Questionnaire-2024/sat_solvers_dpll/0043_sol.tex

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

Conflict in step 4\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
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  % Edge: 1 -> 3
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  % Edge: 1 -> 4
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  \draw (54.0bp,33.5bp) node {$$3$$};
  % Edge: 1 -> 5
  \draw [->] (21.311bp,59.709bp) .. controls (35.439bp,66.854bp) and (62.567bp,80.574bp)  .. (89.756bp,94.325bp);
  \draw (54.0bp,90.5bp) node {$$6$$};
  % Edge: 3 -> 2
  \draw [->] (199.16bp,50.341bp) .. controls (207.09bp,46.306bp) and (218.8bp,40.346bp)  .. (237.68bp,30.744bp);
  % Edge: 4 -> 2
  \draw [->] (156.95bp,12.493bp) .. controls (173.2bp,14.93bp) and (205.73bp,19.81bp)  .. (237.09bp,24.513bp);
  % Edge: 5 -> 3
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  \draw (146.0bp,90.5bp) node {$$1$$};
  % Node: 1
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,55.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,55.0bp) node {$\lnot w$};
\end{scope}
  % Node: 3
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (189.0bp,55.0bp) ellipse (11.0bp and 11.0bp);
  \draw (189.0bp,55.0bp) node {$y$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (146.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (146.0bp,11.0bp) node {$\lnot y$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (100.0bp,99.0bp) ellipse (11.0bp and 11.0bp);
  \draw (100.0bp,99.0bp) node {$\lnot x$};
\end{scope}
  % Node: 2
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (248.0bp,26.0bp) ellipse (11.0bp and 11.0bp);
  \draw (248.0bp,26.0bp) node {$\bot$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; x \lor y \lor w$}
	\AxiomC{$3. \; \lnot y \lor w$}
	\BinaryInfC{$x \lor w$}
	\AxiomC{$6. \; \lnot x \lor w$}
	\BinaryInfC{$w$}
\end{prooftree}

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