Questionnaire-2024/sat_solvers_dpll/1009_sol.tex

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

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

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

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{2}
		\dpllStep{10|11}
		\dpllDecL{1|2}
		\dpllAssi{$a$|$a, \lnot b$}
		\dpllClause{1}{$\lnot a, b$}{$b$|\conflict}
		\dpllClause{2}{$\lnot a, \lnot d$}{$\lnot d$|$\lnot d$}
		\dpllClause{3}{$c, \lnot b$}{$c, \lnot b$|\done}
		\dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$}
		\dpllBCP{ - | - }
		\dpllPL{ - | - }
		\dpllDeci{$\lnot b$| - }
	\end{dplltabular}
}

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