ne {yt restore} if
  5.1821 +fhnumcolors 4 ne {/yt save def} if
  5.1822 +/customcolorimage{
  5.1823 + aload pop
  5.1824 + (_vc_Registration) eq 
  5.1825 + {
  5.1826 +pop pop pop pop separationimage
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  5.1828 + {
  5.1829 +/ik xdf /iy xdf /im xdf /ic xdf
  5.1830 +currentcolortransfer
  5.1831 +{1.0 exch sub ik mul ik sub 1 add}concatprocs 4 1 roll
  5.1832 +{1.0 exch sub iy mul iy sub 1 add}concatprocs 4 1 roll
  5.1833 +{1.0 exch sub im mul im sub 1 add}concatprocs 4 1 roll
  5.1834 +{1.0 exch sub ic mul ic sub 1 add}concatprocs 4 1 roll
  5.1835 +setcolortransfer
  5.1836 +{/dummy xdf dummy}concatprocs{dummy}{dummy}{dummy}
  5.1837 +true 4 colorimage
  5.1838 + }
  5.1839 + ifelse
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  5.1841 +fhnumcolors 4 ne {yt restore} if
  5.1842 +/separationimage{image}ndf
  5.1843 +/newcmykcustomcolor{6 packedarray}ndf
  5.1844 +/inkoverprint false ndf
  5.1845 +/setinkoverprint{pop}ndf 
  5.1846 +/setspotcolor { 
  5.1847 + spots exch get
  5.1848 + dup 4 get (_vc_Registration) eq
  5.1849 + {pop 1 exch sub setseparationgray}
  5.1850 + {0 5 getinterval exch setcustomcolor}
  5.1851 + ifelse
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  5.1853 +/currentcolortransfer{currenttransfer dup dup dup}ndf
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  5.1856 +/sas{}ndf
  5.1857 +/fhsetspreadsize{pop}ndf
  5.1858 +/filler{fill}bdf 
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  5.1860 +/f{closepath F}bdf
  5.1861 +/S{gsave {stroke}fp grestore}bdf
  5.1862 +/s{closepath S}bdf
  5.1863 +/bc4 [0 0 0 0] def 
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  5.1866 + /cosv currentoverprint def
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  5.1868 + /xt xdf       
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  5.1870 + storerect
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  5.1872 + /k2 xdf /y2 xdf /m2 xdf /c2 xdf
  5.1873 + /k1 xdf /y1 xdf /m1 xdf /c1 xdf
  5.1874 + c1 c2 sub abs
  5.1875 + m1 m2 sub abs
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  5.1877 + k1 k2 sub abs
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  5.1881 + dup 2 lt {pop 1} if    
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  5.1883 + currentflat mark    
  5.1884 + currentflat clipflatness  
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  5.1886 + /right right left sub def  
  5.1887 + /botsv top delta sub def  
  5.1888 + {
  5.1889 +{
  5.1890 +W
  5.1891 +xt yt translate 
  5.1892 +ang rotate
  5.1893 +xt neg yt neg translate 
  5.1894 +dup setflat 
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  5.1896 +0 1 numsteps1 
  5.1897 +{
  5.1898 +numsteps1 dup 0 eq {pop 0.5 } { div } ifelse 
  5.1899 +taperfcn /frac xdf
  5.1900 +bc4 0 c2 c1 sub frac mul c1 add put
  5.1901 +bc4 1 m2 m1 sub frac mul m1 add put
  5.1902 +bc4 2 y2 y1 sub frac mul y1 add put
  5.1903 +bc4 3 k2 k1 sub frac mul k1 add put
  5.1904 +bc4 vc
  5.1905 +1 index setflat 
  5.1906 +{ 
  5.1907 +mark {newpath left bottom right delta rectfill}stopped
  5.1908 +{cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if}
  5.1909 +{cleartomark exit}ifelse
  5.1910 +}loop
  5.1911 +/bottom bottom delta sub def
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  5.1913 +}
  5.1914 +gsave stopped grestore
  5.1915 +{exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if}
  5.1916 +{exit}ifelse
  5.1917 + }loop
  5.1918 + cleartomark setflat
  5.1919 + iosv setinkoverprint
  5.1920 + cosv setoverprint
  5.1921 +}bdf
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  5.1923 +/_lfs4 {
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  5.1927 + /xt xdf       
  5.1928 + /ang xdf      
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  5.1931 + /tint2 xdf      
  5.1932 + /tint1 xdf      
  5.1933 + bcs exch 1 exch put    
  5.1934 + tint1 tint2 sub abs    
  5.1935 + bcs 1 get maxspot    
  5.1936 + calcgraysteps mul abs round  
  5.1937 + height abs adjnumsteps   
  5.1938 + dup 2 lt {pop 2} if    
  5.1939 + 1 sub /numsteps1 xdf
  5.1940 + currentflat mark    
  5.1941 + currentflat clipflatness  
  5.1942 + /delta top bottom sub numsteps1 1 add div def 
  5.1943 + /right right left sub def  
  5.1944 + /botsv top delta sub def  
  5.1945 + {
  5.1946 +{
  5.1947 +W
  5.1948 +xt yt translate 
  5.1949 +ang rotate
  5.1950 +xt neg yt neg translate 
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  5.1953 +0 1 numsteps1 
  5.1954 +{
  5.1955 +numsteps1 div taperfcn /frac xdf
  5.1956 +bcs 0
  5.1957 +1.0 tint2 tint1 sub frac mul tint1 add sub
  5.1958 +put bcs vc
  5.1959 +1 index setflat 
  5.1960 +{ 
  5.1961 +mark {newpath left bottom right delta rectfill}stopped
  5.1962 +{cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if}
  5.1963 +{cleartomark exit}ifelse
  5.1964 +}loop
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  5.1966 +}for
  5.1967 +}
  5.1968 +gsave stopped grestore
  5.1969 +{exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if}
  5.1970 +{exit}ifelse
  5.1971 + }loop
  5.1972 + cleartomark setflat
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  5.1974 + cosv setoverprint
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  5.1983 + /yt xdf       
  5.1984 + /xt xdf       
  5.1985 + tint1 tint2 sub abs    
  5.1986 + bcs 1 get maxspot    
  5.1987 + calcgraysteps mul abs round  
  5.1988 + radius abs adjnumsteps   
  5.1989 + dup 2 lt {pop 2} if    
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  5.1991 + radius numsteps1 div 2 div /halfstep xdf 
  5.1992 + currentflat mark    
  5.1993 + currentflat clipflatness  
  5.1994 + {
  5.1995 +{
  5.1996 +dup setflat 
  5.1997 +W 
  5.1998 +0 1 numsteps1 
  5.1999 +{
  5.2000 +dup /radindex xdf
  5.2001 +numsteps1 div /frac xdf
  5.2002 +bcs 0
  5.2003 +tint2 tint1 sub frac mul tint1 add
  5.2004 +put bcs vc
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  5.2008 +{ arc
  5.2009 +radindex numsteps1 ne 
  5.2010 +{
  5.2011 +xt yt 
  5.2012 +radindex 1 add numsteps1 
  5.2013 +div 1 exch sub 
  5.2014 +radius mul halfstep add
  5.2015 +dup xt add yt moveto 
  5.2016 +360 0 arcn 
  5.2017 +} if
  5.2018 +fill
  5.2019 +}stopped
  5.2020 +{cleartomark exch 1.3 mul dup setflat exch 2 copy gt{stop}if}
  5.2021 +{cleartomark exit}ifelse
  5.2022 +}loop
  5.2023 +}for
  5.2024 +}
  5.2025 +gsave stopped grestore
  5.2026 +{exch pop 2 index exch 1.3 mul dup 100 gt{cleartomark setflat stop}if}
  5.2027 +{exit}ifelse
  5.2028 + }loop
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  5.2030 + iosv setinkoverprint
  5.2031 + cosv setoverprint
  5.2032 +}bdf
  5.2033 +/_rfp4 {
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  5.2037 + /k1 xdf /y1 xdf /m1 xdf /c1 xdf
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  5.2040 + /xt xdf       
  5.2041 + c1 c2 sub abs
  5.2042 + m1 m2 sub abs
  5.2043 + y1 y2 sub abs
  5.2044 + k1 k2 sub abs
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  5.2051 + 2 div /halfstep xdf 
  5.2052 + currentflat mark    
  5.2053 + currentflat clipflatness  
  5.2054 + {
  5.2055 +{
  5.2056 +dup setflat 
  5.2057 +W 
  5.2058 +0 1 numsteps1 
  5.2059 +{
  5.2060 +dup /radindex xdf
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  5.2064 +bc4 1 m2 m1 sub frac mul m1 add put
  5.2065 +bc4 2 y2 y1 sub frac mul y1 add put
  5.2066 +bc4 3 k2 k1 sub frac mul k1 add put
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  5.2068 +1 index setflat 
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  5.2071 +{ arc
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  5.2073 +{
  5.2074 +xt yt 
  5.2075 +radindex 1 add 
  5.2076 +numsteps1 dup 0 eq {pop} {div} ifelse 
  5.2077 +1 exch sub 
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  5.2079 +dup xt add yt moveto 
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  5.2085 +{cleartomark exit}ifelse
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  5.2091 +{exit}ifelse
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  5.2107 + ifelse
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  5.2112 +/imgr {1692 1570.1102 2287.2756 2412 } def 
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  5.2115 +/xs 1 def 
  5.2116 +/ys 1 def 
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  5.2122 +/maxsteps 256 def 
  5.2123 +/forcemaxsteps false def 
  5.2124 +vms
  5.2125 +-1845 -1956 translate
  5.2126 +/currentpacking defed{false setpacking}if 
  5.2127 +/spots[
  5.2128 +1 0 0 0 (Process Cyan) false newcmykcustomcolor
  5.2129 +0 1 0 0 (Process Magenta) false newcmykcustomcolor
  5.2130 +0 0 1 0 (Process Yellow) false newcmykcustomcolor
  5.2131 +0 0 0 1 (Process Black) false newcmykcustomcolor
  5.2132 +]def
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  5.2140 +/ta2{ 
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  5.2142 +cwidth cheight rmoveto 
  5.2143 +4 index eq{5 index 5 index rmoveto}if 
  5.2144 +2 index 2 index rmoveto 
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  5.2146 +/ta{exch systemdict/cshow known
  5.2147 +{{/cheight xdf/cwidth xdf tempstr 0 2 index put ta2}exch cshow} 
  5.2148 +{{tempstr 0 2 index put tempstr stringwidth/cheight xdf/cwidth xdf ta2}forall} 
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  5.2152 +/stol{/xt currentlinewidth def 
  5.2153 + setlinewidth vc newpath 
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  5.2155 + xt setlinewidth}bdf 
  5.2156 + 
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  5.2158 + /ts{{false charpath stroke}ta}def exec 
  5.2159 + textopf setoverprint
  5.2160 + }bdf 
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  5.2200 +1933.9 1966.5 1929.4 1968.8 1925.1 1970.7 C
  5.2201 +1917.2 1978.2 1906 1977.9 1897.2 1983.4 C
  5.2202 +1893.2 1985.6 1889.4 1988.6 1885 1990.1 C
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  5.2204 +1883.7 2000.4 1884 2009.9 1883.6 2018.9 C
  5.2205 +1887.7 2024 1893.2 2028.8 1898 2033.8 C
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  5.2231 +1977.3 1969.3 1976 1967.6 1974.8 1968.5 C
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  5.2234 +1928.3 1968.2 1920.6 1974.8 1911.6 1978.4 C
  5.2235 +1901.9 1979.7 1893.9 1986.6 1885 1990.6 C
  5.2236 +1884.3 1991 1884.3 1991.7 1884 1992.3 C
  5.2237 +1884.5 2001 1884.2 2011 1884.3 2019.9 C
  5.2238 +1890.9 2025.3 1895.9 2031.9 1902.3 2037.4 C
  5.2239 +1904.2 2037.9 1905.6 2034.2 1906.8 2035.7 C
  5.2240 +1907.4 2040.9 1905.7 2046.1 1907.3 2050.8 C
  5.2241 +1913.6 2056.2 1919.2 2062.6 1925.1 2067.9 C
  5.2242 +1926.9 2067.8 1928 2066.3 1929.6 2065.7 C
  5.2243 +1929.9 2070.5 1929.2 2076 1930.1 2080.8 C
  5.2244 +1936.5 2086.1 1941.6 2092.8 1948.4 2097.6 C
  5.2245 +1957.3 2093.3 1966.2 2088.8 1975.2 2084.7 C
  5.2246 +[0 0 0 0]  vc
  5.2247 +f 
  5.2248 +S 
  5.2249 +n
  5.2250 +1954.8 2093.8 m
  5.2251 +1961.6 2090.5 1968.2 2087 1975 2084 C
  5.2252 +1975 2082.8 1975.6 2080.9 1974.8 2080.6 C
  5.2253 +1974.3 2075.2 1974.6 2069.6 1974.5 2064 C
  5.2254 +1977.5 2059.7 1984.5 2060 1988.9 2056.4 C
  5.2255 +1989.5 2055.5 1990.5 2055.3 1990.8 2054.4 C
  5.2256 +1991.1 2045.7 1991.4 2036.1 1990.6 2027.8 C
  5.2257 +1990.7 2026.6 1992 2027.3 1992.8 2027.1 C
  5.2258 +1997 2032.4 2002.6 2037.8 2007.6 2042.2 C
  5.2259 +2008.7 2042.3 2007.8 2040.6 2007.4 2040 C
  5.2260 +2002.3 2035.6 1997.5 2030 1992.8 2025.2 C
  5.2261 +1991.6 2024.7 1990.8 2024.9 1990.1 2025.4 C
  5.2262 +1989.4 2024.9 1988.1 2025.2 1987.2 2024.4 C
  5.2263 +1987.1 2025.8 1988.3 2026.5 1989.4 2026.8 C
  5.2264 +1989.4 2026.6 1989.3 2026.2 1989.6 2026.1 C
  5.2265 +1989.9 2026.2 1989.9 2026.6 1989.9 2026.8 C
  5.2266 +1989.8 2026.6 1990 2026.5 1990.1 2026.4 C
  5.2267 +1990.2 2027 1991.1 2028.3 1990.1 2028 C
  5.2268 +1989.9 2037.9 1990.5 2044.1 1989.6 2054.2 C
  5.2269 +1985.9 2058 1979.7 2057.4 1976 2061.2 C
  5.2270 +1974.5 2061.6 1975.2 2059.9 1974.5 2059.5 C
  5.2271 +1973.9 2058 1975.6 2057.8 1975 2056.6 C
  5.2272 +1974.5 2057.1 1974.6 2055.3 1973.6 2055.9 C
  5.2273 +1971.9 2059.3 1974.7 2062.1 1973.1 2065.5 C
  5.2274 +1973.1 2071.2 1972.9 2077 1973.3 2082.5 C
  5.2275 +1967.7 2085.6 1962 2088 1956.3 2090.7 C
  5.2276 +1953.9 2092.4 1951 2093 1948.6 2094.8 C
  5.2277 +1943.7 2089.9 1937.9 2084.3 1933 2079.6 C
  5.2278 +1931.3 2076.1 1933.2 2071.3 1932.3 2067.2 C
  5.2279 +1931.3 2062.9 1933.3 2060.6 1932 2057.6 C
  5.2280 +1932.7 2056.5 1930.9 2053.3 1933.2 2051.8 C
  5.2281 +1936.8 2050.1 1940.1 2046.9 1944 2046.8 C
  5.2282 +1946.3 2049.7 1949.3 2051.9 1952 2054.4 C
  5.2283 +1954.5 2054.2 1956.4 2052.3 1958.7 2051.3 C
  5.2284 +1960.8 2050 1963.2 2049 1965.6 2048.4 C
  5.2285 +1968.3 2050.8 1970.7 2054.3 1973.6 2055.4 C
  5.2286 +1973 2052.2 1969.7 2050.4 1967.6 2048.2 C
  5.2287 +1967.1 2046.7 1968.8 2046.6 1969.5 2045.8 C
  5.2288 +1972.8 2043.3 1980.6 2043.4 1979.3 2038.4 C
  5.2289 +1979.4 2038.6 1979.2 2038.7 1979.1 2038.8 C
  5.2290 +1978.7 2038.6 1978.9 2038.1 1978.8 2037.6 C
  5.2291 +1978.9 2037.9 1978.7 2038 1978.6 2038.1 C
  5.2292 +1978.2 2032.7 1978.4 2027.1 1978.4 2021.6 C
  5.2293 +1979.3 2021.1 1980 2020.2 1981.5 2020.1 C
  5.2294 +1983.5 2020.5 1984 2021.8 1985.1 2023.5 C
  5.2295 +1985.7 2024 1987.4 2023.7 1986 2022.8 C
  5.2296 +1984.7 2021.7 1983.3 2020.8 1983.9 2018.7 C
  5.2297 +1987.2 2015.9 1993 2015.4 1994.9 2011.5 C
  5.2298 +1992.2 2004.9 1999.3 2005.2 2002.1 2002.4 C
  5.2299 +2005.9 2002.7 2004.8 1997.4 2009.1 1999 C
  5.2300 +2011 1999.3 2010 2002.9 2012.7 2002.4 C
  5.2301 +2010.2 2000.7 2009.4 1996.1 2005.5 1998.5 C
  5.2302 +2002.1 2000.3 1999 2002.5 1995.4 2003.8 C
  5.2303 +1995.2 2003.6 1994.9 2003.3 1994.7 2003.1 C
  5.2304 +1994.3 1997 1995.6 1991.1 1994.4 1985.3 C
  5.2305 +1994.3 1986 1993.8 1985 1994 1985.6 C
  5.2306 +1993.8 1995.4 1994.4 2001.6 1993.5 2011.7 C
  5.2307 +1989.7 2015.5 1983.6 2014.9 1979.8 2018.7 C
  5.2308 +1978.3 2019.1 1979.1 2017.4 1978.4 2017 C
  5.2309 +1977.8 2015.5 1979.4 2015.3 1978.8 2014.1 C
  5.2310 +1978.4 2014.6 1978.5 2012.8 1977.4 2013.4 C
  5.2311 +1975.8 2016.8 1978.5 2019.6 1976.9 2023 C
  5.2312 +1977 2028.7 1976.7 2034.5 1977.2 2040 C
  5.2313 +1971.6 2043.1 1965.8 2045.6 1960.1 2048.2 C
  5.2314 +1957.7 2049.9 1954.8 2050.5 1952.4 2052.3 C
  5.2315 +1947.6 2047.4 1941.8 2041.8 1936.8 2037.2 C
  5.2316 +1935.2 2033.6 1937.1 2028.8 1936.1 2024.7 C
  5.2317 +1935.1 2020.4 1937.1 2018.1 1935.9 2015.1 C
  5.2318 +1936.5 2014.1 1934.7 2010.8 1937.1 2009.3 C
  5.2319 +1944.4 2004.8 1952 2000.9 1959.9 1997.8 C
  5.2320 +1963.9 1997 1963.9 2001.9 1966.8 2003.3 C
  5.2321 +1970.3 2006.9 1973.7 2009.9 1976.9 2012.9 C
  5.2322 +1977.9 2013 1977.1 2011.4 1976.7 2010.8 C
  5.2323 +1971.6 2006.3 1966.8 2000.7 1962 1995.9 C
  5.2324 +1960 1995.2 1960.1 1996.6 1958.2 1995.6 C
  5.2325 +1957 1997 1955.1 1998.8 1953.2 1998 C
  5.2326 +1951.7 1994.5 1954.1 1993.4 1952.9 1991.1 C
  5.2327 +1952.1 1990.5 1953.3 1990.2 1953.2 1989.6 C
  5.2328 +1954.2 1986.8 1950.9 1981.4 1954.4 1981.2 C
  5.2329 +1954.7 1981.6 1954.7 1981.7 1955.1 1982 C
  5.2330 +1961.9 1979.1 1967.6 1975 1974.3 1971.6 C
  5.2331 +1974.7 1969.8 1976.7 1969.5 1978.4 1969.7 C
  5.2332 +1980.3 1970 1979.3 1973.6 1982 1973.1 C
  5.2333 +1975.8 1962.2 1968 1975.8 1960.8 1976.7 C
  5.2334 +1956.9 1977.4 1953.3 1982.4 1949.1 1978.8 C
  5.2335 +1946 1975.8 1941.2 1971 1939.5 1969.2 C
  5.2336 +1938.5 1968.6 1938.9 1967.4 1937.8 1966.8 C
  5.2337 +1928.7 1969.4 1920.6 1974.5 1912.4 1979.1 C
  5.2338 +1904 1980 1896.6 1985 1889.3 1989.4 C
  5.2339 +1887.9 1990.4 1885.1 1990.3 1885 1992.5 C
  5.2340 +1885.4 2000.6 1885.2 2012.9 1885.2 2019.9 C
  5.2341 +1886.1 2022 1889.7 2019.5 1888.4 2022.8 C
  5.2342 +1889 2023.3 1889.8 2024.4 1890.3 2024 C
  5.2343 +1891.2 2023.5 1891.8 2028.2 1893.4 2026.6 C
  5.2344 +1894.2 2026.3 1893.9 2027.3 1894.4 2027.6 C
  5.2345 +1893.4 2027.6 1894.7 2028.3 1894.1 2028.5 C
  5.2346 +1894.4 2029.6 1896 2030 1896 2029.2 C
  5.2347 +1896.2 2029 1896.3 2029 1896.5 2029.2 C
  5.2348 +1896.8 2029.8 1897.3 2030 1897 2030.7 C
  5.2349 +1896.5 2030.7 1896.9 2031.5 1897.2 2031.6 C
  5.2350 +1898.3 2034 1899.5 2030.6 1899.6 2033.3 C
  5.2351 +1898.5 2033 1899.6 2034.4 1900.1 2034.8 C
  5.2352 +1901.3 2035.8 1903.2 2034.6 1902.5 2036.7 C
  5.2353 +1904.4 2036.9 1906.1 2032.2 1907.6 2035.5 C
  5.2354 +1907.5 2040.1 1907.7 2044.9 1907.3 2049.4 C
  5.2355 +1908 2050.2 1908.3 2051.4 1909.5 2051.6 C
  5.2356 +1910.1 2051.1 1911.6 2051.1 1911.4 2052.3 C
  5.2357 +1909.7 2052.8 1912.4 2054 1912.6 2054.7 C
  5.2358 +1913.4 2055.2 1913 2053.7 1913.6 2054.4 C
  5.2359 +1913.6 2054.5 1913.6 2055.3 1913.6 2054.7 C
  5.2360 +1913.7 2054.4 1913.9 2054.4 1914 2054.7 C
  5.2361 +1914 2054.9 1914.1 2055.3 1913.8 2055.4 C
  5.2362 +1913.7 2056 1915.2 2057.6 1916 2057.6 C
  5.2363 +1915.9 2057.3 1916.1 2057.2 1916.2 2057.1 C
  5.2364 +1917 2056.8 1916.7 2057.7 1917.2 2058 C
  5.2365 +1917 2058.3 1916.7 2058.3 1916.4 2058.3 C
  5.2366 +1917.1 2059 1917.3 2060.1 1918.4 2060.4 C
  5.2367 +1918.1 2059.2 1919.1 2060.6 1919.1 2059.5 C
  5.2368 +1919 2060.6 1920.6 2060.1 1919.8 2061.2 C
  5.2369 +1919.6 2061.2 1919.3 2061.2 1919.1 2061.2 C
  5.2370 +1919.6 2061.9 1921.4 2064.2 1921.5 2062.6 C
  5.2371 +1922.4 2062.1 1921.6 2063.9 1922.2 2064.3 C
  5.2372 +1922.9 2067.3 1926.1 2064.3 1925.6 2067.2 C
  5.2373 +1927.2 2066.8 1928.4 2064.6 1930.1 2065.2 C
  5.2374 +1931.8 2067.8 1931 2071.8 1930.8 2074.8 C
  5.2375 +1930.6 2076.4 1930.1 2078.6 1930.6 2080.4 C
  5.2376 +1936.6 2085.4 1941.8 2091.6 1948.1 2096.9 C
  5.2377 +1950.7 2096.7 1952.6 2094.8 1954.8 2093.8 C
  5.2378 +[0 0.33 0.33 0.99]  vc
  5.2379 +f 
  5.2380 +S 
  5.2381 +n
  5.2382 +1989.4 2080.6 m
  5.2383 +1996.1 2077.3 2002.7 2073.8 2009.6 2070.8 C
  5.2384 +2009.6 2069.6 2010.2 2067.7 2009.3 2067.4 C
  5.2385 +2008.9 2062 2009.1 2056.4 2009.1 2050.8 C
  5.2386 +2012.3 2046.6 2019 2046.6 2023.5 2043.2 C
  5.2387 +2024 2042.3 2025.1 2042.1 2025.4 2041.2 C
  5.2388 +2025.3 2032.7 2025.6 2023.1 2025.2 2014.6 C
  5.2389 +2025 2015.3 2024.6 2014.2 2024.7 2014.8 C
  5.2390 +2024.5 2024.7 2025.1 2030.9 2024.2 2041 C
  5.2391 +2020.4 2044.8 2014.3 2044.2 2010.5 2048 C
  5.2392 +2009 2048.4 2009.8 2046.7 2009.1 2046.3 C
  5.2393 +2008.5 2044.8 2010.2 2044.6 2009.6 2043.4 C
  5.2394 +2009.1 2043.9 2009.2 2042.1 2008.1 2042.7 C
  5.2395 +2006.5 2046.1 2009.3 2048.9 2007.6 2052.3 C
  5.2396 +2007.7 2058 2007.5 2063.8 2007.9 2069.3 C
  5.2397 +2002.3 2072.4 1996.5 2074.8 1990.8 2077.5 C
  5.2398 +1988.4 2079.2 1985.6 2079.8 1983.2 2081.6 C
  5.2399 +1980.5 2079 1977.9 2076.5 1975.5 2074.1 C
  5.2400 +1975.5 2075.1 1975.5 2076.2 1975.5 2077.2 C
