Questionnaire-2024/sat_solvers_dpll/1023_sol.tex

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

Conflict in step 6\\
\scalebox{0.75}{

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%
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}
\begin{prooftree}
	\AxiomC{$2. \; a \lor d \lor e$}
	\AxiomC{$4. \; c \lor \lnot d \lor e$}
	\BinaryInfC{$a \lor e \lor c$}
	\AxiomC{$7. \; a \lor c \lor \lnot e$}
	\BinaryInfC{$a \lor c$}
\end{prooftree}

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