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