  5.2401 +1977.8 2079.3 1980.3 2081.6 1982.7 2083.7 C
  5.2402 +1985.3 2083.5 1987.1 2081.6 1989.4 2080.6 C
  5.2403 +f 
  5.2404 +S 
  5.2405 +n
  5.2406 +1930.1 2079.9 m
  5.2407 +1931.1 2075.6 1929.2 2071.1 1930.8 2067.2 C
  5.2408 +1930.3 2066.3 1930.1 2064.6 1928.7 2065.5 C
  5.2409 +1927.7 2066.4 1926.5 2067 1925.3 2067.4 C
  5.2410 +1924.5 2066.9 1925.6 2065.7 1924.4 2066 C
  5.2411 +1924.2 2067.2 1923.6 2065.5 1923.2 2065.7 C
  5.2412 +1922.3 2063.6 1917.8 2062.1 1919.6 2060.4 C
  5.2413 +1919.3 2060.5 1919.2 2060.3 1919.1 2060.2 C
  5.2414 +1919.7 2060.9 1918.2 2061 1917.6 2060.2 C
  5.2415 +1917 2059.6 1916.1 2058.8 1916.4 2058 C
  5.2416 +1915.5 2058 1917.4 2057.1 1915.7 2057.8 C
  5.2417 +1914.8 2057.1 1913.4 2056.2 1913.3 2054.9 C
  5.2418 +1913.1 2055.4 1911.3 2054.3 1910.9 2053.2 C
  5.2419 +1910.7 2052.9 1910.2 2052.5 1910.7 2052.3 C
  5.2420 +1911.1 2052.5 1910.9 2052 1910.9 2051.8 C
  5.2421 +1910.5 2051.2 1909.9 2052.6 1909.2 2051.8 C
  5.2422 +1908.2 2051.4 1907.8 2050.2 1907.1 2049.4 C
  5.2423 +1907.5 2044.8 1907.3 2040 1907.3 2035.2 C
  5.2424 +1905.3 2033 1902.8 2039.3 1902.3 2035.7 C
  5.2425 +1899.6 2036 1898.4 2032.5 1896.3 2030.7 C
  5.2426 +1895.7 2030.1 1897.5 2030 1896.3 2029.7 C
  5.2427 +1896.3 2030.6 1895 2029.7 1894.4 2029.2 C
  5.2428 +1892.9 2028.1 1894.2 2027.4 1893.6 2027.1 C
  5.2429 +1892.1 2027.9 1891.7 2025.6 1890.8 2024.9 C
  5.2430 +1891.1 2024.6 1889.1 2024.3 1888.4 2023 C
  5.2431 +1887.5 2022.6 1888.2 2021.9 1888.1 2021.3 C
  5.2432 +1886.7 2022 1885.2 2020.4 1884.8 2019.2 C
  5.2433 +1884.8 2010 1884.6 2000.2 1885 1991.8 C
  5.2434 +1886.9 1989.6 1889.9 1989.3 1892.2 1987.5 C
  5.2435 +1898.3 1982.7 1905.6 1980.1 1912.8 1978.6 C
  5.2436 +1921 1974.2 1928.8 1968.9 1937.8 1966.6 C
  5.2437 +1939.8 1968.3 1938.8 1968.3 1940.4 1970 C
  5.2438 +1945.4 1972.5 1947.6 1981.5 1954.6 1979.3 C
  5.2439 +1952.3 1981 1950.4 1978.4 1948.6 1977.9 C
  5.2440 +1945.1 1973.9 1941.1 1970.6 1938 1966.6 C
  5.2441 +1928.4 1968.5 1920.6 1974.8 1911.9 1978.8 C
  5.2442 +1907.1 1979.2 1902.6 1981.7 1898.2 1983.6 C
  5.2443 +1893.9 1986 1889.9 1989 1885.5 1990.8 C
  5.2444 +1884.9 1991.2 1884.8 1991.8 1884.5 1992.3 C
  5.2445 +1884.9 2001.3 1884.7 2011.1 1884.8 2019.6 C
  5.2446 +1890.6 2025 1896.5 2031.2 1902.3 2036.9 C
  5.2447 +1904.6 2037.6 1905 2033 1907.3 2035.5 C
  5.2448 +1907.2 2040.2 1907 2044.8 1907.1 2049.6 C
  5.2449 +1913.6 2055.3 1918.4 2061.5 1925.1 2067.4 C
  5.2450 +1927.3 2068.2 1929.6 2062.5 1930.6 2066.9 C
  5.2451 +1929.7 2070.7 1930.3 2076 1930.1 2080.1 C
  5.2452 +1935.6 2085.7 1941.9 2090.7 1947.2 2096.7 C
  5.2453 +1942.2 2091.1 1935.5 2085.2 1930.1 2079.9 C
  5.2454 +[0.18 0.18 0 0.78]  vc
  5.2455 +f 
  5.2456 +S 
  5.2457 +n
  5.2458 +1930.8 2061.9 m
  5.2459 +1930.3 2057.8 1931.8 2053.4 1931.1 2050.4 C
  5.2460 +1931.3 2050.3 1931.7 2050.5 1931.6 2050.1 C
  5.2461 +1933 2051.1 1934.4 2049.5 1935.9 2048.7 C
  5.2462 +1937 2046.5 1939.5 2047.1 1941.2 2045.1 C
  5.2463 +1939.7 2042.6 1937.3 2041.2 1935.4 2039.3 C
  5.2464 +1934 2039.7 1934.5 2038.1 1933.7 2037.6 C
  5.2465 +1934 2033.3 1933.1 2027.9 1934.4 2024.4 C
  5.2466 +1934.3 2023.8 1933.9 2022.8 1933 2022.8 C
  5.2467 +1931.6 2023.1 1930.5 2024.4 1929.2 2024.9 C
  5.2468 +1928.4 2024.5 1929.8 2023.5 1928.7 2023.5 C
  5.2469 +1927.7 2024.1 1926.2 2022.6 1925.6 2021.6 C
  5.2470 +1926.9 2021.6 1924.8 2020.6 1925.6 2020.4 C
  5.2471 +1924.7 2021.7 1923.9 2019.6 1923.2 2019.2 C
  5.2472 +1923.3 2018.3 1923.8 2018.1 1923.2 2018 C
  5.2473 +1922.9 2017.8 1922.9 2017.5 1922.9 2017.2 C
  5.2474 +1922.8 2018.3 1921.3 2017.3 1920.3 2018 C
  5.2475 +1916.6 2019.7 1913 2022.1 1910 2024.7 C
  5.2476 +1910 2032.9 1910 2041.2 1910 2049.4 C
  5.2477 +1915.4 2055.2 1920 2058.7 1925.3 2064.8 C
  5.2478 +1927.2 2064 1929 2061.4 1930.8 2061.9 C
  5.2479 +[0 0 0 0]  vc
  5.2480 +f 
  5.2481 +S 
  5.2482 +n
  5.2483 +1907.6 2030.4 m
  5.2484 +1907.5 2027.1 1906.4 2021.7 1908.5 2019.9 C
  5.2485 +1908.8 2020.1 1908.9 2019 1909.2 2019.6 C
  5.2486 +1910 2019.6 1912 2019.2 1913.1 2018.2 C
  5.2487 +1913.7 2016.5 1920.2 2015.7 1917.4 2012.7 C
  5.2488 +1918.2 2011.2 1917 2013.8 1917.2 2012 C
  5.2489 +1916.9 2012.3 1916 2012.4 1915.2 2012 C
  5.2490 +1912.5 2010.5 1916.6 2008.8 1913.6 2009.6 C
  5.2491 +1912.6 2009.2 1911.1 2009 1910.9 2007.6 C
  5.2492 +1911 1999.2 1911.8 1989.8 1911.2 1982.2 C
  5.2493 +1910.1 1981.1 1908.8 1982.2 1907.6 1982.2 C
  5.2494 +1900.8 1986.5 1893.2 1988.8 1887.2 1994.2 C
  5.2495 +1887.2 2002.4 1887.2 2010.7 1887.2 2018.9 C
  5.2496 +1892.6 2024.7 1897.2 2028.2 1902.5 2034.3 C
  5.2497 +1904.3 2033.3 1906.2 2032.1 1907.6 2030.4 C
  5.2498 +f 
  5.2499 +S 
  5.2500 +n
  5.2501 +1910.7 2025.4 m
  5.2502 +1912.7 2022.4 1916.7 2020.8 1919.8 2018.9 C
  5.2503 +1920.2 2018.7 1920.6 2018.6 1921 2018.4 C
  5.2504 +1925 2020 1927.4 2028.5 1932 2024.2 C
  5.2505 +1932.3 2025 1932.5 2023.7 1932.8 2024.4 C
  5.2506 +1932.8 2028 1932.8 2031.5 1932.8 2035 C
  5.2507 +1931.9 2033.9 1932.5 2036.3 1932.3 2036.9 C
  5.2508 +1933.2 2036.4 1932.5 2038.5 1933 2038.4 C
  5.2509 +1933.1 2040.5 1935.6 2042.2 1936.6 2043.2 C
  5.2510 +1936.2 2042.4 1935.1 2040.8 1933.7 2040.3 C
  5.2511 +1932.2 2034.4 1933.8 2029.8 1933 2023.2 C
  5.2512 +1931.1 2024.9 1928.4 2026.4 1926.5 2023.5 C
  5.2513 +1925.1 2021.6 1923 2019.8 1921.5 2018.2 C
  5.2514 +1917.8 2018.9 1915.2 2022.5 1911.6 2023.5 C
  5.2515 +1910.8 2023.8 1911.2 2024.7 1910.4 2025.2 C
  5.2516 +1910.9 2031.8 1910.6 2039.1 1910.7 2045.6 C
  5.2517 +1910.1 2048 1910.7 2045.9 1911.2 2044.8 C
  5.2518 +1910.6 2038.5 1911.2 2031.8 1910.7 2025.4 C
  5.2519 +[0.07 0.06 0 0.58]  vc
  5.2520 +f 
  5.2521 +S 
  5.2522 +n
  5.2523 +1910.7 2048.9 m
  5.2524 +1910.3 2047.4 1911.3 2046.5 1911.6 2045.3 C
  5.2525 +1912.9 2045.3 1913.9 2047.1 1915.2 2045.8 C
  5.2526 +1915.2 2044.9 1916.6 2043.3 1917.2 2042.9 C
  5.2527 +1918.7 2042.9 1919.4 2044.4 1920.5 2043.2 C
  5.2528 +1921.2 2042.2 1921.4 2040.9 1922.4 2040.3 C
  5.2529 +1924.5 2040.3 1925.7 2040.9 1926.8 2039.6 C
  5.2530 +1927.1 2037.9 1926.8 2038.1 1927.7 2037.6 C
  5.2531 +1929 2037.5 1930.4 2037 1931.6 2037.2 C
  5.2532 +1932.3 2038.2 1933.1 2038.7 1932.8 2040.3 C
  5.2533 +1935 2041.8 1935.9 2043.8 1938.5 2044.8 C
  5.2534 +1938.6 2045 1938.3 2045.5 1938.8 2045.3 C
  5.2535 +1939.1 2042.9 1935.4 2044.2 1935.4 2042.2 C
  5.2536 +1932.1 2040.8 1932.8 2037.2 1932 2034.8 C
  5.2537 +1932.3 2034 1932.7 2035.4 1932.5 2034.8 C
  5.2538 +1931.3 2031.8 1935.5 2020.1 1928.9 2025.9 C
  5.2539 +1924.6 2024.7 1922.6 2014.5 1917.4 2020.4 C
  5.2540 +1915.5 2022.8 1912 2022.6 1910.9 2025.4 C
  5.2541 +1911.5 2031.9 1910.9 2038.8 1911.4 2045.3 C
  5.2542 +1911.1 2046.5 1910 2047.4 1910.4 2048.9 C
  5.2543 +1915.1 2054.4 1920.4 2058.3 1925.1 2063.8 C
  5.2544 +1920.8 2058.6 1914.9 2054.3 1910.7 2048.9 C
  5.2545 +[0.4 0.4 0 0]  vc
  5.2546 +f 
  5.2547 +S 
  5.2548 +n
  5.2549 +1934.7 2031.9 m
  5.2550 +1934.6 2030.7 1934.9 2029.5 1934.4 2028.5 C
  5.2551 +1934 2029.5 1934.3 2031.2 1934.2 2032.6 C
  5.2552 +1933.8 2031.7 1934.9 2031.6 1934.7 2031.9 C
  5.2553 +[0.92 0.92 0 0.67]  vc
  5.2554 +f 
  5.2555 +S 
  5.2556 +n
  5.2557 +vmrs
  5.2558 +1934.7 2019.4 m
  5.2559 +1934.1 2015.3 1935.6 2010.9 1934.9 2007.9 C
  5.2560 +1935.1 2007.8 1935.6 2008.1 1935.4 2007.6 C
  5.2561 +1936.8 2008.6 1938.2 2007 1939.7 2006.2 C
  5.2562 +1940.1 2004.3 1942.7 2005 1943.6 2003.8 C
  5.2563 +1945.1 2000.3 1954 2000.8 1950 1996.6 C
  5.2564 +1952.1 1993.3 1948.2 1989.2 1951.2 1985.6 C
  5.2565 +1953 1981.4 1948.4 1982.3 1947.9 1979.8 C
  5.2566 +1945.4 1979.6 1945.1 1975.5 1942.4 1975 C
  5.2567 +1942.4 1972.3 1938 1973.6 1938.5 1970.4 C
  5.2568 +1937.4 1969 1935.6 1970.1 1934.2 1970.2 C
  5.2569 +1927.5 1974.5 1919.8 1976.8 1913.8 1982.2 C
  5.2570 +1913.8 1990.4 1913.8 1998.7 1913.8 2006.9 C
  5.2571 +1919.3 2012.7 1923.8 2016.2 1929.2 2022.3 C
  5.2572 +1931.1 2021.6 1932.8 2018.9 1934.7 2019.4 C
  5.2573 +[0 0 0 0]  vc
  5.2574 +f 
  5.2575 +0.4 w
  5.2576 +2 J
  5.2577 +2 M
  5.2578 +S 
  5.2579 +n
  5.2580 +2024.2 2038.1 m
  5.2581 +2024.1 2029.3 2024.4 2021.7 2024.7 2014.4 C
  5.2582 +2024.4 2013.6 2020.6 2013.4 2021.3 2011.2 C
  5.2583 +2020.5 2010.3 2018.4 2010.6 2018.9 2008.6 C
  5.2584 +2019 2008.8 2018.8 2009 2018.7 2009.1 C
  5.2585 +2018.2 2006.7 2015.2 2007.9 2015.3 2005.5 C
  5.2586 +2014.7 2004.8 2012.4 2005.1 2013.2 2003.6 C
  5.2587 +2012.3 2004.2 2012.8 2002.4 2012.7 2002.6 C
  5.2588 +2009.4 2003.3 2011.2 1998.6 2008.4 1999.2 C
  5.2589 +2007 1999.1 2006.1 1999.4 2005.7 2000.4 C
  5.2590 +2006.9 1998.5 2007.7 2000.5 2009.3 2000.2 C
  5.2591 +2009.2 2003.7 2012.4 2002.1 2012.9 2005.2 C
  5.2592 +2015.9 2005.6 2015.2 2008.6 2017.7 2008.8 C
  5.2593 +2018.4 2009.6 2018.3 2011.4 2019.6 2011 C
  5.2594 +2021.1 2011.7 2021.4 2014.8 2023.7 2015.1 C
  5.2595 +2023.7 2023.5 2023.9 2031.6 2023.5 2040.5 C
  5.2596 +2021.8 2041.7 2020.7 2043.6 2018.4 2043.9 C
  5.2597 +2020.8 2042.7 2025.5 2041.8 2024.2 2038.1 C
  5.2598 +[0 0.87 0.91 0.83]  vc
  5.2599 +f 
  5.2600 +S 
  5.2601 +n
  5.2602 +2023.5 2040 m
  5.2603 +2023.5 2031.1 2023.5 2023.4 2023.5 2015.1 C
  5.2604 +2020.2 2015 2021.8 2010.3 2018.4 2011 C
  5.2605 +2018.6 2007.5 2014.7 2009.3 2014.8 2006.4 C
  5.2606 +2011.8 2006.3 2012.2 2002.3 2009.8 2002.4 C
  5.2607 +2009.7 2001.5 2009.2 2000.1 2008.4 2000.2 C
  5.2608 +2008.7 2000.9 2009.7 2001.2 2009.3 2002.4 C
  5.2609 +2008.4 2004.2 2007.5 2003.1 2007.9 2005.5 C
  5.2610 +2007.9 2010.8 2007.7 2018.7 2008.1 2023.2 C
  5.2611 +2009 2024.3 2007.3 2023.4 2007.9 2024 C
  5.2612 +2007.7 2024.6 2007.3 2026.3 2008.6 2027.1 C
  5.2613 +2009.7 2026.8 2010 2027.6 2010.5 2028 C
  5.2614 +2010.5 2028.2 2010.5 2029.1 2010.5 2028.5 C
  5.2615 +2011.5 2028 2010.5 2030 2011.5 2030 C
  5.2616 +2014.2 2029.7 2012.9 2032.2 2014.8 2032.6 C
  5.2617 +2015.1 2033.6 2015.3 2033 2016 2033.3 C
  5.2618 +2017 2033.9 2016.6 2035.4 2017.2 2036.2 C
  5.2619 +2018.7 2036.4 2019.2 2039 2021.3 2038.4 C
  5.2620 +2021.6 2035.4 2019.7 2029.5 2021.1 2027.3 C
  5.2621 +2020.9 2023.5 2021.5 2018.5 2020.6 2016 C
  5.2622 +2020.9 2013.9 2021.5 2015.4 2022.3 2014.4 C
  5.2623 +2022.2 2015.1 2023.3 2014.8 2023.2 2015.6 C
  5.2624 +2022.7 2019.8 2023.3 2024.3 2022.8 2028.5 C
  5.2625 +2022.3 2028.2 2022.6 2027.6 2022.5 2027.1 C
  5.2626 +2022.5 2027.8 2022.5 2029.2 2022.5 2029.2 C
  5.2627 +2022.6 2029.2 2022.7 2029.1 2022.8 2029 C
  5.2628 +2023.9 2032.8 2022.6 2037 2023 2040.8 C
  5.2629 +2022.3 2041.2 2021.6 2041.5 2021.1 2042.2 C
  5.2630 +2022 2041.2 2022.9 2041.4 2023.5 2040 C
  5.2631 +[0 1 1 0.23]  vc
  5.2632 +f 
  5.2633 +S 
  5.2634 +n
  5.2635 +2009.1 1997.8 m
  5.2636 +2003.8 1997.7 2000.1 2002.4 1995.4 2003.1 C
  5.2637 +1995 1999.5 1995.2 1995 1995.2 1992 C
  5.2638 +1995.2 1995.8 1995 1999.7 1995.4 2003.3 C
  5.2639 +2000.3 2002.2 2003.8 1997.9 2009.1 1997.8 C
  5.2640 +2012.3 2001.2 2015.6 2004.8 2018.7 2008.1 C
  5.2641 +2021.6 2011.2 2027.5 2013.9 2025.9 2019.9 C
  5.2642 +2026.1 2017.9 2025.6 2016.2 2025.4 2014.4 C
  5.2643 +2020.2 2008.4 2014 2003.6 2009.1 1997.8 C
  5.2644 +[0.18 0.18 0 0.78]  vc
  5.2645 +f 
  5.2646 +S 
  5.2647 +n
  5.2648 +2009.3 1997.8 m
  5.2649 +2008.7 1997.4 2007.9 1997.6 2007.2 1997.6 C
  5.2650 +2007.9 1997.6 2008.9 1997.4 2009.6 1997.8 C
  5.2651 +2014.7 2003.6 2020.8 2008.8 2025.9 2014.8 C
  5.2652 +2025.8 2017.7 2026.1 2014.8 2025.6 2014.1 C
  5.2653 +2020.4 2008.8 2014.8 2003.3 2009.3 1997.8 C
  5.2654 +[0.07 0.06 0 0.58]  vc
  5.2655 +f 
  5.2656 +S 
  5.2657 +n
  5.2658 +2009.6 1997.6 m
  5.2659 +2009 1997.1 2008.1 1997.4 2007.4 1997.3 C
  5.2660 +2008.1 1997.4 2009 1997.1 2009.6 1997.6 C
  5.2661 +2014.8 2003.7 2021.1 2008.3 2025.9 2014.4 C
  5.2662 +2021.1 2008.3 2014.7 2003.5 2009.6 1997.6 C
  5.2663 +[0.4 0.4 0 0]  vc
  5.2664 +f 
  5.2665 +S 
  5.2666 +n
  5.2667 +2021.8 2011.5 m
  5.2668 +2021.9 2012.2 2022.3 2013.5 2023.7 2013.6 C
  5.2669 +2023.4 2012.7 2022.8 2011.8 2021.8 2011.5 C
  5.2670 +[0 0.33 0.33 0.99]  vc
  5.2671 +f 
  5.2672 +S 
  5.2673 +n
  5.2674 +2021.1 2042 m
  5.2675 +2022.1 2041.1 2020.9 2040.2 2020.6 2039.6 C
  5.2676 +2018.4 2039.5 2018.1 2036.9 2016.3 2036.4 C
  5.2677 +2015.8 2035.5 2015.3 2033.8 2014.8 2033.6 C
  5.2678 +2012.4 2033.8 2013 2030.4 2010.5 2030.2 C
  5.2679 +2009.6 2028.9 2009.6 2028.3 2008.4 2028 C
  5.2680 +2006.9 2026.7 2007.5 2024.3 2006 2023.2 C
  5.2681 +2006.6 2023.2 2005.7 2023.3 2005.7 2023 C
  5.2682 +2006.4 2022.5 2006.3 2021.1 2006.7 2020.6 C
  5.2683 +2006.6 2015 2006.9 2009 2006.4 2003.8 C
  5.2684 +2006.9 2002.5 2007.6 2001.1 2006.9 2000.7 C
  5.2685 +2004.6 2003.6 2003 2002.9 2000.2 2004.3 C
  5.2686 +1999.3 2005.8 1997.9 2006.3 1996.1 2006.7 C
  5.2687 +1995.7 2008.9 1996 2011.1 1995.9 2012.9 C
  5.2688 +1993.4 2015.1 1990.5 2016.2 1987.7 2017.7 C
  5.2689 +1987.1 2019.3 1991.1 2019.4 1990.4 2021.3 C
  5.2690 +1990.5 2021.5 1991.9 2022.3 1992 2023 C
  5.2691 +1994.8 2024.4 1996.2 2027.5 1998.5 2030 C
  5.2692 +2002.4 2033 2005.2 2037.2 2008.8 2041 C
  5.2693 +2010.2 2041.3 2011.6 2042 2011 2043.9 C
  5.2694 +2011.2 2044.8 2010.1 2045.3 2010.5 2046.3 C
  5.2695 +2013.8 2044.8 2017.5 2043.4 2021.1 2042 C
  5.2696 +[0 0.5 0.5 0.2]  vc
  5.2697 +f 
  5.2698 +S 
  5.2699 +n
  5.2700 +2019.4 2008.8 m
  5.2701 +2018.9 2009.2 2019.3 2009.9 2019.6 2010.3 C
  5.2702 +2022.2 2011.5 2020.3 2009.1 2019.4 2008.8 C
  5.2703 +[0 0.33 0.33 0.99]  vc
  5.2704 +f 
  5.2705 +S 
  5.2706 +n
  5.2707 +2018 2007.4 m
  5.2708 +2015.7 2006.7 2015.3 2003.6 2012.9 2002.8 C
  5.2709 +2013.5 2003.7 2013.5 2005.1 2015.6 2005.2 C
  5.2710 +2016.4 2006.1 2015.7 2007.7 2018 2007.4 C
  5.2711 +f 
  5.2712 +S 
  5.2713 +n
  5.2714 +vmrs
  5.2715 +1993.5 2008.8 m
  5.2716 +1993.4 2000 1993.7 1992.5 1994 1985.1 C
  5.2717 +1993.7 1984.3 1989.9 1984.1 1990.6 1982 C
  5.2718 +1989.8 1981.1 1987.7 1981.4 1988.2 1979.3 C
  5.2719 +1988.3 1979.6 1988.1 1979.7 1988 1979.8 C
  5.2720 +1987.5 1977.5 1984.5 1978.6 1984.6 1976.2 C
  5.2721 +1983.9 1975.5 1981.7 1975.8 1982.4 1974.3 C
  5.2722 +1981.6 1974.9 1982.1 1973.1 1982 1973.3 C
  5.2723 +1979 1973.7 1980 1968.8 1976.9 1969.7 C
  5.2724 +1975.9 1969.8 1975.3 1970.3 1975 1971.2 C
  5.2725 +1976.2 1969.2 1977 1971.2 1978.6 1970.9 C
  5.2726 +1978.5 1974.4 1981.7 1972.8 1982.2 1976 C
  5.2727 +1985.2 1976.3 1984.5 1979.3 1987 1979.6 C
  5.2728 +1987.7 1980.3 1987.5 1982.1 1988.9 1981.7 C
  5.2729 +1990.4 1982.4 1990.7 1985.5 1993 1985.8 C
  5.2730 +1992.9 1994.3 1993.2 2002.3 1992.8 2011.2 C
  5.2731 +1991.1 2012.4 1990 2014.4 1987.7 2014.6 C
  5.2732 +1990.1 2013.4 1994.7 2012.6 1993.5 2008.8 C
  5.2733 +[0 0.87 0.91 0.83]  vc
  5.2734 +f 
  5.2735 +0.4 w
  5.2736 +2 J
  5.2737 +2 M
  5.2738 +S 
  5.2739 +n
  5.2740 +1992.8 2010.8 m
  5.2741 +1992.8 2001.8 1992.8 1994.1 1992.8 1985.8 C
  5.2742 +1989.5 1985.7 1991.1 1981.1 1987.7 1981.7 C
  5.2743 +1987.9 1978.2 1983.9 1980 1984.1 1977.2 C
  5.2744 +1981.1 1977 1981.5 1973 1979.1 1973.1 C
  5.2745 +1979 1972.2 1978.5 1970.9 1977.6 1970.9 C
  5.2746 +1977.9 1971.6 1979 1971.9 1978.6 1973.1 C
  5.2747 +1977.6 1974.9 1976.8 1973.9 1977.2 1976.2 C
  5.2748 +1977.2 1981.5 1977 1989.4 1977.4 1994 C
  5.2749 +1978.3 1995 1976.6 1994.1 1977.2 1994.7 C
  5.2750 +1977 1995.3 1976.6 1997 1977.9 1997.8 C
  5.2751 +1979 1997.5 1979.3 1998.3 1979.8 1998.8 C
  5.2752 +1979.8 1998.9 1979.8 1999.8 1979.8 1999.2 C
  5.2753 +1980.8 1998.7 1979.7 2000.7 1980.8 2000.7 C
  5.2754 +1983.5 2000.4 1982.1 2003 1984.1 2003.3 C
  5.2755 +1984.4 2004.3 1984.5 2003.7 1985.3 2004 C
  5.2756 +1986.3 2004.6 1985.9 2006.1 1986.5 2006.9 C
  5.2757 +1988 2007.1 1988.4 2009.7 1990.6 2009.1 C
  5.2758 +1990.9 2006.1 1989 2000.2 1990.4 1998 C
  5.2759 +1990.2 1994.3 1990.8 1989.2 1989.9 1986.8 C
  5.2760 +1990.2 1984.7 1990.8 1986.2 1991.6 1985.1 C
  5.2761 +1991.5 1985.9 1992.6 1985.5 1992.5 1986.3 C
  5.2762 +1992 1990.5 1992.6 1995 1992 1999.2 C
  5.2763 +1991.6 1998.9 1991.9 1998.3 1991.8 1997.8 C
  5.2764 +1991.8 1998.5 1991.8 2000 1991.8 2000 C
  5.2765 +1991.9 1999.9 1992 1999.8 1992 1999.7 C
  5.2766 +1993.2 2003.5 1991.9 2007.7 1992.3 2011.5 C
  5.2767 +1991.6 2012 1990.9 2012.2 1990.4 2012.9 C
  5.2768 +1991.3 2011.9 1992.2 2012.1 1992.8 2010.8 C
  5.2769 +[0 1 1 0.23]  vc
  5.2770 +f 
  5.2771 +S 
  5.2772 +n
  5.2773 +1978.4 1968.5 m
  5.2774 +1977 1969.2 1975.8 1968.2 1974.5 1969 C
  5.2775 +1968.3 1973 1961.6 1976 1955.1 1979.1 C
  5.2776 +1962 1975.9 1968.8 1972.5 1975.5 1968.8 C
  5.2777 +1976.5 1968.8 1977.6 1968.8 1978.6 1968.8 C
  5.2778 +1981.7 1972.1 1984.8 1975.7 1988 1978.8 C
  5.2779 +1990.9 1981.9 1996.8 1984.6 1995.2 1990.6 C
  5.2780 +1995.3 1988.6 1994.9 1986.9 1994.7 1985.1 C
  5.2781 +1989.5 1979.1 1983.3 1974.3 1978.4 1968.5 C
  5.2782 +[0.18 0.18 0 0.78]  vc
  5.2783 +f 
  5.2784 +S 
  5.2785 +n
  5.2786 +1978.4 1968.3 m
  5.2787 +1977.9 1968.7 1977.1 1968.5 1976.4 1968.5 C
  5.2788 +1977.3 1968.8 1978.1 1967.9 1978.8 1968.5 C
  5.2789 +1984 1974.3 1990.1 1979.5 1995.2 1985.6 C
  5.2790 +1995.1 1988.4 1995.3 1985.6 1994.9 1984.8 C
  5.2791 +1989.5 1979.4 1983.9 1973.8 1978.4 1968.3 C
  5.2792 +[0.07 0.06 0 0.58]  vc
  5.2793 +f 
  5.2794 +S 
  5.2795 +n
  5.2796 +1978.6 1968 m
  5.2797 +1977.9 1968 1977.4 1968.6 1978.4 1968 C
  5.2798 +1983.9 1973.9 1990.1 1979.1 1995.2 1985.1 C
  5.2799 +1990.2 1979 1983.8 1974.1 1978.6 1968 C
  5.2800 +[0.4 0.4 0 0]  vc
  5.2801 +f 
  5.2802 +S 
  5.2803 +n
  5.2804 +1991.1 1982.2 m
  5.2805 +1991.2 1982.9 1991.6 1984.2 1993 1984.4 C
  5.2806 +1992.6 1983.5 1992.1 1982.5 1991.1 1982.2 C
  5.2807 +[0 0.33 0.33 0.99]  vc
  5.2808 +f 
  5.2809 +S 
  5.2810 +n
  5.2811 +1990.4 2012.7 m
  5.2812 +1991.4 2011.8 1990.2 2010.9 1989.9 2010.3 C
  5.2813 +1987.7 2010.2 1987.4 2007.6 1985.6 2007.2 C
  5.2814 +1985.1 2006.2 1984.6 2004.5 1984.1 2004.3 C
  5.2815 +1981.7 2004.5 1982.3 2001.2 1979.8 2000.9 C
  5.2816 +1978.8 1999.6 1978.8 1999.1 1977.6 1998.8 C
  5.2817 +1976.1 1997.4 1976.7 1995 1975.2 1994 C
  5.2818 +1975.8 1994 1975 1994 1975 1993.7 C
  5.2819 +1975.7 1993.2 1975.6 1991.8 1976 1991.3 C
  5.2820 +1975.9 1985.7 1976.1 1979.7 1975.7 1974.5 C
  5.2821 +1976.2 1973.3 1976.9 1971.8 1976.2 1971.4 C
  5.2822 +1973.9 1974.3 1972.2 1973.6 1969.5 1975 C
  5.2823 +1967.9 1977.5 1963.8 1977.1 1961.8 1980 C
  5.2824 +1959 1980 1957.6 1983 1954.8 1982.9 C
  5.2825 +1953.8 1984.2 1954.8 1985.7 1955.1 1987.2 C
  5.2826 +1956.2 1989.5 1959.7 1990.1 1959.9 1991.8 C
  5.2827 +1965.9 1998 1971.8 2005.2 1978.1 2011.7 C
  5.2828 +1979.5 2012 1980.9 2012.7 1980.3 2014.6 C
  5.2829 +1980.5 2015.6 1979.4 2016 1979.8 2017 C
  5.2830 +1983 2015.6 1986.8 2014.1 1990.4 2012.7 C
  5.2831 +[0 0.5 0.5 0.2]  vc
  5.2832 +f 
  5.2833 +S 
  5.2834 +n
  5.2835 +1988.7 1979.6 m
  5.2836 +1988.2 1979.9 1988.6 1980.6 1988.9 1981 C
