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

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

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 1 -> 4
  \draw [->] (21.966bp,69.373bp) .. controls (35.227bp,72.53bp) and (58.98bp,78.186bp)  .. (86.047bp,84.63bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,87.5bp) node {$$3$$};
  % Edge: 1 -> 5
  \draw [->] (21.417bp,62.714bp) .. controls (26.77bp,60.427bp) and (33.652bp,57.735bp)  .. (40.0bp,56.0bp) .. controls (51.702bp,52.801bp) and (65.111bp,50.597bp)  .. (85.949bp,47.957bp);
  \draw (54.0bp,63.5bp) node {$$4$$};
  % Edge: 3 -> 2
  \draw [->] (193.67bp,47.438bp) .. controls (201.41bp,44.585bp) and (212.51bp,40.495bp)  .. (231.47bp,33.51bp);
  % Edge: 4 -> 3
  \draw [->] (107.62bp,83.519bp) .. controls (118.86bp,79.383bp) and (137.97bp,72.139bp)  .. (154.0bp,65.0bp) .. controls (157.18bp,63.585bp) and (160.52bp,62.002bp)  .. (172.77bp,55.877bp);
  \draw (140.0bp,84.5bp) node {$$2$$};
  % Edge: 5 -> 3
  \draw [->] (108.3bp,47.49bp) .. controls (121.47bp,48.118bp) and (144.58bp,49.218bp)  .. (171.88bp,50.518bp);
  \draw (140.0bp,57.5bp) node {$$2$$};
  % Edge: 5 -> 6
  \draw [->] (106.56bp,41.131bp) .. controls (111.96bp,37.593bp) and (119.2bp,33.173bp)  .. (126.0bp,30.0bp) .. controls (137.72bp,24.533bp) and (151.47bp,19.844bp)  .. (172.24bp,13.608bp);
  \draw (140.0bp,37.5bp) node {$$5$$};
  % Edge: 6 -> 2
  \draw [->] (193.67bp,14.223bp) .. controls (201.24bp,16.746bp) and (212.02bp,20.339bp)  .. (231.09bp,26.697bp);
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,67.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,67.0bp) node {$\lnot a$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,87.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,87.0bp) node {$\lnot b$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,47.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,47.0bp) node {$c$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (242.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (242.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,51.0bp) node {$d$};
\end{scope}
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,11.0bp) node {$\lnot d$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$2. \; b \lor \lnot c \lor d$}
	\AxiomC{$5. \; \lnot c \lor \lnot d$}
	\BinaryInfC{$b \lor \lnot c$}
	\AxiomC{$3. \; a \lor \lnot b$}
	\BinaryInfC{$\lnot c \lor a$}
	\AxiomC{$4. \; a \lor c$}
	\BinaryInfC{$a$}
\end{prooftree}

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

