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

Conflict in step 4\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 1 -> 4
  \draw [->] (22.3bp,31.0bp) .. controls (35.47bp,31.0bp) and (58.583bp,31.0bp)  .. (85.878bp,31.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,38.5bp) node {$$3$$};
  % 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 [->] (107.97bp,33.373bp) .. controls (121.23bp,36.53bp) and (144.98bp,42.186bp)  .. (172.05bp,48.63bp);
  \draw (140.0bp,50.5bp) node {$$2$$};
  % Edge: 4 -> 5
  \draw [->] (107.11bp,26.371bp) .. controls (112.48bp,23.828bp) and (119.48bp,20.828bp)  .. (126.0bp,19.0bp) .. controls (137.65bp,15.733bp) and (151.06bp,13.758bp)  .. (171.92bp,11.639bp);
  \draw (140.0bp,26.5bp) node {$$4$$};
  % Edge: 5 -> 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,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,31.0bp) node {$a$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,31.0bp) node {$\lnot c$};
\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 {$\lnot b$};
\end{scope}
  % Node: 5
\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 {$b$};
\end{scope}
%
\end{tikzpicture}


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

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

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

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 0 -> 4
  \draw [->] (1.0536bp,31.0bp) .. controls (2.5071bp,31.0bp) and (33.188bp,31.0bp)  .. (64.696bp,31.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (33.0bp,38.5bp) node {$$6$$};
  % Edge: 2 -> 1
  \draw [->] (172.67bp,47.438bp) .. controls (180.41bp,44.585bp) and (191.51bp,40.495bp)  .. (210.47bp,33.51bp);
  % Edge: 3 -> 1
  \draw [->] (172.67bp,14.223bp) .. controls (180.24bp,16.746bp) and (191.02bp,20.339bp)  .. (210.09bp,26.697bp);
  % Edge: 4 -> 2
  \draw [->] (86.966bp,33.373bp) .. controls (100.23bp,36.53bp) and (123.98bp,42.186bp)  .. (151.05bp,48.63bp);
  \draw (119.0bp,50.5bp) node {$$1$$};
  % Edge: 4 -> 3
  \draw [->] (86.111bp,26.371bp) .. controls (91.482bp,23.828bp) and (98.482bp,20.828bp)  .. (105.0bp,19.0bp) .. controls (116.65bp,15.733bp) and (130.06bp,13.758bp)  .. (150.92bp,11.639bp);
  \draw (119.0bp,26.5bp) node {$$5$$};
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,31.0bp) node {$\lnot a$};
\end{scope}
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (221.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (221.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,51.0bp) node {$b$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,11.0bp) node {$\lnot b$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; a \lor b$}
	\AxiomC{$5. \; a \lor \lnot b$}
	\BinaryInfC{$a$}
	\AxiomC{$6. \; \lnot a$}
	\BinaryInfC{$\bot$}
\end{prooftree}