\hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{4} \dpllStep{1|2|3|4} \dpllDecL{0|0|1|1} \dpllAssi{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, e$} \dpllClause{1}{$\lnot a, d$}{$\lnot a, d$|\done|\done|\done} \dpllClause{2}{$\lnot d, c, \lnot a$}{$\lnot d, c, \lnot a$|\done|\done|\done} \dpllClause{3}{$\lnot b, e$}{$\lnot b, e$|$\lnot b, e$|$e$|\done} \dpllClause{4}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot b, \lnot e$|$\lnot e$|\conflict} \dpllClause{5}{$\lnot b, f$}{$\lnot b, f$|$\lnot b, f$|$f$|$f$} \dpllClause{6}{$b, \lnot f$}{$b, \lnot f$|$b, \lnot f$|\done|\done} \dpllBCP{ - | - |$e$| - } \dpllPL{$\lnot a$| - | - | - } \dpllDeci{ - |$b$| - | - } \end{dplltabular} } Conflict in step 4\\ \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: 1 -> 3 \draw [->] (21.966bp,33.373bp) .. controls (35.227bp,36.53bp) and (58.98bp,42.186bp) .. (86.047bp,48.63bp); \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (54.0bp,50.5bp) node {$$3$$}; % Edge: 1 -> 4 \draw [->] (21.111bp,26.371bp) .. controls (26.482bp,23.828bp) and (33.482bp,20.828bp) .. (40.0bp,19.0bp) .. controls (51.65bp,15.733bp) and (65.057bp,13.758bp) .. (85.923bp,11.639bp); \draw (54.0bp,26.5bp) node {$$4$$}; % Edge: 3 -> 2 \draw [->] (107.67bp,47.438bp) .. controls (115.41bp,44.585bp) and (126.51bp,40.495bp) .. (145.47bp,33.51bp); % Edge: 4 -> 2 \draw [->] (107.67bp,14.223bp) .. controls (115.24bp,16.746bp) and (126.02bp,20.339bp) .. (145.09bp,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 {$b$}; \end{scope} % Node: 3 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (97.0bp,51.0bp) ellipse (11.0bp and 11.0bp); \draw (97.0bp,51.0bp) node {$e$}; \end{scope} % Node: 4 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (97.0bp,11.0bp) ellipse (11.0bp and 11.0bp); \draw (97.0bp,11.0bp) node {$\lnot e$}; \end{scope} % Node: 2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (156.0bp,30.0bp) ellipse (11.0bp and 11.0bp); \draw (156.0bp,30.0bp) node {$\bot$}; \end{scope} % \end{tikzpicture} } \begin{prooftree} \AxiomC{$3. \; \lnot b \lor e$} \AxiomC{$4. \; \lnot b \lor \lnot e$} \BinaryInfC{$\lnot b$} \end{prooftree} \hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{3} \dpllStep{5|6|7} \dpllDecL{0|0|0} \dpllAssi{$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, \lnot f$} \dpllClause{1}{$\lnot a, d$}{\done|\done|\done} \dpllClause{2}{$\lnot d, c, \lnot a$}{\done|\done|\done} \dpllClause{3}{$\lnot b, e$}{$\lnot b, e$|\done|\done} \dpllClause{4}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|\done|\done} \dpllClause{5}{$\lnot b, f$}{$\lnot b, f$|\done|\done} \dpllClause{6}{$b, \lnot f$}{$b, \lnot f$|$\lnot f$|\done} \dpllClause{7}{$\lnot b$}{$\lnot b$|\done|\done} \dpllBCP{$\lnot b$|$\lnot f$| - } \dpllPL{ - | - | - } \dpllDeci{ - | - |SAT} \end{dplltabular} }