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228 lines
8.8 KiB
228 lines
8.8 KiB
\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{6}
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\dpllStep{1|2|3|4|5|6}
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\dpllDecL{0|1|2|2|2|2}
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\dpllAssi{ - |$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, e$|\makecell{$\lnot a, \lnot b, e, $ \\ $\lnot c$}|\makecell{$\lnot a, \lnot b, e, $ \\ $\lnot c, \lnot d$}}
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\dpllClause{1}{$\lnot b, d, e$}{$\lnot b, d, e$|$\lnot b, d, e$|\done|\done|\done|\done}
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\dpllClause{2}{$b, e$}{$b, e$|$b, e$|$e$|\done|\done|\done}
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\dpllClause{3}{$c, d$}{$c, d$|$c, d$|$c, d$|$c, d$|$d$|\conflict}
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\dpllClause{4}{$\lnot a, \lnot e$}{$\lnot a, \lnot e$|\done|\done|\done|\done|\done}
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\dpllClause{5}{$a, \lnot c, \lnot e$}{$a, \lnot c, \lnot e$|$\lnot c, \lnot e$|$\lnot c, \lnot e$|$\lnot c$|\done|\done}
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\dpllClause{6}{$c, \lnot d$}{$c, \lnot d$|$c, \lnot d$|$c, \lnot d$|$c, \lnot d$|$\lnot d$|\done}
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\dpllClause{7}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot b, \lnot d$|\done|\done|\done|\done}
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\dpllBCP{ - | - |$e$|$\lnot c$|$\lnot d$| - }
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\dpllPL{ - | - | - | - | - | - }
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\dpllDeci{$\lnot a$|$\lnot b$| - | - | - | - }
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\end{dplltabular}
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}
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Conflict in step 6\\
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\scalebox{0.75}{
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\begin{tikzpicture}[>=latex,line join=bevel,]
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\pgfsetlinewidth{1bp}
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%%
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\pgfsetcolor{black}
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% Edge: 1 -> 4
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\draw [->] (22.3bp,52.0bp) .. controls (35.47bp,52.0bp) and (58.583bp,52.0bp) .. (85.878bp,52.0bp);
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (54.0bp,59.5bp) node {$$2$$};
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% Edge: 2 -> 6
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\draw [->] (108.16bp,10.852bp) .. controls (119.58bp,9.9047bp) and (138.53bp,9.3716bp) .. (154.0bp,14.0bp) .. controls (157.82bp,15.143bp) and (161.65bp,16.935bp) .. (173.72bp,24.413bp);
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\draw (140.0bp,21.5bp) node {$$5$$};
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% Edge: 4 -> 6
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\draw [->] (107.97bp,49.509bp) .. controls (121.23bp,46.193bp) and (144.98bp,40.255bp) .. (172.05bp,33.488bp);
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\draw (140.0bp,51.5bp) node {$$5$$};
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% Edge: 5 -> 3
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\draw [->] (279.67bp,47.438bp) .. controls (287.41bp,44.585bp) and (298.51bp,40.495bp) .. (317.47bp,33.51bp);
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% Edge: 6 -> 5
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\draw [->] (193.97bp,33.373bp) .. controls (207.23bp,36.53bp) and (230.98bp,42.186bp) .. (258.05bp,48.63bp);
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\draw (226.0bp,50.5bp) node {$$3$$};
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% Edge: 6 -> 7
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\draw [->] (193.11bp,26.371bp) .. controls (198.48bp,23.828bp) and (205.48bp,20.828bp) .. (212.0bp,19.0bp) .. controls (223.65bp,15.733bp) and (237.06bp,13.758bp) .. (257.92bp,11.639bp);
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\draw (226.0bp,26.5bp) node {$$6$$};
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% Edge: 7 -> 3
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\draw [->] (279.67bp,14.223bp) .. controls (287.24bp,16.746bp) and (298.02bp,20.339bp) .. (317.09bp,26.697bp);
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% Node: 1
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (11.0bp,52.0bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,52.0bp) node {$\lnot b$};
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\end{scope}
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% Node: 4
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (97.0bp,52.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,52.0bp) node {$e$};
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\end{scope}
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% Node: 2
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (97.0bp,12.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,12.0bp) node {$\lnot a$};
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\end{scope}
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% Node: 6
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (183.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,31.0bp) node {$\lnot c$};
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\end{scope}
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% Node: 3
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (328.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (328.0bp,30.0bp) node {$\bot$};
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\end{scope}
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% Node: 5
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (269.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (269.0bp,51.0bp) node {$d$};
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\end{scope}
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% Node: 7
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (269.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (269.0bp,11.0bp) node {$\lnot d$};
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\end{scope}
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%
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\end{tikzpicture}
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}
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\begin{prooftree}
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\AxiomC{$3. \; c \lor d$}
