Questionnaire-2024/sat_solvers_dpll/1025_sol.tex

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

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

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%%
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\end{scope}
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  % Node: 3
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  \draw (226.0bp,69.5bp) node {$\lnot e$};
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  % Node: 4
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  \draw (269.0bp,30.5bp) node {$\lnot d$};
\end{scope}
  % Node: 7
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  \draw (355.0bp,30.5bp) node {$e$};
\end{scope}
  % Node: 5
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,30.5bp) node {$c$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$8. \; \lnot b \lor d \lor e$}
	\AxiomC{$5. \; \lnot c \lor \lnot d$}
	\BinaryInfC{$\lnot b \lor e \lor \lnot c$}
	\AxiomC{$3. \; \lnot b \lor \lnot e$}
	\BinaryInfC{$\lnot b \lor \lnot c$}
	\AxiomC{$6. \; \lnot b \lor c$}
	\BinaryInfC{$\lnot b$}
	\AxiomC{$7. \; a \lor b$}
	\BinaryInfC{$a$}
\end{prooftree}

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

Conflict in step 10\\
\scalebox{0.75}{

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%%
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  % Edge: 0 -> 5
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  % Edge: 3 -> 4
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  % Node: 1
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  \draw (307.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 2
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  % Node: 3
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\end{scope}
  % Node: 4
\begin{scope}
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  \draw (248.0bp,11.0bp) node {$\lnot b$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$2. \; b \lor c$}
	\AxiomC{$6. \; \lnot b \lor c$}
	\BinaryInfC{$c$}
	\AxiomC{$4. \; \lnot a \lor \lnot c$}
	\BinaryInfC{$\lnot a$}
	\AxiomC{$9. \; a$}
	\BinaryInfC{$\bot$}
\end{prooftree}