\hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{5} \dpllStep{10|11|12|13|14} \dpllDecL{0|0|0|0|0} \dpllAssi{$a$|$a, b$|$a, b, d$|\makecell{$a, b, d, $ \\ $\lnot c$}|\makecell{$a, b, d, $ \\ $\lnot c, \lnot e$}} \dpllClause{1}{$\lnot a, b, c$}{$b, c$|\done|\done|\done|\done} \dpllClause{2}{$a, c$}{\done|\done|\done|\done|\done} \dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|\done|\done|\done|\done} \dpllClause{4}{$\lnot b, d$}{$\lnot b, d$|$d$|\done|\done|\done} \dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c$|\done|\done} \dpllClause{6}{$c, e$}{$c, e$|$c, e$|$c, e$|$e$|\conflict} \dpllClause{7}{$c, \lnot e$}{$c, \lnot e$|$c, \lnot e$|$c, \lnot e$|$\lnot e$|\done} \dpllClause{8}{$a$}{\done|\done|\done|\done|\done} \dpllClause{9}{$b$}{$b$|\done|\done|\done|\done} \dpllBCP{$b$|$d$|$\lnot c$|$\lnot e$| - } \dpllPL{ - | - | - | - | - } \dpllDeci{ - | - | - | - |UNSAT} \end{dplltabular} } Conflict in step 14\\ \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: 0 -> 6 \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 {$$9$$}; % Edge: 2 -> 3 \draw [->] (173.3bp,31.0bp) .. controls (186.47bp,31.0bp) and (209.58bp,31.0bp) .. (236.88bp,31.0bp); \draw (205.0bp,38.5bp) node {$$5$$}; % Edge: 3 -> 4 \draw [->] (258.97bp,33.373bp) .. controls (272.23bp,36.53bp) and (295.98bp,42.186bp) .. (323.05bp,48.63bp); \draw (291.0bp,50.5bp) node {$$6$$}; % Edge: 3 -> 5 \draw [->] (258.11bp,26.371bp) .. controls (263.48bp,23.828bp) and (270.48bp,20.828bp) .. (277.0bp,19.0bp) .. controls (288.65bp,15.733bp) and (302.06bp,13.758bp) .. (322.92bp,11.639bp); \draw (291.0bp,26.5bp) node {$$7$$}; % Edge: 4 -> 1 \draw [->] (344.67bp,47.438bp) .. controls (352.41bp,44.585bp) and (363.51bp,40.495bp) .. (382.47bp,33.51bp); % Edge: 5 -> 1 \draw [->] (344.67bp,14.223bp) .. controls (352.24bp,16.746bp) and (363.02bp,20.339bp) .. (382.09bp,26.697bp); % Edge: 6 -> 2 \draw [->] (87.3bp,31.0bp) .. controls (100.47bp,31.0bp) and (123.58bp,31.0bp) .. (150.88bp,31.0bp); \draw (119.0bp,38.5bp) node {$$4$$}; % Node: 6 \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 {$b$}; \end{scope} % Node: 1 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (393.0bp,30.0bp) ellipse (11.0bp and 11.0bp); \draw (393.0bp,30.0bp) node {$\bot$}; \end{scope} % Node: 2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (162.0bp,31.0bp) ellipse (11.0bp and 11.0bp); \draw (162.0bp,31.0bp) node {$d$}; \end{scope} % Node: 3 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (248.0bp,31.0bp) ellipse (11.0bp and 11.0bp); \draw (248.0bp,31.0bp) node {$\lnot c$}; \end{scope} % Node: 4 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (334.0bp,51.0bp) ellipse (11.0bp and 11.0bp); \draw (334.0bp,51.0bp) node {$e$}; \end{scope} % Node: 5 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (334.0bp,11.0bp) ellipse (11.0bp and 11.0bp); \draw (334.0bp,11.0bp) node {$\lnot e$}; \end{scope} % \end{tikzpicture} } \begin{prooftree} \AxiomC{$6. \; c \lor e$} \AxiomC{$7. \; c \lor \lnot e$} \BinaryInfC{$c$} \AxiomC{$5. \; \lnot c \lor \lnot d$} \BinaryInfC{$\lnot d$} \AxiomC{$4. \; \lnot b \lor d$} \BinaryInfC{$\lnot b$} \AxiomC{$9. \; b$} \BinaryInfC{$\bot$} \end{prooftree}