\hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{5} \dpllStep{1|2|3|4|5} \dpllDecL{0|1|1|1|1} \dpllAssi{ - |$\lnot a$|$\lnot a, c$|$\lnot a, c, b$|\makecell{$\lnot a, c, b, $ \\ $\lnot d$}} \dpllClause{1}{$\lnot a, b, c$}{$\lnot a, b, c$|\done|\done|\done|\done} \dpllClause{2}{$a, c$}{$a, c$|$c$|\done|\done|\done} \dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|$b$|\done|\done} \dpllClause{4}{$\lnot b, d$}{$\lnot b, d$|$\lnot b, d$|$\lnot b, d$|$d$|\conflict} \dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot d$|$\lnot d$|\done} \dpllClause{6}{$c, e$}{$c, e$|$c, e$|\done|\done|\done} \dpllClause{7}{$c, \lnot e$}{$c, \lnot e$|$c, \lnot e$|\done|\done|\done} \dpllBCP{ - |$c$|$b$|$\lnot d$| - } \dpllPL{ - | - | - | - | - } \dpllDeci{$\lnot a$| - | - | - | - } \end{dplltabular} } Conflict in step 5\\ \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: 1 -> 3 \draw [->] (22.3bp,30.5bp) .. controls (35.47bp,30.5bp) and (58.583bp,30.5bp) .. (85.878bp,30.5bp); \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (54.0bp,38.0bp) node {$$2$$}; % Edge: 3 -> 4 \draw [->] (107.97bp,32.873bp) .. controls (121.23bp,36.03bp) and (144.98bp,41.686bp) .. (172.05bp,48.13bp); \draw (140.0bp,50.0bp) node {$$3$$}; % Edge: 3 -> 6 \draw [->] (107.07bp,25.696bp) .. controls (112.42bp,23.094bp) and (119.42bp,20.094bp) .. (126.0bp,18.5bp) .. controls (152.72bp,12.025bp) and (184.6bp,10.902bp) .. (215.0bp,11.119bp); \draw (140.0bp,26.0bp) node {$$5$$}; % Edge: 4 -> 5 \draw [->] (194.3bp,50.5bp) .. controls (207.47bp,50.5bp) and (230.58bp,50.5bp) .. (257.88bp,50.5bp); \draw (226.0bp,58.0bp) node {$$4$$}; % Edge: 5 -> 2 \draw [->] (279.16bp,46.162bp) .. controls (287.01bp,42.445bp) and (298.56bp,36.972bp) .. (317.68bp,27.917bp); % Edge: 6 -> 2 \draw [->] (236.95bp,12.694bp) .. controls (253.12bp,14.634bp) and (285.4bp,18.508bp) .. (316.79bp,22.275bp); % Node: 1 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (11.0bp,30.5bp) ellipse (11.0bp and 11.0bp); \draw (11.0bp,30.5bp) node {$\lnot a$}; \end{scope} % Node: 3 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (97.0bp,30.5bp) ellipse (11.0bp and 11.0bp); \draw (97.0bp,30.5bp) node {$c$}; \end{scope} % Node: 2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (328.0bp,23.5bp) ellipse (11.0bp and 11.0bp); \draw (328.0bp,23.5bp) node {$\bot$}; \end{scope} % Node: 4 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (183.0bp,50.5bp) ellipse (11.0bp and 11.0bp); \draw (183.0bp,50.5bp) node {$b$}; \end{scope} % Node: 6 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (226.0bp,11.5bp) ellipse (11.0bp and 11.0bp); \draw (226.0bp,11.5bp) node {$\lnot d$}; \end{scope} % Node: 5 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (269.0bp,50.5bp) ellipse (11.0bp and 11.0bp); \draw (269.0bp,50.5bp) node {$d$}; \end{scope} % \end{tikzpicture} } \begin{prooftree} \AxiomC{$4. \; \lnot b \lor d$} \AxiomC{$3. \; b \lor \lnot c$} \BinaryInfC{$d \lor \lnot c$} \AxiomC{$5. \; \lnot c \lor \lnot d$} \BinaryInfC{$\lnot c$} \AxiomC{$2. \; a \lor c$} \BinaryInfC{$a$} \end{prooftree} \hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{4} \dpllStep{6|7|8|9} \dpllDecL{0|0|1|1} \dpllAssi{ - |$a$|$a, \lnot b$|$a, \lnot b, \lnot c$} \dpllClause{1}{$\lnot a, b, c$}{$\lnot a, b, c$|$b, c$|$c$|\conflict} \dpllClause{2}{$a, c$}{$a, c$|\done|\done|\done} \dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|$\lnot c$|\done} \dpllClause{4}{$\lnot b, d$}{$\lnot b, d$|$\lnot b, d$|\done|\done} \dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c, \lnot d$|\done} \dpllClause{6}{$c, e$}{$c, e$|$c, e$|$c, e$|$e$} \dpllClause{7}{$c, \lnot e$}{$c, \lnot e$|$c, \lnot e$|$c, \lnot e$|$\lnot e$} \dpllClause{8}{$a$}{$a$|\done|\done|\done} \dpllBCP{$a$| - |$\lnot c$| - } \dpllPL{ - | - | - | - } \dpllDeci{ - |$\lnot b$| - | - } \end{dplltabular} } Conflict in step 9\\ \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: 0 -> 5 \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 {$$8$$}; % 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 -> 4 \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 {$$3$$}; % Edge: 3 -> 2 \draw [->] (172.67bp,47.438bp) .. controls (180.41bp,44.585bp) and (191.51bp,40.495bp) .. (210.47bp,33.51bp); % Edge: 4 -> 2 \draw [->] (172.67bp,14.223bp) .. controls (180.24bp,16.746bp) and (191.02bp,20.339bp) .. (210.09bp,26.697bp); % Edge: 5 -> 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 {$$1$$}; % Node: 5 \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 {$a$}; \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 {$\lnot b$}; \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 {$c$}; \end{scope} % Node: 4 \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 {$\lnot c$}; \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{$1. \; \lnot a \lor b \lor c$} \AxiomC{$8. \; a$} \BinaryInfC{$b \lor c$} \AxiomC{$3. \; b \lor \lnot c$} \BinaryInfC{$b$} \end{prooftree}