Questionnaire-2024/sat_solvers_dpll/1027_sol_second_part.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{6}
		\dpllStep{12|13|14|15|16|17}
		\dpllDecL{0|0|0|0|0|0}
		\dpllAssi{ - |$a$|$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $d$}|\makecell{$a, b, c, $ \\ $d, \lnot e$}}
		\dpllClause{1}{$a, b, c$}{$a, b, c$|\done|\done|\done|\done|\done}
		\dpllClause{2}{$\lnot a, b$}{$\lnot a, b$|$b$|\done|\done|\done|\done}
		\dpllClause{3}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$c$|\done|\done|\done}
		\dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\done|\done}
		\dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$e$|$e$|\conflict}
		\dpllClause{6}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done}
		\dpllClause{7}{$a, b$}{$a, b$|\done|\done|\done|\done|\done}
		\dpllClause{8}{$a$}{$a$|\done|\done|\done|\done|\done}
		\dpllBCP{$a$|$b$|$c$|$d$|$\lnot e$| - }
		\dpllPL{ - | - | - | - | - | - }
		\dpllDeci{ - | - | - | - | - |UNSAT}
	\end{dplltabular}
}

Conflict in step 17\\
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%%
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%
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}
\begin{prooftree}
	\AxiomC{$6. \; \lnot d \lor \lnot e$}
	\AxiomC{$4. \; \lnot c \lor d$}
	\BinaryInfC{$\lnot e \lor \lnot c$}
	\AxiomC{$5. \; \lnot c \lor e$}
	\BinaryInfC{$\lnot c$}
	\AxiomC{$3. \; \lnot b \lor c$}
	\BinaryInfC{$\lnot b$}
	\AxiomC{$2. \; \lnot a \lor b$}
	\BinaryInfC{$\lnot a$}
	\AxiomC{$8. \; a$}
	\BinaryInfC{$\bot$}
\end{prooftree}