\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{5}
		\dpllStep{1|2|3|4|5}
		\dpllDecL{0|1|1|1|1}
		\dpllAssi{ - |$\lnot a$|$\lnot a, \lnot c$|$\lnot a, \lnot c, b$|\makecell{$\lnot a, \lnot c, b, $ \\ $\lnot d$}}
		\dpllClause{1}{$\lnot b, c, d$}{$\lnot b, c, d$|$\lnot b, c, d$|$\lnot b, d$|$d$|\conflict}
		\dpllClause{2}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot d$|\done}
		\dpllClause{3}{$a, \lnot c$}{$a, \lnot c$|$\lnot c$|\done|\done|\done}
		\dpllClause{4}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|\done|\done|\done}
		\dpllClause{5}{$b, c$}{$b, c$|$b, c$|$b$|\done|\done}
		\dpllClause{6}{$\lnot a, \lnot e$}{$\lnot a, \lnot e$|\done|\done|\done|\done}
		\dpllBCP{ - |$\lnot c$|$b$|$\lnot d$| - }
		\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 -> 5
  \draw [->] (22.3bp,56.0bp) .. controls (35.47bp,56.0bp) and (58.583bp,56.0bp)  .. (85.878bp,56.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,63.5bp) node {$$3$$};
  % Edge: 3 -> 2
  \draw [->] (285.67bp,47.438bp) .. controls (293.41bp,44.585bp) and (304.51bp,40.495bp)  .. (323.47bp,33.51bp);
  % Edge: 4 -> 2
  \draw [->] (285.67bp,14.223bp) .. controls (293.24bp,16.746bp) and (304.02bp,20.339bp)  .. (323.09bp,26.697bp);
  % Edge: 5 -> 3
  \draw [->] (107.41bp,59.835bp) .. controls (112.76bp,61.808bp) and (119.64bp,64.004bp)  .. (126.0bp,65.0bp) .. controls (149.1bp,68.621bp) and (199.96bp,74.429bp)  .. (246.0bp,64.0bp) .. controls (249.24bp,63.266bp) and (252.55bp,62.125bp)  .. (265.02bp,56.363bp);
  \draw (186.0bp,76.5bp) node {$$1$$};
  % Edge: 5 -> 6
  \draw [->] (107.98bp,53.247bp) .. controls (121.94bp,49.395bp) and (147.6bp,42.318bp)  .. (175.14bp,34.721bp);
  \draw (140.0bp,56.5bp) node {$$5$$};
  % Edge: 6 -> 3
  \draw [->] (196.98bp,34.18bp) .. controls (210.88bp,37.215bp) and (236.36bp,42.779bp)  .. (264.14bp,48.846bp);
  \draw (232.0bp,52.5bp) node {$$1$$};
  % Edge: 6 -> 4
  \draw [->] (196.37bp,28.221bp) .. controls (202.46bp,25.881bp) and (210.6bp,22.959bp)  .. (218.0bp,21.0bp) .. controls (229.76bp,17.886bp) and (243.17bp,15.453bp)  .. (263.98bp,12.283bp);
  \draw (232.0bp,28.5bp) node {$$2$$};
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,56.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,56.0bp) node {$\lnot a$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,56.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,56.0bp) node {$\lnot c$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (334.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (334.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (275.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (275.0bp,51.0bp) node {$d$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (275.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (275.0bp,11.0bp) node {$\lnot d$};
\end{scope}
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (186.0bp,32.0bp) ellipse (11.0bp and 11.0bp);
  \draw (186.0bp,32.0bp) node {$b$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; \lnot b \lor c \lor d$}
	\AxiomC{$2. \; \lnot b \lor \lnot d$}
	\BinaryInfC{$\lnot b \lor c$}
	\AxiomC{$5. \; b \lor c$}
	\BinaryInfC{$c$}
	\AxiomC{$3. \; a \lor \lnot c$}
