\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{4}
		\dpllStep{1|2|3|4}
		\dpllDecL{0|0|1|1}
		\dpllAssi{ - |$\lnot y$|$\lnot y, \lnot w$|$\lnot y, \lnot w, \lnot x$}
		\dpllClause{1}{$x, y, w$}{$x, y, w$|$x, w$|$x$|\conflict}
		\dpllClause{2}{$\lnot x, z$}{$\lnot x, z$|$\lnot x, z$|$\lnot x, z$|\done}
		\dpllClause{3}{$\lnot y, w$}{$\lnot y, w$|\done|\done|\done}
		\dpllClause{4}{$\lnot z, \lnot w$}{$\lnot z, \lnot w$|$\lnot z, \lnot w$|\done|\done}
		\dpllClause{5}{$\lnot y$}{$\lnot y$|\done|\done|\done}
		\dpllClause{6}{$\lnot x, w$}{$\lnot x, w$|$\lnot x, w$|$\lnot x$|\done}
		\dpllBCP{$\lnot y$| - |$\lnot x$| - }
		\dpllPL{ - | - | - | - }
		\dpllDeci{ - |$\lnot w$| - | - }
	\end{dplltabular}
}

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

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 0 -> 4
  \draw [->] (1.0536bp,87.0bp) .. controls (2.5071bp,87.0bp) and (33.188bp,87.0bp)  .. (64.696bp,87.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (33.0bp,94.5bp) node {$$5$$};
  % Edge: 1 -> 3
  \draw [->] (86.966bp,31.61bp) .. controls (100.23bp,35.083bp) and (123.98bp,41.304bp)  .. (151.05bp,48.393bp);
  \draw (119.0bp,51.5bp) node {$$1$$};
  % Edge: 1 -> 5
  \draw [->] (85.269bp,22.367bp) .. controls (90.57bp,18.542bp) and (97.789bp,14.087bp)  .. (105.0bp,12.0bp) .. controls (116.51bp,8.6691bp) and (129.91bp,8.3126bp)  .. (150.85bp,9.6198bp);
  \draw (119.0bp,19.5bp) node {$$6$$};
  % Edge: 3 -> 2
  \draw [->] (172.67bp,47.438bp) .. controls (180.41bp,44.585bp) and (191.51bp,40.495bp)  .. (210.47bp,33.51bp);
  % Edge: 4 -> 3
  \draw [->] (86.31bp,83.01bp) .. controls (99.682bp,77.279bp) and (124.62bp,66.591bp)  .. (151.65bp,55.008bp);
  \draw (119.0bp,81.5bp) node {$$1$$};
  % Edge: 5 -> 2
  \draw [->] (172.67bp,14.223bp) .. controls (180.24bp,16.746bp) and (191.02bp,20.339bp)  .. (210.09bp,26.697bp);
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,87.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,87.0bp) node {$\lnot y$};
\end{scope}
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,29.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,29.0bp) node {$\lnot w$};
\end{scope}
  % Node: 3
\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 {$x$};
\end{scope}
  % Node: 5
\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 {$\lnot x$};
\end{scope}
  % Node: 2
\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}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; x \lor y \lor w$}
	\AxiomC{$5. \; \lnot y$}
	\BinaryInfC{$x \lor w$}
	\AxiomC{$6. \; \lnot x \lor w$}
	\BinaryInfC{$w$}
\end{prooftree}

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{4}
		\dpllStep{5|6|7|8}
		\dpllDecL{0|0|0|0}
		\dpllAssi{$\lnot y$|$\lnot y, w$|$\lnot y, w, \lnot z$|\makecell{$\lnot y, w, \lnot z, $ \\ $\lnot x$}}
		\dpllClause{1}{$x, y, w$}{$x, w$|\done|\done|\done}
		\dpllClause{2}{$\lnot x, z$}{$\lnot x, z$|$\lnot x, z$|$\lnot x$|\done}
		\dpllClause{3}{$\lnot y, w$}{\done|\done|\done|\done}
		\dpllClause{4}{$\lnot z, \lnot w$}{$\lnot z, \lnot w$|$\lnot z$|\done|\done}
		\dpllClause{5}{$\lnot y$}{\done|\done|\done|\done}
		\dpllClause{6}{$\lnot x, w$}{$\lnot x, w$|\done|\done|\done}
		\dpllClause{7}{$w$}{$w$|\done|\done|\done}
		\dpllBCP{$w$|$\lnot z$|$\lnot x$| - }
		\dpllPL{ - | - | - | - }
		\dpllDeci{ - | - | - |SAT}
	\end{dplltabular}
}

