Questionnaire-2024/sat_solvers_dpll/0038_sol.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{6}
		\dpllStep{1|2|3|4|5|6}
		\dpllDecL{0|0|0|1|1|1}
		\dpllAssi{ - |$a$|$a, b$|$a, b, \lnot c$|\makecell{$a, b, \lnot c, $ \\ $\lnot d$}|\makecell{$a, b, \lnot c, $ \\ $\lnot d, \lnot e$}}
		\dpllClause{1}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c, \lnot d$|\done|\done|\done}
		\dpllClause{2}{$c, e$}{$c, e$|$c, e$|$c, e$|$e$|$e$|\conflict}
		\dpllClause{3}{$\lnot d, c$}{$\lnot d, c$|$\lnot d, c$|$\lnot d, c$|$\lnot d$|\done|\done}
		\dpllClause{4}{$d, \lnot e$}{$d, \lnot e$|$d, \lnot e$|$d, \lnot e$|$d, \lnot e$|$\lnot e$|\done}
		\dpllClause{5}{$b, \lnot d$}{$b, \lnot d$|$b, \lnot d$|\done|\done|\done|\done}
		\dpllClause{6}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|\done|\done}
		\dpllClause{7}{$a, c$}{$a, c$|\done|\done|\done|\done|\done}
		\dpllBCP{ - | - | - |$\lnot d$|$\lnot e$| - }
		\dpllPL{$a$|$b$| - | - | - | - }
		\dpllDeci{ - | - |$\lnot c$| - | - | - }
	\end{dplltabular}
}

Conflict in step 6\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 1 -> 3
  \draw [->] (21.965bp,32.491bp) .. controls (42.831bp,35.613bp) and (91.46bp,42.888bp)  .. (129.08bp,48.516bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,46.5bp) node {$$2$$};
  % Edge: 1 -> 4
  \draw [->] (20.22bp,24.026bp) .. controls (25.504bp,19.994bp) and (32.72bp,15.28bp)  .. (40.0bp,13.0bp) .. controls (51.438bp,9.4177bp) and (64.837bp,8.8202bp)  .. (85.817bp,9.7781bp);
  \draw (54.0bp,20.5bp) node {$$3$$};
  % Edge: 3 -> 2
  \draw [->] (150.95bp,48.009bp) .. controls (167.28bp,44.745bp) and (200.03bp,38.194bp)  .. (231.09bp,31.983bp);
  % Edge: 4 -> 5
  \draw [->] (108.3bp,11.0bp) .. controls (121.47bp,11.0bp) and (144.58bp,11.0bp)  .. (171.88bp,11.0bp);
  \draw (140.0bp,18.5bp) node {$$4$$};
  % Edge: 5 -> 2
  \draw [->] (193.67bp,14.223bp) .. controls (201.24bp,16.746bp) and (212.02bp,20.339bp)  .. (231.09bp,26.697bp);
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,31.0bp) node {$\lnot c$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (140.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
  \draw (140.0bp,50.0bp) node {$e$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,11.0bp) node {$\lnot d$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (242.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (242.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,11.0bp) node {$\lnot e$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$4. \; d \lor \lnot e$}
	\AxiomC{$2. \; c \lor e$}
	\BinaryInfC{$d \lor c$}
	\AxiomC{$3. \; \lnot d \lor c$}
	\BinaryInfC{$c$}
\end{prooftree}

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{4}
		\dpllStep{7|8|9|10}
		\dpllDecL{0|0|0|0}
		\dpllAssi{$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $\lnot d$}|\makecell{$a, b, c, $ \\ $\lnot d, \lnot e$}}
		\dpllClause{1}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot d$|\done|\done}
		\dpllClause{2}{$c, e$}{$c, e$|\done|\done|\done}
		\dpllClause{3}{$\lnot d, c$}{$\lnot d, c$|\done|\done|\done}
		\dpllClause{4}{$d, \lnot e$}{$d, \lnot e$|$d, \lnot e$|$\lnot e$|\done}
		\dpllClause{5}{$b, \lnot d$}{\done|\done|\done|\done}
		\dpllClause{6}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|\done|\done}
		\dpllClause{7}{$a, c$}{\done|\done|\done|\done}
		\dpllClause{8}{$c$}{$c$|\done|\done|\done}
		\dpllBCP{$c$|$\lnot d$|$\lnot e$| - }
		\dpllPL{ - | - | - | - }
		\dpllDeci{ - | - | - |SAT}
	\end{dplltabular}
}