Questionnaire-2024/sat_solvers_dpll/1011_sol.tex

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

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

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{7}
		\dpllStep{8|9|10|11|12|13|14}
		\dpllDecL{0|1|2|3|4|5|5}
		\dpllAssi{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, c$|\makecell{$\lnot a, b, c, $ \\ $d$}|\makecell{$\lnot a, b, c, $ \\ $d, e$}|\makecell{$\lnot a, b, c, $ \\ $d, e, \lnot f$}}
		\dpllClause{1}{$\lnot d, \lnot b, \lnot a$}{$\lnot d, \lnot b, \lnot a$|\done|\done|\done|\done|\done|\done}
		\dpllClause{2}{$\lnot e, a, \lnot f$}{$\lnot e, a, \lnot f$|$\lnot e, \lnot f$|$\lnot e, \lnot f$|$\lnot e, \lnot f$|$\lnot e, \lnot f$|$\lnot f$|\done}
		\dpllClause{3}{$\lnot a, c, b$}{$\lnot a, c, b$|\done|\done|\done|\done|\done|\done}
		\dpllClause{4}{$f, a, e$}{$f, a, e$|$f, e$|$f, e$|$f, e$|$f, e$|\done|\done}
		\dpllClause{5}{$d, \lnot a, \lnot b$}{$d, \lnot a, \lnot b$|\done|\done|\done|\done|\done|\done}
		\dpllClause{6}{$\lnot a, \lnot c, b$}{$\lnot a, \lnot c, b$|\done|\done|\done|\done|\done|\done}
		\dpllBCP{ - | - | - | - | - |$\lnot f$| - }
		\dpllPL{ - | - | - | - | - | - | - }
		\dpllDeci{$\lnot a$|$b$|$c$|$d$|$e$| - |SAT}
	\end{dplltabular}
}