Questionnaire-2024/sat_solvers_dpll/0042_sol.tex

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

Conflict in step 5\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 1 -> 3
  \draw [->] (21.966bp,33.373bp) .. controls (35.227bp,36.53bp) and (58.98bp,42.186bp)  .. (86.047bp,48.63bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,50.5bp) node {$$3$$};
  % Edge: 1 -> 4
  \draw [->] (21.111bp,26.371bp) .. controls (26.482bp,23.828bp) and (33.482bp,20.828bp)  .. (40.0bp,19.0bp) .. controls (51.65bp,15.733bp) and (65.057bp,13.758bp)  .. (85.923bp,11.639bp);
  \draw (54.0bp,26.5bp) node {$$7$$};
  % Edge: 3 -> 2
  \draw [->] (107.67bp,47.438bp) .. controls (115.41bp,44.585bp) and (126.51bp,40.495bp)  .. (145.47bp,33.51bp);
  % Edge: 4 -> 2
  \draw [->] (107.67bp,14.223bp) .. controls (115.24bp,16.746bp) and (126.02bp,20.339bp)  .. (145.09bp,26.697bp);
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,31.0bp) node {$\lnot c$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,51.0bp) node {$\lnot d$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,11.0bp) node {$d$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (156.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (156.0bp,30.0bp) node {$\bot$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$3. \; \lnot d \lor c$}
	\AxiomC{$7. \; d \lor c$}
	\BinaryInfC{$c$}
\end{prooftree}

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