Questionnaire-2024/sat_solvers_dpll/0054_sol.tex

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

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

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%%
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  % Edge: 1 -> 3
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  % Edge: 1 -> 4
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  % Edge: 1 -> 5
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  % Edge: 3 -> 2
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  \draw (146.0bp,90.5bp) node {$$1$$};
  % Node: 1
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  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,55.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,55.0bp) node {$\lnot a$};
\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 {$\lnot d$};
\end{scope}
  % Node: 4
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (146.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (146.0bp,11.0bp) node {$d$};
\end{scope}
  % Node: 5
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (100.0bp,99.0bp) ellipse (11.0bp and 11.0bp);
  \draw (100.0bp,99.0bp) node {$\lnot b$};
\end{scope}
  % Node: 2
\begin{scope}
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  \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{$1. \; b \lor \lnot d \lor a$}
	\AxiomC{$5. \; a \lor d$}
	\BinaryInfC{$b \lor a$}
	\AxiomC{$8. \; a \lor \lnot b$}
	\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{ - |$a$|$a, c$|$a, c, \lnot b$|\makecell{$a, c, \lnot b, $ \\ $\lnot d$}}
		\dpllClause{1}{$b, \lnot d, a$}{$b, \lnot d, a$|\done|\done|\done|\done}
		\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
		\dpllClause{3}{$\lnot a, b, c$}{$\lnot a, b, c$|$b, c$|\done|\done|\done}
		\dpllClause{4}{$\lnot b, e$}{$\lnot b, e$|$\lnot b, e$|$\lnot b, e$|\done|\done}
		\dpllClause{5}{$a, d$}{$a, d$|\done|\done|\done|\done}
		\dpllClause{6}{$a, \lnot c$}{$a, \lnot c$|\done|\done|\done|\done}
		\dpllClause{7}{$\lnot a, \lnot e, \lnot d$}{$\lnot a, \lnot e, \lnot d$|$\lnot e, \lnot d$|$\lnot e, \lnot d$|$\lnot e, \lnot d$|\done}
		\dpllClause{8}{$a, \lnot b$}{$a, \lnot b$|\done|\done|\done|\done}
		\dpllClause{9}{$a$}{$a$|\done|\done|\done|\done}
		\dpllBCP{$a$|$c$| - | - | - }
		\dpllPL{ - | - |$\lnot b$|$\lnot d$| - }
		\dpllDeci{ - | - | - | - |SAT}
	\end{dplltabular}
}