\hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{6} \dpllStep{12|13|14|15|16|17} \dpllDecL{0|0|0|0|0|0} \dpllAssi{ - |$a$|$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $d$}|\makecell{$a, b, c, $ \\ $d, \lnot e$}} \dpllClause{1}{$a, b, c$}{$a, b, c$|\done|\done|\done|\done|\done} \dpllClause{2}{$\lnot a, b$}{$\lnot a, b$|$b$|\done|\done|\done|\done} \dpllClause{3}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$c$|\done|\done|\done} \dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\done|\done} \dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$e$|$e$|\conflict} \dpllClause{6}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done} \dpllClause{7}{$a, b$}{$a, b$|\done|\done|\done|\done|\done} \dpllClause{8}{$a$}{$a$|\done|\done|\done|\done|\done} \dpllBCP{$a$|$b$|$c$|$d$|$\lnot e$| - } \dpllPL{ - | - | - | - | - | - } \dpllDeci{ - | - | - | - | - |UNSAT} \end{dplltabular} } Conflict in step 17\\ \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: 0 -> 7 \draw [->] (1.0536bp,30.0bp) .. controls (2.5071bp,30.0bp) and (33.188bp,30.0bp) .. (64.696bp,30.0bp); \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (33.0bp,37.5bp) node {$$8$$}; % Edge: 2 -> 3 \draw [->] (173.3bp,30.0bp) .. controls (186.47bp,30.0bp) and (209.58bp,30.0bp) .. (236.88bp,30.0bp); \draw (205.0bp,37.5bp) node {$$3$$}; % Edge: 3 -> 4 \draw [->] (258.97bp,32.373bp) .. controls (272.23bp,35.53bp) and (295.98bp,41.186bp) .. (323.05bp,47.63bp); \draw (291.0bp,49.5bp) node {$$4$$}; % Edge: 3 -> 5 \draw [->] (258.07bp,25.196bp) .. controls (263.42bp,22.594bp) and (270.42bp,19.594bp) .. (277.0bp,18.0bp) .. controls (303.72bp,11.525bp) and (335.6bp,10.402bp) .. (366.0bp,10.619bp); \draw (291.0bp,25.5bp) node {$$5$$}; % Edge: 4 -> 6 \draw [->] (345.3bp,50.0bp) .. controls (358.47bp,50.0bp) and (381.58bp,50.0bp) .. (408.88bp,50.0bp); \draw (377.0bp,57.5bp) node {$$6$$}; % Edge: 5 -> 1 \draw [->] (387.95bp,12.194bp) .. controls (404.12bp,14.134bp) and (436.4bp,18.008bp) .. (467.79bp,21.775bp); % Edge: 6 -> 1 \draw [->] (430.16bp,45.662bp) .. controls (438.01bp,41.945bp) and (449.56bp,36.472bp) .. (468.68bp,27.417bp); % Edge: 7 -> 2 \draw [->] (87.3bp,30.0bp) .. controls (100.47bp,30.0bp) and (123.58bp,30.0bp) .. (150.88bp,30.0bp); \draw (119.0bp,37.5bp) node {$$2$$}; % Node: 7 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (76.0bp,30.0bp) ellipse (11.0bp and 11.0bp); \draw (76.0bp,30.0bp) node {$a$}; \end{scope} % Node: 1 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (479.0bp,23.0bp) ellipse (11.0bp and 11.0bp); \draw (479.0bp,23.0bp) node {$\bot$}; \end{scope} % Node: 2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (162.0bp,30.0bp) ellipse (11.0bp and 11.0bp); \draw (162.0bp,30.0bp) node {$b$}; \end{scope} % Node: 3 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (248.0bp,30.0bp) ellipse (11.0bp and 11.0bp); \draw (248.0bp,30.0bp) node {$c$}; \end{scope} % Node: 4 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (334.0bp,50.0bp) ellipse (11.0bp and 11.0bp); \draw (334.0bp,50.0bp) node {$d$}; \end{scope} % Node: 5 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (377.0bp,11.0bp) ellipse (11.0bp and 11.0bp); \draw (377.0bp,11.0bp) node {$e$}; \end{scope} % Node: 6 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (420.0bp,50.0bp) ellipse (11.0bp and 11.0bp); \draw (420.0bp,50.0bp) node {$\lnot e$}; \end{scope} % \end{tikzpicture} } \begin{prooftree} \AxiomC{$6. \; \lnot d \lor \lnot e$} \AxiomC{$4. \; \lnot c \lor d$} \BinaryInfC{$\lnot e \lor \lnot c$} \AxiomC{$5. \; \lnot c \lor e$} \BinaryInfC{$\lnot c$} \AxiomC{$3. \; \lnot b \lor c$} \BinaryInfC{$\lnot b$} \AxiomC{$2. \; \lnot a \lor b$} \BinaryInfC{$\lnot a$} \AxiomC{$8. \; a$} \BinaryInfC{$\bot$} \end{prooftree}