Questionnaire-2024/sat_solvers_dpll/ex1_sol.tex

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

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

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%%
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  % Node: 1
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  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,67.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,67.0bp) node {$\lnot a$};
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  % Node: 4
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  \draw (183.0bp,51.0bp) node {$d$};
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  \draw (183.0bp,11.0bp) node {$\lnot d$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$2. \; b \lor \lnot c \lor d$}
	\AxiomC{$5. \; \lnot c \lor \lnot d$}
	\BinaryInfC{$b \lor \lnot c$}
	\AxiomC{$3. \; a \lor \lnot b$}
	\BinaryInfC{$\lnot c \lor a$}
	\AxiomC{$4. \; a \lor c$}
	\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{ - |$a$|$a, c$|$a, c, \lnot d$|\makecell{$a, c, \lnot d, $ \\ $b$}}
		\dpllClause{1}{$a, \lnot b, c$}{$a, \lnot b, c$|\done|\done|\done|\done}
		\dpllClause{2}{$b, \lnot c, d$}{$b, \lnot c, d$|$b, \lnot c, d$|$b, d$|$b$|\done}
		\dpllClause{3}{$a, \lnot b$}{$a, \lnot b$|\done|\done|\done|\done}
		\dpllClause{4}{$a, c$}{$a, c$|\done|\done|\done|\done}
		\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot d$|\done|\done}
		\dpllClause{6}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
		\dpllClause{7}{$a$}{$a$|\done|\done|\done|\done}
		\dpllBCP{$a$|$c$|$\lnot d$|$b$| - }
		\dpllPL{ - | - | - | - | - }
		\dpllDeci{ - | - | - | - |SAT}
	\end{dplltabular}
}