	\BinaryInfC{$a$}
\end{prooftree}

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

Conflict in step 11\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 0 -> 7
  \draw [->] (1.0536bp,56.0bp) .. controls (2.5071bp,56.0bp) and (33.188bp,56.0bp)  .. (64.696bp,56.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (33.0bp,63.5bp) node {$$7$$};
  % Edge: 2 -> 1
  \draw [->] (436.67bp,47.438bp) .. controls (444.41bp,44.585bp) and (455.51bp,40.495bp)  .. (474.47bp,33.51bp);
  % Edge: 3 -> 1
  \draw [->] (436.67bp,14.223bp) .. controls (444.24bp,16.746bp) and (455.02bp,20.339bp)  .. (474.09bp,26.697bp);
  % Edge: 4 -> 2
  \draw [->] (258.41bp,59.835bp) .. controls (263.76bp,61.808bp) and (270.64bp,64.004bp)  .. (277.0bp,65.0bp) .. controls (300.93bp,68.751bp) and (353.64bp,72.391bp)  .. (397.0bp,63.0bp) .. controls (400.2bp,62.306bp) and (403.5bp,61.244bp)  .. (415.96bp,55.925bp);
  \draw (337.0bp,75.5bp) node {$$1$$};
  % Edge: 4 -> 5
  \draw [->] (258.98bp,53.247bp) .. controls (272.94bp,49.395bp) and (298.6bp,42.318bp)  .. (326.14bp,34.721bp);
  \draw (291.0bp,55.5bp) node {$$5$$};
  % Edge: 5 -> 2
  \draw [->] (347.98bp,34.18bp) .. controls (361.88bp,37.215bp) and (387.36bp,42.779bp)  .. (415.14bp,48.846bp);
  \draw (383.0bp,51.5bp) node {$$1$$};
  % Edge: 5 -> 3
  \draw [->] (347.33bp,27.798bp) .. controls (353.39bp,25.214bp) and (361.54bp,22.021bp)  .. (369.0bp,20.0bp) .. controls (380.71bp,16.83bp) and (394.12bp,14.627bp)  .. (414.95bp,11.971bp);
  \draw (383.0bp,27.5bp) node {$$2$$};
  % Edge: 6 -> 4
  \draw [->] (173.3bp,56.0bp) .. controls (186.47bp,56.0bp) and (209.58bp,56.0bp)  .. (236.88bp,56.0bp);
  \draw (205.0bp,63.5bp) node {$$4$$};
  % Edge: 7 -> 6
  \draw [->] (87.3bp,56.0bp) .. controls (100.47bp,56.0bp) and (123.58bp,56.0bp)  .. (150.88bp,56.0bp);
  \draw (119.0bp,63.5bp) node {$$6$$};
  % Node: 7
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,56.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,56.0bp) node {$a$};
\end{scope}
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (485.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (485.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (426.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (426.0bp,51.0bp) node {$d$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (426.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (426.0bp,11.0bp) node {$\lnot d$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (248.0bp,56.0bp) ellipse (11.0bp and 11.0bp);
  \draw (248.0bp,56.0bp) node {$\lnot c$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (337.0bp,32.0bp) ellipse (11.0bp and 11.0bp);
  \draw (337.0bp,32.0bp) node {$b$};
\end{scope}
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,56.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,56.0bp) node {$\lnot e$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; \lnot b \lor c \lor d$}
	\AxiomC{$2. \; \lnot b \lor \lnot d$}
	\BinaryInfC{$\lnot b \lor c$}
	\AxiomC{$5. \; b \lor c$}
	\BinaryInfC{$c$}
	\AxiomC{$4. \; \lnot c \lor e$}
	\BinaryInfC{$e$}
	\AxiomC{$6. \; \lnot a \lor \lnot e$}
	\BinaryInfC{$\lnot a$}
	\AxiomC{$7. \; a$}
	\BinaryInfC{$\bot$}
\end{prooftree}

