\hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{5} \dpllStep{12|13|14|15|16} \dpllDecL{0|0|0|0|0} \dpllAssi{ - |$a$|$a, \lnot e$|$a, \lnot e, b$|\makecell{$a, \lnot e, b, $ \\ $\lnot d$}} \dpllClause{1}{$\lnot b, d, e$}{$\lnot b, d, e$|$\lnot b, d, e$|$\lnot b, d$|$d$|\conflict} \dpllClause{2}{$b, e$}{$b, e$|$b, e$|$b$|\done|\done} \dpllClause{3}{$c, d$}{$c, d$|$c, d$|$c, d$|$c, d$|$c$} \dpllClause{4}{$\lnot a, \lnot e$}{$\lnot a, \lnot e$|$\lnot e$|\done|\done|\done} \dpllClause{5}{$a, \lnot c, \lnot e$}{$a, \lnot c, \lnot e$|\done|\done|\done|\done} \dpllClause{6}{$c, \lnot d$}{$c, \lnot d$|$c, \lnot d$|$c, \lnot d$|$c, \lnot d$|\done} \dpllClause{7}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot d$|\done} \dpllClause{8}{$a, b$}{$a, b$|\done|\done|\done|\done} \dpllClause{9}{$a$}{$a$|\done|\done|\done|\done} \dpllBCP{$a$|$\lnot e$|$b$|$\lnot d$| - } \dpllPL{ - | - | - | - | - } \dpllDeci{ - | - | - | - |UNSAT} \end{dplltabular} } Conflict in step 16\\ \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: 0 -> 6 \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 {$$9$$}; % Edge: 2 -> 1 \draw [->] (350.67bp,47.438bp) .. controls (358.41bp,44.585bp) and (369.51bp,40.495bp) .. (388.47bp,33.51bp); % Edge: 3 -> 2 \draw [->] (261.98bp,34.18bp) .. controls (275.88bp,37.215bp) and (301.36bp,42.779bp) .. (329.14bp,48.846bp); \draw (297.0bp,51.5bp) node {$$1$$}; % Edge: 3 -> 5 \draw [->] (261.33bp,27.798bp) .. controls (267.39bp,25.214bp) and (275.54bp,22.021bp) .. (283.0bp,20.0bp) .. controls (294.71bp,16.83bp) and (308.12bp,14.627bp) .. (328.95bp,11.971bp); \draw (297.0bp,27.5bp) node {$$7$$}; % Edge: 4 -> 2 \draw [->] (172.41bp,59.835bp) .. controls (177.76bp,61.808bp) and (184.64bp,64.004bp) .. (191.0bp,65.0bp) .. controls (214.93bp,68.751bp) and (267.64bp,72.391bp) .. (311.0bp,63.0bp) .. controls (314.2bp,62.306bp) and (317.5bp,61.244bp) .. (329.96bp,55.925bp); \draw (251.0bp,75.5bp) node {$$1$$}; % Edge: 4 -> 3 \draw [->] (172.98bp,53.247bp) .. controls (186.94bp,49.395bp) and (212.6bp,42.318bp) .. (240.14bp,34.721bp); \draw (205.0bp,55.5bp) node {$$2$$}; % Edge: 5 -> 1 \draw [->] (350.67bp,14.223bp) .. controls (358.24bp,16.746bp) and (369.02bp,20.339bp) .. (388.09bp,26.697bp); % Edge: 6 -> 4 \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 {$$4$$}; % Node: 6 \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 (399.0bp,30.0bp) ellipse (11.0bp and 11.0bp); \draw (399.0bp,30.0bp) node {$\bot$}; \end{scope} % Node: 2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (340.0bp,51.0bp) ellipse (11.0bp and 11.0bp); \draw (340.0bp,51.0bp) node {$d$}; \end{scope} % Node: 3 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (251.0bp,32.0bp) ellipse (11.0bp and 11.0bp); \draw (251.0bp,32.0bp) node {$b$}; \end{scope} % Node: 5 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (340.0bp,11.0bp) ellipse (11.0bp and 11.0bp); \draw (340.0bp,11.0bp) node {$\lnot d$}; \end{scope} % Node: 4 \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{$1. \; \lnot b \lor d \lor e$} \AxiomC{$7. \; \lnot b \lor \lnot d$} \BinaryInfC{$\lnot b \lor e$} \AxiomC{$2. \; b \lor e$} \BinaryInfC{$e$} \AxiomC{$4. \; \lnot a \lor \lnot e$} \BinaryInfC{$\lnot a$} \AxiomC{$9. \; a$} \BinaryInfC{$\bot$} \end{prooftree}