Questionnaire-2024/sat_solvers_dpll/0022_sol.tex

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

Conflict in step 7\\
\scalebox{0.75}{

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%%
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  % Edge: 1 -> 3
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  \draw (312.0bp,57.5bp) node {$$7$$};
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  \draw (226.0bp,18.5bp) node {$$6$$};
  % Node: 1
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  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,31.0bp) node {$\lnot a$};
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  % Node: 3
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  \pgfsetstrokecolor{strokecol}
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  \draw (97.0bp,31.0bp) node {$b$};
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  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,51.0bp) node {$\lnot c$};
\end{scope}
  % Node: 8
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  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,11.0bp) node {$e$};
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  % Node: 4
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  \draw (269.0bp,50.0bp) node {$d$};
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  % Node: 7
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  \draw (355.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
  \draw (355.0bp,50.0bp) node {$\lnot f$};
\end{scope}
  % Node: 6
\begin{scope}
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  \draw (312.0bp,11.0bp) node {$f$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$6. \; \lnot e \lor f$}
	\AxiomC{$7. \; \lnot d \lor \lnot f$}
	\BinaryInfC{$\lnot e \lor \lnot d$}
	\AxiomC{$3. \; c \lor d$}
	\BinaryInfC{$\lnot e \lor c$}
	\AxiomC{$4. \; \lnot b \lor \lnot c$}
	\BinaryInfC{$\lnot e \lor \lnot b$}
	\AxiomC{$9. \; \lnot b \lor e$}
	\BinaryInfC{$\lnot b$}
	\AxiomC{$1. \; a \lor b$}
	\BinaryInfC{$a$}
\end{prooftree}

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