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265 lines
7.2 KiB
265 lines
7.2 KiB
%\input{util/ltl_macros}
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\newcommand{\dom}{\ensuremath\mathcal{A}}
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\newcommand{\boolDom}{\ensuremath\mathbb{B}}
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\newcommand{\N}{\ensuremath\mathbb{N}}
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%\newcommand{\Z}{\ensuremath\mathbb{Z}}
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\newcommand{\Q}{\ensuremath\mathbb{Q}}
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\newcommand{\R}{\ensuremath\mathbb{R}}
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\renewcommand{\phi}{\varphi}
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\renewcommand{\implies}{\rightarrow}
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\newcommand{\imp}{\rightarrow}
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\newcommand{\entails}{\enspace \vdash \enspace}
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%\newcommand{\model}{\enspace \vDash \enspace}
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\newcommand{\ent}{\enspace \vdash \enspace}
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\newcommand{\nmodel}{\enspace \nvDash \enspace}
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\newcommand{\nent}{\enspace \nvdash \enspace}
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\newcommand{\eqv}{\leftrightarrow}
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\newcommand{\biimp}{\leftrightarrow}
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\newcommand{\lxor}{\oplus}
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\newcommand{\nentails}{\nvdash}
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\newcommand{\nmodels}{\nvDash}
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\newcommand{\Model}{\ensuremath{\mathcal{M}}}
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\newcommand{\impi}{\ensuremath{\imp_i}}
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\newcommand{\impe}{\ensuremath{\imp_e}}
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\newcommand{\andi}{\ensuremath{\land_i}}
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\newcommand{\ande}{\ensuremath{\land_e}}
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\newcommand{\ori}{\ensuremath{\lor_i}}
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\newcommand{\ore}{\ensuremath{\lor_e}}
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\newcommand{\negi}{\ensuremath{\neg_i}}
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\newcommand{\nege}{\ensuremath{\neg_e}}
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\newcommand{\bote}{\ensuremath{\bot_e}\xspace}
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\newcommand{\negnege}{\ensuremath{\neg\neg_e}\xspace}
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\newcommand{\negnegi}{\ensuremath{\neg\neg_i}\xspace}
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\newcommand{\foralli}{\ensuremath{\forall_i}\xspace}
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\newcommand{\foralle}{\ensuremath{\forall_e}\xspace}
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\newcommand{\existi}{\ensuremath{\exists_i}\xspace}
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\newcommand{\existe}{\ensuremath{\exists_e}\xspace}
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\newcommand{\prem}{\text{\scriptsize premise}} %% \prem = premise
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\newcommand{\assum}{\text{\scriptsize assumption}} %% \assum = assumption
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\newcommand{\freshVar}[1]{\text{\scriptsize fresh~{#1}}}
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\newcommand{\MT}{\text{MT}~}
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\newcommand{\PBC}{\text{PBC}~}
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\newcommand{\LEM}{\text{LEM}}
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\newcommand{\copying}{\text{\scriptsize copy}~}
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\newcommand{\true}{\ensuremath{\top}}
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\newcommand{\false}{\ensuremath{\bot}}
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\newcommand{\F}{\textbf{F}}
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\newcommand{\T}{\textbf{T}}
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\newcommand{\variableOrder}[1]{
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\foreach\variable in {#1}
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{\ensuremath{~\variable<}}%% FIXME
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}
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% multiple choice itemize
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\newcommand{\ticked}{\ensuremath{\boxtimes}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% TSEITIN rules
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\newcommand{\tseitinOr}[3]{
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\def\CHI{#1}%
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\def\PHI{#2}%
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\def\PSI{#3}%
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\ensuremath{(\lnot \PHI \lor \CHI) \land (\lnot \PSI \lor \CHI) \land (\lnot \CHI \lor \PHI \lor \PSI)}%
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}
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\newcommand{\tseitinAnd}[3]{
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\def\CHI{#1}%
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\def\PHI{#2}%
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\def\PSI{#3}%
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\ensuremath{(\lnot \CHI \lor \PHI) \land (\lnot \CHI \lor \PSI) \land (\lnot \PHI \lor \lnot \PSI \lor \CHI)}%
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}
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\newcommand{\tseitinNot}[2]{
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\def\CHI{#1}%
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\def\PHI{#2}%
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\ensuremath{(\lnot \CHI \lor \lnot \PHI) \land (\CHI \lor \PHI)}%
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DPLL helper
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\newenvironment{dpllCNFInput}%
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{\begin{enumerate}[leftmargin=2.0em,itemindent=2.45em,label=Clause {\arabic*}:]}%
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{\end{enumerate}}%
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\newenvironment{dplltabular}[1]
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{\begin{tabular}{ |l|*{#1}{c|} } \hline}
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{\end{tabular}}
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\ExplSyntaxOn
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\NewDocumentCommand{\dpllrow}{m}
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{
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\seq_set_split:Nnn \l_row {|} { #1 }
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\seq_use:Nn \l_row { & }
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\\
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\hline
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}
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\seq_new:N \l_row % allocate a sequence
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\ExplSyntaxOff
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\newcommand{\dpllStep}[1]{
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Step & \dpllrow{#1}
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}
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\newcommand{\dpllDecL}[1]{
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Decision Level & \dpllrow{#1}
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}
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\newcommand{\dpllAssi}[1]{
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Assignment & \dpllrow{#1}
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}
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\newcommand{\dpllBCP}[1]{
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BCP & \dpllrow{#1}
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}
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\newcommand{\dpllPL}[1]{
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PL & \dpllrow{#1}
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}
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\newcommand{\dpllDeci}[1]{
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Decision & \dpllrow{#1}
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}
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\newcommand{\dpllClause}[3]{
