Questionnaire-2024/sat_solvers_dpll/0021_sol.tex

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

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

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%%
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  % Edge: 0 -> 4
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  % Edge: 1 -> 3
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  % Edge: 1 -> 5
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  \draw (119.0bp,19.5bp) node {$$6$$};
  % Edge: 3 -> 2
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  % Edge: 4 -> 3
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  % Edge: 5 -> 2
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  % Node: 4
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  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,87.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,87.0bp) node {$\lnot y$};
\end{scope}
  % Node: 1
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,29.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,29.0bp) node {$\lnot w$};
\end{scope}
  % Node: 3
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,51.0bp) node {$x$};
\end{scope}
  % Node: 5
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,11.0bp) node {$\lnot x$};
\end{scope}
  % Node: 2
\begin{scope}
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  \draw (221.0bp,30.0bp) node {$\bot$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; x \lor y \lor w$}
	\AxiomC{$5. \; \lnot y$}
	\BinaryInfC{$x \lor w$}
	\AxiomC{$6. \; \lnot x \lor w$}
	\BinaryInfC{$w$}
\end{prooftree}

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