  5.2837 +1991.4 1982.2 1989.6 1979.9 1988.7 1979.6 C
  5.2838 +[0 0.33 0.33 0.99]  vc
  5.2839 +f 
  5.2840 +S 
  5.2841 +n
  5.2842 +1987.2 1978.1 m
  5.2843 +1985 1977.5 1984.6 1974.3 1982.2 1973.6 C
  5.2844 +1982.7 1974.5 1982.8 1975.8 1984.8 1976 C
  5.2845 +1985.7 1976.9 1985 1978.4 1987.2 1978.1 C
  5.2846 +f 
  5.2847 +S 
  5.2848 +n
  5.2849 +1975.5 2084 m
  5.2850 +1975.5 2082 1975.3 2080 1975.7 2078.2 C
  5.2851 +1978.8 2079 1980.9 2085.5 1984.8 2083.5 C
  5.2852 +1993 2078.7 2001.6 2075 2010 2070.8 C
  5.2853 +2010.1 2064 2009.9 2057.2 2010.3 2050.6 C
  5.2854 +2014.8 2046.2 2020.9 2045.7 2025.6 2042 C
  5.2855 +2026.1 2035.1 2025.8 2028 2025.9 2021.1 C
  5.2856 +2025.8 2027.8 2026.1 2034.6 2025.6 2041.2 C
  5.2857 +2022.2 2044.9 2017.6 2046.8 2012.9 2048 C
  5.2858 +2012.5 2049.5 2010.4 2049.4 2009.8 2051.1 C
  5.2859 +2009.9 2057.6 2009.6 2064.2 2010 2070.5 C
  5.2860 +2001.2 2075.4 1992 2079.1 1983.2 2084 C
  5.2861 +1980.3 2082.3 1977.8 2079.2 1975.2 2077.5 C
  5.2862 +1974.9 2079.9 1977.2 2084.6 1973.3 2085.2 C
  5.2863 +1964.7 2088.6 1956.8 2093.7 1948.1 2097.2 C
  5.2864 +1949 2097.3 1949.6 2096.9 1950.3 2096.7 C
  5.2865 +1958.4 2091.9 1967.1 2088.2 1975.5 2084 C
  5.2866 +[0.18 0.18 0 0.78]  vc
  5.2867 +f 
  5.2868 +S 
  5.2869 +n
  5.2870 +vmrs
  5.2871 +1948.6 2094.5 m
  5.2872 +1950.2 2093.7 1951.8 2092.9 1953.4 2092.1 C
  5.2873 +1951.8 2092.9 1950.2 2093.7 1948.6 2094.5 C
  5.2874 +[0 0.87 0.91 0.83]  vc
  5.2875 +f 
  5.2876 +0.4 w
  5.2877 +2 J
  5.2878 +2 M
  5.2879 +S 
  5.2880 +n
  5.2881 +1971.6 2082.3 m
  5.2882 +1971.6 2081.9 1970.7 2081.1 1970.9 2081.3 C
  5.2883 +1970.7 2081.6 1970.6 2081.6 1970.4 2081.3 C
  5.2884 +1970.8 2080.1 1968.7 2081.7 1968.3 2080.8 C
  5.2885 +1966.6 2080.9 1966.7 2078 1964.2 2078.2 C
  5.2886 +1964.8 2075 1960.1 2075.8 1960.1 2072.9 C
  5.2887 +1958 2072.3 1957.5 2069.3 1955.3 2069.3 C
  5.2888 +1953.9 2070.9 1948.8 2067.8 1950 2072 C
  5.2889 +1949 2074 1943.2 2070.6 1944 2074.8 C
  5.2890 +1942.2 2076.6 1937.6 2073.9 1938 2078.2 C
  5.2891 +1936.7 2078.6 1935 2078.6 1933.7 2078.2 C
  5.2892 +1933.5 2080 1936.8 2080.7 1937.3 2082.8 C
  5.2893 +1939.9 2083.5 1940.6 2086.4 1942.6 2088 C
  5.2894 +1945.2 2089.2 1946 2091.3 1948.4 2093.6 C
  5.2895 +1956 2089.5 1963.9 2086.1 1971.6 2082.3 C
  5.2896 +[0 0.01 1 0]  vc
  5.2897 +f 
  5.2898 +S 
  5.2899 +n
  5.2900 +1958.2 2089.7 m
  5.2901 +1956.4 2090 1955.6 2091.3 1953.9 2091.9 C
  5.2902 +1955.6 2091.9 1956.5 2089.7 1958.2 2089.7 C
  5.2903 +[0 0.87 0.91 0.83]  vc
  5.2904 +f 
  5.2905 +S 
  5.2906 +n
  5.2907 +1929.9 2080.4 m
  5.2908 +1929.5 2077.3 1929.7 2073.9 1929.6 2070.8 C
  5.2909 +1929.8 2074.1 1929.2 2077.8 1930.1 2080.8 C
  5.2910 +1935.8 2085.9 1941.4 2091.3 1946.9 2096.9 C
  5.2911 +1941.2 2091 1935.7 2086 1929.9 2080.4 C
  5.2912 +[0.4 0.4 0 0]  vc
  5.2913 +f 
  5.2914 +S 
  5.2915 +n
  5.2916 +1930.1 2080.4 m
  5.2917 +1935.8 2086 1941.5 2090.7 1946.9 2096.7 C
  5.2918 +1941.5 2090.9 1935.7 2085.8 1930.1 2080.4 C
  5.2919 +[0.07 0.06 0 0.58]  vc
  5.2920 +f 
  5.2921 +S 
  5.2922 +n
  5.2923 +1940.9 2087.1 m
  5.2924 +1941.7 2088 1944.8 2090.6 1943.6 2089.2 C
  5.2925 +1942.5 2089 1941.6 2087.7 1940.9 2087.1 C
  5.2926 +[0 0.87 0.91 0.83]  vc
  5.2927 +f 
  5.2928 +S 
  5.2929 +n
  5.2930 +1972.8 2082.8 m
  5.2931 +1973 2075.3 1972.4 2066.9 1973.3 2059.5 C
  5.2932 +1972.5 2058.9 1972.8 2057.3 1973.1 2056.4 C
  5.2933 +1974.8 2055.2 1973.4 2055.5 1972.4 2055.4 C
  5.2934 +1970.1 2053.2 1967.9 2050.9 1965.6 2048.7 C
  5.2935 +1960.9 2049.9 1956.9 2052.7 1952.4 2054.7 C
  5.2936 +1949.3 2052.5 1946.3 2049.5 1943.6 2046.8 C
  5.2937 +1939.9 2047.7 1936.8 2050.1 1933.5 2051.8 C
  5.2938 +1930.9 2054.9 1933.5 2056.2 1932.3 2059.7 C
  5.2939 +1933.2 2059.7 1932.2 2060.5 1932.5 2060.2 C
  5.2940 +1933.2 2062.5 1931.6 2064.6 1932.5 2067.4 C
  5.2941 +1932.9 2069.7 1932.7 2072.2 1932.8 2074.6 C
  5.2942 +1933.6 2070.6 1932.2 2066.3 1933 2062.6 C
  5.2943 +1934.4 2058.2 1929.8 2053.5 1935.2 2051.1 C
  5.2944 +1937.7 2049.7 1940.2 2048 1942.8 2046.8 C
  5.2945 +1945.9 2049.2 1948.8 2052 1951.7 2054.7 C
  5.2946 +1952.7 2054.7 1953.6 2054.6 1954.4 2054.2 C
  5.2947 +1958.1 2052.5 1961.7 2049.3 1965.9 2049.2 C
  5.2948 +1968.2 2052.8 1975.2 2055 1972.6 2060.9 C
  5.2949 +1973.3 2062.4 1972.2 2065.2 1972.6 2067.6 C
  5.2950 +1972.7 2072.6 1972.4 2077.7 1972.8 2082.5 C
  5.2951 +1968.1 2084.9 1963.5 2087.5 1958.7 2089.5 C
  5.2952 +1963.5 2087.4 1968.2 2085 1972.8 2082.8 C
  5.2953 +f 
  5.2954 +S 
  5.2955 +n
  5.2956 +1935.2 2081.1 m
  5.2957 +1936.8 2083.4 1938.6 2084.6 1940.4 2086.6 C
  5.2958 +1938.8 2084.4 1936.7 2083.4 1935.2 2081.1 C
  5.2959 +f 
  5.2960 +S 
  5.2961 +n
  5.2962 +1983.2 2081.3 m
  5.2963 +1984.8 2080.5 1986.3 2079.7 1988 2078.9 C
  5.2964 +1986.3 2079.7 1984.8 2080.5 1983.2 2081.3 C
  5.2965 +f 
  5.2966 +S 
  5.2967 +n
  5.2968 +2006.2 2069.1 m
  5.2969 +2006.2 2068.7 2005.2 2067.9 2005.5 2068.1 C
  5.2970 +2005.3 2068.4 2005.2 2068.4 2005 2068.1 C
  5.2971 +2005.4 2066.9 2003.3 2068.5 2002.8 2067.6 C
  5.2972 +2001.2 2067.7 2001.2 2064.8 1998.8 2065 C
  5.2973 +1999.4 2061.8 1994.7 2062.6 1994.7 2059.7 C
  5.2974 +1992.4 2059.5 1992.4 2055.8 1990.1 2056.8 C
  5.2975 +1985.9 2059.5 1981.1 2061 1976.9 2063.8 C
  5.2976 +1977.2 2067.6 1974.9 2074.2 1978.8 2075.8 C
  5.2977 +1979.6 2077.8 1981.7 2078.4 1982.9 2080.4 C
  5.2978 +1990.6 2076.3 1998.5 2072.9 2006.2 2069.1 C
  5.2979 +[0 0.01 1 0]  vc
  5.2980 +f 
  5.2981 +S 
  5.2982 +n
  5.2983 +vmrs
  5.2984 +1992.8 2076.5 m
  5.2985 +1991 2076.8 1990.2 2078.1 1988.4 2078.7 C
  5.2986 +1990.2 2078.7 1991 2076.5 1992.8 2076.5 C
  5.2987 +[0 0.87 0.91 0.83]  vc
  5.2988 +f 
  5.2989 +0.4 w
  5.2990 +2 J
  5.2991 +2 M
  5.2992 +S 
  5.2993 +n
  5.2994 +1975.5 2073.4 m
  5.2995 +1976.1 2069.7 1973.9 2064.6 1977.4 2062.4 C
  5.2996 +1973.9 2064.5 1976.1 2069.9 1975.5 2073.6 C
  5.2997 +1976 2074.8 1979.3 2077.4 1978.1 2076 C
  5.2998 +1977 2075.7 1975.8 2074.5 1975.5 2073.4 C
  5.2999 +f 
  5.3000 +S 
  5.3001 +n
  5.3002 +2007.4 2069.6 m
  5.3003 +2007.6 2062.1 2007 2053.7 2007.9 2046.3 C
  5.3004 +2007.1 2045.7 2007.3 2044.1 2007.6 2043.2 C
  5.3005 +2009.4 2042 2007.9 2042.3 2006.9 2042.2 C
  5.3006 +2002.2 2037.4 1996.7 2032.4 1992.5 2027.3 C
  5.3007 +1992 2027.3 1991.6 2027.3 1991.1 2027.3 C
  5.3008 +1991.4 2035.6 1991.4 2045.6 1991.1 2054.4 C
  5.3009 +1990.5 2055.5 1988.4 2056.6 1990.6 2055.4 C
  5.3010 +1991.6 2055.4 1991.6 2054.1 1991.6 2053.2 C
  5.3011 +1990.8 2044.7 1991.9 2035.4 1991.6 2027.6 C
  5.3012 +1991.8 2027.6 1992 2027.6 1992.3 2027.6 C
  5.3013 +1997 2032.8 2002.5 2037.7 2007.2 2042.9 C
  5.3014 +2007.3 2044.8 2006.7 2047.4 2007.6 2048.4 C
  5.3015 +2006.9 2055.1 2007.1 2062.5 2007.4 2069.3 C
  5.3016 +2002.7 2071.7 1998.1 2074.3 1993.2 2076.3 C
  5.3017 +1998 2074.2 2002.7 2071.8 2007.4 2069.6 C
  5.3018 +f 
  5.3019 +S 
  5.3020 +n
  5.3021 +2006.7 2069.1 m
  5.3022 +2006.3 2068.6 2005.9 2067.7 2005.7 2066.9 C
  5.3023 +2005.7 2059.7 2005.9 2051.4 2005.5 2045.1 C
  5.3024 +2004.9 2045.3 2004.7 2044.5 2004.3 2045.3 C
  5.3025 +2005.1 2045.3 2004.2 2045.8 2004.8 2046 C
  5.3026 +2004.8 2052.2 2004.8 2059.2 2004.8 2064.5 C
  5.3027 +2005.7 2065.7 2005.1 2065.7 2005 2066.7 C
  5.3028 +2003.8 2067 2002.7 2067.2 2001.9 2066.4 C
  5.3029 +2001.3 2064.6 1998 2063.1 1998 2061.9 C
  5.3030 +1996.1 2062.3 1996.6 2058.3 1994.2 2058.8 C
  5.3031 +1992.6 2057.7 1992.7 2054.8 1989.9 2056.6 C
  5.3032 +1985.6 2059.3 1980.9 2060.8 1976.7 2063.6 C
  5.3033 +1976 2066.9 1976 2071.2 1976.7 2074.6 C
  5.3034 +1977.6 2070.8 1973.1 2062.1 1980.5 2061.2 C
  5.3035 +1984.3 2060.3 1987.5 2058.2 1990.8 2056.4 C
  5.3036 +1991.7 2056.8 1992.9 2057.2 1993.5 2059.2 C
  5.3037 +1994.3 2058.6 1994.4 2060.6 1994.7 2059.2 C
  5.3038 +1995.3 2062.7 1999.2 2061.4 1998.8 2064.8 C
  5.3039 +2001.8 2065.4 2002.5 2068.4 2005.2 2067.4 C
  5.3040 +2004.9 2067.9 2006 2068 2006.4 2069.1 C
  5.3041 +2001.8 2071.1 1997.4 2073.9 1992.8 2075.8 C
  5.3042 +1997.5 2073.8 2002 2071.2 2006.7 2069.1 C
  5.3043 +[0 0.2 1 0]  vc
  5.3044 +f 
  5.3045 +S 
  5.3046 +n
  5.3047 +1988.7 2056.6 m
  5.3048 +1985.1 2058.7 1981.1 2060.1 1977.6 2061.9 C
  5.3049 +1981.3 2060.5 1985.6 2058.1 1988.7 2056.6 C
  5.3050 +[0 0.87 0.91 0.83]  vc
  5.3051 +f 
  5.3052 +S 
  5.3053 +n
  5.3054 +1977.9 2059.5 m
  5.3055 +1975.7 2064.5 1973.7 2054.7 1975.2 2060.9 C
  5.3056 +1976 2060.6 1977.6 2059.7 1977.9 2059.5 C
  5.3057 +f 
  5.3058 +S 
  5.3059 +n
  5.3060 +1989.6 2051.3 m
  5.3061 +1990.1 2042.3 1989.8 2036.6 1989.9 2028 C
  5.3062 +1989.8 2027 1990.8 2028.3 1990.1 2027.3 C
  5.3063 +1988.9 2026.7 1986.7 2026.9 1986.8 2024.7 C
  5.3064 +1987.4 2023 1985.9 2024.6 1985.1 2023.7 C
  5.3065 +1984.1 2021.4 1982.5 2020.5 1980.3 2020.6 C
  5.3066 +1979.9 2020.8 1979.5 2021.1 1979.3 2021.6 C
  5.3067 +1979.7 2025.8 1978.4 2033 1979.6 2038.1 C
  5.3068 +1983.7 2042.9 1968.8 2044.6 1978.8 2042.7 C
  5.3069 +1979.3 2042.3 1979.6 2041.9 1980 2041.5 C
  5.3070 +1980 2034.8 1980 2027 1980 2021.6 C
  5.3071 +1981.3 2020.5 1981.7 2021.5 1982.9 2021.8 C
  5.3072 +1983.6 2024.7 1986.1 2023.8 1986.8 2026.4 C
  5.3073 +1987.1 2027.7 1988.6 2027.1 1989.2 2028.3 C
  5.3074 +1989.1 2036.7 1989.3 2044.8 1988.9 2053.7 C
  5.3075 +1987.2 2054.9 1986.2 2056.8 1983.9 2057.1 C
  5.3076 +1986.3 2055.9 1990.9 2055 1989.6 2051.3 C
  5.3077 +f 
  5.3078 +S 
  5.3079 +n
  5.3080 +1971.6 2078.9 m
  5.3081 +1971.4 2070.5 1972.1 2062.2 1971.6 2055.9 C
  5.3082 +1969.9 2053.7 1967.6 2051.7 1965.6 2049.6 C
  5.3083 +1961.4 2050.4 1957.6 2053.6 1953.4 2055.2 C
  5.3084 +1949.8 2055.6 1948.2 2051.2 1945.5 2049.6 C
  5.3085 +1945.1 2048.8 1944.5 2047.9 1943.6 2047.5 C
  5.3086 +1940.1 2047.8 1937.3 2051 1934 2052.3 C
  5.3087 +1933.7 2052.6 1933.7 2053 1933.2 2053.2 C
  5.3088 +1933.7 2060.8 1933.4 2067.2 1933.5 2074.6 C
  5.3089 +1933.8 2068.1 1934 2060.9 1933.2 2054 C
  5.3090 +1935.3 2050.9 1939.3 2049.6 1942.4 2047.5 C
  5.3091 +1942.8 2047.5 1943.4 2047.4 1943.8 2047.7 C
  5.3092 +1947.1 2050.2 1950.3 2057.9 1955.3 2054.4 C
  5.3093 +1955.4 2054.4 1955.5 2054.3 1955.6 2054.2 C
  5.3094 +1955.9 2057.6 1956.1 2061.8 1955.3 2064.8 C
  5.3095 +1955.4 2064.3 1955.1 2063.8 1955.6 2063.6 C
  5.3096 +1956 2066.6 1955.3 2068.7 1958.7 2069.8 C
  5.3097 +1959.2 2071.7 1961.4 2071.7 1962 2074.1 C
  5.3098 +1964.4 2074.2 1964 2077.7 1967.3 2078.4 C
  5.3099 +1967 2079.7 1968.1 2079.9 1969 2080.1 C
  5.3100 +1971.1 2079.9 1970 2079.2 1970.4 2078 C
  5.3101 +1969.5 2077.2 1970.3 2075.9 1969.7 2075.1 C
  5.3102 +1970.1 2069.8 1970.1 2063.6 1969.7 2058.8 C
  5.3103 +1969.2 2058.5 1970 2058.1 1970.2 2057.8 C
  5.3104 +1970.4 2058.3 1971.2 2057.7 1971.4 2058.3 C
  5.3105 +1971.5 2065.3 1971.2 2073.6 1971.6 2081.1 C
  5.3106 +1974.1 2081.4 1969.8 2084.3 1972.4 2082.5 C
  5.3107 +1971.9 2081.4 1971.6 2080.2 1971.6 2078.9 C
  5.3108 +[0 0.4 1 0]  vc
  5.3109 +f 
  5.3110 +S 
  5.3111 +n
  5.3112 +1952.4 2052 m
  5.3113 +1954.1 2051.3 1955.6 2050.4 1957.2 2049.6 C
  5.3114 +1955.6 2050.4 1954.1 2051.3 1952.4 2052 C
  5.3115 +[0 0.87 0.91 0.83]  vc
  5.3116 +f 
  5.3117 +S 
  5.3118 +n
  5.3119 +1975.5 2039.8 m
  5.3120 +1975.5 2039.4 1974.5 2038.7 1974.8 2038.8 C
  5.3121 +1974.6 2039.1 1974.5 2039.1 1974.3 2038.8 C
  5.3122 +1974.6 2037.6 1972.5 2039.3 1972.1 2038.4 C
  5.3123 +1970.4 2038.4 1970.5 2035.5 1968 2035.7 C
  5.3124 +1968.6 2032.5 1964 2033.3 1964 2030.4 C
  5.3125 +1961.9 2029.8 1961.4 2026.8 1959.2 2026.8 C
  5.3126 +1957.7 2028.5 1952.6 2025.3 1953.9 2029.5 C
  5.3127 +1952.9 2031.5 1947 2028.2 1947.9 2032.4 C
  5.3128 +1946 2034.2 1941.5 2031.5 1941.9 2035.7 C
  5.3129 +1940.6 2036.1 1938.9 2036.1 1937.6 2035.7 C
  5.3130 +1937.3 2037.5 1940.7 2038.2 1941.2 2040.3 C
  5.3131 +1943.7 2041.1 1944.4 2043.9 1946.4 2045.6 C
  5.3132 +1949.1 2046.7 1949.9 2048.8 1952.2 2051.1 C
  5.3133 +1959.9 2047.1 1967.7 2043.6 1975.5 2039.8 C
  5.3134 +[0 0.01 1 0]  vc
  5.3135 +f 
  5.3136 +S 
  5.3137 +n
  5.3138 +vmrs
  5.3139 +1962 2047.2 m
  5.3140 +1960.2 2047.5 1959.5 2048.9 1957.7 2049.4 C
  5.3141 +1959.5 2049.5 1960.3 2047.2 1962 2047.2 C
  5.3142 +[0 0.87 0.91 0.83]  vc
  5.3143 +f 
  5.3144 +0.4 w
  5.3145 +2 J
  5.3146 +2 M
  5.3147 +S 
  5.3148 +n
  5.3149 +2012.4 2046.3 m
  5.3150 +2010.3 2051.3 2008.3 2041.5 2009.8 2047.7 C
  5.3151 +2010.5 2047.4 2012.2 2046.5 2012.4 2046.3 C
  5.3152 +f 
  5.3153 +S 
  5.3154 +n
  5.3155 +1944.8 2044.6 m
  5.3156 +1945.5 2045.6 1948.6 2048.1 1947.4 2046.8 C
  5.3157 +1946.3 2046.5 1945.5 2045.2 1944.8 2044.6 C
  5.3158 +f 
  5.3159 +S 
  5.3160 +n
  5.3161 +1987.2 2054.9 m
  5.3162 +1983.7 2057.3 1979.6 2058 1976 2060.2 C
  5.3163 +1974.7 2058.2 1977.2 2055.8 1974.3 2054.9 C
  5.3164 +1973.1 2052 1970.4 2050.2 1968 2048 C
  5.3165 +1968 2047.7 1968 2047.4 1968.3 2047.2 C
  5.3166 +1969.5 2046.1 1983 2040.8 1972.4 2044.8 C
  5.3167 +1971.2 2046.6 1967.9 2046 1968 2048.2 C
  5.3168 +1970.5 2050.7 1973.8 2052.6 1974.3 2055.6 C
  5.3169 +1975.1 2055 1975.7 2056.7 1975.7 2057.1 C
  5.3170 +1975.7 2058.2 1974.8 2059.3 1975.5 2060.4 C
  5.3171 +1979.3 2058.2 1983.9 2057.7 1987.2 2054.9 C
  5.3172 +[0.18 0.18 0 0.78]  vc
  5.3173 +f 
  5.3174 +S 
  5.3175 +n
  5.3176 +1967.8 2047.5 m
  5.3177 +1968.5 2047 1969.1 2046.5 1969.7 2046 C
  5.3178 +1969.1 2046.5 1968.5 2047 1967.8 2047.5 C
  5.3179 +[0 0.87 0.91 0.83]  vc
  5.3180 +f 
  5.3181 +S 
  5.3182 +n
  5.3183 +1976.7 2040.3 m
  5.3184 +1976.9 2032.8 1976.3 2024.4 1977.2 2017 C
  5.3185 +1976.4 2016.5 1976.6 2014.8 1976.9 2013.9 C
  5.3186 +1978.7 2012.7 1977.2 2013 1976.2 2012.9 C
  5.3187 +1971.5 2008.1 1965.9 2003.1 1961.8 1998 C
  5.3188 +1960.9 1998 1960.1 1998 1959.2 1998 C
  5.3189 +1951.5 2001.1 1944.3 2005.5 1937.1 2009.6 C
  5.3190 +1935 2012.9 1937 2013.6 1936.1 2017.2 C
  5.3191 +1937.1 2017.2 1936 2018 1936.4 2017.7 C
  5.3192 +1937 2020.1 1935.5 2022.1 1936.4 2024.9 C
  5.3193 +1936.8 2027.2 1936.5 2029.7 1936.6 2032.1 C
  5.3194 +1937.4 2028.2 1936 2023.8 1936.8 2020.1 C
  5.3195 +1938.3 2015.7 1933.6 2011 1939 2008.6 C
  5.3196 +1945.9 2004.5 1953.1 2000.3 1960.6 1998.3 C
  5.3197 +1960.9 1998.3 1961.3 1998.3 1961.6 1998.3 C
  5.3198 +1966.2 2003.5 1971.8 2008.4 1976.4 2013.6 C
  5.3199 +1976.6 2015.5 1976 2018.1 1976.9 2019.2 C
  5.3200 +1976.1 2025.8 1976.4 2033.2 1976.7 2040 C
  5.3201 +1971.9 2042.4 1967.4 2045 1962.5 2047 C
  5.3202 +1967.3 2044.9 1972 2042.6 1976.7 2040.3 C
  5.3203 +f 
  5.3204 +S 
  5.3205 +n
  5.3206 +1939 2038.6 m
  5.3207 +1940.6 2040.9 1942.5 2042.1 1944.3 2044.1 C
  5.3208 +1942.7 2041.9 1940.6 2040.9 1939 2038.6 C
  5.3209 +f 
  5.3210 +S 
  5.3211 +n
  5.3212 +2006.2 2065.7 m
  5.3213 +2006 2057.3 2006.7 2049 2006.2 2042.7 C
  5.3214 +2002.1 2038.4 1997.7 2033.4 1993 2030 C
  5.3215 +1992.9 2029.3 1992.5 2028.6 1992 2028.3 C
  5.3216 +1992.1 2036.6 1991.9 2046.2 1992.3 2054.9 C
  5.3217 +1990.8 2056.2 1989 2056.7 1987.5 2058 C
  5.3218 +1988.7 2057.7 1990.7 2054.4 1993 2056.4 C
  5.3219 +1993.4 2058.8 1996 2058.2 1996.6 2060.9 C
  5.3220 +1999 2061 1998.5 2064.5 2001.9 2065.2 C
  5.3221 +2001.5 2066.5 2002.7 2066.7 2003.6 2066.9 C
  5.3222 +2005.7 2066.7 2004.6 2066 2005 2064.8 C
  5.3223 +2004 2064 2004.8 2062.7 2004.3 2061.9 C
  5.3224 +2004.6 2056.6 2004.6 2050.4 2004.3 2045.6 C
  5.3225 +2003.7 2045.3 2004.6 2044.9 2004.8 2044.6 C
  5.3226 +2005 2045.1 2005.7 2044.5 2006 2045.1 C
  5.3227 +2006 2052.1 2005.8 2060.4 2006.2 2067.9 C
  5.3228 +2008.7 2068.2 2004.4 2071.1 2006.9 2069.3 C
  5.3229 +2006.4 2068.2 2006.2 2067 2006.2 2065.7 C
  5.3230 +[0 0.4 1 0]  vc
  5.3231 +f 
  5.3232 +S 
  5.3233 +n
  5.3234 +2021.8 2041.7 m
  5.3235 +2018.3 2044.1 2014.1 2044.8 2010.5 2047 C
  5.3236 +2009.3 2045 2011.7 2042.6 2008.8 2041.7 C
  5.3237 +2004.3 2035.1 1997.6 2030.9 1993 2024.4 C
  5.3238 +1992.1 2024 1991.5 2024.3 1990.8 2024 C
  5.3239 +1993.2 2023.9 1995.3 2027.1 1996.8 2029 C
  5.3240 +2000.4 2032.6 2004.9 2036.9 2008.4 2040.8 C
  5.3241 +2008.2 2043.1 2011.4 2042.8 2009.8 2045.8 C
  5.3242 +2009.8 2046.3 2009.7 2046.9 2010 2047.2 C
  5.3243 +2013.8 2045 2018.5 2044.5 2021.8 2041.7 C
  5.3244 +[0.18 0.18 0 0.78]  vc
  5.3245 +f 
  5.3246 +S 
  5.3247 +n
  5.3248 +2001.6 2034 m
  5.3249 +2000.7 2033.1 1999.9 2032.3 1999 2031.4 C
  5.3250 +1999.9 2032.3 2000.7 2033.1 2001.6 2034 C
  5.3251 +[0 0.87 0.91 0.83]  vc
  5.3252 +f 
  5.3253 +S 
  5.3254 +n
  5.3255 +vmrs
  5.3256 +1989.4 2024.4 m
  5.3257 +1989.5 2025.4 1988.6 2024.3 1988.9 2024.7 C
  5.3258 +1990.5 2025.8 1990.7 2024.2 1992.8 2024.9 C
  5.3259 +1993.8 2025.9 1995 2027.1 1995.9 2028 C
  5.3260 +1994.3 2026 1991.9 2023.4 1989.4 2024.4 C
  5.3261 +[0 0.87 0.91 0.83]  vc
  5.3262 +f 
  5.3263 +0.4 w
  5.3264 +2 J
  5.3265 +2 M
  5.3266 +S 
  5.3267 +n
  5.3268 +1984.8 2019.9 m
  5.3269 +1984.6 2018.6 1986.3 2017.2 1987.7 2016.8 C
  5.3270 +1987.2 2017.5 1982.9 2017.9 1984.4 2020.6 C
  5.3271 +1984.1 2019.9 1984.9 2020 1984.8 2019.9 C
  5.3272 +f 
  5.3273 +S 
  5.3274 +n
  5.3275 +1981.7 2017 m
  5.3276 +1979.6 2022 1977.6 2012.3 1979.1 2018.4 C
  5.3277 +1979.8 2018.1 1981.5 2017.2 1981.7 2017 C
  5.3278 +f 
  5.3279 +S 
  5.3280 +n
  5.3281 +1884.3 2019.2 m
  5.3282 +1884.7 2010.5 1884.5 2000.6 1884.5 1991.8 C
  5.3283 +1886.6 1989.3 1889.9 1988.9 1892.4 1987 C
  5.3284 +1890.8 1988.7 1886 1989.1 1884.3 1992.3 C
  5.3285 +1884.7 2001 1884.5 2011.3 1884.5 2019.9 C
  5.3286 +1891 2025.1 1895.7 2031.5 1902 2036.9 C
  5.3287 +1896.1 2031 1890 2024.9 1884.3 2019.2 C
  5.3288 +[0.07 0.06 0 0.58]  vc
  5.3289 +f 
  5.3290 +S 
  5.3291 +n
  5.3292 +1884 2019.4 m
  5.3293 +1884.5 2010.6 1884.2 2000.4 1884.3 1991.8 C
  5.3294 +1884.8 1990.4 1887.8 1989 1884.8 1990.8 C
  5.3295 +1884.3 1991.3 1884.3 1992 1884 1992.5 C
  5.3296 +1884.5 2001.2 1884.2 2011.1 1884.3 2019.9 C
  5.3297 +1887.9 2023.1 1891.1 2026.4 1894.4 2030 C
  5.3298 +1891.7 2026.1 1887.1 2022.9 1884 2019.4 C
  5.3299 +[0.4 0.4 0 0]  vc
  5.3300 +f 
  5.3301 +S 
  5.3302 +n
  5.3303 +1885 2011.7 m
  5.3304 +1885 2006.9 1885 2001.9 1885 1997.1 C
  5.3305 +1885 2001.9 1885 2006.9 1885 2011.7 C
  5.3306 +[0 0.87 0.91 0.83]  vc
  5.3307 +f 
  5.3308 +S 
  5.3309 +n
  5.3310 +1975.5 2036.4 m
  5.3311 +1975.2 2028 1976 2019.7 1975.5 2013.4 C
  5.3312 +1971.1 2008.5 1965.6 2003.6 1961.6 1999 C
  5.3313 +1958.8 1998 1956 2000 1953.6 2001.2 C
  5.3314 +1948.2 2004.7 1941.9 2006.5 1937.1 2010.8 C
  5.3315 +1937.5 2018.3 1937.3 2024.7 1937.3 2032.1 C
  5.3316 +1937.6 2025.6 1937.9 2018.4 1937.1 2011.5 C
  5.3317 +1937.3 2011 1937.6 2010.5 1937.8 2010 C
  5.3318 +1944.6 2005.7 1951.9 2002.3 1959.2 1999 C
  5.3319 +1960.1 1998.5 1960.1 1999.8 1960.4 2000.4 C
  5.3320 +1959.7 2006.9 1959.7 2014.2 1959.4 2021.1 C
  5.3321 +1959 2021.1 1959.2 2021.9 1959.2 2022.3 C
  5.3322 +1959.2 2021.9 1959 2021.3 1959.4 2021.1 C
