Questionnaire-2024/sat_solvers_dpll/0017_sol.tex

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

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

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