Questionnaire-2024/sat_solvers_dpll/0024_sol.tex

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

Conflict in step 6\\
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%%
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\end{scope}
%
\end{tikzpicture}


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

Conflict in step 12\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
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%%
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\end{scope}
%
\end{tikzpicture}


}
\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{3}
		\dpllStep{13|14|15}
		\dpllDecL{0|0|0}
		\dpllAssi{$c$|$c, e$|$c, e, \lnot a$}
		\dpllClause{1}{$a, \lnot c, \lnot e$}{$a, \lnot e$|$a$|\conflict}
		\dpllClause{2}{$\lnot a, \lnot e$}{$\lnot a, \lnot e$|$\lnot a$|\done}
		\dpllClause{3}{$b, e$}{$b, e$|\done|\done}
		\dpllClause{4}{$\lnot b, d, e$}{$\lnot b, d, e$|\done|\done}
		\dpllClause{5}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot b, \lnot d$}
		\dpllClause{6}{$c, \lnot d$}{\done|\done|\done}
		\dpllClause{7}{$c, d$}{\done|\done|\done}
		\dpllClause{8}{$c$}{\done|\done|\done}
		\dpllClause{9}{$e$}{$e$|\done|\done}
		\dpllBCP{$e$|$\lnot a$| - }
		\dpllPL{ - | - | - }
		\dpllDeci{ - | - |UNSAT}
	\end{dplltabular}
}