Questionnaire-2024/sat_solvers_dpll/1026_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{ - |$a$|$a, \lnot e$|$a, \lnot e, b$|\makecell{$a, \lnot e, b, $ \\ $\lnot d$}}
		\dpllClause{1}{$\lnot b, d, e$}{$\lnot b, d, e$|$\lnot b, d, e$|$\lnot b, d$|$d$|\conflict}
		\dpllClause{2}{$b, e$}{$b, e$|$b, e$|$b$|\done|\done}
		\dpllClause{3}{$c, d$}{$c, d$|$c, d$|$c, d$|$c, d$|$c$}
		\dpllClause{4}{$\lnot a, \lnot e$}{$\lnot a, \lnot e$|$\lnot e$|\done|\done|\done}
		\dpllClause{5}{$a, \lnot c, \lnot e$}{$a, \lnot c, \lnot e$|\done|\done|\done|\done}
		\dpllClause{6}{$c, \lnot d$}{$c, \lnot d$|$c, \lnot d$|$c, \lnot d$|$c, \lnot d$|\done}
		\dpllClause{7}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot d$|\done}
		\dpllClause{8}{$a, b$}{$a, b$|\done|\done|\done|\done}
		\dpllClause{9}{$a$}{$a$|\done|\done|\done|\done}
		\dpllBCP{$a$|$\lnot e$|$b$|$\lnot d$| - }
		\dpllPL{ - | - | - | - | - }
		\dpllDeci{ - | - | - | - |UNSAT}
	\end{dplltabular}
}

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

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%%
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%
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}
\begin{prooftree}
	\AxiomC{$1. \; \lnot b \lor d \lor e$}
	\AxiomC{$7. \; \lnot b \lor \lnot d$}
	\BinaryInfC{$\lnot b \lor e$}
	\AxiomC{$2. \; b \lor e$}
	\BinaryInfC{$e$}
	\AxiomC{$4. \; \lnot a \lor \lnot e$}
	\BinaryInfC{$\lnot a$}
	\AxiomC{$9. \; a$}
	\BinaryInfC{$\bot$}
\end{prooftree}