  5.3323 +1959.8 2024.1 1959.2 2026.2 1962.5 2027.3 C
  5.3324 +1963 2029.2 1965.3 2029.2 1965.9 2031.6 C
  5.3325 +1968.3 2031.8 1967.8 2035.2 1971.2 2036 C
  5.3326 +1970.8 2037.2 1971.9 2037.5 1972.8 2037.6 C
  5.3327 +1974.9 2037.4 1973.9 2036.7 1974.3 2035.5 C
  5.3328 +1973.3 2034.7 1974.1 2033.4 1973.6 2032.6 C
  5.3329 +1973.9 2027.3 1973.9 2021.1 1973.6 2016.3 C
  5.3330 +1973 2016 1973.9 2015.6 1974 2015.3 C
  5.3331 +1974.3 2015.9 1975 2015.3 1975.2 2015.8 C
  5.3332 +1975.3 2022.8 1975.1 2031.2 1975.5 2038.6 C
  5.3333 +1977.9 2039 1973.7 2041.8 1976.2 2040 C
  5.3334 +1975.7 2039 1975.5 2037.8 1975.5 2036.4 C
  5.3335 +[0 0.4 1 0]  vc
  5.3336 +f 
  5.3337 +S 
  5.3338 +n
  5.3339 +1991.1 2012.4 m
  5.3340 +1987.5 2014.8 1983.4 2015.6 1979.8 2017.7 C
  5.3341 +1978.5 2015.7 1981 2013.3 1978.1 2012.4 C
  5.3342 +1973.6 2005.8 1966.8 2001.6 1962.3 1995.2 C
  5.3343 +1961.4 1994.7 1960.8 1995 1960.1 1994.7 C
  5.3344 +1962.5 1994.6 1964.6 1997.8 1966.1 1999.7 C
  5.3345 +1969.7 2003.3 1974.2 2007.6 1977.6 2011.5 C
  5.3346 +1977.5 2013.8 1980.6 2013.5 1979.1 2016.5 C
  5.3347 +1979.1 2017 1979 2017.6 1979.3 2018 C
  5.3348 +1983.1 2015.7 1987.8 2015.2 1991.1 2012.4 C
  5.3349 +[0.18 0.18 0 0.78]  vc
  5.3350 +f 
  5.3351 +S 
  5.3352 +n
  5.3353 +1970.9 2004.8 m
  5.3354 +1970 2003.9 1969.2 2003 1968.3 2002.1 C
  5.3355 +1969.2 2003 1970 2003.9 1970.9 2004.8 C
  5.3356 +[0 0.87 0.91 0.83]  vc
  5.3357 +f 
  5.3358 +S 
  5.3359 +n
  5.3360 +1887.9 1994.9 m
  5.3361 +1888.5 1992.3 1891.4 1992.2 1893.2 1990.8 C
  5.3362 +1898.4 1987.5 1904 1984.8 1909.5 1982.2 C
  5.3363 +1909.7 1982.7 1910.3 1982.1 1910.4 1982.7 C
  5.3364 +1909.5 1990.5 1910.1 1996.4 1910 2004.5 C
  5.3365 +1909.1 2003.4 1909.7 2005.8 1909.5 2006.4 C
  5.3366 +1910.4 2006 1909.7 2008 1910.2 2007.9 C
  5.3367 +1911.3 2010.6 1912.5 2012.6 1915.7 2013.4 C
  5.3368 +1915.8 2013.7 1915.5 2014.4 1916 2014.4 C
  5.3369 +1916.3 2015 1915.4 2016 1915.2 2016 C
  5.3370 +1916.1 2015.5 1916.5 2014.5 1916 2013.6 C
  5.3371 +1913.4 2013.3 1913.1 2010.5 1910.9 2009.8 C
  5.3372 +1910.7 2008.8 1910.4 2007.9 1910.2 2006.9 C
  5.3373 +1911.1 1998.8 1909.4 1990.7 1910.7 1982.4 C
  5.3374 +1910 1982.1 1908.9 1982.1 1908.3 1982.4 C
  5.3375 +1901.9 1986.1 1895 1988.7 1888.8 1993 C
  5.3376 +1888 1993.4 1888.4 1994.3 1887.6 1994.7 C
  5.3377 +1888.1 2001.3 1887.8 2008.6 1887.9 2015.1 C
  5.3378 +1887.3 2017.5 1887.9 2015.4 1888.4 2014.4 C
  5.3379 +1887.8 2008 1888.4 2001.3 1887.9 1994.9 C
  5.3380 +[0.07 0.06 0 0.58]  vc
  5.3381 +f 
  5.3382 +S 
  5.3383 +n
  5.3384 +vmrs
  5.3385 +1887.9 2018.4 m
  5.3386 +1887.5 2016.9 1888.5 2016 1888.8 2014.8 C
  5.3387 +1890.1 2014.8 1891.1 2016.6 1892.4 2015.3 C
  5.3388 +1892.4 2014.4 1893.8 2012.9 1894.4 2012.4 C
  5.3389 +1895.9 2012.4 1896.6 2013.9 1897.7 2012.7 C
  5.3390 +1898.4 2011.7 1898.6 2010.4 1899.6 2009.8 C
  5.3391 +1901.7 2009.9 1902.9 2010.4 1904 2009.1 C
  5.3392 +1904.3 2007.4 1904 2007.6 1904.9 2007.2 C
  5.3393 +1906.2 2007 1907.6 2006.5 1908.8 2006.7 C
  5.3394 +1910.6 2008.2 1909.8 2011.5 1912.6 2012 C
  5.3395 +1912.4 2013 1913.8 2012.7 1914 2013.2 C
  5.3396 +1911.5 2011.1 1909.1 2007.9 1909.2 2004.3 C
  5.3397 +1909.5 2003.5 1909.9 2004.9 1909.7 2004.3 C
  5.3398 +1909.9 1996.2 1909.3 1990.5 1910.2 1982.7 C
  5.3399 +1909.5 1982.6 1909.5 1982.6 1908.8 1982.7 C
  5.3400 +1903.1 1985.7 1897 1987.9 1891.7 1992 C
  5.3401 +1890.5 1993 1888.2 1992.9 1888.1 1994.9 C
  5.3402 +1888.7 2001.4 1888.1 2008.4 1888.6 2014.8 C
  5.3403 +1888.3 2016 1887.2 2016.9 1887.6 2018.4 C
  5.3404 +1892.3 2023.9 1897.6 2027.9 1902.3 2033.3 C
  5.3405 +1898 2028.2 1892.1 2023.8 1887.9 2018.4 C
  5.3406 +[0.4 0.4 0 0]  vc
  5.3407 +f 
  5.3408 +0.4 w
  5.3409 +2 J
  5.3410 +2 M
  5.3411 +S 
  5.3412 +n
  5.3413 +1910.9 1995.2 m
  5.3414 +1910.4 1999.8 1911 2003.3 1910.9 2008.1 C
  5.3415 +1910.9 2003.8 1910.9 1999.2 1910.9 1995.2 C
  5.3416 +[0.18 0.18 0 0.78]  vc
  5.3417 +f 
  5.3418 +S 
  5.3419 +n
  5.3420 +1911.2 2004.3 m
  5.3421 +1911.2 2001.9 1911.2 1999.7 1911.2 1997.3 C
  5.3422 +1911.2 1999.7 1911.2 2001.9 1911.2 2004.3 C
  5.3423 +[0 0.87 0.91 0.83]  vc
  5.3424 +f 
  5.3425 +S 
  5.3426 +n
  5.3427 +1958.7 1995.2 m
  5.3428 +1959 1995.6 1956.2 1995 1956.5 1996.8 C
  5.3429 +1955.8 1997.6 1954.2 1998.5 1953.6 1997.3 C
  5.3430 +1953.6 1990.8 1954.9 1989.6 1953.4 1983.9 C
  5.3431 +1953.4 1983.3 1953.3 1982.1 1954.4 1982 C
  5.3432 +1955.5 1982.6 1956.5 1981.3 1957.5 1981 C
  5.3433 +1956.3 1981.8 1954.7 1982.6 1953.9 1981.5 C
  5.3434 +1951.4 1983 1954.7 1988.8 1952.9 1990.6 C
  5.3435 +1953.8 1990.6 1953.2 1992.7 1953.4 1993.7 C
  5.3436 +1953.8 1994.5 1952.3 1996.1 1953.2 1997.8 C
  5.3437 +1956.3 1999.4 1957.5 1994 1959.9 1995.6 C
  5.3438 +1962 1994.4 1963.7 1997.7 1965.2 1998.8 C
  5.3439 +1963.5 1996.7 1961.2 1994.1 1958.7 1995.2 C
  5.3440 +f 
  5.3441 +S 
  5.3442 +n
  5.3443 +1945 2000.7 m
  5.3444 +1945.4 1998.7 1945.4 1997.9 1945 1995.9 C
  5.3445 +1944.5 1995.3 1944.2 1992.6 1945.7 1993.2 C
  5.3446 +1946 1992.2 1948.7 1992.5 1948.4 1990.6 C
  5.3447 +1947.5 1990.3 1948.1 1988.7 1947.9 1988.2 C
  5.3448 +1948.9 1987.8 1950.5 1986.8 1950.5 1984.6 C
  5.3449 +1951.5 1980.9 1946.7 1983 1947.2 1979.8 C
  5.3450 +1944.5 1979.9 1945.2 1976.6 1943.1 1976.7 C
  5.3451 +1941.8 1975.7 1942.1 1972.7 1939.2 1973.8 C
  5.3452 +1938.2 1974.6 1939.3 1971.6 1938.3 1970.9 C
  5.3453 +1938.8 1969.2 1933.4 1970.3 1937.3 1970 C
  5.3454 +1939.4 1971.2 1937.2 1973 1937.6 1974.3 C
  5.3455 +1937.2 1976.3 1937.1 1981.2 1937.8 1984.1 C
  5.3456 +1938.8 1982.3 1937.9 1976.6 1938.5 1973.1 C
  5.3457 +1938.9 1975 1938.5 1976.4 1939.7 1977.2 C
  5.3458 +1939.5 1983.5 1938.9 1991.3 1940.2 1997.3 C
  5.3459 +1939.4 1999.1 1938.6 1997.1 1937.8 1997.1 C
  5.3460 +1937.4 1996.7 1937.6 1996.1 1937.6 1995.6 C
  5.3461 +1936.5 1998.5 1940.1 1998.4 1940.9 2000.7 C
  5.3462 +1942.1 2000.4 1943.2 2001.3 1943.1 2002.4 C
  5.3463 +1943.6 2003.1 1941.1 2004.6 1942.8 2003.8 C
  5.3464 +1943.9 2002.5 1942.6 2000.6 1945 2000.7 C
  5.3465 +[0.65 0.65 0 0.42]  vc
  5.3466 +f 
  5.3467 +S 
  5.3468 +n
  5.3469 +1914.5 2006.4 m
  5.3470 +1914.1 2004.9 1915.2 2004 1915.5 2002.8 C
  5.3471 +1916.7 2002.8 1917.8 2004.6 1919.1 2003.3 C
  5.3472 +1919 2002.4 1920.4 2000.9 1921 2000.4 C
  5.3473 +1922.5 2000.4 1923.2 2001.9 1924.4 2000.7 C
  5.3474 +1925 1999.7 1925.3 1998.4 1926.3 1997.8 C
  5.3475 +1928.4 1997.9 1929.5 1998.4 1930.6 1997.1 C
  5.3476 +1930.9 1995.4 1930.7 1995.6 1931.6 1995.2 C
  5.3477 +1932.8 1995 1934.3 1994.5 1935.4 1994.7 C
  5.3478 +1936.1 1995.8 1936.9 1996.2 1936.6 1997.8 C
  5.3479 +1938.9 1999.4 1939.7 2001.3 1942.4 2002.4 C
  5.3480 +1942.4 2002.5 1942.2 2003 1942.6 2002.8 C
  5.3481 +1942.9 2000.4 1939.2 2001.8 1939.2 1999.7 C
  5.3482 +1936.2 1998.6 1937 1995.3 1935.9 1993.5 C
  5.3483 +1937.1 1986.5 1935.2 1977.9 1937.6 1971.2 C
  5.3484 +1937.6 1970.3 1936.6 1971 1936.4 1970.4 C
  5.3485 +1930.2 1973.4 1924 1976 1918.4 1980 C
  5.3486 +1917.2 1981 1914.9 1980.9 1914.8 1982.9 C
  5.3487 +1915.3 1989.4 1914.7 1996.4 1915.2 2002.8 C
  5.3488 +1914.9 2004 1913.9 2004.9 1914.3 2006.4 C
  5.3489 +1919 2011.9 1924.2 2015.9 1928.9 2021.3 C
  5.3490 +1924.6 2016.2 1918.7 2011.8 1914.5 2006.4 C
  5.3491 +[0.4 0.4 0 0]  vc
  5.3492 +f 
  5.3493 +S 
  5.3494 +n
  5.3495 +1914.5 1982.9 m
  5.3496 +1915.1 1980.3 1918 1980.2 1919.8 1978.8 C
  5.3497 +1925 1975.5 1930.6 1972.8 1936.1 1970.2 C
  5.3498 +1939.4 1970.6 1936.1 1974.2 1936.6 1976.4 C
  5.3499 +1936.5 1981.9 1936.8 1987.5 1936.4 1992.8 C
  5.3500 +1935.9 1992.8 1936.2 1993.5 1936.1 1994 C
  5.3501 +1937.1 1993.6 1936.2 1995.9 1936.8 1995.9 C
  5.3502 +1937 1998 1939.5 1999.7 1940.4 2000.7 C
  5.3503 +1940.1 1998.6 1935 1997.2 1937.6 1993.7 C
  5.3504 +1938.3 1985.7 1935.9 1976.8 1937.8 1970.7 C
  5.3505 +1936.9 1969.8 1935.4 1970.3 1934.4 1970.7 C
  5.3506 +1928.3 1974.4 1921.4 1976.7 1915.5 1981 C
  5.3507 +1914.6 1981.4 1915.1 1982.3 1914.3 1982.7 C
  5.3508 +1914.7 1989.3 1914.5 1996.6 1914.5 2003.1 C
  5.3509 +1913.9 2005.5 1914.5 2003.4 1915 2002.4 C
  5.3510 +1914.5 1996 1915.1 1989.3 1914.5 1982.9 C
  5.3511 +[0.07 0.06 0 0.58]  vc
  5.3512 +f 
  5.3513 +S 
  5.3514 +n
  5.3515 +1939.2 1994.9 m
  5.3516 +1939.3 1995 1939.4 1995.1 1939.5 1995.2 C
  5.3517 +1939.1 1989 1939.3 1981.6 1939 1976.7 C
  5.3518 +1938.6 1976.3 1938.6 1974.6 1938.5 1973.3 C
  5.3519 +1938.7 1976.1 1938.1 1979.4 1939 1981.7 C
  5.3520 +1937.3 1986 1937.7 1991.6 1938 1996.4 C
  5.3521 +1937.3 1994.3 1939.6 1996.2 1939.2 1994.9 C
  5.3522 +[0.18 0.18 0 0.78]  vc
  5.3523 +f 
  5.3524 +S 
  5.3525 +n
  5.3526 +1938.3 1988.4 m
  5.3527 +1938.5 1990.5 1937.9 1994.1 1938.8 1994.7 C
  5.3528 +1937.9 1992.6 1939 1990.6 1938.3 1988.4 C
  5.3529 +[0 0.87 0.91 0.83]  vc
  5.3530 +f 
  5.3531 +S 
  5.3532 +n
  5.3533 +1938.8 1985.8 m
  5.3534 +1938.5 1985.9 1938.4 1985.7 1938.3 1985.6 C
  5.3535 +1938.4 1986.2 1938 1989.5 1938.8 1987.2 C
  5.3536 +1938.8 1986.8 1938.8 1986.3 1938.8 1985.8 C
  5.3537 +f 
  5.3538 +S 
  5.3539 +n
  5.3540 +vmrs
  5.3541 +1972.8 2062.1 m
  5.3542 +1971.9 2061 1972.5 2059.4 1972.4 2058 C
  5.3543 +1972.2 2063.8 1971.9 2073.7 1972.4 2081.3 C
  5.3544 +1972.5 2074.9 1971.9 2067.9 1972.8 2062.1 C
  5.3545 +[0 1 1 0.36]  vc
  5.3546 +f 
  5.3547 +0.4 w
  5.3548 +2 J
  5.3549 +2 M
  5.3550 +S 
  5.3551 +n
  5.3552 +1940.2 2071.7 m
  5.3553 +1941.3 2072 1943.1 2072.3 1944 2071.5 C
  5.3554 +1943.6 2069.9 1945.2 2069.1 1946 2068.8 C
  5.3555 +1950 2071.1 1948.7 2065.9 1951.7 2066.2 C
  5.3556 +1953.5 2063.9 1956.9 2069.4 1955.6 2063.8 C
  5.3557 +1955.5 2064.2 1955.7 2064.8 1955.3 2065 C
  5.3558 +1954.3 2063.7 1956.2 2063.6 1955.6 2062.1 C
  5.3559 +1954.5 2060 1958.3 2050.3 1952.2 2055.6 C
  5.3560 +1949.1 2053.8 1946 2051 1943.8 2048 C
  5.3561 +1940.3 2048 1937.5 2051.3 1934.2 2052.5 C
  5.3562 +1933.1 2054.6 1934.4 2057.3 1934 2060 C
  5.3563 +1934 2065.1 1934 2069.7 1934 2074.6 C
  5.3564 +1934.4 2069 1934.1 2061.5 1934.2 2054.9 C
  5.3565 +1934.6 2054.5 1935.3 2054.7 1935.9 2054.7 C
  5.3566 +1937 2055.3 1935.9 2056.1 1935.9 2056.8 C
  5.3567 +1936.5 2063 1935.6 2070.5 1935.9 2074.6 C
  5.3568 +1936.7 2074.4 1937.3 2075.2 1938 2074.6 C
  5.3569 +1937.9 2073.6 1939.1 2072.1 1940.2 2071.7 C
  5.3570 +[0 0.2 1 0]  vc
  5.3571 +f 
  5.3572 +S 
  5.3573 +n
  5.3574 +1933.2 2074.1 m
  5.3575 +1933.2 2071.5 1933.2 2069 1933.2 2066.4 C
  5.3576 +1933.2 2069 1933.2 2071.5 1933.2 2074.1 C
  5.3577 +[0 1 1 0.36]  vc
  5.3578 +f 
  5.3579 +S 
  5.3580 +n
  5.3581 +2007.4 2048.9 m
  5.3582 +2006.5 2047.8 2007.1 2046.2 2006.9 2044.8 C
  5.3583 +2006.7 2050.6 2006.5 2060.5 2006.9 2068.1 C
  5.3584 +2007.1 2061.7 2006.5 2054.7 2007.4 2048.9 C
  5.3585 +f 
  5.3586 +S 
  5.3587 +n
  5.3588 +1927.2 2062.4 m
  5.3589 +1925.8 2060.1 1928.1 2058.2 1927 2056.4 C
  5.3590 +1927.3 2055.5 1926.5 2053.5 1926.8 2051.8 C
  5.3591 +1926.8 2052.8 1926 2052.5 1925.3 2052.5 C
  5.3592 +1924.1 2052.8 1925 2050.5 1924.4 2050.1 C
  5.3593 +1925.3 2050.2 1925.4 2048.8 1926.3 2049.4 C
  5.3594 +1926.5 2052.3 1928.4 2047.2 1928.4 2051.1 C
  5.3595 +1928.9 2050.5 1929 2051.4 1928.9 2051.8 C
  5.3596 +1928.9 2052 1928.9 2052.3 1928.9 2052.5 C
  5.3597 +1929.4 2051.4 1928.9 2049 1930.1 2048.2 C
  5.3598 +1928.9 2047.1 1930.5 2047.1 1930.4 2046.5 C
  5.3599 +1931.9 2046.2 1933.1 2046.1 1934.7 2046.5 C
  5.3600 +1934.6 2046.9 1935.2 2047.9 1934.4 2048.4 C
  5.3601 +1936.9 2048.1 1933.6 2043.8 1935.9 2043.9 C
  5.3602 +1935.7 2043.9 1934.8 2041.3 1933.2 2041.7 C
  5.3603 +1932.5 2041.6 1932.4 2039.6 1932.3 2041 C
  5.3604 +1930.8 2042.6 1929 2040.6 1927.7 2042 C
  5.3605 +1927.5 2041.4 1927.1 2040.9 1927.2 2040.3 C
  5.3606 +1927.8 2040.6 1927.4 2039.1 1928.2 2038.6 C
  5.3607 +1929.4 2038 1930.5 2038.8 1931.3 2037.9 C
  5.3608 +1931.7 2039 1932.5 2038.6 1931.8 2037.6 C
  5.3609 +1930.9 2037 1928.7 2037.8 1928.2 2037.9 C
  5.3610 +1926.7 2037.8 1928 2039 1927 2038.8 C
  5.3611 +1927.4 2040.4 1925.6 2040.8 1925.1 2041 C
  5.3612 +1924.3 2040.4 1923.2 2040.5 1922.2 2040.5 C
  5.3613 +1921.4 2041.7 1921 2043.9 1919.3 2043.9 C
  5.3614 +1918.8 2043.4 1917.2 2043.3 1916.4 2043.4 C
  5.3615 +1915.9 2044.4 1915.7 2046 1914.3 2046.5 C
  5.3616 +1913.1 2046.6 1912 2044.5 1911.4 2046.3 C
  5.3617 +1912.8 2046.5 1913.8 2047.4 1915.7 2047 C
  5.3618 +1916.9 2047.7 1915.6 2048.8 1916 2049.4 C
  5.3619 +1915.4 2049.3 1913.9 2050.3 1913.3 2051.1 C
  5.3620 +1913.9 2054.1 1916 2050.2 1916.7 2053 C
  5.3621 +1916.9 2053.8 1915.5 2054.1 1916.7 2054.4 C
  5.3622 +1917 2054.7 1920.2 2054.3 1919.3 2056.6 C
  5.3623 +1918.8 2056.1 1920.2 2058.6 1920.3 2057.6 C
  5.3624 +1921.2 2057.9 1922.1 2057.5 1922.4 2059 C
  5.3625 +1922.3 2059.1 1922.2 2059.3 1922 2059.2 C
  5.3626 +1922.1 2059.7 1922.4 2060.3 1922.9 2060.7 C
  5.3627 +1923.2 2060.1 1923.8 2060.4 1924.6 2060.7 C
  5.3628 +1925.9 2062.6 1923.2 2062 1925.6 2063.6 C
  5.3629 +1926.1 2063.1 1927.3 2062.5 1927.2 2062.4 C
  5.3630 +[0.21 0.21 0 0]  vc
  5.3631 +f 
  5.3632 +S 
  5.3633 +n
  5.3634 +1933.2 2063.3 m
  5.3635 +1933.2 2060.7 1933.2 2058.2 1933.2 2055.6 C
  5.3636 +1933.2 2058.2 1933.2 2060.7 1933.2 2063.3 C
  5.3637 +[0 1 1 0.36]  vc
  5.3638 +f 
  5.3639 +S 
  5.3640 +n
  5.3641 +1965.2 2049.2 m
  5.3642 +1967.1 2050.1 1969.9 2053.7 1972.1 2056.4 C
  5.3643 +1970.5 2054 1967.6 2051.3 1965.2 2049.2 C
  5.3644 +f 
  5.3645 +S 
  5.3646 +n
  5.3647 +1991.8 2034.8 m
  5.3648 +1991.7 2041.5 1992 2048.5 1991.6 2055.2 C
  5.3649 +1990.5 2056.4 1991.9 2054.9 1991.8 2054.4 C
  5.3650 +1991.8 2047.9 1991.8 2041.3 1991.8 2034.8 C
  5.3651 +f 
  5.3652 +S 
  5.3653 +n
  5.3654 +1988.9 2053.2 m
  5.3655 +1988.9 2044.3 1988.9 2036.6 1988.9 2028.3 C
  5.3656 +1985.7 2028.2 1987.2 2023.5 1983.9 2024.2 C
  5.3657 +1983.9 2022.4 1982 2021.6 1981 2021.3 C
  5.3658 +1980.6 2021.1 1980.6 2021.7 1980.3 2021.6 C
  5.3659 +1980.3 2027 1980.3 2034.8 1980.3 2041.5 C
  5.3660 +1979.3 2043.2 1977.6 2043 1976.2 2043.6 C
  5.3661 +1977.1 2043.8 1978.5 2043.2 1978.8 2044.1 C
  5.3662 +1978.5 2045.3 1979.9 2045.3 1980.3 2045.8 C
  5.3663 +1980.5 2046.8 1980.7 2046.2 1981.5 2046.5 C
  5.3664 +1982.4 2047.1 1982 2048.6 1982.7 2049.4 C
  5.3665 +1984.2 2049.6 1984.6 2052.2 1986.8 2051.6 C
  5.3666 +1987.1 2048.6 1985.1 2042.7 1986.5 2040.5 C
  5.3667 +1986.3 2036.7 1986.9 2031.7 1986 2029.2 C
  5.3668 +1986.3 2027.1 1986.9 2028.6 1987.7 2027.6 C
  5.3669 +1987.7 2028.3 1988.7 2028 1988.7 2028.8 C
  5.3670 +1988.1 2033 1988.7 2037.5 1988.2 2041.7 C
  5.3671 +1987.8 2041.4 1988 2040.8 1988 2040.3 C
  5.3672 +1988 2041 1988 2042.4 1988 2042.4 C
  5.3673 +1988 2042.4 1988.1 2042.3 1988.2 2042.2 C
  5.3674 +1989.3 2046 1988 2050.2 1988.4 2054 C
  5.3675 +1987.8 2054.4 1987.1 2054.7 1986.5 2055.4 C
  5.3676 +1987.4 2054.4 1988.4 2054.6 1988.9 2053.2 C
  5.3677 +[0 1 1 0.23]  vc
  5.3678 +f 
  5.3679 +S 
  5.3680 +n
  5.3681 +1950.8 2054.4 m
  5.3682 +1949.7 2053.4 1948.7 2052.3 1947.6 2051.3 C
  5.3683 +1948.7 2052.3 1949.7 2053.4 1950.8 2054.4 C
  5.3684 +[0 1 1 0.36]  vc
  5.3685 +f 
  5.3686 +S 
  5.3687 +n
  5.3688 +vmrs
  5.3689 +2006.7 2043.2 m
  5.3690 +2004.5 2040.8 2002.4 2038.4 2000.2 2036 C
  5.3691 +2002.4 2038.4 2004.5 2040.8 2006.7 2043.2 C
  5.3692 +[0 1 1 0.36]  vc
  5.3693 +f 
  5.3694 +0.4 w
  5.3695 +2 J
  5.3696 +2 M
  5.3697 +S 
  5.3698 +n
  5.3699 +1976.7 2019.6 m
  5.3700 +1975.8 2018.6 1976.4 2016.9 1976.2 2015.6 C
  5.3701 +1976 2021.3 1975.8 2031.2 1976.2 2038.8 C
  5.3702 +1976.4 2032.4 1975.8 2025.5 1976.7 2019.6 C
  5.3703 +f 
  5.3704 +S 
  5.3705 +n
  5.3706 +1988.4 2053.5 m
  5.3707 +1988.6 2049.2 1988.1 2042.8 1988 2040 C
  5.3708 +1988.4 2040.4 1988.1 2041 1988.2 2041.5 C
  5.3709 +1988.3 2037.2 1988 2032.7 1988.4 2028.5 C
  5.3710 +1987.6 2027.1 1987.2 2028.6 1986.8 2028 C
  5.3711 +1985.9 2028.5 1986.5 2029.7 1986.3 2030.4 C
  5.3712 +1986.9 2029.8 1986.6 2031 1987 2031.2 C
  5.3713 +1987.4 2039.6 1985 2043 1987.2 2050.4 C
  5.3714 +1987.2 2051.6 1985.9 2052.3 1984.6 2051.3 C
  5.3715 +1981.9 2049.7 1982.9 2047 1980.3 2046.5 C
  5.3716 +1980.3 2045.2 1978.1 2046.2 1978.6 2043.9 C
  5.3717 +1975.6 2043.3 1979.3 2045.6 1979.6 2046.5 C
  5.3718 +1980.8 2046.6 1981.5 2048.5 1982.2 2049.9 C
  5.3719 +1983.7 2050.8 1984.8 2052.8 1986.5 2053 C
  5.3720 +1986.7 2053.5 1987.5 2054.1 1987 2054.7 C
  5.3721 +1987.4 2053.9 1988.3 2054.3 1988.4 2053.5 C
  5.3722 +[0 1 1 0.23]  vc
  5.3723 +f 
  5.3724 +S 
  5.3725 +n
  5.3726 +1988 2038.1 m
  5.3727 +1988 2036.7 1988 2035.4 1988 2034 C
  5.3728 +1988 2035.4 1988 2036.7 1988 2038.1 C
  5.3729 +[0 1 1 0.36]  vc
  5.3730 +f 
  5.3731 +S 
  5.3732 +n
  5.3733 +1999.7 2035.7 m
  5.3734 +1997.6 2033.5 1995.4 2031.2 1993.2 2029 C
  5.3735 +1995.4 2031.2 1997.6 2033.5 1999.7 2035.7 C
  5.3736 +f 
  5.3737 +S 
  5.3738 +n
  5.3739 +1944 2029.2 m
  5.3740 +1945.2 2029.5 1946.9 2029.8 1947.9 2029 C
  5.3741 +1947.4 2027.4 1949 2026.7 1949.8 2026.4 C
  5.3742 +1953.9 2028.6 1952.6 2023.4 1955.6 2023.7 C
  5.3743 +1957.4 2021.4 1960.7 2027 1959.4 2021.3 C
  5.3744 +1959.3 2021.7 1959.6 2022.3 1959.2 2022.5 C
  5.3745 +1958.1 2021.2 1960.1 2021.1 1959.4 2019.6 C
  5.3746 +1959.1 2012.7 1959.9 2005.1 1959.6 1999.2 C
  5.3747 +1955.3 2000.1 1951.3 2003.1 1947.2 2005 C
  5.3748 +1943.9 2006 1941.2 2008.7 1938 2010 C
  5.3749 +1936.9 2012.1 1938.2 2014.8 1937.8 2017.5 C
  5.3750 +1937.8 2022.6 1937.8 2027.3 1937.8 2032.1 C
  5.3751 +1938.2 2026.5 1938 2019 1938 2012.4 C
  5.3752 +1938.5 2012 1939.2 2012.3 1939.7 2012.2 C
  5.3753 +1940.8 2012.8 1939.7 2013.6 1939.7 2014.4 C
  5.3754 +1940.4 2020.5 1939.4 2028 1939.7 2032.1 C
  5.3755 +1940.6 2031.9 1941.2 2032.7 1941.9 2032.1 C
  5.3756 +1941.7 2031.2 1943 2029.7 1944 2029.2 C
  5.3757 +[0 0.2 1 0]  vc
  5.3758 +f 
  5.3759 +S 
  5.3760 +n
  5.3761 +1937.1 2031.6 m
  5.3762 +1937.1 2029.1 1937.1 2026.5 1937.1 2024 C
  5.3763 +1937.1 2026.5 1937.1 2029.1 1937.1 2031.6 C
  5.3764 +[0 1 1 0.36]  vc
  5.3765 +f 
  5.3766 +S 
  5.3767 +n
  5.3768 +1991.8 2028 m
  5.3769 +1992.5 2027.8 1993.2 2029.9 1994 2030.2 C
  5.3770 +1992.9 2029.6 1993.1 2028.1 1991.8 2028 C
  5.3771 +[0 1 1 0.23]  vc
  5.3772 +f 
  5.3773 +S 
  5.3774 +n
  5.3775 +1991.8 2027.8 m
  5.3776 +1992.4 2027.6 1992.6 2028.3 1993 2028.5 C
  5.3777 +1992.6 2028.2 1992.2 2027.6 1991.6 2027.8 C
  5.3778 +1991.6 2028.5 1991.6 2029.1 1991.6 2029.7 C
  5.3779 +1991.6 2029.1 1991.4 2028.3 1991.8 2027.8 C
  5.3780 +[0 1 1 0.36]  vc
  5.3781 +f 
  5.3782 +S 
  5.3783 +n
  5.3784 +1985.8 2025.4 m
  5.3785 +1985.3 2025.2 1984.8 2024.7 1984.1 2024.9 C
  5.3786 +1983.3 2025.3 1983.6 2027.3 1983.9 2027.6 C
  5.3787 +1985 2028 1986.9 2026.9 1985.8 2025.4 C
  5.3788 +[0 1 1 0.23]  vc
  5.3789 +f 
  5.3790 +S 
  5.3791 +n
  5.3792 +vmrs
  5.3793 +1993.5 2024.4 m