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\def\ITEM{#1}%
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\def\CLAUSE{#2}%
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Cl. \ITEM: \CLAUSE & \dpllrow{#3}
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}
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\ExplSyntaxOn
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\NewDocumentCommand{\clause}{m}
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{
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\seq_set_split:Nnn \l_clause {;} { #1 }
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\seq_use:Nn \l_clause { \lor }
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}
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\seq_new:N \l_clause % allocate a sequence
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\ExplSyntaxOff
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\ExplSyntaxOn
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\NewDocumentCommand{\cube}{m}
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{
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\seq_set_split:Nnn \l_cube {;} { #1 }
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\seq_use:Nn \l_cube { \land }
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}
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\seq_new:N \l_cube % allocate a sequence
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\ExplSyntaxOff
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\newcommand{\cmark}{\ding{51}}
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\newcommand{\xmark}{\ding{55}}
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\newcommand{\done}{\cmark}
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\newcommand{\conflict}{\{\} \xmark}
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\NewEnviron{conflictgraph}[1][1.5cm]{%
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\begin{tikzpicture}[->,
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>=stealth',
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shorten >=1pt,
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auto,
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node distance=#1,
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thick,
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base node/.style={circle,draw,minimum size=20pt},
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real node/.style={double,circle,draw,minimum size=20pt}]
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\BODY
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\end{tikzpicture}
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}
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\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
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\node[shape=circle,draw,inner sep=1.5pt] (char) {#1};}}
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\tikzset{
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line/.style={-},
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dot/.style={decoration={
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markings,
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mark=at position #1 with {\draw circle (2pt);}},postaction={decorate}},
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fulldot/.style={decoration={
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markings,
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mark=at position #1 with {\fill circle (2pt);}},postaction={decorate}},
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}
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\newenvironment{scprooftree}[1]%
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{\gdef\scalefactor{#1}\begin{center}\proofSkipAmount \leavevmode}%
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{\scalebox{\scalefactor}{\DisplayProof}\proofSkipAmount \end{center} }
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\tikzset{
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line/.style={-},
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dot/.style={decoration={
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markings,
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mark=at position #1 with {\draw circle (2pt);}},postaction={decorate}},
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fulldot/.style={decoration={
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markings,
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mark=at position #1 with {\fill circle (2pt);}},postaction={decorate}},
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% BDD helper
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\newenvironment{cofactors}
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{\begin{tabbing}}
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{\end{tabbing}}
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\NewEnviron{bdd}[1][3em]{%
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\begin{tikzpicture}[node distance=#1,
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base node/.style={circle,draw,minimum size=20pt},
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func node/.style={rectangle,draw,minimum size=10pt},
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cofactor/.style={circle,draw,minimum size=10pt},
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phantom/.style={circle,draw,inner sep=0pt,minimum size=0pt}]
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\BODY
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\end{tikzpicture}
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}
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\newcommand{\funcEdge}[3][]{
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\path[] (#2) edge [#1] (#3);
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}
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\newcommand{\thenEdge}[3][]{
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\path[] (#2) edge [#1] (#3);
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}
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\newcommand{\elseEdge}[3][]{
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\path[] (#2) edge [#1] node [midway,draw,circle,fill=white,transform shape,inner sep=0pt,minimum size=0.3em] (ref) {} (#3);
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}
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\newcommand{\negatedEdge}[3][]{
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\path[] (#2) edge [#1] node [midway,draw,circle,fill=black,transform shape,inner sep=0pt,minimum size=0.3em] (ref) {} (#3);
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\NewEnviron{egraph}[1][1.5cm]{%
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\begin{tikzpicture}[-,
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>=stealth',
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shorten >=1pt,
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auto,
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node distance=#1,
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thick,
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base node/.style={circle,draw,minimum size=20pt}]
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\BODY
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\end{tikzpicture}
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}
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\newcommand{\chord}[2]{
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\draw[dashed,red] (#1) -- (#2);
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}
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\newcommand{\egraphFuncConstraint}[3]{%
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&((e_{#1=#2}~\land~e_{#2=#3})~\imp~e_{#1=#3})~\land\\
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&((e_{#1=#2}~\land~e_{#1=#3})~\imp~e_{#2=#3})~\land\\
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&((e_{#1=#3}~\land~e_{#2=#3})~\imp~e_{#1=#2})
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}
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\newcommand{\eq}[2]{
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e_{#1=#2}
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}
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\newcommand{\ackermannFuncConstraint}[3]{%
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(#2=#3~\imp~#1_{#2}=#1_{#3})
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}
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\newcommand{\DNF}[1]{\ensuremath{\text{DNF}(#1})}
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\newcommand{\CNF}[1]{\ensuremath{\text{CNF}(#1})}
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\newcommand{\satUnsatAss}[2]{{\color{blue}\ensuremath{#1}}|{\color{red}\ensuremath{#2}}}
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