Questionnaire-2024/sat_solvers_dpll/0044_sol.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{6}
		\dpllStep{1|2|3|4|5|6}
		\dpllDecL{0|1|1|1|1|1}
		\dpllAssi{ - |$\lnot u$|$\lnot u, \lnot v$|$\lnot u, \lnot v, \lnot x$|\makecell{$\lnot u, \lnot v, \lnot x, $ \\ $\lnot y$}|\makecell{$\lnot u, \lnot v, \lnot x, $ \\ $\lnot y, \lnot z$}}
		\dpllClause{1}{$u, \lnot v$}{$u, \lnot v$|$\lnot v$|\done|\done|\done|\done}
		\dpllClause{2}{$\lnot u, w$}{$\lnot u, w$|\done|\done|\done|\done|\done}
		\dpllClause{3}{$v, \lnot x$}{$v, \lnot x$|$v, \lnot x$|$\lnot x$|\done|\done|\done}
		\dpllClause{4}{$w, \lnot y$}{$w, \lnot y$|$w, \lnot y$|$w, \lnot y$|$w, \lnot y$|\done|\done}
		\dpllClause{5}{$v, \lnot y$}{$v, \lnot y$|$v, \lnot y$|$\lnot y$|$\lnot y$|\done|\done}
		\dpllClause{6}{$\lnot w, z$}{$\lnot w, z$|$\lnot w, z$|$\lnot w, z$|$\lnot w, z$|$\lnot w, z$|$\lnot w$}
		\dpllClause{7}{$z, x$}{$z, x$|$z, x$|$z, x$|$z$|$z$|\conflict}
		\dpllClause{8}{$y, \lnot z$}{$y, \lnot z$|$y, \lnot z$|$y, \lnot z$|$y, \lnot z$|$\lnot z$|\done}
		\dpllBCP{ - |$\lnot v$|$\lnot x$|$\lnot y$|$\lnot z$| - }
		\dpllPL{ - | - | - | - | - | - }
		\dpllDeci{$\lnot u$| - | - | - | - | - }
	\end{dplltabular}
}

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

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 1 -> 3
  \draw [->] (22.3bp,31.0bp) .. controls (35.47bp,31.0bp) and (58.583bp,31.0bp)  .. (85.878bp,31.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,38.5bp) node {$$1$$};
  % Edge: 3 -> 4
  \draw [->] (107.97bp,33.373bp) .. controls (121.23bp,36.53bp) and (144.98bp,42.186bp)  .. (172.05bp,48.63bp);
  \draw (140.0bp,50.5bp) node {$$3$$};
  % Edge: 3 -> 5
  \draw [->] (107.11bp,26.371bp) .. controls (112.48bp,23.828bp) and (119.48bp,20.828bp)  .. (126.0bp,19.0bp) .. controls (137.65bp,15.733bp) and (151.06bp,13.758bp)  .. (171.92bp,11.639bp);
  \draw (140.0bp,26.5bp) node {$$5$$};
  % Edge: 4 -> 6
  \draw [->] (194.3bp,51.0bp) .. controls (207.47bp,51.0bp) and (230.58bp,51.0bp)  .. (257.88bp,51.0bp);
  \draw (226.0bp,58.5bp) node {$$7$$};
  % Edge: 5 -> 7
  \draw [->] (194.3bp,11.0bp) .. controls (207.47bp,11.0bp) and (230.58bp,11.0bp)  .. (257.88bp,11.0bp);
  \draw (226.0bp,18.5bp) node {$$8$$};
  % Edge: 6 -> 2
  \draw [->] (279.67bp,47.438bp) .. controls (287.41bp,44.585bp) and (298.51bp,40.495bp)  .. (317.47bp,33.51bp);
  % Edge: 7 -> 2
  \draw [->] (279.67bp,14.223bp) .. controls (287.24bp,16.746bp) and (298.02bp,20.339bp)  .. (317.09bp,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 {$\lnot u$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,31.0bp) node {$\lnot v$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (328.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (328.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,51.0bp) node {$\lnot x$};
\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 {$\lnot y$};
\end{scope}
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (269.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (269.0bp,51.0bp) node {$z$};
\end{scope}
  % Node: 7
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (269.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (269.0bp,11.0bp) node {$\lnot z$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$8. \; y \lor \lnot z$}
	\AxiomC{$7. \; z \lor x$}
	\BinaryInfC{$y \lor x$}
	\AxiomC{$3. \; v \lor \lnot x$}
	\BinaryInfC{$y \lor v$}
	\AxiomC{$5. \; v \lor \lnot y$}
	\BinaryInfC{$v$}
	\AxiomC{$1. \; u \lor \lnot v$}
	\BinaryInfC{$u$}
\end{prooftree}

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{6}
		\dpllStep{7|8|9|10|11|12}
		\dpllDecL{0|0|0|0|0|0}
		\dpllAssi{ - |$u$|$u, w$|$u, w, z$|\makecell{$u, w, z, $ \\ $y$}|\makecell{$u, w, z, $ \\ $y, v$}}
		\dpllClause{1}{$u, \lnot v$}{$u, \lnot v$|\done|\done|\done|\done|\done}
		\dpllClause{2}{$\lnot u, w$}{$\lnot u, w$|$w$|\done|\done|\done|\done}
		\dpllClause{3}{$v, \lnot x$}{$v, \lnot x$|$v, \lnot x$|$v, \lnot x$|$v, \lnot x$|$v, \lnot x$|\done}
		\dpllClause{4}{$w, \lnot y$}{$w, \lnot y$|$w, \lnot y$|\done|\done|\done|\done}
		\dpllClause{5}{$v, \lnot y$}{$v, \lnot y$|$v, \lnot y$|$v, \lnot y$|$v, \lnot y$|$v$|\done}
		\dpllClause{6}{$\lnot w, z$}{$\lnot w, z$|$\lnot w, z$|$z$|\done|\done|\done}
		\dpllClause{7}{$z, x$}{$z, x$|$z, x$|$z, x$|\done|\done|\done}
		\dpllClause{8}{$y, \lnot z$}{$y, \lnot z$|$y, \lnot z$|$y, \lnot z$|$y$|\done|\done}
		\dpllClause{9}{$u$}{$u$|\done|\done|\done|\done|\done}
		\dpllBCP{$u$|$w$|$z$|$y$|$v$| - }
		\dpllPL{ - | - | - | - | - | - }
		\dpllDeci{ - | - | - | - | - |SAT}
	\end{dplltabular}
}