  5.3794 +1992.4 2023.7 1991.3 2022.9 1990.1 2023.2 C
  5.3795 +1990.7 2023.7 1989.8 2023.8 1989.4 2023.7 C
  5.3796 +1989.1 2023.7 1988.6 2023.9 1988.4 2023.5 C
  5.3797 +1988.5 2023.2 1988.3 2022.7 1988.7 2022.5 C
  5.3798 +1989 2022.6 1988.9 2023 1988.9 2023.2 C
  5.3799 +1989.1 2022.8 1990.4 2022.3 1990.6 2021.3 C
  5.3800 +1990.4 2021.8 1990 2021.3 1990.1 2021.1 C
  5.3801 +1990.1 2020.9 1990.1 2020.1 1990.1 2020.6 C
  5.3802 +1989.9 2021.1 1989.5 2020.6 1989.6 2020.4 C
  5.3803 +1989.6 2019.8 1988.7 2019.6 1988.2 2019.2 C
  5.3804 +1987.5 2018.7 1987.7 2020.2 1987 2019.4 C
  5.3805 +1987.5 2020.4 1986 2021.1 1987.5 2021.8 C
  5.3806 +1986.8 2023.1 1986.6 2021.1 1986 2021.1 C
  5.3807 +1986.1 2020.1 1985.9 2019 1986.3 2018.2 C
  5.3808 +1986.7 2018.4 1986.5 2019 1986.5 2019.4 C
  5.3809 +1986.5 2018.7 1986.4 2017.8 1987.2 2017.7 C
  5.3810 +1986.5 2017.2 1985.5 2019.3 1985.3 2020.4 C
  5.3811 +1986.2 2022 1987.3 2023.5 1989.2 2024.2 C
  5.3812 +1990.8 2024.3 1991.6 2022.9 1993.2 2024.4 C
  5.3813 +1993.8 2025.4 1995 2026.6 1995.9 2027.1 C
  5.3814 +1995 2026.5 1994.1 2025.5 1993.5 2024.4 C
  5.3815 +[0 1 1 0.36]  vc
  5.3816 +f 
  5.3817 +0.4 w
  5.3818 +2 J
  5.3819 +2 M
  5.3820 +[0 0.5 0.5 0.2]  vc
  5.3821 +S 
  5.3822 +n
  5.3823 +2023 2040.3 m
  5.3824 +2023.2 2036 2022.7 2029.6 2022.5 2026.8 C
  5.3825 +2022.9 2027.2 2022.7 2027.8 2022.8 2028.3 C
  5.3826 +2022.8 2024 2022.6 2019.5 2023 2015.3 C
  5.3827 +2022.2 2013.9 2021.7 2015.4 2021.3 2014.8 C
  5.3828 +2020.4 2015.3 2021 2016.5 2020.8 2017.2 C
  5.3829 +2021.4 2016.6 2021.1 2017.8 2021.6 2018 C
  5.3830 +2022 2026.4 2019.6 2029.8 2021.8 2037.2 C
  5.3831 +2021.7 2038.4 2020.5 2039.1 2019.2 2038.1 C
  5.3832 +2016.5 2036.5 2017.5 2033.8 2014.8 2033.3 C
  5.3833 +2014.9 2032 2012.6 2033 2013.2 2030.7 C
  5.3834 +2011.9 2030.8 2011.2 2030.1 2010.8 2029.2 C
  5.3835 +2010.8 2029.1 2010.8 2028.2 2010.8 2028.8 C
  5.3836 +2010 2028.8 2010.4 2026.5 2008.6 2027.3 C
  5.3837 +2007.9 2026.6 2007.3 2025.9 2007.9 2027.1 C
  5.3838 +2009.7 2028 2010 2030.1 2012.2 2030.9 C
  5.3839 +2012.9 2032.1 2013.7 2033.6 2015.1 2033.6 C
  5.3840 +2015.7 2035.1 2016.9 2036.7 2018.4 2038.4 C
  5.3841 +2019.8 2039.3 2022 2039.4 2021.6 2041.5 C
  5.3842 +2021.9 2040.7 2022.9 2041.1 2023 2040.3 C
  5.3843 +[0 1 1 0.23]  vc
  5.3844 +f 
  5.3845 +S 
  5.3846 +n
  5.3847 +2022.5 2024.9 m
  5.3848 +2022.5 2023.5 2022.5 2022.2 2022.5 2020.8 C
  5.3849 +2022.5 2022.2 2022.5 2023.5 2022.5 2024.9 C
  5.3850 +[0 1 1 0.36]  vc
  5.3851 +f 
  5.3852 +S 
  5.3853 +n
  5.3854 +1983.2 2022.8 m
  5.3855 +1982.4 2022.5 1982.1 2021.6 1981.2 2022.3 C
  5.3856 +1981.1 2022.9 1980.5 2024 1981 2024.2 C
  5.3857 +1981.8 2024.6 1982.9 2024.4 1983.2 2022.8 C
  5.3858 +[0 1 1 0.23]  vc
  5.3859 +f 
  5.3860 +S 
  5.3861 +n
  5.3862 +1931.1 2019.9 m
  5.3863 +1929.6 2017.7 1932 2015.7 1930.8 2013.9 C
  5.3864 +1931.1 2013 1930.3 2011 1930.6 2009.3 C
  5.3865 +1930.6 2010.3 1929.8 2010 1929.2 2010 C
  5.3866 +1928 2010.3 1928.8 2008.1 1928.2 2007.6 C
  5.3867 +1929.1 2007.8 1929.3 2006.3 1930.1 2006.9 C
  5.3868 +1930.3 2009.8 1932.2 2004.8 1932.3 2008.6 C
  5.3869 +1932.7 2008 1932.8 2009 1932.8 2009.3 C
  5.3870 +1932.8 2009.6 1932.8 2009.8 1932.8 2010 C
  5.3871 +1933.2 2009 1932.7 2006.6 1934 2005.7 C
  5.3872 +1932.7 2004.6 1934.3 2004.6 1934.2 2004 C
  5.3873 +1935.8 2003.7 1937 2003.6 1938.5 2004 C
  5.3874 +1938.5 2004.5 1939.1 2005.4 1938.3 2006 C
  5.3875 +1940.7 2005.7 1937.4 2001.3 1939.7 2001.4 C
  5.3876 +1939.5 2001.4 1938.6 1998.8 1937.1 1999.2 C
  5.3877 +1936.3 1999.1 1936.2 1997.1 1936.1 1998.5 C
  5.3878 +1934.7 2000.1 1932.9 1998.2 1931.6 1999.5 C
  5.3879 +1931.3 1998.9 1930.9 1998.5 1931.1 1997.8 C
  5.3880 +1931.6 1998.2 1931.3 1996.6 1932 1996.1 C
  5.3881 +1933.2 1995.5 1934.3 1996.4 1935.2 1995.4 C
  5.3882 +1935.5 1996.5 1936.3 1996.1 1935.6 1995.2 C
  5.3883 +1934.7 1994.5 1932.5 1995.3 1932 1995.4 C
  5.3884 +1930.5 1995.3 1931.9 1996.5 1930.8 1996.4 C
  5.3885 +1931.2 1997.9 1929.5 1998.3 1928.9 1998.5 C
  5.3886 +1928.1 1997.9 1927.1 1998 1926 1998 C
  5.3887 +1925.3 1999.2 1924.8 2001.4 1923.2 2001.4 C
  5.3888 +1922.6 2000.9 1921 2000.9 1920.3 2000.9 C
  5.3889 +1919.7 2001.9 1919.6 2003.5 1918.1 2004 C
  5.3890 +1916.9 2004.1 1915.8 2002 1915.2 2003.8 C
  5.3891 +1916.7 2004 1917.6 2004.9 1919.6 2004.5 C
  5.3892 +1920.7 2005.2 1919.4 2006.3 1919.8 2006.9 C
  5.3893 +1919.2 2006.9 1917.7 2007.8 1917.2 2008.6 C
  5.3894 +1917.8 2011.6 1919.8 2007.8 1920.5 2010.5 C
  5.3895 +1920.8 2011.3 1919.3 2011.6 1920.5 2012 C
  5.3896 +1920.8 2012.3 1924 2011.8 1923.2 2014.1 C
  5.3897 +1922.6 2013.6 1924.1 2016.1 1924.1 2015.1 C
  5.3898 +1925.1 2015.4 1925.9 2015 1926.3 2016.5 C
  5.3899 +1926.2 2016.6 1926 2016.8 1925.8 2016.8 C
  5.3900 +1925.9 2017.2 1926.2 2017.8 1926.8 2018.2 C
  5.3901 +1927.1 2017.6 1927.7 2018 1928.4 2018.2 C
  5.3902 +1929.7 2020.1 1927.1 2019.5 1929.4 2021.1 C
  5.3903 +1929.9 2020.7 1931.1 2020 1931.1 2019.9 C
  5.3904 +[0.21 0.21 0 0]  vc
  5.3905 +f 
  5.3906 +S 
  5.3907 +n
  5.3908 +1937.1 2020.8 m
  5.3909 +1937.1 2018.3 1937.1 2015.7 1937.1 2013.2 C
  5.3910 +1937.1 2015.7 1937.1 2018.3 1937.1 2020.8 C
  5.3911 +[0 1 1 0.36]  vc
  5.3912 +f 
  5.3913 +S 
  5.3914 +n
  5.3915 +2020.4 2012.2 m
  5.3916 +2019.8 2012 2019.3 2011.5 2018.7 2011.7 C
  5.3917 +2017.9 2012.1 2018.1 2014.1 2018.4 2014.4 C
  5.3918 +2019.6 2014.8 2021.4 2013.7 2020.4 2012.2 C
  5.3919 +[0 1 1 0.23]  vc
  5.3920 +f 
  5.3921 +S 
  5.3922 +n
  5.3923 +1976 2013.9 m
  5.3924 +1973.8 2011.5 1971.6 2009.1 1969.5 2006.7 C
  5.3925 +1971.6 2009.1 1973.8 2011.5 1976 2013.9 C
  5.3926 +[0 1 1 0.36]  vc
  5.3927 +f 
  5.3928 +S 
  5.3929 +n
  5.3930 +1995.4 2012.7 m
  5.3931 +1996.1 2010.3 1993.8 2006.2 1997.3 2005.7 C
  5.3932 +1998.9 2005.4 2000 2003.7 2001.4 2003.1 C
  5.3933 +2003.9 2003.1 2005.3 2001.3 2006.9 1999.7 C
  5.3934 +2004.5 2003.5 2000 2002.2 1997.6 2005.7 C
  5.3935 +1996.5 2005.9 1994.8 2006.1 1995.2 2007.6 C
  5.3936 +1995.7 2009.4 1995.2 2011.6 1994.7 2012.9 C
  5.3937 +1992 2015.8 1987.8 2015.7 1985.3 2018.7 C
  5.3938 +1988.3 2016.3 1992.3 2015.3 1995.4 2012.7 C
  5.3939 +[0.18 0.18 0 0.78]  vc
  5.3940 +f 
  5.3941 +S 
  5.3942 +n
  5.3943 +1995.6 2012.4 m
  5.3944 +1995.6 2011.2 1995.6 2010 1995.6 2008.8 C
  5.3945 +1995.6 2010 1995.6 2011.2 1995.6 2012.4 C
  5.3946 +[0 1 1 0.36]  vc
  5.3947 +f 
  5.3948 +S 
  5.3949 +n
  5.3950 +vmrs
  5.3951 +2017.7 2009.6 m
  5.3952 +2016.9 2009.3 2016.7 2008.4 2015.8 2009.1 C
  5.3953 +2014.2 2010.6 2016 2010.6 2016.5 2011.5 C
  5.3954 +2017.2 2010.9 2018.1 2010.8 2017.7 2009.6 C
  5.3955 +[0 1 1 0.23]  vc
  5.3956 +f 
  5.3957 +0.4 w
  5.3958 +2 J
  5.3959 +2 M
  5.3960 +S 
  5.3961 +n
  5.3962 +2014.4 2006.4 m
  5.3963 +2013.5 2006.8 2012.1 2005.6 2012 2006.7 C
  5.3964 +2013 2007.3 2011.9 2009.2 2012.9 2008.4 C
  5.3965 +2014.2 2008.3 2014.6 2007.8 2014.4 2006.4 C
  5.3966 +f 
  5.3967 +S 
  5.3968 +n
  5.3969 +1969 2006.4 m
  5.3970 +1966.5 2003.8 1964 2001.2 1961.6 1998.5 C
  5.3971 +1964 2001.2 1966.5 2003.8 1969 2006.4 C
  5.3972 +[0 1 1 0.36]  vc
  5.3973 +f 
  5.3974 +S 
  5.3975 +n
  5.3976 +2012 2005.2 m
  5.3977 +2012.2 2004.2 2011.4 2003.3 2010.3 2003.3 C
  5.3978 +2009 2003.6 2010 2004.7 2009.6 2004.8 C
  5.3979 +2009.3 2005.7 2011.4 2006.7 2012 2005.2 C
  5.3980 +[0 1 1 0.23]  vc
  5.3981 +f 
  5.3982 +S 
  5.3983 +n
  5.3984 +1962.8 1995.2 m
  5.3985 +1961.7 1994.4 1960.6 1993.7 1959.4 1994 C
  5.3986 +1959.5 1994.9 1957.5 1994.1 1956.8 1994.7 C
  5.3987 +1955.9 1995.5 1956.7 1997 1955.1 1997.3 C
  5.3988 +1956.9 1996.7 1956.8 1994 1959.2 1994.7 C
  5.3989 +1961.1 1991 1968.9 2003.2 1962.8 1995.2 C
  5.3990 +[0 1 1 0.36]  vc
  5.3991 +f 
  5.3992 +S 
  5.3993 +n
  5.3994 +1954.6 1995.6 m
  5.3995 +1955.9 1994.7 1955.1 1989.8 1955.3 1988 C
  5.3996 +1954.5 1988.3 1954.9 1986.6 1954.4 1986 C
  5.3997 +1955.7 1989.2 1953.9 1991.1 1954.8 1994.2 C
  5.3998 +1954.5 1995.9 1953.5 1995.3 1953.9 1997.3 C
  5.3999 +1955.3 1998.3 1953.2 1995.5 1954.6 1995.6 C
  5.4000 +f 
  5.4001 +S 
  5.4002 +n
  5.4003 +1992.3 2011 m
  5.4004 +1992.5 2006.7 1992 2000.3 1991.8 1997.6 C
  5.4005 +1992.2 1997.9 1992 1998.5 1992 1999 C
  5.4006 +1992.1 1994.7 1991.9 1990.2 1992.3 1986 C
  5.4007 +1991.4 1984.6 1991 1986.1 1990.6 1985.6 C
  5.4008 +1989.7 1986 1990.3 1987.2 1990.1 1988 C
  5.4009 +1990.7 1987.4 1990.4 1988.5 1990.8 1988.7 C
  5.4010 +1991.3 1997.1 1988.9 2000.6 1991.1 2007.9 C
  5.4011 +1991 2009.1 1989.8 2009.9 1988.4 2008.8 C
  5.4012 +1985.7 2007.2 1986.8 2004.5 1984.1 2004 C
  5.4013 +1984.2 2002.7 1981.9 2003.7 1982.4 2001.4 C
  5.4014 +1981.2 2001.5 1980.5 2000.8 1980 2000 C
  5.4015 +1980 1999.8 1980 1998.9 1980 1999.5 C
  5.4016 +1979.3 1999.5 1979.7 1997.2 1977.9 1998 C
  5.4017 +1977.2 1997.3 1976.6 1996.7 1977.2 1997.8 C
  5.4018 +1979 1998.7 1979.3 2000.8 1981.5 2001.6 C
  5.4019 +1982.2 2002.8 1983 2004.3 1984.4 2004.3 C
  5.4020 +1985 2005.8 1986.2 2007.5 1987.7 2009.1 C
  5.4021 +1989 2010 1991.3 2010.2 1990.8 2012.2 C
  5.4022 +1991.2 2011.4 1992.2 2011.8 1992.3 2011 C
  5.4023 +[0 1 1 0.23]  vc
  5.4024 +f 
  5.4025 +S 
  5.4026 +n
  5.4027 +1991.8 1995.6 m
  5.4028 +1991.8 1994.3 1991.8 1992.9 1991.8 1991.6 C
  5.4029 +1991.8 1992.9 1991.8 1994.3 1991.8 1995.6 C
  5.4030 +[0 1 1 0.36]  vc
  5.4031 +f 
  5.4032 +S 
  5.4033 +n
  5.4034 +1959.2 1994.2 m
  5.4035 +1958.8 1993.3 1960.7 1993.9 1961.1 1993.7 C
  5.4036 +1961.5 1993.9 1961.2 1994.4 1961.8 1994.2 C
  5.4037 +1960.9 1994 1960.8 1992.9 1959.9 1992.5 C
  5.4038 +1959.6 1993.5 1958.3 1993.5 1958.2 1994.2 C
  5.4039 +1958.1 1994.1 1958 1994 1958 1994 C
  5.4040 +1957.2 1994.9 1958 1993.4 1956.8 1993 C
  5.4041 +1955.6 1992.5 1956 1991 1956.3 1989.9 C
  5.4042 +1956.5 1989.8 1956.6 1990 1956.8 1990.1 C
  5.4043 +1957.1 1989 1956 1989.1 1955.8 1988.2 C
  5.4044 +1955.1 1990.4 1956.2 1995 1954.8 1995.9 C
  5.4045 +1954.1 1995.5 1954.5 1996.5 1954.4 1997.1 C
  5.4046 +1955 1996.8 1954.8 1997.4 1955.6 1996.8 C
  5.4047 +1956 1996 1956.3 1993.2 1958.7 1994.2 C
  5.4048 +1958.9 1994.2 1959.7 1994.2 1959.2 1994.2 C
  5.4049 +[0 1 1 0.23]  vc
  5.4050 +f 
  5.4051 +S 
  5.4052 +n
  5.4053 +1958.2 1994 m
  5.4054 +1958.4 1993.5 1959.7 1993.1 1959.9 1992 C
  5.4055 +1959.7 1992.5 1959.3 1992 1959.4 1991.8 C
  5.4056 +1959.4 1991.6 1959.4 1990.8 1959.4 1991.3 C
  5.4057 +1959.2 1991.8 1958.8 1991.3 1958.9 1991.1 C
  5.4058 +1958.9 1990.5 1958 1990.3 1957.5 1989.9 C
  5.4059 +1956.8 1989.5 1956.9 1991 1956.3 1990.1 C
  5.4060 +1956.7 1991 1955.4 1992.1 1956.5 1992.3 C
  5.4061 +1956.8 1993.5 1958.3 1992.9 1957.2 1994 C
  5.4062 +1957.8 1994.3 1958.1 1992.4 1958.2 1994 C
  5.4063 +[0 0.5 0.5 0.2]  vc
  5.4064 +f 
  5.4065 +S 
  5.4066 +n
  5.4067 +vmrs
  5.4068 +1954.4 1982.7 m
  5.4069 +1956.1 1982.7 1954.1 1982.5 1953.9 1982.9 C
  5.4070 +1953.9 1983.7 1953.7 1984.7 1954.1 1985.3 C
  5.4071 +1954.4 1984.2 1953.6 1983.6 1954.4 1982.7 C
  5.4072 +[0 1 1 0.36]  vc
  5.4073 +f 
  5.4074 +0.4 w
  5.4075 +2 J
  5.4076 +2 M
  5.4077 +S 
  5.4078 +n
  5.4079 +1989.6 1982.9 m
  5.4080 +1989.1 1982.7 1988.6 1982.3 1988 1982.4 C
  5.4081 +1987.2 1982.8 1987.4 1984.8 1987.7 1985.1 C
  5.4082 +1988.9 1985.6 1990.7 1984.4 1989.6 1982.9 C
  5.4083 +[0 1 1 0.23]  vc
  5.4084 +f 
  5.4085 +S 
  5.4086 +n
  5.4087 +1987 1980.3 m
  5.4088 +1986.2 1980 1986 1979.1 1985.1 1979.8 C
  5.4089 +1983.5 1981.4 1985.3 1981.4 1985.8 1982.2 C
  5.4090 +1986.5 1981.7 1987.4 1981.5 1987 1980.3 C
  5.4091 +f 
  5.4092 +S 
  5.4093 +n
  5.4094 +1983.6 1977.2 m
  5.4095 +1982.7 1977.5 1981.4 1976.3 1981.2 1977.4 C
  5.4096 +1982.3 1978 1981.2 1979.9 1982.2 1979.1 C
  5.4097 +1983.5 1979 1983.9 1978.5 1983.6 1977.2 C
  5.4098 +f 
  5.4099 +S 
  5.4100 +n
  5.4101 +1981.2 1976 m
  5.4102 +1981.5 1974.9 1980.6 1974 1979.6 1974 C
  5.4103 +1978.3 1974.3 1979.3 1975.4 1978.8 1975.5 C
  5.4104 +1978.6 1976.4 1980.7 1977.4 1981.2 1976 C
  5.4105 +f 
  5.4106 +S 
  5.4107 +n
  5.4108 +1972.1 2082.3 m
  5.4109 +1971.8 2081.8 1971.3 2080.9 1971.2 2080.1 C
  5.4110 +1971.1 2072.9 1971.3 2064.6 1970.9 2058.3 C
  5.4111 +1970.3 2058.5 1970.1 2057.7 1969.7 2058.5 C
  5.4112 +1970.6 2058.5 1969.7 2059 1970.2 2059.2 C
  5.4113 +1970.2 2065.4 1970.2 2072.4 1970.2 2077.7 C
  5.4114 +1971.1 2078.9 1970.6 2078.9 1970.4 2079.9 C
  5.4115 +1969.2 2080.2 1968.2 2080.4 1967.3 2079.6 C
  5.4116 +1966.8 2077.8 1963.4 2076.3 1963.5 2075.1 C
  5.4117 +1961.5 2075.5 1962 2071.5 1959.6 2072 C
  5.4118 +1959.2 2070 1956.5 2069.3 1955.8 2067.6 C
  5.4119 +1956 2068.4 1955.3 2069.7 1956.5 2069.8 C
  5.4120 +1958.6 2068.9 1958.1 2073.5 1960.1 2072.4 C
  5.4121 +1960.7 2075.9 1964.7 2074.6 1964.2 2078 C
  5.4122 +1967.2 2078.6 1967.9 2081.6 1970.7 2080.6 C
  5.4123 +1970.3 2081.1 1971.5 2081.2 1971.9 2082.3 C
  5.4124 +1967.2 2084.3 1962.9 2087.1 1958.2 2089 C
  5.4125 +1962.9 2087 1967.4 2084.4 1972.1 2082.3 C
  5.4126 +[0 0.2 1 0]  vc
  5.4127 +f 
  5.4128 +S 
  5.4129 +n
  5.4130 +1971.9 2080.1 m
  5.4131 +1971.9 2075.1 1971.9 2070 1971.9 2065 C
  5.4132 +1971.9 2070 1971.9 2075.1 1971.9 2080.1 C
  5.4133 +[0 1 1 0.23]  vc
  5.4134 +f 
  5.4135 +S 
  5.4136 +n
  5.4137 +2010.8 2050.6 m
  5.4138 +2013.2 2049 2010.5 2050.1 2010.5 2051.3 C
  5.4139 +2010.5 2057.7 2010.5 2064.1 2010.5 2070.5 C
  5.4140 +2008.7 2072.4 2006 2073.3 2003.6 2074.4 C
  5.4141 +2016.4 2073.7 2008 2058.4 2010.8 2050.6 C
  5.4142 +[0.4 0.4 0 0]  vc
  5.4143 +f 
  5.4144 +S 
  5.4145 +n
  5.4146 +2006.4 2066.9 m
  5.4147 +2006.4 2061.9 2006.4 2056.8 2006.4 2051.8 C
  5.4148 +2006.4 2056.8 2006.4 2061.9 2006.4 2066.9 C
  5.4149 +[0 1 1 0.23]  vc
  5.4150 +f 
  5.4151 +S 
  5.4152 +n
  5.4153 +1971.9 2060.7 m
  5.4154 +1972.2 2060.3 1971.4 2068.2 1972.4 2061.9 C
  5.4155 +1971.8 2061.6 1972.4 2060.9 1971.9 2060.7 C
  5.4156 +f 
  5.4157 +S 
  5.4158 +n
  5.4159 +vmrs
  5.4160 +1986.5 2055.2 m
  5.4161 +1987.5 2054.3 1986.3 2053.4 1986 2052.8 C
  5.4162 +1983.8 2052.7 1983.6 2050.1 1981.7 2049.6 C
  5.4163 +1981.2 2048.7 1980.8 2047 1980.3 2046.8 C
  5.4164 +1978.5 2047 1978 2044.6 1976.7 2043.9 C
  5.4165 +1974 2044.4 1972 2046.6 1969.2 2047 C
  5.4166 +1969 2047.2 1968.8 2047.5 1968.5 2047.7 C
  5.4167 +1970.6 2049.6 1973.1 2051.3 1974.3 2054.2 C
  5.4168 +1975.7 2054.5 1977 2055.2 1976.4 2057.1 C
  5.4169 +1976.7 2058 1975.5 2058.5 1976 2059.5 C
  5.4170 +1979.2 2058 1983 2056.6 1986.5 2055.2 C
  5.4171 +[0 0.5 0.5 0.2]  vc
  5.4172 +f 
  5.4173 +0.4 w
  5.4174 +2 J
  5.4175 +2 M
  5.4176 +S 
  5.4177 +n
  5.4178 +1970.2 2054.2 m
  5.4179 +1971.5 2055.3 1972.5 2056.8 1972.1 2058.3 C
  5.4180 +1972.8 2056.5 1971.6 2055.6 1970.2 2054.2 C
  5.4181 +[0 1 1 0.23]  vc
  5.4182 +f 
  5.4183 +S 
  5.4184 +n
  5.4185 +1992 2052.5 m
  5.4186 +1992 2053.4 1992.2 2054.4 1991.8 2055.2 C
  5.4187 +1992.2 2054.4 1992 2053.4 1992 2052.5 C
  5.4188 +f 
  5.4189 +S 
  5.4190 +n
  5.4191 +1957.2 2053 m
  5.4192 +1958.1 2052.6 1959 2052.2 1959.9 2051.8 C
  5.4193 +1959 2052.2 1958.1 2052.6 1957.2 2053 C
  5.4194 +f 
  5.4195 +S 
  5.4196 +n
  5.4197 +2006.4 2047.5 m
  5.4198 +2006.8 2047.1 2006 2055 2006.9 2048.7 C
  5.4199 +2006.4 2048.4 2007 2047.7 2006.4 2047.5 C
  5.4200 +f 
  5.4201 +S 
  5.4202 +n
  5.4203 +2004.8 2041 m
  5.4204 +2006.1 2042.1 2007.1 2043.6 2006.7 2045.1 C
  5.4205 +2007.3 2043.3 2006.2 2042.4 2004.8 2041 C
  5.4206 +f 
  5.4207 +S 
  5.4208 +n
  5.4209 +1976 2039.8 m
  5.4210 +1975.6 2039.3 1975.2 2038.4 1975 2037.6 C
  5.4211 +1974.9 2030.4 1975.2 2022.1 1974.8 2015.8 C
  5.4212 +1974.2 2016 1974 2015.3 1973.6 2016 C
  5.4213 +1974.4 2016 1973.5 2016.5 1974 2016.8 C
  5.4214 +1974 2022.9 1974 2030 1974 2035.2 C
  5.4215 +1974.9 2036.4 1974.4 2036.4 1974.3 2037.4 C
  5.4216 +1973.1 2037.7 1972 2037.9 1971.2 2037.2 C
  5.4217 +1970.6 2035.3 1967.3 2033.9 1967.3 2032.6 C
  5.4218 +1965.3 2033 1965.9 2029.1 1963.5 2029.5 C
  5.4219 +1963 2027.6 1960.4 2026.8 1959.6 2025.2 C
  5.4220 +1959.8 2025.9 1959.2 2027.2 1960.4 2027.3 C
  5.4221 +1962.5 2026.4 1961.9 2031 1964 2030 C
  5.4222 +1964.6 2033.4 1968.5 2032.1 1968 2035.5 C
  5.4223 +1971 2036.1 1971.8 2039.1 1974.5 2038.1 C
  5.4224 +1974.2 2038.7 1975.3 2038.7 1975.7 2039.8 C
  5.4225 +1971 2041.8 1966.7 2044.6 1962 2046.5 C
  5.4226 +1966.8 2044.5 1971.3 2041.9 1976 2039.8 C
  5.4227 +[0 0.2 1 0]  vc
  5.4228 +f 
  5.4229 +S 
  5.4230 +n
  5.4231 +1975.7 2037.6 m
  5.4232 +1975.7 2032.6 1975.7 2027.6 1975.7 2022.5 C
  5.4233 +1975.7 2027.6 1975.7 2032.6 1975.7 2037.6 C
  5.4234 +[0 1 1 0.23]  vc
  5.4235 +f 
  5.4236 +S 
  5.4237 +n
  5.4238 +1992 2035.5 m
  5.4239 +1992 2034.2 1992 2032.9 1992 2031.6 C
  5.4240 +1992 2032.9 1992 2034.2 1992 2035.5 C
  5.4241 +f 
  5.4242 +S 
  5.4243 +n
  5.4244 +2015.3 2036 m
  5.4245 +2015.4 2034.1 2013.3 2034 2012.9 2033.3 C
  5.4246 +2011.5 2031 2009.3 2029.4 2007.4 2028 C
  5.4247 +2006.9 2027.1 2006.6 2023.8 2005 2024.9 C
  5.4248 +2004 2024.9 2002.9 2024.9 2001.9 2024.9 C
  5.4249 +2001.4 2026.5 2001 2028.4 2003.8 2028.3 C
  5.4250 +2006.6 2030.4 2008.9 2033.7 2011.2 2036.2 C
  5.4251 +2011.8 2036.4 2012.9 2035.8 2012.9 2036.7 C
  5.4252 +2013 2035.5 2015.3 2037.4 2015.3 2036 C
  5.4253 +[0 0 0 0]  vc
  5.4254 +f 
  5.4255 +S 
  5.4256 +n
  5.4257 +vmrs
  5.4258 +2009.1 2030.4 m
  5.4259 +2009.1 2029 2007.5 2029.4 2006.9 2028.3 C
  5.4260 +2007.2 2027.1 2006.5 2025.5 2005.7 2024.7 C
  5.4261 +2004.6 2025.1 2003.1 2024.9 2001.9 2024.9 C
  5.4262 +2001.8 2026.2 2000.9 2027 2002.4 2028 C
  5.4263 +2004.5 2027.3 2004.9 2029.4 2006.9 2029 C
  5.4264 +2007 2030.2 2007.6 2030.7 2008.4 2031.4 C
  5.4265 +2008.8 2031.5 2009.1 2031.1 2009.1 2030.4 C
  5.4266 +[0 0 0 0.18]  vc
  5.4267 +f 
  5.4268 +0.4 w
  5.4269 +2 J
  5.4270 +2 M
  5.4271 +S 
  5.4272 +n
  5.4273 +2003.8 2029.5 m
  5.4274 +2003 2029.4 2001.9 2029.1 2002.4 2030.4 C
  5.4275 +2003.1 2031.3 2005.2 2030.3 2003.8 2029.5 C
  5.4276 +[0 1 1 0.23]  vc
  5.4277 +f 
  5.4278 +S 
  5.4279 +n
  5.4280 +1999.2 2025.2 m
  5.4281 +1999.1 2025.6 1998 2025.7 1998.8 2026.6 C
  5.4282 +2000.9 2028.5 1999.5 2023.4 1999.2 2025.2 C
  5.4283 +f 
  5.4284 +S 
  5.4285 +n
  5.4286 +2007.6 2024.2 m
  5.4287 +2007.6 2022.9 2008.4 2024.2 2007.6 2022.8 C
  5.4288 +2007.6 2017.5 2007.8 2009.1 2007.4 2003.8 C
  5.4289 +2007.9 2003.7 2008.7 2002.8 2009.1 2002.1 C
  5.4290 +2009.6 2000.8 2008.3 2000.8 2007.9 2000.2 C
  5.4291 +2004.9 2000 2008.9 2001.3 2007.2 2002.1 C
  5.4292 +2006.7 2007.7 2007 2015.1 2006.9 2021.1 C
  5.4293 +2006.7 2022.1 2005.4 2022.8 2006.2 2023.5 C
  5.4294 +2006.6 2023.1 2008 2025.9 2007.6 2024.2 C
  5.4295 +f 
  5.4296 +S 
  5.4297 +n
  5.4298 +1989.9 2023.5 m
  5.4299 +1989.5 2022.6 1991.4 2023.2 1991.8 2023 C
  5.4300 +1992.2 2023.2 1991.9 2023.7 1992.5 2023.5 C
  5.4301 +1991.6 2023.2 1991.6 2022.2 1990.6 2021.8 C
