Questionnaire-2024/sat_solvers_dpll/0036_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{ - |$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, \lnot c$|\makecell{$\lnot a, \lnot b, \lnot c, $ \\ $\lnot e$}|\makecell{$\lnot a, \lnot b, \lnot c, $ \\ $\lnot e, \lnot d$}}
		\dpllClause{1}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot b, \lnot e$|\done|\done|\done|\done}
		\dpllClause{2}{$a, d, e$}{$a, d, e$|$d, e$|$d, e$|$d, e$|$d$|\conflict}
		\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|$\lnot c$|\done|\done|\done}
		\dpllClause{4}{$c, \lnot d, e$}{$c, \lnot d, e$|$c, \lnot d, e$|$c, \lnot d, e$|$\lnot d, e$|$\lnot d$|\done}
		\dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|\done|\done|\done}
		\dpllClause{6}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done|\done}
		\dpllClause{7}{$a, b, \lnot e$}{$a, b, \lnot e$|$b, \lnot e$|$\lnot e$|$\lnot e$|\done|\done}
		\dpllBCP{ - | - |$\lnot c$|$\lnot e$|$\lnot d$| - }
		\dpllPL{ - | - | - | - | - | - }
		\dpllDeci{$\lnot a$|$\lnot b$| - | - | - | - }
	\end{dplltabular}
}

Conflict in step 6\\
\scalebox{0.75}{

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%%
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  % Node: 4
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  \draw (189.0bp,47.5bp) node {$d$};
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  % Node: 3
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  % Node: 6
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\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$2. \; a \lor d \lor e$}
	\AxiomC{$4. \; c \lor \lnot d \lor e$}
	\BinaryInfC{$a \lor e \lor c$}
	\AxiomC{$7. \; a \lor b \lor \lnot e$}
	\BinaryInfC{$a \lor c \lor b$}
	\AxiomC{$3. \; b \lor \lnot c$}
	\BinaryInfC{$a \lor b$}
\end{prooftree}

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

Conflict in step 11\\
\scalebox{0.75}{

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%%
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\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$4. \; c \lor \lnot d \lor e$}
	\AxiomC{$2. \; a \lor d \lor e$}
	\BinaryInfC{$c \lor e \lor a$}
	\AxiomC{$5. \; \lnot c \lor e$}
	\BinaryInfC{$e \lor a$}
	\AxiomC{$1. \; \lnot b \lor \lnot e$}
	\BinaryInfC{$a \lor \lnot b$}
	\AxiomC{$8. \; a \lor b$}
	\BinaryInfC{$a$}
\end{prooftree}