Questionnaire-2024/sat_solvers_dpll/0036_sol_second_part.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{5}
		\dpllStep{12|13|14|15|16}
		\dpllDecL{0|0|0|0|0}
		\dpllAssi{ - |$a$|$a, c$|$a, c, b$|\makecell{$a, c, b, $ \\ $\lnot e$}}
		\dpllClause{1}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot b, \lnot e$|$\lnot b, \lnot e$|$\lnot e$|\done}
		\dpllClause{2}{$a, d, e$}{$a, d, e$|\done|\done|\done|\done}
		\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|$b$|\done|\done}
		\dpllClause{4}{$c, \lnot d, e$}{$c, \lnot d, e$|$c, \lnot d, e$|\done|\done|\done}
		\dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$e$|$e$|\conflict}
		\dpllClause{6}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
		\dpllClause{7}{$a, b, \lnot e$}{$a, b, \lnot e$|\done|\done|\done|\done}
		\dpllClause{8}{$a, b$}{$a, b$|\done|\done|\done|\done}
		\dpllClause{9}{$a$}{$a$|\done|\done|\done|\done}
		\dpllBCP{$a$|$c$|$b$|$\lnot e$| - }
		\dpllPL{ - | - | - | - | - }
		\dpllDeci{ - | - | - | - |UNSAT}
	\end{dplltabular}
}

Conflict in step 16\\
\scalebox{0.75}{

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%%
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  \draw (162.0bp,30.0bp) node {$c$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; \lnot b \lor \lnot e$}
	\AxiomC{$3. \; b \lor \lnot c$}
	\BinaryInfC{$\lnot e \lor \lnot c$}
	\AxiomC{$5. \; \lnot c \lor e$}
	\BinaryInfC{$\lnot c$}
	\AxiomC{$6. \; \lnot a \lor c$}
	\BinaryInfC{$\lnot a$}
	\AxiomC{$9. \; a$}
	\BinaryInfC{$\bot$}
\end{prooftree}