  5.4302 +1990.4 2022.8 1989 2022.8 1988.9 2023.5 C
  5.4303 +1988.5 2023 1988.7 2022.6 1988.7 2023.5 C
  5.4304 +1989.1 2023.5 1990.2 2023.5 1989.9 2023.5 C
  5.4305 +f 
  5.4306 +[0 0.5 0.5 0.2]  vc
  5.4307 +S 
  5.4308 +n
  5.4309 +2003.3 2023.5 m
  5.4310 +2003.1 2023.3 2003.1 2023.2 2003.3 2023 C
  5.4311 +2003.7 2023.1 2003.9 2022.9 2003.8 2022.5 C
  5.4312 +2003.4 2022.2 2001.2 2022.3 2002.4 2023 C
  5.4313 +2002.6 2022.9 2002.7 2023.1 2002.8 2023.2 C
  5.4314 +2000.7 2023.7 2003.9 2023.4 2003.3 2023.5 C
  5.4315 +[0 1 1 0.23]  vc
  5.4316 +f 
  5.4317 +S 
  5.4318 +n
  5.4319 +1986.8 2019.4 m
  5.4320 +1987.8 2019.8 1987.5 2018.6 1987.2 2018 C
  5.4321 +1986.2 2017.8 1987.3 2020.5 1986.3 2019.2 C
  5.4322 +1986.3 2017.7 1986.3 2020.6 1986.3 2021.3 C
  5.4323 +1988.5 2023.1 1985.6 2020.3 1986.8 2019.4 C
  5.4324 +f 
  5.4325 +S 
  5.4326 +n
  5.4327 +1975.7 2018.2 m
  5.4328 +1976.1 2017.8 1975.2 2025.7 1976.2 2019.4 C
  5.4329 +1975.7 2019.2 1976.3 2018.4 1975.7 2018.2 C
  5.4330 +f 
  5.4331 +S 
  5.4332 +n
  5.4333 +1974 2011.7 m
  5.4334 +1975.4 2012.8 1976.4 2014.3 1976 2015.8 C
  5.4335 +1976.6 2014 1975.5 2013.1 1974 2011.7 C
  5.4336 +f 
  5.4337 +S 
  5.4338 +n
  5.4339 +1984.6 2006.7 m
  5.4340 +1984.7 2004.8 1982.6 2004.8 1982.2 2004 C
  5.4341 +1980.8 2001.7 1978.6 2000.1 1976.7 1998.8 C
  5.4342 +1976.1 1997.8 1975.8 1994.5 1974.3 1995.6 C
  5.4343 +1973.3 1995.6 1972.2 1995.6 1971.2 1995.6 C
  5.4344 +1970.7 1997.2 1970.3 1999.1 1973.1 1999 C
  5.4345 +1975.8 2001.2 1978.2 2004.4 1980.5 2006.9 C
  5.4346 +1981.1 2007.1 1982.1 2006.5 1982.2 2007.4 C
  5.4347 +1982.3 2006.2 1984.5 2008.1 1984.6 2006.7 C
  5.4348 +[0 0 0 0]  vc
  5.4349 +f 
  5.4350 +S 
  5.4351 +n
  5.4352 +vmrs
  5.4353 +1978.4 2001.2 m
  5.4354 +1978.4 1999.7 1976.8 2000.1 1976.2 1999 C
  5.4355 +1976.5 1997.8 1975.8 1996.2 1975 1995.4 C
  5.4356 +1973.9 1995.8 1972.4 1995.6 1971.2 1995.6 C
  5.4357 +1971 1997 1970.2 1997.7 1971.6 1998.8 C
  5.4358 +1973.8 1998 1974.2 2000.1 1976.2 1999.7 C
  5.4359 +1976.3 2000.9 1976.9 2001.4 1977.6 2002.1 C
  5.4360 +1978.1 2002.2 1978.4 2001.8 1978.4 2001.2 C
  5.4361 +[0 0 0 0.18]  vc
  5.4362 +f 
  5.4363 +0.4 w
  5.4364 +2 J
  5.4365 +2 M
  5.4366 +S 
  5.4367 +n
  5.4368 +1973.1 2000.2 m
  5.4369 +1972.3 2000.1 1971.2 1999.8 1971.6 2001.2 C
  5.4370 +1972.4 2002 1974.5 2001 1973.1 2000.2 C
  5.4371 +[0 1 1 0.23]  vc
  5.4372 +f 
  5.4373 +S 
  5.4374 +n
  5.4375 +1960.8 1998.5 m
  5.4376 +1961.6 1998.2 1962.6 2000.3 1963.2 2000.9 C
  5.4377 +1962.3 2000.1 1962.2 1998.7 1960.8 1998.5 C
  5.4378 +f 
  5.4379 +S 
  5.4380 +n
  5.4381 +1968.5 1995.9 m
  5.4382 +1968.4 1996.4 1967.3 1996.4 1968 1997.3 C
  5.4383 +1970.1 1999.2 1968.8 1994.1 1968.5 1995.9 C
  5.4384 +f 
  5.4385 +S 
  5.4386 +n
  5.4387 +1976.9 1994.9 m
  5.4388 +1976.9 1993.7 1977.6 1994.9 1976.9 1993.5 C
  5.4389 +1976.9 1988.2 1977.1 1979.8 1976.7 1974.5 C
  5.4390 +1977.2 1974.5 1978 1973.5 1978.4 1972.8 C
  5.4391 +1978.8 1971.5 1977.6 1971.5 1977.2 1970.9 C
  5.4392 +1974.2 1970.7 1978.2 1972 1976.4 1972.8 C
  5.4393 +1976 1978.4 1976.3 1985.8 1976.2 1991.8 C
  5.4394 +1976 1992.8 1974.6 1993.5 1975.5 1994.2 C
  5.4395 +1975.9 1993.8 1977.3 1996.6 1976.9 1994.9 C
  5.4396 +f 
  5.4397 +S 
  5.4398 +n
  5.4399 +1972.6 1994.2 m
  5.4400 +1972.4 1994 1972.4 1993.9 1972.6 1993.7 C
  5.4401 +1973 1993.8 1973.1 1993.7 1973.1 1993.2 C
  5.4402 +1972.7 1992.9 1970.5 1993.1 1971.6 1993.7 C
  5.4403 +1971.9 1993.7 1972 1993.8 1972.1 1994 C
  5.4404 +1970 1994.4 1973.1 1994.1 1972.6 1994.2 C
  5.4405 +f 
  5.4406 +S 
  5.4407 +n
  5.4408 +1948.1 2093.8 m
  5.4409 +1947 2092.7 1945.9 2091.6 1944.8 2090.4 C
  5.4410 +1945.9 2091.6 1947 2092.7 1948.1 2093.8 C
  5.4411 +[0 0.4 1 0]  vc
  5.4412 +f 
  5.4413 +S 
  5.4414 +n
  5.4415 +1953.4 2091.4 m
  5.4416 +1954.8 2090.7 1956.3 2090 1957.7 2089.2 C
  5.4417 +1956.3 2090 1954.8 2090.7 1953.4 2091.4 C
  5.4418 +[0 0.2 1 0]  vc
  5.4419 +f 
  5.4420 +S 
  5.4421 +n
  5.4422 +1954.1 2091.4 m
  5.4423 +1956.6 2089.6 1957.2 2089.6 1954.1 2091.4 C
  5.4424 +[0 0.4 1 0]  vc
  5.4425 +f 
  5.4426 +S 
  5.4427 +n
  5.4428 +1962.3 2087.3 m
  5.4429 +1963.7 2086.6 1965.2 2085.9 1966.6 2085.2 C
  5.4430 +1965.2 2085.9 1963.7 2086.6 1962.3 2087.3 C
  5.4431 +f 
  5.4432 +S 
  5.4433 +n
  5.4434 +vmrs
  5.4435 +1967.1 2084.9 m
  5.4436 +1968.3 2084.4 1969.7 2083.8 1970.9 2083.2 C
  5.4437 +1969.7 2083.8 1968.3 2084.4 1967.1 2084.9 C
  5.4438 +[0 0.4 1 0]  vc
  5.4439 +f 
  5.4440 +0.4 w
  5.4441 +2 J
  5.4442 +2 M
  5.4443 +S 
  5.4444 +n
  5.4445 +1982.7 2080.6 m
  5.4446 +1981.5 2079.5 1980.5 2078.4 1979.3 2077.2 C
  5.4447 +1980.5 2078.4 1981.5 2079.5 1982.7 2080.6 C
  5.4448 +f 
  5.4449 +S 
  5.4450 +n
  5.4451 +1988 2078.2 m
  5.4452 +1989.4 2077.5 1990.8 2076.8 1992.3 2076 C
  5.4453 +1990.8 2076.8 1989.4 2077.5 1988 2078.2 C
  5.4454 +[0 0.2 1 0]  vc
  5.4455 +f 
  5.4456 +S 
  5.4457 +n
  5.4458 +1988.7 2078.2 m
  5.4459 +1991.1 2076.4 1991.8 2076.4 1988.7 2078.2 C
  5.4460 +[0 0.4 1 0]  vc
  5.4461 +f 
  5.4462 +S 
  5.4463 +n
  5.4464 +1976.2 2063.8 m
  5.4465 +1978.6 2062.2 1976 2063.3 1976 2064.5 C
  5.4466 +1976.1 2067.8 1975.5 2071.4 1976.4 2074.4 C
  5.4467 +1975.7 2071.1 1975.9 2067.2 1976.2 2063.8 C
  5.4468 +f 
  5.4469 +S 
  5.4470 +n
  5.4471 +1996.8 2074.1 m
  5.4472 +1998.3 2073.4 1999.7 2072.7 2001.2 2072 C
  5.4473 +1999.7 2072.7 1998.3 2073.4 1996.8 2074.1 C
  5.4474 +f 
  5.4475 +S 
  5.4476 +n
  5.4477 +2001.6 2071.7 m
  5.4478 +2002.9 2071.2 2004.2 2070.6 2005.5 2070 C
  5.4479 +2004.2 2070.6 2002.9 2071.2 2001.6 2071.7 C
  5.4480 +f 
  5.4481 +S 
  5.4482 +n
  5.4483 +1981.5 2060.7 m
  5.4484 +1980.2 2061.2 1978.9 2061.5 1977.9 2062.6 C
  5.4485 +1978.9 2061.5 1980.2 2061.2 1981.5 2060.7 C
  5.4486 +f 
  5.4487 +S 
  5.4488 +n
  5.4489 +1982 2060.4 m
  5.4490 +1982.7 2060.1 1983.6 2059.8 1984.4 2059.5 C
  5.4491 +1983.6 2059.8 1982.7 2060.1 1982 2060.4 C
  5.4492 +f 
  5.4493 +S 
  5.4494 +n
  5.4495 +1952 2051.3 m
  5.4496 +1950.8 2050.2 1949.7 2049.1 1948.6 2048 C
  5.4497 +1949.7 2049.1 1950.8 2050.2 1952 2051.3 C
  5.4498 +f 
  5.4499 +S 
  5.4500 +n
  5.4501 +vmrs
  5.4502 +1977.4 2047.7 m
  5.4503 +1975.8 2047.8 1974.8 2046.1 1974.5 2045.3 C
  5.4504 +1974.9 2044.4 1976 2044.5 1976.7 2044.8 C
  5.4505 +1977.9 2045 1977 2048.4 1979.3 2047.5 C
  5.4506 +1979.9 2047.5 1980.8 2048.6 1979.8 2049.2 C
  5.4507 +1978.2 2050.4 1980.8 2049.5 1980.3 2049.4 C
  5.4508 +1981.4 2049.8 1980.3 2048.4 1980.3 2048 C
  5.4509 +1979.8 2047.5 1979 2046.6 1978.4 2046.5 C
  5.4510 +1977.3 2045.9 1977.2 2043.3 1975.2 2044.6 C
  5.4511 +1974.7 2045.3 1973.6 2045 1973.3 2045.8 C
  5.4512 +1975 2046.3 1975.8 2049.8 1978.1 2049.4 C
  5.4513 +1978.4 2050.9 1978.7 2048.5 1977.9 2049.2 C
  5.4514 +1977.7 2048.7 1977.2 2047.8 1977.4 2047.7 C
  5.4515 +[0 0.5 0.5 0.2]  vc
  5.4516 +f 
  5.4517 +0.4 w
  5.4518 +2 J
  5.4519 +2 M
  5.4520 +S 
  5.4521 +n
  5.4522 +1957.2 2048.9 m
  5.4523 +1958.7 2048.2 1960.1 2047.5 1961.6 2046.8 C
  5.4524 +1960.1 2047.5 1958.7 2048.2 1957.2 2048.9 C
  5.4525 +[0 0.2 1 0]  vc
  5.4526 +f 
  5.4527 +S 
  5.4528 +n
  5.4529 +1958 2048.9 m
  5.4530 +1960.4 2047.1 1961.1 2047.1 1958 2048.9 C
  5.4531 +[0 0.4 1 0]  vc
  5.4532 +f 
  5.4533 +S 
  5.4534 +n
  5.4535 +1966.1 2044.8 m
  5.4536 +1967.6 2044.1 1969 2043.4 1970.4 2042.7 C
  5.4537 +1969 2043.4 1967.6 2044.1 1966.1 2044.8 C
  5.4538 +f 
  5.4539 +S 
  5.4540 +n
  5.4541 +1970.9 2042.4 m
  5.4542 +1972.2 2041.9 1973.5 2041.3 1974.8 2040.8 C
  5.4543 +1973.5 2041.3 1972.2 2041.9 1970.9 2042.4 C
  5.4544 +f 
  5.4545 +S 
  5.4546 +n
  5.4547 +2012 2034.5 m
  5.4548 +2010.4 2034.6 2009.3 2032.9 2009.1 2032.1 C
  5.4549 +2009.4 2031 2010.3 2031.3 2011.2 2031.6 C
  5.4550 +2012.5 2031.8 2011.6 2035.2 2013.9 2034.3 C
  5.4551 +2014.4 2034.3 2015.4 2035.4 2014.4 2036 C
  5.4552 +2012.7 2037.2 2015.3 2036.3 2014.8 2036.2 C
  5.4553 +2015.9 2036.6 2014.8 2035.2 2014.8 2034.8 C
  5.4554 +2014.4 2034.3 2013.6 2033.4 2012.9 2033.3 C
  5.4555 +2011.5 2031 2009.3 2029.4 2007.4 2028 C
  5.4556 +2007.5 2026.5 2007.3 2027.9 2007.2 2028.3 C
  5.4557 +2007.9 2028.8 2008.7 2029.1 2009.3 2030 C
  5.4558 +2009.6 2030.7 2009 2031.9 2008.4 2031.6 C
  5.4559 +2006.7 2031 2007.7 2028 2005 2028.8 C
  5.4560 +2004.8 2028.6 2004.3 2028.2 2003.8 2028.3 C
  5.4561 +2006.6 2030.4 2008.9 2033.7 2011.2 2036.2 C
  5.4562 +2011.8 2036.4 2012.9 2035.8 2012.9 2036.7 C
  5.4563 +2012.7 2036.1 2011.8 2035 2012 2034.5 C
  5.4564 +[0 0.5 0.5 0.2]  vc
  5.4565 +f 
  5.4566 +S 
  5.4567 +n
  5.4568 +1981.2 2005.2 m
  5.4569 +1979.7 2005.3 1978.6 2003.6 1978.4 2002.8 C
  5.4570 +1978.7 2001.8 1979.6 2002.1 1980.5 2002.4 C
  5.4571 +1981.8 2002.5 1980.9 2005.9 1983.2 2005 C
  5.4572 +1983.7 2005.1 1984.7 2006.1 1983.6 2006.7 C
  5.4573 +1982 2007.9 1984.6 2007 1984.1 2006.9 C
  5.4574 +1985.2 2007.3 1984.1 2006 1984.1 2005.5 C
  5.4575 +1983.6 2005 1982.9 2004.1 1982.2 2004 C
  5.4576 +1980.8 2001.7 1978.6 2000.1 1976.7 1998.8 C
  5.4577 +1976.7 1997.2 1976.6 1998.6 1976.4 1999 C
  5.4578 +1977.2 1999.5 1978 1999.8 1978.6 2000.7 C
  5.4579 +1978.8 2001.5 1978.3 2002.7 1977.6 2002.4 C
  5.4580 +1976 2001.8 1977 1998.7 1974.3 1999.5 C
  5.4581 +1974.1 1999.3 1973.6 1998.9 1973.1 1999 C
  5.4582 +1975.8 2001.2 1978.2 2004.4 1980.5 2006.9 C
  5.4583 +1981.1 2007.1 1982.1 2006.5 1982.2 2007.4 C
  5.4584 +1982 2006.8 1981.1 2005.7 1981.2 2005.2 C
  5.4585 +f 
  5.4586 +S 
  5.4587 +n
  5.4588 +1966.8 1976.4 m
  5.4589 +1969.4 1973 1974.4 1974.6 1976.2 1970.4 C
  5.4590 +1972.7 1974 1968 1975.1 1964 1977.4 C
  5.4591 +1960.9 1979.9 1957.1 1981.8 1953.9 1982.7 C
  5.4592 +1958.4 1981.1 1962.6 1978.8 1966.8 1976.4 C
  5.4593 +[0.18 0.18 0 0.78]  vc
  5.4594 +f 
  5.4595 +S 
  5.4596 +n
  5.4597 +1948.4 2093.8 m
  5.4598 +1949.8 2093.1 1951.2 2092.5 1952.7 2091.9 C
  5.4599 +1951.2 2092.5 1949.8 2093.1 1948.4 2093.8 C
  5.4600 +[0 0.2 1 0]  vc
  5.4601 +f 
  5.4602 +S 
  5.4603 +n
  5.4604 +1948.1 2093.6 m
  5.4605 +1947.3 2092.8 1946.5 2091.9 1945.7 2091.2 C
  5.4606 +1946.5 2091.9 1947.3 2092.8 1948.1 2093.6 C
  5.4607 +f 
  5.4608 +S 
  5.4609 +n
  5.4610 +vmrs
  5.4611 +1942.1 2087.8 m
  5.4612 +1943.5 2088.4 1944.3 2089.5 1945.2 2090.7 C
  5.4613 +1944.8 2089.3 1943.3 2088.3 1942.1 2087.8 C
  5.4614 +[0 0.2 1 0]  vc
  5.4615 +f 
  5.4616 +0.4 w
  5.4617 +2 J
  5.4618 +2 M
  5.4619 +S 
  5.4620 +n
  5.4621 +1933.5 2078.4 m
  5.4622 +1933.5 2078 1933.2 2079 1933.7 2079.4 C
  5.4623 +1935 2080.4 1936.2 2081.3 1937.1 2082.8 C
  5.4624 +1936.7 2080.7 1933.7 2080.7 1933.5 2078.4 C
  5.4625 +f 
  5.4626 +S 
  5.4627 +n
  5.4628 +1982.9 2080.6 m
  5.4629 +1984.4 2079.9 1985.8 2079.3 1987.2 2078.7 C
  5.4630 +1985.8 2079.3 1984.4 2079.9 1982.9 2080.6 C
  5.4631 +f 
  5.4632 +S 
  5.4633 +n
  5.4634 +1982.7 2080.4 m
  5.4635 +1981.9 2079.6 1981.1 2078.7 1980.3 2078 C
  5.4636 +1981.1 2078.7 1981.9 2079.6 1982.7 2080.4 C
  5.4637 +f 
  5.4638 +S 
  5.4639 +n
  5.4640 +1977.4 2075.1 m
  5.4641 +1977.9 2075.3 1979.1 2076.4 1979.8 2077.5 C
  5.4642 +1979 2076.8 1978.7 2075.1 1977.4 2075.1 C
  5.4643 +f 
  5.4644 +S 
  5.4645 +n
  5.4646 +1952.2 2051.3 m
  5.4647 +1953.6 2050.7 1955.1 2050.1 1956.5 2049.4 C
  5.4648 +1955.1 2050.1 1953.6 2050.7 1952.2 2051.3 C
  5.4649 +f 
  5.4650 +S 
  5.4651 +n
  5.4652 +1952 2051.1 m
  5.4653 +1951.2 2050.3 1950.3 2049.5 1949.6 2048.7 C
  5.4654 +1950.3 2049.5 1951.2 2050.3 1952 2051.1 C
  5.4655 +f 
  5.4656 +S 
  5.4657 +n
  5.4658 +1946 2045.3 m
  5.4659 +1947.3 2045.9 1948.1 2047 1949.1 2048.2 C
  5.4660 +1948.6 2046.8 1947.1 2045.8 1946 2045.3 C
  5.4661 +f 
  5.4662 +S 
  5.4663 +n
  5.4664 +1937.3 2036 m
  5.4665 +1937.4 2035.5 1937 2036.5 1937.6 2036.9 C
  5.4666 +1938.8 2037.9 1940.1 2038.8 1940.9 2040.3 C
  5.4667 +1940.6 2038.2 1937.6 2038.2 1937.3 2036 C
  5.4668 +f 
  5.4669 +S 
  5.4670 +n
  5.4671 +1935.2 2073.2 m
  5.4672 +1936.4 2069.9 1935.8 2061.8 1935.6 2056.4 C
  5.4673 +1935.8 2055.9 1936.3 2055.7 1936.1 2055.2 C
  5.4674 +1935.7 2054.7 1935 2055 1934.4 2054.9 C
  5.4675 +1934.4 2061.5 1934.4 2068.7 1934.4 2074.6 C
  5.4676 +1935.7 2075.1 1936 2073.7 1935.2 2073.2 C
  5.4677 +[0 0.01 1 0]  vc
  5.4678 +f 
  5.4679 +S 
  5.4680 +n
  5.4681 +vmrs
  5.4682 +1939 2030.7 m
  5.4683 +1940.3 2027.4 1939.7 2019.3 1939.5 2013.9 C
  5.4684 +1939.7 2013.5 1940.1 2013.2 1940 2012.7 C
  5.4685 +1939.5 2012.3 1938.8 2012.5 1938.3 2012.4 C
  5.4686 +1938.3 2019 1938.3 2026.2 1938.3 2032.1 C
  5.4687 +1939.5 2032.7 1939.8 2031.2 1939 2030.7 C
  5.4688 +[0 0.01 1 0]  vc
  5.4689 +f 
  5.4690 +0.4 w
  5.4691 +2 J
  5.4692 +2 M
  5.4693 +S 
  5.4694 +n
  5.4695 +1975.2 2077.2 m
  5.4696 +1975.3 2077.3 1975.4 2077.4 1975.5 2077.5 C
  5.4697 +1974.7 2073.2 1974.9 2067.5 1975.2 2063.6 C
  5.4698 +1975.4 2064 1974.6 2063.9 1974.8 2064.3 C
  5.4699 +1974.9 2069.9 1974.3 2076.5 1975.2 2081.1 C
  5.4700 +1974.9 2079.9 1974.9 2078.4 1975.2 2077.2 C
  5.4701 +[0.92 0.92 0 0.67]  vc
  5.4702 +f 
  5.4703 +S 
  5.4704 +n
  5.4705 +1930.8 2067.4 m
  5.4706 +1931.5 2070.1 1929.6 2072.1 1930.6 2074.6 C
  5.4707 +1931 2072.6 1930.8 2069.8 1930.8 2067.4 C
  5.4708 +f 
  5.4709 +S 
  5.4710 +n
  5.4711 +2010 2050.1 m
  5.4712 +2009.8 2050.5 2009.5 2050.9 2009.3 2051.1 C
  5.4713 +2009.5 2056.7 2008.9 2063.3 2009.8 2067.9 C
  5.4714 +2009.5 2062.1 2009.3 2054.7 2010 2050.1 C
  5.4715 +f 
  5.4716 +S 
  5.4717 +n
  5.4718 +1930.1 2060.9 m
  5.4719 +1929.3 2057.1 1930.7 2054.8 1929.9 2051.3 C
  5.4720 +1930.2 2050.2 1931.1 2049.6 1931.8 2049.2 C
  5.4721 +1931.4 2049.6 1930.4 2049.5 1930.1 2050.1 C
  5.4722 +1928.4 2054.8 1933.4 2063.5 1925.3 2064.3 C
  5.4723 +1927.2 2063.9 1928.5 2062.1 1930.1 2060.9 C
  5.4724 +[0.07 0.06 0 0.58]  vc
  5.4725 +f 
  5.4726 +S 
  5.4727 +n
  5.4728 +1929.6 2061.2 m
  5.4729 +1929.6 2057.6 1929.6 2054.1 1929.6 2050.6 C
  5.4730 +1930 2049.9 1930.5 2049.4 1931.1 2049.2 C
  5.4731 +1930 2048.6 1930.5 2050.2 1929.4 2049.6 C
  5.4732 +1928 2054.4 1932.8 2063 1925.3 2064 C
  5.4733 +1926.9 2063.3 1928.3 2062.4 1929.6 2061.2 C
  5.4734 +[0.4 0.4 0 0]  vc
  5.4735 +f 
  5.4736 +S 
  5.4737 +n
  5.4738 +1930.8 2061.6 m
  5.4739 +1930.5 2058 1931.6 2054 1930.8 2051.3 C
  5.4740 +1930.3 2054.5 1930.9 2058.5 1930.4 2061.9 C
  5.4741 +1930.5 2061.2 1931 2062.2 1930.8 2061.6 C
  5.4742 +[0.92 0.92 0 0.67]  vc
  5.4743 +f 
  5.4744 +S 
  5.4745 +n
  5.4746 +1941.2 2045.1 m
  5.4747 +1939.7 2042.6 1937.3 2041.2 1935.4 2039.3 C
  5.4748 +1934.2 2040 1933.7 2036.4 1934 2039.3 C
  5.4749 +1934.9 2040.1 1936.1 2039.9 1936.8 2040.8 C
  5.4750 +1935.3 2044.2 1942.3 2041.7 1939.5 2046 C
  5.4751 +1937.1 2048.5 1940.5 2045.6 1941.2 2045.1 C
  5.4752 +f 
  5.4753 +S 
  5.4754 +n
  5.4755 +1910 2045.8 m
  5.4756 +1910 2039.4 1910 2033 1910 2026.6 C
  5.4757 +1910 2033 1910 2039.4 1910 2045.8 C
  5.4758 +f 
  5.4759 +S 
  5.4760 +n
  5.4761 +1978.8 2022.3 m
  5.4762 +1979.1 2021.7 1979.4 2020.4 1978.6 2021.6 C
  5.4763 +1978.6 2026.9 1978.6 2033 1978.6 2037.6 C
  5.4764 +1979.2 2037 1979.1 2038.2 1979.1 2038.6 C
  5.4765 +1978.7 2033.6 1978.9 2026.8 1978.8 2022.3 C
  5.4766 +f 
  5.4767 +S 
  5.4768 +n
  5.4769 +vmrs
  5.4770 +2026.1 2041.2 m
  5.4771 +2026.1 2034.8 2026.1 2028.3 2026.1 2021.8 C
  5.4772 +2026.1 2028.5 2026.3 2035.4 2025.9 2042 C
  5.4773 +2024.4 2042.9 2022.9 2044.1 2021.3 2044.8 C
  5.4774 +2023.1 2044 2025.1 2042.8 2026.1 2041.2 C
  5.4775 +[0.07 0.06 0 0.58]  vc
  5.4776 +f 
  5.4777 +0.4 w
  5.4778 +2 J
  5.4779 +2 M
  5.4780 +S 
  5.4781 +n
  5.4782 +2026.4 2021.8 m
  5.4783 +2026.3 2028.5 2026.5 2035.4 2026.1 2042 C
  5.4784 +2025.6 2042.8 2024.7 2042.7 2024.2 2043.4 C
  5.4785 +2024.7 2042.7 2025.5 2042.7 2026.1 2042.2 C
  5.4786 +2026.5 2035.5 2026.3 2027.9 2026.4 2021.8 C
  5.4787 +[0.4 0.4 0 0]  vc
  5.4788 +f 
  5.4789 +S 
  5.4790 +n
  5.4791 +2025.6 2038.4 m
  5.4792 +2025.6 2033 2025.6 2027.6 2025.6 2022.3 C
  5.4793 +2025.6 2027.6 2025.6 2033 2025.6 2038.4 C
  5.4794 +[0.92 0.92 0 0.67]  vc
  5.4795 +f 
  5.4796 +S 
  5.4797 +n
  5.4798 +1934 2023.5 m
  5.4799 +1934 2024.7 1933.8 2026 1934.2 2027.1 C
  5.4800 +1934 2025.5 1934.7 2024.6 1934 2023.5 C
  5.4801 +f 
  5.4802 +S 
  5.4803 +n
  5.4804 +1928.2 2023.5 m
  5.4805 +1928 2024.6 1927.4 2023.1 1926.8 2023.2 C
  5.4806 +1926.2 2021 1921.4 2019.3 1923.2 2018 C
  5.4807 +1922.7 2016.5 1923.2 2019.3 1922.2 2018.2 C
  5.4808 +1924.4 2020.4 1926.2 2023.3 1928.9 2024.9 C
  5.4809 +1927.9 2024.2 1929.8 2023.5 1928.2 2023.5 C
  5.4810 +[0.18 0.18 0 0.78]  vc
  5.4811 +f 
  5.4812 +S 
  5.4813 +n
  5.4814 +1934 2019.2 m
  5.4815 +1932 2019.6 1930.8 2022.6 1928.7 2021.8 C
  5.4816 +1924.5 2016.5 1918.2 2011.8 1914 2006.7 C
  5.4817 +1914 2005.7 1914 2004.6 1914 2003.6 C
  5.4818 +1913.6 2004.3 1913.9 2005.8 1913.8 2006.9 C
  5.4819 +1919 2012.4 1924.1 2016.5 1929.2 2022.3 C
  5.4820 +1931 2021.7 1932.2 2019.8 1934 2019.2 C
  5.4821 +f 
  5.4822 +S 
  5.4823 +n
  5.4824 +1928.7 2024.9 m
  5.4825 +1926.3 2022.7 1924.1 2020.4 1921.7 2018.2 C
  5.4826 +1924.1 2020.4 1926.3 2022.7 1928.7 2024.9 C
  5.4827 +[0.65 0.65 0 0.42]  vc
  5.4828 +f 
  5.4829 +S 
  5.4830 +n
  5.4831 +1914.3 2006.7 m
  5.4832 +1918.7 2011.8 1924.5 2016.4 1928.9 2021.6 C
  5.4833 +1924.2 2016.1 1919 2012.1 1914.3 2006.7 C
  5.4834 +[0.07 0.06 0 0.58]  vc
  5.4835 +f 
  5.4836 +S 
  5.4837 +n
  5.4838 +1924.8 2020.8 m
  5.4839 +1921.2 2016.9 1925.6 2022.5 1926 2021.1 C
  5.4840 +1924.2 2021 1926.7 2019.6 1924.8 2020.8 C
  5.4841 +[0.92 0.92 0 0.67]  vc
  5.4842 +f 
  5.4843 +S 
  5.4844 +n
  5.4845 +1934 2018.4 m
  5.4846 +1933.2 2014.7 1934.5 2012.3 1933.7 2008.8 C
  5.4847 +1934 2007.8 1935 2007.2 1935.6 2006.7 C
  5.4848 +1935.3 2007.1 1934.3 2007 1934 2007.6 C
  5.4849 +1932.2 2012.3 1937.2 2021 1929.2 2021.8 C
  5.4850 +1931.1 2021.4 1932.3 2019.6 1934 2018.4 C
  5.4851 +[0.07 0.06 0 0.58]  vc
  5.4852 +f 
  5.4853 +S 
  5.4854 +n
  5.4855 +vmrs
  5.4856 +1933.5 2018.7 m
  5.4857 +1933.5 2015.1 1933.5 2011.7 1933.5 2008.1 C
  5.4858 +1933.8 2007.4 1934.3 2006.9 1934.9 2006.7 C
  5.4859 +1933.8 2006.1 1934.3 2007.7 1933.2 2007.2 C
  5.4860 +1931.9 2012 1936.7 2020.5 1929.2 2021.6 C
  5.4861 +1930.7 2020.8 1932.2 2019.9 1933.5 2018.7 C
  5.4862 +[0.4 0.4 0 0]  vc
  5.4863 +f 
  5.4864 +0.4 w
  5.4865 +2 J
  5.4866 +2 M
  5.4867 +S 
  5.4868 +n
  5.4869 +1934.7 2019.2 m
  5.4870 +1934.3 2015.6 1935.4 2011.5 1934.7 2008.8 C
  5.4871 +1934.1 2012 1934.7 2016 1934.2 2019.4 C
  5.4872 +1934.4 2018.7 1934.8 2019.8 1934.7 2019.2 C
  5.4873 +[0.92 0.92 0 0.67]  vc
  5.4874 +f 
  5.4875 +S 
  5.4876 +n
  5.4877 +1917.6 2013.6 m
  5.4878 +1917.8 2011.1 1916.8 2014.2 1917.2 2012.2 C
  5.4879 +1916.3 2012.9 1914.8 2011.8 1914.3 2010.8 C
  5.4880 +1914.2 2010.5 1914.4 2010.4 1914.5 2010.3 C
