Questionnaire-2024/sat_solvers_dpll/0047_sol.tex

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

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

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 1 -> 5
  \draw [->] (21.08bp,83.506bp) .. controls (26.44bp,80.758bp) and (33.44bp,77.508bp)  .. (40.0bp,75.5bp) .. controls (51.601bp,71.949bp) and (65.006bp,69.732bp)  .. (85.898bp,67.281bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,83.0bp) node {$$3$$};
  % Edge: 1 -> 6
  \draw [->] (21.966bp,90.636bp) .. controls (35.227bp,93.477bp) and (58.98bp,98.567bp)  .. (86.047bp,104.37bp);
  \draw (54.0bp,107.0bp) node {$$5$$};
  % Edge: 3 -> 5
  \draw [->] (21.717bp,33.396bp) .. controls (33.05bp,36.904bp) and (52.243bp,43.253bp)  .. (68.0bp,50.5bp) .. controls (71.462bp,52.092bp) and (75.062bp,53.969bp)  .. (87.382bp,61.048bp);
  \draw (54.0bp,58.0bp) node {$$3$$};
  % Edge: 5 -> 4
  \draw [->] (107.67bp,69.723bp) .. controls (115.24bp,72.246bp) and (126.02bp,75.839bp)  .. (145.09bp,82.197bp);
  % Edge: 6 -> 4
  \draw [->] (107.67bp,102.94bp) .. controls (115.41bp,100.08bp) and (126.51bp,95.995bp)  .. (145.47bp,89.01bp);
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,88.5bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,88.5bp) node {$\lnot c$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,66.5bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,66.5bp) node {$\lnot e$};
\end{scope}
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,106.5bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,106.5bp) node {$e$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,128.5bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,128.5bp) node {$\lnot b$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,30.5bp) node {$\lnot a$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (156.0bp,85.5bp) ellipse (11.0bp and 11.0bp);
  \draw (156.0bp,85.5bp) node {$\bot$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$3. \; a \lor c \lor \lnot e$}
	\AxiomC{$5. \; c \lor e$}
	\BinaryInfC{$a \lor c$}
\end{prooftree}

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