Questionnaire-2024/sat_solvers_dpll/1022_sol.tex

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

Conflict in step 5\\
\scalebox{0.75}{

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  \pgfsetlinewidth{1bp}
%%
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  % Edge: 1 -> 3
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  % Edge: 1 -> 4
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  % Edge: 3 -> 5
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  % Edge: 4 -> 2
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  % Edge: 5 -> 6
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  \draw (226.0bp,58.0bp) node {$$5$$};
  % Edge: 6 -> 2
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  % Node: 1
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,30.5bp) node {$\lnot a$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,50.5bp) node {$b$};
\end{scope}
  % Node: 4
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (140.0bp,11.5bp) ellipse (11.0bp and 11.0bp);
  \draw (140.0bp,11.5bp) node {$\lnot d$};
\end{scope}
  % Node: 2
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (328.0bp,23.5bp) ellipse (11.0bp and 11.0bp);
  \draw (328.0bp,23.5bp) node {$\bot$};
\end{scope}
  % Node: 5
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  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,50.5bp) node {$c$};
\end{scope}
  % Node: 6
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (269.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
  \draw (269.0bp,50.5bp) node {$d$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$5. \; \lnot c \lor d$}
	\AxiomC{$4. \; \lnot b \lor c$}
	\BinaryInfC{$d \lor \lnot b$}
	\AxiomC{$1. \; a \lor b$}
	\BinaryInfC{$d \lor a$}
	\AxiomC{$3. \; a \lor \lnot d$}
	\BinaryInfC{$a$}
\end{prooftree}

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