Questionnaire-2024/sat_solvers_dpll/0053_sol_second_part.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{5}
		\dpllStep{10|11|12|13|14}
		\dpllDecL{0|0|0|0|0}
		\dpllAssi{$a$|$a, b$|$a, b, d$|\makecell{$a, b, d, $ \\ $\lnot c$}|\makecell{$a, b, d, $ \\ $\lnot c, \lnot e$}}
		\dpllClause{1}{$\lnot a, b, c$}{$b, c$|\done|\done|\done|\done}
		\dpllClause{2}{$a, c$}{\done|\done|\done|\done|\done}
		\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|\done|\done|\done|\done}
		\dpllClause{4}{$\lnot b, d$}{$\lnot b, d$|$d$|\done|\done|\done}
		\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c$|\done|\done}
		\dpllClause{6}{$c, e$}{$c, e$|$c, e$|$c, e$|$e$|\conflict}
		\dpllClause{7}{$c, \lnot e$}{$c, \lnot e$|$c, \lnot e$|$c, \lnot e$|$\lnot e$|\done}
		\dpllClause{8}{$a$}{\done|\done|\done|\done|\done}
		\dpllClause{9}{$b$}{$b$|\done|\done|\done|\done}
		\dpllBCP{$b$|$d$|$\lnot c$|$\lnot e$| - }
		\dpllPL{ - | - | - | - | - }
		\dpllDeci{ - | - | - | - |UNSAT}
	\end{dplltabular}
}

Conflict in step 14\\
\scalebox{0.75}{

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%%
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  % Edge: 0 -> 6
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  \draw (76.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,31.0bp) node {$b$};
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  % Node: 1
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  \draw (334.0bp,11.0bp) node {$\lnot e$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$6. \; c \lor e$}
	\AxiomC{$7. \; c \lor \lnot e$}
	\BinaryInfC{$c$}
	\AxiomC{$5. \; \lnot c \lor \lnot d$}
	\BinaryInfC{$\lnot d$}
	\AxiomC{$4. \; \lnot b \lor d$}
	\BinaryInfC{$\lnot b$}
	\AxiomC{$9. \; b$}
	\BinaryInfC{$\bot$}
\end{prooftree}