  5.4881 +1913.9 2008.8 1913.9 2011.9 1914.3 2012 C
  5.4882 +1916.3 2012 1917.6 2013.6 1916.7 2015.6 C
  5.4883 +1913.7 2017.4 1919.6 2014.8 1917.6 2013.6 C
  5.4884 +f 
  5.4885 +S 
  5.4886 +n
  5.4887 +1887.2 2015.3 m
  5.4888 +1887.2 2008.9 1887.2 2002.5 1887.2 1996.1 C
  5.4889 +1887.2 2002.5 1887.2 2008.9 1887.2 2015.3 C
  5.4890 +f 
  5.4891 +S 
  5.4892 +n
  5.4893 +1916.7 2014.4 m
  5.4894 +1917 2012.1 1913 2013 1913.8 2010.8 C
  5.4895 +1912.1 2009.8 1910.9 2009.4 1910.7 2007.9 C
  5.4896 +1910.4 2010.6 1913.4 2010.4 1914 2012.4 C
  5.4897 +1914.9 2012.8 1916.6 2012.9 1916.4 2014.4 C
  5.4898 +1916.9 2015.1 1914.5 2016.6 1916.2 2015.8 C
  5.4899 +1916.4 2015.3 1916.7 2015 1916.7 2014.4 C
  5.4900 +[0.65 0.65 0 0.42]  vc
  5.4901 +f 
  5.4902 +S 
  5.4903 +n
  5.4904 +1914 2009.3 m
  5.4905 +1912.8 2010.9 1909.6 2005.3 1911.9 2009.8 C
  5.4906 +1912.3 2009.6 1913.6 2010.2 1914 2009.3 C
  5.4907 +[0.92 0.92 0 0.67]  vc
  5.4908 +f 
  5.4909 +S 
  5.4910 +n
  5.4911 +1951.2 1998.8 m
  5.4912 +1949 1996.4 1951.5 1994 1950.3 1991.8 C
  5.4913 +1949.1 1989.1 1954 1982.7 1948.8 1981.2 C
  5.4914 +1949.2 1981.5 1951 1982.4 1950.8 1983.6 C
  5.4915 +1951.9 1988.6 1947.1 1986.5 1948.1 1990.4 C
  5.4916 +1948.5 1990.3 1948.7 1990.7 1948.6 1991.1 C
  5.4917 +1949 1992.5 1947.3 1991.9 1948.1 1992.5 C
  5.4918 +1947.1 1992.7 1945.7 1993.5 1945.2 1994.7 C
  5.4919 +1944.5 1996.8 1947.7 2000.5 1943.8 2001.4 C
  5.4920 +1943.4 2002 1943.7 2004 1942.4 2004.5 C
  5.4921 +1945.2 2002.2 1948.9 2000.9 1951.2 1998.8 C
  5.4922 +f 
  5.4923 +S 
  5.4924 +n
  5.4925 +1994.9 1993 m
  5.4926 +1995.1 1996.5 1994.5 2000.3 1995.4 2003.6 C
  5.4927 +1994.5 2000.3 1995.1 1996.5 1994.9 1993 C
  5.4928 +f 
  5.4929 +S 
  5.4930 +n
  5.4931 +1913.8 2003.3 m
  5.4932 +1913.8 1996.9 1913.8 1990.5 1913.8 1984.1 C
  5.4933 +1913.8 1990.5 1913.8 1996.9 1913.8 2003.3 C
  5.4934 +f 
  5.4935 +S 
  5.4936 +n
  5.4937 +1941.9 1998 m
  5.4938 +1940.5 1997.3 1940.7 1999.4 1940.7 2000 C
  5.4939 +1942.8 2001.3 1942.6 1998.8 1941.9 1998 C
  5.4940 +[0 0 0 0]  vc
  5.4941 +f 
  5.4942 +S 
  5.4943 +n
  5.4944 +vmrs
  5.4945 +1942.1 1999.2 m
  5.4946 +1942.2 1998.9 1941.8 1998.8 1941.6 1998.5 C
  5.4947 +1940.4 1998 1940.7 1999.7 1940.7 2000 C
  5.4948 +1941.6 2000.3 1942.6 2000.4 1942.1 1999.2 C
  5.4949 +[0.92 0.92 0 0.67]  vc
  5.4950 +f 
  5.4951 +0.4 w
  5.4952 +2 J
  5.4953 +2 M
  5.4954 +S 
  5.4955 +n
  5.4956 +1940 1997.1 m
  5.4957 +1939.8 1996 1939.7 1995.9 1939.2 1995.2 C
  5.4958 +1939.1 1995.3 1938.5 1997.9 1937.8 1996.4 C
  5.4959 +1938 1997.3 1939.4 1998.6 1940 1997.1 C
  5.4960 +f 
  5.4961 +S 
  5.4962 +n
  5.4963 +1911.2 1995.9 m
  5.4964 +1911.2 1991.6 1911.3 1987.2 1911.4 1982.9 C
  5.4965 +1911.3 1987.2 1911.2 1991.6 1911.2 1995.9 C
  5.4966 +f 
  5.4967 +S 
  5.4968 +n
  5.4969 +1947.2 1979.1 m
  5.4970 +1945.1 1978.8 1944.6 1975.7 1942.4 1975 C
  5.4971 +1940.5 1972.6 1942.2 1973.7 1942.4 1975.7 C
  5.4972 +1945.8 1975.5 1944.2 1979.8 1947.6 1979.6 C
  5.4973 +1948.3 1982.3 1948.5 1980 1947.2 1979.1 C
  5.4974 +f 
  5.4975 +S 
  5.4976 +n
  5.4977 +1939.5 1973.3 m
  5.4978 +1940.1 1972.6 1939.8 1974.2 1940.2 1973.1 C
  5.4979 +1939.1 1972.8 1938.8 1968.5 1935.9 1969.7 C
  5.4980 +1937.4 1969.2 1938.5 1970.6 1939 1971.4 C
  5.4981 +1939.2 1972.7 1938.6 1973.9 1939.5 1973.3 C
  5.4982 +f 
  5.4983 +S 
  5.4984 +n
  5.4985 +1975.2 2073.2 m
  5.4986 +1975.2 2070.2 1975.2 2067.2 1975.2 2064.3 C
  5.4987 +1975.2 2067.2 1975.2 2070.2 1975.2 2073.2 C
  5.4988 +[0.18 0.18 0 0.78]  vc
  5.4989 +f 
  5.4990 +S 
  5.4991 +n
  5.4992 +1929.9 2065.7 m
  5.4993 +1928.1 2065.6 1926 2068.8 1924.1 2066.9 C
  5.4994 +1918.1 2060.9 1912.9 2055.7 1907.1 2049.9 C
  5.4995 +1906.7 2047.1 1906.9 2043.9 1906.8 2041 C
  5.4996 +1906.8 2043.9 1906.8 2046.8 1906.8 2049.6 C
  5.4997 +1913.2 2055.5 1918.7 2061.9 1925.1 2067.6 C
  5.4998 +1927.1 2067.9 1928.6 2064.4 1930.1 2066.2 C
  5.4999 +1929.7 2070.3 1929.9 2074.7 1929.9 2078.9 C
  5.5000 +1929.6 2074.4 1930.5 2070.1 1929.9 2065.7 C
  5.5001 +[0.07 0.06 0 0.58]  vc
  5.5002 +f 
  5.5003 +S 
  5.5004 +n
  5.5005 +1930.1 2061.6 m
  5.5006 +1928.1 2062.1 1927 2065.1 1924.8 2064.3 C
  5.5007 +1920.7 2058.9 1914.4 2054.3 1910.2 2049.2 C
  5.5008 +1910.2 2048.1 1910.2 2047.1 1910.2 2046 C
  5.5009 +1909.8 2046.8 1910 2048.3 1910 2049.4 C
  5.5010 +1915.1 2054.9 1920.3 2059 1925.3 2064.8 C
  5.5011 +1927.1 2064.2 1928.4 2062.3 1930.1 2061.6 C
  5.5012 +[0.18 0.18 0 0.78]  vc
  5.5013 +f 
  5.5014 +S 
  5.5015 +n
  5.5016 +1932 2049.9 m
  5.5017 +1932.3 2050.3 1932 2050.4 1932.8 2050.4 C
  5.5018 +1932 2050.4 1932.2 2049.2 1931.3 2049.6 C
  5.5019 +1931.4 2050.5 1930.3 2050.4 1930.4 2051.3 C
  5.5020 +1931.1 2051.1 1930.7 2049.4 1932 2049.9 C
  5.5021 +f 
  5.5022 +S 
  5.5023 +n
  5.5024 +1938.3 2046 m
  5.5025 +1936.3 2046.8 1935.2 2047.2 1934.2 2048.9 C
  5.5026 +1935.3 2047.7 1936.8 2046.2 1938.3 2046 C
  5.5027 +[0.4 0.4 0 0]  vc
  5.5028 +f 
  5.5029 +S 
  5.5030 +n
  5.5031 +vmrs
  5.5032 +1938.3 2047 m
  5.5033 +1937.9 2046.9 1936.6 2047.1 1936.1 2048 C
  5.5034 +1936.5 2047.5 1937.3 2046.7 1938.3 2047 C
  5.5035 +[0.18 0.18 0 0.78]  vc
  5.5036 +f 
  5.5037 +0.4 w
  5.5038 +2 J
  5.5039 +2 M
  5.5040 +S 
  5.5041 +n
  5.5042 +1910.2 2043.2 m
  5.5043 +1910.1 2037.5 1910 2031.8 1910 2026.1 C
  5.5044 +1910 2031.8 1910.1 2037.5 1910.2 2043.2 C
  5.5045 +f 
  5.5046 +S 
  5.5047 +n
  5.5048 +1933.5 2032.1 m
  5.5049 +1933.7 2035.2 1932.8 2035.8 1933.7 2038.6 C
  5.5050 +1933.3 2036.6 1934.6 2018 1933.5 2032.1 C
  5.5051 +f 
  5.5052 +S 
  5.5053 +n
  5.5054 +1907.3 2021.8 m
  5.5055 +1906.6 2025.9 1909.4 2032.6 1903.2 2034 C
  5.5056 +1902.8 2034.1 1902.4 2033.9 1902 2033.8 C
  5.5057 +1897.9 2028.5 1891.6 2023.8 1887.4 2018.7 C
  5.5058 +1887.4 2017.7 1887.4 2016.6 1887.4 2015.6 C
  5.5059 +1887 2016.3 1887.2 2017.8 1887.2 2018.9 C
  5.5060 +1892.3 2024.4 1897.5 2028.5 1902.5 2034.3 C
  5.5061 +1904.3 2033.6 1905.7 2032 1907.3 2030.9 C
  5.5062 +1907.3 2027.9 1907.3 2024.9 1907.3 2021.8 C
  5.5063 +f 
  5.5064 +S 
  5.5065 +n
  5.5066 +1933.7 2023.2 m
  5.5067 +1932 2021.7 1931.1 2024.9 1929.4 2024.9 C
  5.5068 +1931.2 2024.7 1932.4 2021.5 1933.7 2023.2 C
  5.5069 +f 
  5.5070 +S 
  5.5071 +n
  5.5072 +1989.2 2024.4 m
  5.5073 +1987.4 2023.7 1985.8 2022.2 1985.1 2020.4 C
  5.5074 +1984.6 2020.1 1986 2018.9 1985.1 2019.2 C
  5.5075 +1985.6 2020.8 1984.1 2019.4 1984.6 2021.1 C
  5.5076 +1986.3 2022.3 1988.1 2025.3 1989.2 2024.4 C
  5.5077 +f 
  5.5078 +S 
  5.5079 +n
  5.5080 +1904.4 2031.9 m
  5.5081 +1903 2029.7 1905.3 2027.7 1904.2 2025.9 C
  5.5082 +1904.5 2025 1903.7 2023 1904 2021.3 C
  5.5083 +1904 2022.3 1903.2 2022 1902.5 2022 C
  5.5084 +1901.3 2022.3 1902.2 2020.1 1901.6 2019.6 C
  5.5085 +1902.5 2019.8 1902.6 2018.3 1903.5 2018.9 C
  5.5086 +1903.7 2021.8 1905.6 2016.8 1905.6 2020.6 C
  5.5087 +1905.9 2020 1906.3 2020.8 1906.1 2021.1 C
  5.5088 +1905.8 2022.7 1906.7 2020.4 1906.4 2019.9 C
  5.5089 +1906.4 2018.5 1908.2 2017.8 1906.8 2016.5 C
  5.5090 +1906.9 2015.7 1907.7 2017.1 1907.1 2016.3 C
  5.5091 +1908.5 2015.8 1910.3 2015.1 1911.6 2016 C
  5.5092 +1912.2 2016.2 1911.9 2018 1911.6 2018 C
  5.5093 +1914.5 2017.1 1910.4 2013.6 1913.3 2013.4 C
  5.5094 +1912.4 2011.3 1910.5 2011.8 1909.5 2010 C
  5.5095 +1910 2010.5 1909 2010.8 1908.8 2011.2 C
  5.5096 +1907.5 2009.9 1906.1 2011.7 1904.9 2011.5 C
  5.5097 +1904.7 2010.9 1904.3 2010.5 1904.4 2009.8 C
  5.5098 +1905 2010.2 1904.6 2008.6 1905.4 2008.1 C
  5.5099 +1906.6 2007.5 1907.7 2008.4 1908.5 2007.4 C
  5.5100 +1908.9 2008.5 1909.7 2008.1 1909 2007.2 C
  5.5101 +1908.1 2006.5 1905.9 2007.3 1905.4 2007.4 C
  5.5102 +1903.9 2007.3 1905.2 2008.5 1904.2 2008.4 C
  5.5103 +1904.6 2009.9 1902.8 2010.3 1902.3 2010.5 C
  5.5104 +1901.5 2009.9 1900.4 2010 1899.4 2010 C
  5.5105 +1898.6 2011.2 1898.2 2013.4 1896.5 2013.4 C
  5.5106 +1896 2012.9 1894.4 2012.9 1893.6 2012.9 C
  5.5107 +1893.1 2013.9 1892.9 2015.5 1891.5 2016 C
  5.5108 +1890.3 2016.1 1889.2 2014 1888.6 2015.8 C
  5.5109 +1890 2016 1891 2016.9 1892.9 2016.5 C
  5.5110 +1894.1 2017.2 1892.8 2018.3 1893.2 2018.9 C
  5.5111 +1892.6 2018.9 1891.1 2019.8 1890.5 2020.6 C
  5.5112 +1891.1 2023.6 1893.2 2019.8 1893.9 2022.5 C
  5.5113 +1894.1 2023.3 1892.7 2023.6 1893.9 2024 C
  5.5114 +1894.2 2024.3 1897.4 2023.8 1896.5 2026.1 C
  5.5115 +1896 2025.6 1897.4 2028.1 1897.5 2027.1 C
  5.5116 +1898.4 2027.4 1899.3 2027 1899.6 2028.5 C
  5.5117 +1899.5 2028.6 1899.4 2028.8 1899.2 2028.8 C
  5.5118 +1899.3 2029.2 1899.6 2029.8 1900.1 2030.2 C
  5.5119 +1900.4 2029.6 1901 2030 1901.8 2030.2 C
  5.5120 +1903.1 2032.1 1900.4 2031.5 1902.8 2033.1 C
  5.5121 +1903.3 2032.7 1904.5 2032 1904.4 2031.9 C
  5.5122 +[0.21 0.21 0 0]  vc
  5.5123 +f 
  5.5124 +S 
  5.5125 +n
  5.5126 +1909.2 2019.4 m
  5.5127 +1908.8 2020.3 1910.2 2019.8 1909.2 2019.2 C
  5.5128 +1908.3 2019.3 1907.6 2020.2 1907.6 2021.3 C
  5.5129 +1908.5 2021 1907.6 2019 1909.2 2019.4 C
  5.5130 +[0.18 0.18 0 0.78]  vc
  5.5131 +f 
  5.5132 +S 
  5.5133 +n
  5.5134 +1915.5 2015.6 m
  5.5135 +1913.5 2016.3 1912.4 2016.8 1911.4 2018.4 C
  5.5136 +1912.5 2017.2 1914 2015.7 1915.5 2015.6 C
  5.5137 +[0.4 0.4 0 0]  vc
  5.5138 +f 
  5.5139 +S 
  5.5140 +n
  5.5141 +1915.5 2016.5 m
  5.5142 +1915.1 2016.4 1913.8 2016.6 1913.3 2017.5 C
  5.5143 +1913.7 2017 1914.5 2016.2 1915.5 2016.5 C
  5.5144 +[0.18 0.18 0 0.78]  vc
  5.5145 +f 
  5.5146 +S 
  5.5147 +n
  5.5148 +vmrs
  5.5149 +1887.4 2012.7 m
  5.5150 +1887.3 2007 1887.2 2001.3 1887.2 1995.6 C
  5.5151 +1887.2 2001.3 1887.3 2007 1887.4 2012.7 C
  5.5152 +[0.18 0.18 0 0.78]  vc
  5.5153 +f 
  5.5154 +0.4 w
  5.5155 +2 J
  5.5156 +2 M
  5.5157 +S 
  5.5158 +n
  5.5159 +1935.9 2007.4 m
  5.5160 +1936.2 2007.8 1935.8 2007.9 1936.6 2007.9 C
  5.5161 +1935.9 2007.9 1936.1 2006.7 1935.2 2007.2 C
  5.5162 +1935.2 2008.1 1934.1 2007.9 1934.2 2008.8 C
  5.5163 +1935 2008.7 1934.6 2006.9 1935.9 2007.4 C
  5.5164 +f 
  5.5165 +S 
  5.5166 +n
  5.5167 +1942.1 2003.6 m
  5.5168 +1940.1 2004.3 1939.1 2004.8 1938 2006.4 C
  5.5169 +1939.1 2005.2 1940.6 2003.7 1942.1 2003.6 C
  5.5170 +[0.4 0.4 0 0]  vc
  5.5171 +f 
  5.5172 +S 
  5.5173 +n
  5.5174 +1942.1 2004.5 m
  5.5175 +1941.8 2004.4 1940.4 2004.6 1940 2005.5 C
  5.5176 +1940.4 2005 1941.2 2004.2 1942.1 2004.5 C
  5.5177 +[0.18 0.18 0 0.78]  vc
  5.5178 +f 
  5.5179 +S 
  5.5180 +n
  5.5181 +1914 2000.7 m
  5.5182 +1914 1995 1913.9 1989.3 1913.8 1983.6 C
  5.5183 +1913.9 1989.3 1914 1995 1914 2000.7 C
  5.5184 +f 
  5.5185 +S 
  5.5186 +n
  5.5187 +1941.6 1998.3 m
  5.5188 +1943.4 2001.9 1942.4 1996 1940.9 1998.3 C
  5.5189 +1941.2 1998.3 1941.4 1998.3 1941.6 1998.3 C
  5.5190 +f 
  5.5191 +S 
  5.5192 +n
  5.5193 +1954.8 1989.9 m
  5.5194 +1953.9 1989.6 1954.7 1991.6 1953.9 1991.1 C
  5.5195 +1954.5 1993.1 1953.6 1998 1954.6 1993.2 C
  5.5196 +1954 1992.2 1954.7 1990.7 1954.8 1989.9 C
  5.5197 +f 
  5.5198 +S 
  5.5199 +n
  5.5200 +1947.6 1992.5 m
  5.5201 +1946.2 1993.5 1944.9 1993 1944.8 1994.7 C
  5.5202 +1945.5 1994 1947 1992.2 1947.6 1992.5 C
  5.5203 +f 
  5.5204 +S 
  5.5205 +n
  5.5206 +1910.7 1982.2 m
  5.5207 +1910.3 1981.8 1909.7 1982 1909.2 1982 C
  5.5208 +1909.7 1982 1910.3 1981.9 1910.7 1982.2 C
  5.5209 +1911 1987.1 1910 1992.6 1910.7 1997.3 C
  5.5210 +1910.7 1992.3 1910.7 1987.2 1910.7 1982.2 C
  5.5211 +[0.65 0.65 0 0.42]  vc
  5.5212 +f 
  5.5213 +S 
  5.5214 +n
  5.5215 +1910.9 1992.8 m
  5.5216 +1910.9 1991.3 1910.9 1989.7 1910.9 1988.2 C
  5.5217 +1910.9 1989.7 1910.9 1991.3 1910.9 1992.8 C
  5.5218 +[0.18 0.18 0 0.78]  vc
  5.5219 +f 
  5.5220 +S 
  5.5221 +n
  5.5222 +vmrs
  5.5223 +1953.6 1983.6 m
  5.5224 +1954.1 1985.3 1953.2 1988.6 1954.8 1989.4 C
  5.5225 +1954.1 1987.9 1954.4 1985.4 1953.6 1983.6 C
  5.5226 +[0.18 0.18 0 0.78]  vc
  5.5227 +f 
  5.5228 +0.4 w
  5.5229 +2 J
  5.5230 +2 M
  5.5231 +S 
  5.5232 +n
  5.5233 +1910.7 1982 m
  5.5234 +1911.6 1982.9 1911 1984.4 1911.2 1985.6 C
  5.5235 +1911 1984.4 1911.6 1982.9 1910.7 1982 C
  5.5236 +f 
  5.5237 +S 
  5.5238 +n
  5.5239 +1947.2 1979.6 m
  5.5240 +1947.5 1980.6 1948.3 1980.6 1947.4 1979.6 C
  5.5241 +1946.2 1979.4 1945.7 1978.8 1947.2 1979.6 C
  5.5242 +f 
  5.5243 +S 
  5.5244 +n
  5.5245 +1930.4 2061.4 m
  5.5246 +1930.4 2058 1930.4 2053.5 1930.4 2051.1 C
  5.5247 +1930.7 2054.6 1929.8 2057.4 1930.1 2061.2 C
  5.5248 +1929.5 2061.9 1929.7 2061.2 1930.4 2061.4 C
  5.5249 +[0.65 0.65 0 0.42]  vc
  5.5250 +f 
  5.5251 +S 
  5.5252 +n
  5.5253 +1939.5 2044.8 m
  5.5254 +1940 2041.5 1935.2 2044.3 1936.4 2040.8 C
  5.5255 +1934.9 2040.9 1934.1 2039.7 1933.5 2038.6 C
  5.5256 +1933.3 2035.4 1933.2 2040 1934 2040.3 C
  5.5257 +1936.2 2040.6 1936.3 2043.6 1938.5 2043.4 C
  5.5258 +1939.7 2044.2 1939.4 2045.6 1938.3 2046.5 C
  5.5259 +1939.1 2046.6 1939.6 2045.6 1939.5 2044.8 C
  5.5260 +f 
  5.5261 +S 
  5.5262 +n
  5.5263 +1910.4 2045.3 m
  5.5264 +1910.4 2039.5 1910.4 2033.6 1910.4 2027.8 C
  5.5265 +1910.4 2033.6 1910.4 2039.5 1910.4 2045.3 C
  5.5266 +f 
  5.5267 +S 
  5.5268 +n
  5.5269 +1906.8 2030.9 m
  5.5270 +1907.6 2026.8 1905 2020.8 1909 2018.7 C
  5.5271 +1906.5 2018.9 1906.8 2022.4 1906.8 2024.7 C
  5.5272 +1906.4 2028.2 1907.9 2032 1903 2033.8 C
  5.5273 +1902.2 2034 1903.8 2033.4 1904.2 2033.1 C
  5.5274 +1905.1 2032.4 1905.9 2031.5 1906.8 2030.9 C
  5.5275 +[0.07 0.06 0 0.58]  vc
  5.5276 +f 
  5.5277 +S 
  5.5278 +n
  5.5279 +1907.1 2030.7 m
  5.5280 +1907.1 2028.8 1907.1 2027 1907.1 2025.2 C
  5.5281 +1907.1 2027 1907.1 2028.8 1907.1 2030.7 C
  5.5282 +[0.65 0.65 0 0.42]  vc
  5.5283 +f 
  5.5284 +S 
  5.5285 +n
  5.5286 +1932 2023.2 m
  5.5287 +1932.2 2023.6 1931.7 2023.7 1931.6 2024 C
  5.5288 +1932 2023.7 1932.3 2022.8 1933 2023 C
  5.5289 +1933.9 2024.3 1933.3 2026.2 1933.5 2027.8 C
  5.5290 +1933.5 2026.4 1934.9 2022.2 1932 2023.2 C
  5.5291 +f 
  5.5292 +S 
  5.5293 +n
  5.5294 +2026.1 2021.6 m
  5.5295 +2026.1 2020.8 2026.1 2019.9 2026.1 2019.2 C
  5.5296 +2026.1 2019.9 2026.1 2020.8 2026.1 2021.6 C
  5.5297 +f 
  5.5298 +S 
  5.5299 +n
  5.5300 +vmrs
  5.5301 +1934.2 2018.9 m
  5.5302 +1934.2 2015.5 1934.2 2011 1934.2 2008.6 C
  5.5303 +1934.5 2012.1 1933.7 2014.9 1934 2018.7 C
  5.5304 +1933.4 2019.5 1933.5 2018.7 1934.2 2018.9 C
  5.5305 +[0.65 0.65 0 0.42]  vc
  5.5306 +f 
  5.5307 +0.4 w
  5.5308 +2 J
  5.5309 +2 M
  5.5310 +S 
  5.5311 +n
  5.5312 +1887.6 2014.8 m
  5.5313 +1887.6 2009 1887.6 2003.1 1887.6 1997.3 C
  5.5314 +1887.6 2003.1 1887.6 2009 1887.6 2014.8 C
  5.5315 +f 
  5.5316 +S 
  5.5317 +n
  5.5318 +1914.3 2002.8 m
  5.5319 +1914.3 1997 1914.3 1991.1 1914.3 1985.3 C
  5.5320 +1914.3 1991.1 1914.3 1997 1914.3 2002.8 C
  5.5321 +f 
  5.5322 +S 
  5.5323 +n
  5.5324 +1995.4 1992.3 m
  5.5325 +1995.4 1991.5 1995.4 1990.7 1995.4 1989.9 C
  5.5326 +1995.4 1990.7 1995.4 1991.5 1995.4 1992.3 C
  5.5327 +f 
  5.5328 +S 
  5.5329 +n
  5.5330 +1896 1988.4 m
  5.5331 +1896.9 1988 1897.8 1987.7 1898.7 1987.2 C
  5.5332 +1897.8 1987.7 1896.9 1988 1896 1988.4 C
  5.5333 +f 
  5.5334 +S 
  5.5335 +n
  5.5336 +1899.4 1986.8 m
  5.5337 +1900.4 1986.3 1901.3 1985.8 1902.3 1985.3 C
  5.5338 +1901.3 1985.8 1900.4 1986.3 1899.4 1986.8 C
  5.5339 +f 
  5.5340 +S 
  5.5341 +n
  5.5342 +1902.8 1985.1 m
  5.5343 +1905.2 1984 1905.2 1984 1902.8 1985.1 C
  5.5344 +f 
  5.5345 +S 
  5.5346 +n
  5.5347 +1949.1 1983.4 m
  5.5348 +1950.2 1984.4 1947.8 1984.6 1949.3 1985.1 C
  5.5349 +1949.5 1984.4 1949.6 1984.1 1949.1 1983.4 C
  5.5350 +[0.07 0.06 0 0.58]  vc
  5.5351 +f 
  5.5352 +S 
  5.5353 +n
  5.5354 +1906.1 1983.4 m
  5.5355 +1908.6 1982 1908.6 1982 1906.1 1983.4 C
  5.5356 +[0.65 0.65 0 0.42]  vc
  5.5357 +f 
  5.5358 +S 
  5.5359 +n
  5.5360 +1922.7 1976.4 m
  5.5361 +1923.6 1976 1924.4 1975.7 1925.3 1975.2 C
  5.5362 +1924.4 1975.7 1923.6 1976 1922.7 1976.4 C
  5.5363 +f 
  5.5364 +S 
  5.5365 +n
  5.5366 +vmrs
  5.5367 +1926 1974.8 m
  5.5368 +1927 1974.3 1928 1973.8 1928.9 1973.3 C
  5.5369 +1928 1973.8 1927 1974.3 1926 1974.8 C
  5.5370 +[0.65 0.65 0 0.42]  vc
  5.5371 +f 
  5.5372 +0.4 w
  5.5373 +2 J
  5.5374 +2 M
  5.5375 +S 
  5.5376 +n
  5.5377 +1929.4 1973.1 m
  5.5378 +1931.9 1972 1931.9 1972 1929.4 1973.1 C
  5.5379 +f 
  5.5380 +S 
  5.5381 +n
  5.5382 +1932.8 1971.4 m
  5.5383 +1935.3 1970 1935.3 1970 1932.8 1971.4 C
  5.5384 +f 
  5.5385 +S 
  5.5386 +n
  5.5387 +1949.6 2097.2 m
  5.5388 +1951.1 2096.4 1952.6 2095.5 1954.1 2094.8 C
  5.5389 +1952.6 2095.5 1951.1 2096.4 1949.6 2097.2 C
  5.5390 +[0.07 0.06 0 0.58]  vc
  5.5391 +f 
  5.5392 +S 
  5.5393 +n
  5.5394 +1955.1 2094.3 m
  5.5395 +1956.7 2093.5 1958.3 2092.7 1959.9 2091.9 C
  5.5396 +1958.3 2092.7 1956.7 2093.5 1955.1 2094.3 C
  5.5397 +f 
  5.5398 +S 
  5.5399 +n
  5.5400 +1960.4 2091.6 m
  5.5401 +1961.3 2091.2 1962.1 2090.9 1963 2090.4 C
  5.5402 +1962.1 2090.9 1961.3 2091.2 1960.4 2091.6 C
  5.5403 +f 
  5.5404 +S 
  5.5405 +n
  5.5406 +1963.5 2090.2 m
  5.5407 +1964.4 2089.7 1965.2 2089.2 1966.1 2088.8 C
  5.5408 +1965.2 2089.2 1964.4 2089.7 1963.5 2090.2 C
  5.5409 +f 
  5.5410 +S 
  5.5411 +n
  5.5412 +1966.6 2088.5 m
  5.5413 +1969.5 2087.1 1972.4 2085.8 1975.2 2084.4 C
  5.5414 +1972.4 2085.8 1969.5 2087.1 1966.6 2088.5 C
  5.5415 +f 
  5.5416 +S 
  5.5417 +n
  5.5418 +1965.2 2086.1 m
  5.5419 +1965.9 2085.7 1966.8 2085.3 1967.6 2084.9 C
  5.5420 +1966.8 2085.3 1965.9 2085.7 1965.2 2086.1 C
  5.5421 +f 
  5.5422 +S 
  5.5423 +n
  5.5424 +1968.3 2084.7 m
  5.5425 +1969.2 2084.3 1970 2083.9 1970.9 2083.5 C
  5.5426 +1970 2083.9 1969.2 2084.3 1968.3 2084.7 C
  5.5427 +f 
  5.5428 +S 
  5.5429 +n
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  5.5431 +1984.1 2084 m
  5.5432 +1985.6 2083.2 1987.2 2082.3 1988.7 2081.6 C
  5.5433 +1987.2 2082.3 1985.6 2083.2 1984.1 2084 C
  5.5434 +[0.07 0.06 0 0.58]  vc
  5.5435 +f 
  5.5436 +0.4 w
  5.5437 +2 J
  5.5438 +2 M
  5.5439 +S 
  5.5440 +n
  5.5441 +1976 2078.7 m
  5.5442 +1978.1 2080.1 1980 2082 1982 2083.7 C
  5.5443 +1980 2081.9 1977.9 2080.3 1976 2078.2 C
  5.5444 +1975.5 2079.9 1975.8 2081.9 1975.7 2083.7 C
  5.5445 +1975.8 2082 1975.5 2080.2 1976 2078.7 C
  5.5446 +f 
  5.5447 +S 
  5.5448 +n
  5.5449 +1989.6 2081.1 m
  5.5450 +1991.3 2080.3 1992.8 2079.5 1994.4 2078.7 C
  5.5451 +1992.8 2079.5 1991.3 2080.3 1989.6 2081.1 C
  5.5452 +f 
  5.5453 +S 
  5.5454 +n
  5.5455 +1933.2 2074.6 m
  5.5456 +1932.4 2076.2 1932.8 2077.5 1933 2078.7 C
  5.5457 +1933 2077.6 1932.9 2074.8 1933.2 2074.6 C
  5.5458 +f 
  5.5459 +S 
  5.5460 +n
  5.5461 +1994.9 2078.4 m
  5.5462 +1995.8 2078 1996.7 2077.7 1997.6 2077.2 C
  5.5463 +1996.7 2077.7 1995.8 2078 1994.9 2078.4 C
  5.5464 +f 
  5.5465 +S 
  5.5466 +n
  5.5467 +1998 2077 m
  5.5468 +1998.9 2076.5 1999.8 2076 2000.7 2075.6 C
  5.5469 +1999.8 2076 1998.9 2076.5 1998 2077 C
  5.5470 +f 
  5.5471 +S 
  5.5472 +n
  5.5473 +2001.2 2075.3 m
  5.5474 +2004 2073.9 2006.9 2072.6 2009.8 2071.2 C
  5.5475 +2006.9 2072.6 2004 2073.9 2001.2 2075.3 C
  5.5476 +f 
  5.5477 +S 
  5.5478 +n
  5.5479 +1980.5 2060.7 m
  5.5480 +1979.9 2060.7 1976.7 2062.8 1975.7 2064.5 C
  5.5481 +1975.7 2067.5 1975.7 2070.5 1975.7 2073.4 C
  5.5482 +1976.3 2068.7 1973.9 2061.6 1980.5 2060.7 C
  5.5483 +f 
  5.5484 +S 
  5.5485 +n
  5.5486 +1999.7 2072.9 m
  5.5487 +2000.5 2072.5 2001.3 2072.1 2002.1 2071.7 C
  5.5488 +2001.3 2072.1 2000.5 2072.5 1999.7 2072.9 C
  5.5489 +f 
  5.5490 +S 
  5.5491 +n
  5.5492 +2002.8 2071.5 m
  5.5493 +2003.7 2071.1 2004.6 2070.7 2005.5 2070.3 C
  5.5494 +2004.6 2070.7 2003.7 2071.1 2002.8 2071.5 C
  5.5495 +f 
  5.5496 +S 
  5.5497 +n
  5.5498 +vmrs
  5.5499 +2015.1 2047.5 m
  5.5500 +2014.4 2047.5 2011.2 2049.6 2010.3 2051.3 C
  5.5501 +2010.3 2057.7 2010.3 2064.1 2010.3 2070.5 C
  5.5502 +2010.3 2063.9 2010.1 2057.1 2010.5 2050.6 C
  5.5503 +2012 2049.3 2013.5 2048.3 2015.1 2047.5 C
  5.5504 +[0.07 0.06 0 0.58]  vc
  5.5505 +f 
  5.5506 +0.4 w
  5.5507 +2 J
  5.5508 +2 M
  5.5509 +S 
  5.5510 +n
  5.5511 +1910.4 2049.2 m
  5.5512 +1914.8 2054.3 1920.7 2058.9 1925.1 2064 C
  5.5513 +1920.4 2058.6 1915.1 2054.6 1910.4 2049.2 C
  5.5514 +f 
  5.5515 +S 
  5.5516 +n
  5.5517 +1988.2 2057.3 m
  5.5518 +1989.1 2056.8 1989.9 2056.2 1990.8 2055.6 C
  5.5519 +1989.9 2056.2 1989.1 2056.8 1988.2 2057.3 C
  5.5520 +f 
  5.5521 +S 
  5.5522 +n
  5.5523 +1991.6 2051.3 m
  5.5524 +1991.6 2046.3 1991.6 2041.2 1991.6 2036.2 C
  5.5525 +1991.6 2041.2 1991.6 2046.3 1991.6 2051.3 C
  5.5526 +f 
  5.5527 +S 
  5.5528 +n
  5.5529 +1935.6 2047.5 m
  5.5530 +1932.9 2051.7 1939.7 2043.8 1935.6 2047.5 C
  5.5531 +f 
  5.5532 +S 
  5.5533 +n
  5.5534 +1938.8 2043.9 m
  5.5535 +1938.1 2043.3 1938.2 2043.7 1937.3 2043.4 C
  5.5536 +1938.7 2043 1938.2 2044.9 1939 2045.3 C
  5.5537 +1938.2 2045.3 1938.7 2046.6 1937.8 2046.5 C
  5.5538 +1939.1 2046.2 1939.1 2044.5 1938.8 2043.9 C
  5.5539 +f 
  5.5540 +S 
  5.5541 +n
  5.5542 +1972.4 2045.6 m
  5.5543 +1973.4 2045 1974.5 2044.4 1975.5 2043.9 C
  5.5544 +1974.5 2044.4 1973.4 2045 1972.4 2045.6 C
  5.5545 +f 
  5.5546 +S 
  5.5547 +n
  5.5548 +1969 2043.6 m
  5.5549 +1969.8 2043.2 1970.6 2042.9 1971.4 2042.4 C
  5.5550 +1970.6 2042.9 1969.8 2043.2 1969 2043.6 C
  5.5551 +f 
  5.5552 +S 
  5.5553 +n
  5.5554 +1972.1 2042.2 m
  5.5555 +1973 2041.8 1973.9 2041.4 1974.8 2041 C
  5.5556 +1973.9 2041.4 1973 2041.8 1972.1 2042.2 C
  5.5557 +f 
  5.5558 +S 
  5.5559 +n
  5.5560 +1906.6 2035 m
  5.5561 +1905 2034.7 1904.8 2036.6 1903.5 2036.9 C
  5.5562 +1904.9 2037 1905.8 2033.4 1907.1 2035.7 C
  5.5563 +1907.1 2037.2 1907.1 2038.6 1907.1 2040 C
  5.5564 +1906.9 2038.4 1907.5 2036.4 1906.6 2035 C
  5.5565 +f 
  5.5566 +S 
  5.5567 +n
  5.5568 +vmrs
  5.5569 +1937.1 2032.1 m
  5.5570 +1936.2 2033.7 1936.6 2035 1936.8 2036.2 C
  5.5571 +1936.8 2035.1 1936.8 2032.4 1937.1 2032.1 C
  5.5572 +[0.07 0.06 0 0.58]  vc
  5.5573 +f 
  5.5574 +0.4 w
  5.5575 +2 J
  5.5576 +2 M
  5.5577 +S 
  5.5578 +n
  5.5579 +1887.6 2018.7 m
  5.5580 +1892 2023.8 1897.9 2028.4 1902.3 2033.6 C
  5.5581 +1897.6 2028.1 1892.3 2024.1 1887.6 2018.7 C
  5.5582 +f 
  5.5583 +S 
  5.5584 +n
  5.5585 +1999.7 2031.4 m
  5.5586 +1998.7 2030.3 1997.6 2029.2 1996.6 2028 C
  5.5587 +1997.6 2029.2 1998.7 2030.3 1999.7 2031.4 C
  5.5588 +f 
  5.5589 +S 
  5.5590 +n
  5.5591 +1912.8 2017 m
  5.5592 +1910.6 2021.1 1913.6 2015.3 1914.5 2016 C
  5.5593 +1914 2016.3 1913.4 2016.7 1912.8 2017 C
  5.5594 +f 
  5.5595 +S 
  5.5596 +n
  5.5597 +1939.5 2005 m
  5.5598 +1936.7 2009.2 1943.6 2001.3 1939.5 2005 C
  5.5599 +f 
  5.5600 +S 
  5.5601 +n
  5.5602 +1942.6 2001.4 m
  5.5603 +1941.9 2000.8 1942 2001.2 1941.2 2000.9 C
  5.5604 +1942.5 2000.6 1942.1 2002.4 1942.8 2002.8 C
  5.5605 +1942 2002.8 1942.5 2004.1 1941.6 2004 C
  5.5606 +1943 2003.7 1942.9 2002.1 1942.6 2001.4 C
  5.5607 +f 
  5.5608 +S 
  5.5609 +n
  5.5610 +2006.2 2000.7 m
  5.5611 +2005.4 2001.5 2004 2002.8 2004 2002.8 C
  5.5612 +2004.5 2002.4 2005.5 2001.4 2006.2 2000.7 C
  5.5613 +f 
  5.5614 +S 
  5.5615 +n
  5.5616 +1998.5 2001.6 m
  5.5617 +1997.7 2002 1996.8 2002.4 1995.9 2002.6 C
  5.5618 +1995.5 1999.3 1995.7 1995.7 1995.6 1992.3 C
  5.5619 +1995.6 1995.7 1995.6 1999.2 1995.6 2002.6 C
  5.5620 +1996.6 2002.4 1997.7 2002.2 1998.5 2001.6 C
  5.5621 +[0.4 0.4 0 0]  vc
  5.5622 +f 
  5.5623 +S 
  5.5624 +n
  5.5625 +1996.1 2002.8 m
  5.5626 +1995.9 2002.8 1995.8 2002.8 1995.6 2002.8 C
  5.5627 +1995.2 1999.5 1995.5 1995.9 1995.4 1992.5 C
  5.5628 +1995.4 1995.9 1995.4 1999.4 1995.4 2002.8 C
  5.5629 +1996.4 2003.1 1998.2 2001.6 1996.1 2002.8 C
  5.5630 +[0.07 0.06 0 0.58]  vc
  5.5631 +f 
  5.5632 +S 
  5.5633 +n
  5.5634 +1969 2002.1 m
  5.5635 +1968 2001 1966.9 1999.9 1965.9 1998.8 C
  5.5636 +1966.9 1999.9 1968 2001 1969 2002.1 C
  5.5637 +f 
  5.5638 +S 
  5.5639 +n
  5.5640 +vmrs
  5.5641 +2000 2001.2 m
  5.5642 +2002.1 2000 2004.1 1998.9 2006.2 1997.8 C
  5.5643 +2004.1 1998.9 2002.1 2000 2000 2001.2 C
  5.5644 +[0.07 0.06 0 0.58]  vc
  5.5645 +f 
  5.5646 +0.4 w
  5.5647 +2 J
  5.5648 +2 M
  5.5649 +S 
  5.5650 +n
  5.5651 +1895.8 1984.8 m
  5.5652 +1898.3 1983.6 1900.8 1982.3 1903.2 1981 C
  5.5653 +1900.8 1982.3 1898.3 1983.6 1895.8 1984.8 C
  5.5654 +f 
  5.5655 +S 
  5.5656 +n
  5.5657 +1905.2 1980.3 m
  5.5658 +1906.4 1979.9 1907.6 1979.5 1908.8 1979.1 C
  5.5659 +1907.6 1979.5 1906.4 1979.9 1905.2 1980.3 C
  5.5660 +f 
  5.5661 +S 
  5.5662 +n
  5.5663 +1964.7 1977.4 m
  5.5664 +1963.8 1977.5 1962.5 1980.2 1960.8 1980 C
  5.5665 +1962.5 1980.2 1963.3 1978 1964.7 1977.4 C
  5.5666 +f 
  5.5667 +S 
  5.5668 +n
  5.5669 +1952 1979.6 m
  5.5670 +1955.2 1979.2 1955.2 1979.2 1952 1979.6 C
  5.5671 +f 
  5.5672 +S 
  5.5673 +n
  5.5674 +1937.8 1966.4 m
  5.5675 +1941.2 1969.5 1946.1 1976.4 1951.5 1979.3 C
  5.5676 +1946.1 1976.7 1942.8 1970.4 1937.8 1966.4 C
  5.5677 +f 
  5.5678 +S 
  5.5679 +n
  5.5680 +1911.9 1978.6 m
  5.5681 +1914.3 1977.4 1916.7 1976.2 1919.1 1975 C
  5.5682 +1916.7 1976.2 1914.3 1977.4 1911.9 1978.6 C
  5.5683 +f 
  5.5684 +S 
  5.5685 +n
  5.5686 +1975.5 1971.4 m
  5.5687 +1974.6 1972.2 1973.3 1973.6 1973.3 1973.6 C
  5.5688 +1973.7 1973.1 1974.8 1972.1 1975.5 1971.4 C
  5.5689 +f 
  5.5690 +S 
  5.5691 +n
  5.5692 +1922.4 1972.8 m
  5.5693 +1924.9 1971.6 1927.4 1970.3 1929.9 1969 C
  5.5694 +1927.4 1970.3 1924.9 1971.6 1922.4 1972.8 C
  5.5695 +f 
  5.5696 +S 
  5.5697 +n
  5.5698 +1969.2 1971.9 m
  5.5699 +1971.1 1970.9 1972.9 1969.8 1974.8 1968.8 C
  5.5700 +1972.9 1969.8 1971.1 1970.9 1969.2 1971.9 C
  5.5701 +f 
  5.5702 +S 
  5.5703 +n
  5.5704 +vmrs
  5.5705 +1931.8 1968.3 m
  5.5706 +1933 1967.9 1934.2 1967.5 1935.4 1967.1 C
  5.5707 +1934.2 1967.5 1933 1967.9 1931.8 1968.3 C
  5.5708 +[0.07 0.06 0 0.58]  vc
  5.5709 +f 
  5.5710 +0.4 w
  5.5711 +2 J
  5.5712 +2 M
  5.5713 +S 
  5.5714 +n
  5.5715 +1940.7 2072.4 m
  5.5716 +1941.5 2072.4 1942.3 2072.3 1943.1 2072.2 C
  5.5717 +1942.3 2072.3 1941.5 2072.4 1940.7 2072.4 C
  5.5718 +[0 0 0 0.18]  vc
  5.5719 +f 
  5.5720 +S 
  5.5721 +n
  5.5722 +1948.6 2069.3 m
  5.5723 +1947 2069.5 1945.7 2068.9 1944.8 2069.8 C
  5.5724 +1945.9 2068.5 1948.4 2070.2 1948.6 2069.3 C
  5.5725 +f 
  5.5726 +S 
  5.5727 +n
  5.5728 +1954.6 2066.4 m
  5.5729 +1954.7 2067.9 1955.6 2067.3 1955.6 2068.8 C
  5.5730 +1955.4 2067.8 1956 2066.6 1954.6 2066.4 C
  5.5731 +f 
  5.5732 +S 
  5.5733 +n
  5.5734 +1929.2 2061.2 m
  5.5735 +1927.8 2062.1 1926.3 2064.1 1924.8 2063.3 C
  5.5736 +1926.3 2064.6 1928 2062 1929.2 2061.2 C
  5.5737 +f 
  5.5738 +S 
  5.5739 +n
  5.5740 +1924.4 2067.4 m
  5.5741 +1918.5 2061.6 1912.7 2055.9 1906.8 2050.1 C
  5.5742 +1912.7 2055.9 1918.5 2061.6 1924.4 2067.4 C
  5.5743 +[0.4 0.4 0 0]  vc
  5.5744 +f 
  5.5745 +S 
  5.5746 +n
  5.5747 +1924.6 2062.8 m
  5.5748 +1923.9 2062.1 1923.2 2061.2 1922.4 2060.4 C
  5.5749 +1923.2 2061.2 1923.9 2062.1 1924.6 2062.8 C
  5.5750 +[0 0 0 0.18]  vc
  5.5751 +f 
  5.5752 +S 
  5.5753 +n
  5.5754 +1919.3 2057.3 m
  5.5755 +1917.5 2055.6 1915.7 2053.8 1913.8 2052 C
  5.5756 +1915.7 2053.8 1917.5 2055.6 1919.3 2057.3 C
  5.5757 +f 
  5.5758 +S 
  5.5759 +n
  5.5760 +1929.2 2055.2 m
  5.5761 +1929.2 2054.2 1929.2 2053.2 1929.2 2052.3 C
  5.5762 +1929.2 2053.2 1929.2 2054.2 1929.2 2055.2 C
  5.5763 +f 
  5.5764 +S 
  5.5765 +n
  5.5766 +1926.3 2049.6 m
  5.5767 +1925.4 2049 1925.4 2050.5 1924.4 2050.4 C
  5.5768 +1925.3 2051.3 1924.5 2051.9 1925.6 2052.5 C
  5.5769 +1926.9 2052.6 1926 2050.6 1926.3 2049.6 C
  5.5770 +f 
  5.5771 +S 
  5.5772 +n
  5.5773 +vmrs
  5.5774 +1911.2 2046.8 m
  5.5775 +1910.1 2048.9 1911.9 2050.1 1913.1 2051.3 C
  5.5776 +1912.1 2049.9 1910.6 2048.8 1911.2 2046.8 C
  5.5777 +[0 0 0 0.18]  vc
  5.5778 +f 
  5.5779 +0.4 w
  5.5780 +2 J
  5.5781 +2 M
  5.5782 +S 
  5.5783 +n
  5.5784 +1934 2048.7 m
  5.5785 +1932.6 2048.7 1930.1 2047.7 1929.6 2049.4 C
  5.5786 +1930.9 2048.6 1933.3 2049 1934 2048.7 C
  5.5787 +f 
  5.5788 +S 
  5.5789 +n
  5.5790 +1980 2048.4 m
  5.5791 +1979.5 2046.8 1976.3 2047.9 1977.2 2045.6 C
  5.5792 +1976.8 2045.1 1976.1 2044.7 1975.2 2044.8 C
  5.5793 +1973.7 2046 1976.3 2046.4 1976.7 2047.5 C
  5.5794 +1977.8 2047.2 1978.2 2050 1979.6 2049.2 C
  5.5795 +1980 2049 1979.6 2048.6 1980 2048.4 C
  5.5796 +f 
  5.5797 +S 
  5.5798 +n
  5.5799 +1938.3 2045.6 m
  5.5800 +1938.2 2044.4 1936.8 2043.8 1935.9 2043.4 C
  5.5801 +1936.4 2044.4 1939.1 2044.3 1937.6 2045.8 C
  5.5802 +1937 2046.1 1935.9 2046.1 1935.9 2046.8 C
  5.5803 +1936.7 2046.3 1937.8 2046.2 1938.3 2045.6 C
  5.5804 +f 
  5.5805 +S 
  5.5806 +n
  5.5807 +1932.5 2040 m
  5.5808 +1932.8 2038.1 1932 2038.9 1932.3 2040.3 C
  5.5809 +1933.1 2040.3 1932.7 2041.7 1933.7 2041.5 C
  5.5810 +1933.1 2041 1932.9 2040.5 1932.5 2040 C
  5.5811 +f 
  5.5812 +S 
  5.5813 +n
  5.5814 +2014.6 2035.2 m
  5.5815 +2014.1 2033.6 2010.9 2034.7 2011.7 2032.4 C
  5.5816 +2011.3 2031.9 2009.4 2030.7 2009.3 2032.1 C
  5.5817 +2009.5 2033.7 2012.9 2033.8 2012.4 2035.7 C
  5.5818 +2013 2036.4 2014.2 2036.5 2014.6 2035.2 C
  5.5819 +f 
  5.5820 +S 
  5.5821 +n
  5.5822 +1906.4 2030.7 m
  5.5823 +1905 2031.6 1903.5 2033.6 1902 2032.8 C
  5.5824 +1903.4 2034 1905.6 2031.4 1906.4 2030.7 C
  5.5825 +f 
  5.5826 +S 
  5.5827 +n
  5.5828 +1901.8 2037.2 m
  5.5829 +1899.5 2034.8 1897.2 2032.5 1894.8 2030.2 C
  5.5830 +1897.2 2032.5 1899.5 2034.8 1901.8 2037.2 C
  5.5831 +[0.4 0.4 0 0]  vc
  5.5832 +f 
  5.5833 +S 
  5.5834 +n
  5.5835 +1901.8 2032.4 m
  5.5836 +1901.1 2031.6 1900.4 2030.7 1899.6 2030 C
  5.5837 +1900.4 2030.7 1901.1 2031.6 1901.8 2032.4 C
  5.5838 +[0 0 0 0.18]  vc
  5.5839 +f 
  5.5840 +S 
  5.5841 +n
  5.5842 +1944.5 2030 m
  5.5843 +1945.3 2029.9 1946.1 2029.8 1946.9 2029.7 C
  5.5844 +1946.1 2029.8 1945.3 2029.9 1944.5 2030 C
  5.5845 +f 
  5.5846 +S 
  5.5847 +n
  5.5848 +vmrs
  5.5849 +1997.8 2027.8 m
  5.5850 +1997.7 2027.9 1997.6 2028.1 1997.3 2028 C
  5.5851 +1997.4 2029.1 1998.5 2029.5 1999.2 2030 C
  5.5852 +2000.1 2029.5 1998.9 2028 1997.8 2027.8 C
  5.5853 +[0 0 0 0.18]  vc
  5.5854 +f 
  5.5855 +0.4 w
  5.5856 +2 J
  5.5857 +2 M
  5.5858 +S 
  5.5859 +n
  5.5860 +1906.4 2029.2 m
  5.5861 +1906.4 2026.6 1906.4 2024 1906.4 2021.3 C
  5.5862 +1906.4 2024 1906.4 2026.6 1906.4 2029.2 C
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     6.1 Binary file doc-src/gfx/isabelle_nitpick.pdf has changed
     7.1 --- a/doc-src/manual.bib	Thu Oct 22 09:50:29 2009 +0200
     7.2 +++ b/doc-src/manual.bib	Thu Oct 22 14:45:20 2009 +0200
     7.3 @@ -49,7 +49,7 @@
     7.4  
     7.5  @Unpublished{abrial93,
     7.6    author	= {J. R. Abrial and G. Laffitte},
     7.7 -  title		= {Towards the Mechanization of the Proofs of some Classical
     7.8 +  title		= {Towards the Mechanization of the Proofs of Some Classical
     7.9  		  Theorems of Set Theory},
    7.10    note		= {preprint},
    7.11    year		= 1993,
    7.12 @@ -73,6 +73,17 @@
    7.13    crossref	= {types93},
    7.14    pages		= {213-237}}
    7.15  
    7.16 +@inproceedings{andersson-1993,
    7.17 +  author = "Arne Andersson",
    7.18 +  title = "Balanced Search Trees Made Simple",
    7.19 +  editor = "F. K. H. A. Dehne and N. Santoro and S. Whitesides",
    7.20 +  booktitle = "WADS 1993",
    7.21 +  series = LNCS,
    7.22 +  volume = {709},
    7.23 +  pages = "61--70",
    7.24 +  year = 1993,
    7.25 +  publisher = Springer}
    7.26 +
    7.27  @book{andrews86,
    7.28    author	= "Peter Andrews",
    7.29    title		= "An Introduction to Mathematical Logic and Type Theory: to Truth
    7.30 @@ -167,6 +178,15 @@
    7.31    author          = "Stefan Berghofer and Tobias Nipkow",
    7.32    pages           = "38--52"}
    7.33  
    7.34 +@inproceedings{berghofer-nipkow-2004,
    7.35 +  author = {Stefan Berghofer and Tobias Nipkow},
    7.36 +  title = {Random Testing in {I}sabelle/{HOL}},
    7.37 +  pages = {230--239},
    7.38 +  editor = "J. Cuellar and Z. Liu",
    7.39 +  booktitle = {{SEFM} 2004},
    7.40 +  publisher = IEEE,
    7.41 +  year = 2004}
    7.42 +
    7.43  @InProceedings{Berghofer-Nipkow:2002,
    7.44    author =       {Stefan Berghofer and Tobias Nipkow},
    7.45    title =        {Executing Higher Order Logic},
    7.46 @@ -200,6 +220,14 @@
    7.47  title="Introduction to Functional Programming using Haskell",
    7.48  publisher=PH,year=1998}
    7.49  
    7.50 +@inproceedings{blanchette-nipkow-2009,
    7.51 +  title = "Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder (Extended Abstract)",
    7.52 +  author = "Jasmin Christian Blanchette and Tobias Nipkow",
    7.53 +  booktitle = "{TAP} 2009: Short Papers",
    7.54 +  editor = "Catherine Dubois",
    7.55 +  publisher = "ETH Technical Report 630",
    7.56 +  year = 2009}
    7.57 +
    7.58  @Article{boyer86,
    7.59    author	= {Robert Boyer and Ewing Lusk and William McCune and Ross
    7.60  		   Overbeek and Mark Stickel and Lawrence Wos},
    7.61 @@ -241,7 +269,7 @@
    7.62  }
    7.63  
    7.64  @InProceedings{bulwahn-et-al:2008:imperative,
    7.65 -  author   = {Lukas Bulwahn and Alexander Krauss and Florian Haftmann and Levent Erkök and John Matthews},
    7.66 +  author   = {Lukas Bulwahn and Alexander Krauss and Florian Haftmann and Levent Erkök and John Matthews},
    7.67    title    = {Imperative Functional Programming with {Isabelle/HOL}},
    7.68    crossref = {tphols2008},
    7.69  }
    7.70 @@ -597,6 +625,12 @@
    7.71    year =    2003,
    7.72    note =    {\url{http://www.haskell.org/definition/}}}
    7.73  
    7.74 +@book{jackson-2006,
    7.75 +  author = "Daniel Jackson",
    7.76 +  title = "Software Abstractions: Logic, Language, and Analysis",
    7.77 +  publisher = MIT,
    7.78 +  year = 2006}
    7.79 +
    7.80  %K
    7.81  
    7.82  @InProceedings{kammueller-locales,
    7.83 @@ -878,10 +912,11 @@
    7.84  
    7.85  @Book{isa-tutorial,
    7.86    author	= {Tobias Nipkow and Lawrence C. Paulson and Markus Wenzel},
    7.87 -  title		= {Isabelle/HOL: A Proof Assistant for Higher-Order Logic},
    7.88 -  publisher	= {Springer},
    7.89 +  title		= {Isabelle/{HOL}: A Proof Assistant for Higher-Order Logic},
    7.90 +  publisher	= Springer,
    7.91    year		= 2002,
    7.92 -  note		= {LNCS Tutorial 2283}}
    7.93 +  series    = LNCS,
    7.94 +  volume    = 2283}
    7.95  
    7.96  @Article{noel,
    7.97    author	= {Philippe No{\"e}l},
    7.98 @@ -1021,7 +1056,7 @@
    7.99                     Essays in Honor of {Robin Milner}},
   7.100    booktitle	= {Proof, Language, and Interaction: 
   7.101                     Essays in Honor of {Robin Milner}},
   7.102 -  publisher	= {MIT Press},
   7.103 +  publisher	= MIT,
   7.104    year		= 2000,
   7.105    editor	= {Gordon Plotkin and Colin Stirling and Mads Tofte}}
   7.106  
   7.107 @@ -1236,6 +1271,12 @@
   7.108    number =       4
   7.109  }
   7.110  
   7.111 +@misc{sledgehammer-2009,
   7.112 +  key = "Sledgehammer",
   7.113 +  title = "The {S}ledgehammer: Let Automatic Theorem Provers
   7.114 +Write Your {I}s\-a\-belle Scripts",
   7.115 +  note = "\url{http://www.cl.cam.ac.uk/research/hvg/Isabelle/sledgehammer.html}"}
   7.116 +
   7.117  @inproceedings{slind-tfl,
   7.118    author	= {Konrad Slind},
   7.119    title		= {Function Definition in Higher Order Logic},
   7.120 @@ -1295,6 +1336,27 @@
   7.121  title={Haskell: The Craft of Functional Programming},
   7.122  publisher={Addison-Wesley},year=1999}
   7.123  
   7.124 +@misc{kodkod-2009,
   7.125 +  author = "Emina Torlak",
   7.126 +  title = {Kodkod: Constraint Solver for Relational Logic},
   7.127 +  note = "\url{http://alloy.mit.edu/kodkod/}"}
   7.128 +
   7.129 +@misc{kodkod-2009-options,
   7.130 +  author = "Emina Torlak",
   7.131 +  title = "Kodkod {API}: Class {Options}",
   7.132 +  note = "\url{http://alloy.mit.edu/kodkod/docs/kodkod/engine/config/Options.html}"}
   7.133 +
   7.134 +@inproceedings{torlak-jackson-2007,
   7.135 +  title = "Kodkod: A Relational Model Finder",
   7.136 +  author = "Emina Torlak and Daniel Jackson",
   7.137 +  editor = "Orna Grumberg and Michael Huth",
   7.138 +  booktitle = "TACAS 2007",
   7.139 +  series = LNCS,
   7.140 +  volume = {4424},
   7.141 +  pages = "632--647",
   7.142 +  year = 2007,
   7.143 +  publisher = Springer}
   7.144 +
   7.145  @Unpublished{Trybulec:1993:MizarFeatures,
   7.146    author = 	 {A. Trybulec},
   7.147    title = 	 {Some Features of the {Mizar} Language},
   7.148 @@ -1320,6 +1382,13 @@
   7.149    year          = 1989
   7.150  }
   7.151  
   7.152 +@phdthesis{weber-2008,
   7.153 +  author = "Tjark Weber",
   7.154 +  title = "SAT-Based Finite Model Generation for Higher-Order Logic",
   7.155 +  school = {Dept.\ of Informatics, T.U. M\"unchen},
   7.156 +  type = "{Ph.D.}\ thesis",
   7.157 +  year = 2008}
   7.158 +
   7.159  @Misc{x-symbol,
   7.160    author =	 {Christoph Wedler},
   7.161    title =	 {Emacs package ``{X-Symbol}''},
   7.162 @@ -1570,7 +1639,7 @@
   7.163  			Essays in Honor of {Larry Wos}},
   7.164    booktitle	= {Automated Reasoning and its Applications: 
   7.165  			Essays in Honor of {Larry Wos}},
   7.166 -  publisher	= {MIT Press},
   7.167 +  publisher	= MIT,
   7.168    year		= 1997,
   7.169    editor	= {Robert Veroff}}
   7.170  
   7.171 @@ -1669,3 +1738,8 @@
   7.172    title         = {{ML} Modules and {Haskell} Type Classes: A Constructive Comparison},
   7.173    author        = {Stefan Wehr et. al.}
   7.174  }
   7.175 +
   7.176 +@misc{wikipedia-2009-aa-trees,
   7.177 +  key = "Wikipedia",
   7.178 +  title = "Wikipedia: {AA} Tree",
   7.179 +  note = "\url{http://en.wikipedia.org/wiki/AA_tree}"}