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\AxiomC{$6. \; c \lor \lnot d$}
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\BinaryInfC{$c$}
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\AxiomC{$5. \; a \lor \lnot c \lor \lnot e$}
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\BinaryInfC{$a \lor \lnot e$}
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\AxiomC{$2. \; b \lor e$}
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\BinaryInfC{$a \lor b$}
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\end{prooftree}
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\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{5}
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\dpllStep{7|8|9|10|11}
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\dpllDecL{1|1|1|1|1}
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\dpllAssi{$\lnot a$|$\lnot a, b$|$\lnot a, b, \lnot d$|\makecell{$\lnot a, b, \lnot d, $ \\ $c$}|\makecell{$\lnot a, b, \lnot d, $ \\ $c, \lnot e$}}
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\dpllClause{1}{$\lnot b, d, e$}{$\lnot b, d, e$|$d, e$|$e$|$e$|\conflict}
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\dpllClause{2}{$b, e$}{$b, e$|\done|\done|\done|\done}
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\dpllClause{3}{$c, d$}{$c, d$|$c, d$|$c$|\done|\done}
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\dpllClause{4}{$\lnot a, \lnot e$}{\done|\done|\done|\done|\done}
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\dpllClause{5}{$a, \lnot c, \lnot e$}{$\lnot c, \lnot e$|$\lnot c, \lnot e$|$\lnot c, \lnot e$|$\lnot e$|\done}
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\dpllClause{6}{$c, \lnot d$}{$c, \lnot d$|$c, \lnot d$|\done|\done|\done}
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\dpllClause{7}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot d$|\done|\done|\done}
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\dpllClause{8}{$a, b$}{$b$|\done|\done|\done|\done}
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\dpllBCP{$b$|$\lnot d$|$c$|$\lnot e$| - }
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\dpllPL{ - | - | - | - | - }
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\dpllDeci{ - | - | - | - | - }
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\end{dplltabular}
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}
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Conflict in step 11\\
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\scalebox{0.75}{
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\begin{tikzpicture}[>=latex,line join=bevel,]
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\pgfsetlinewidth{1bp}
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%%
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\pgfsetcolor{black}
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% Edge: 1 -> 5
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\draw [->] (21.668bp,76.625bp) .. controls (37.13bp,82.146bp) and (68.489bp,91.962bp) .. (96.0bp,91.962bp) .. controls (96.0bp,91.962bp) and (96.0bp,91.962bp) .. (276.0bp,91.962bp) .. controls (301.27bp,91.962bp) and (327.17bp,77.264bp) .. (351.77bp,59.755bp);
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (186.0bp,99.462bp) node {$$5$$};
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% Edge: 1 -> 7
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\draw [->] (21.31bp,69.082bp) .. controls (34.682bp,63.511bp) and (59.622bp,53.119bp) .. (86.648bp,41.859bp);
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\draw (54.0bp,68.462bp) node {$$8$$};
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% Edge: 3 -> 2
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\draw [->] (286.28bp,13.897bp) .. controls (309.78bp,16.033bp) and (367.77bp,21.304bp) .. (408.81bp,25.035bp);
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% Edge: 4 -> 5
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\draw [->] (286.3bp,52.962bp) .. controls (299.47bp,52.962bp) and (322.58bp,52.962bp) .. (349.88bp,52.962bp);
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\draw (318.0bp,60.462bp) node {$$5$$};
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% Edge: 5 -> 2
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\draw [->] (371.16bp,48.624bp) .. controls (379.01bp,44.906bp) and (390.56bp,39.434bp) .. (409.68bp,30.379bp);
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% Edge: 6 -> 3
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\draw [->] (196.33bp,33.514bp) .. controls (202.39bp,30.755bp) and (210.54bp,27.303bp) .. (218.0bp,24.962bp) .. controls (229.69bp,21.294bp) and (243.1bp,18.377bp) .. (263.94bp,14.536bp);
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\draw (232.0bp,32.462bp) node {$$1$$};
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% Edge: 6 -> 4
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\draw [->] (196.98bp,39.683bp) .. controls (210.8bp,42.066bp) and (236.09bp,46.425bp) .. (263.87bp,51.215bp);
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\draw (232.0bp,56.462bp) node {$$3$$};
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% Edge: 7 -> 3
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\draw [->] (106.65bp,32.3bp) .. controls (120.01bp,23.928bp) and (146.76bp,8.629bp) .. (172.0bp,2.9618bp) .. controls (200.25bp,-3.3831bp) and (233.81bp,2.3811bp) .. (264.31bp,9.9958bp);
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\draw (186.0bp,10.462bp) node {$$1$$};
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% Edge: 7 -> 6
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\draw [->] (108.32bp,37.962bp) .. controls (122.2bp,37.962bp) and (147.16bp,37.962bp) .. (174.96bp,37.962bp);
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\draw (140.0bp,45.462bp) node {$$7$$};
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% Node: 1
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (11.0bp,72.96bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,72.962bp) node {$\lnot a$};
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\end{scope}
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% Node: 5
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (361.0bp,52.96bp) ellipse (11.0bp and 11.0bp);
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\draw (361.0bp,52.962bp) node {$\lnot e$};
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\end{scope}
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% Node: 7
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (97.0bp,37.96bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,37.962bp) node {$b$};
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\end{scope}
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% Node: 2
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (420.0bp,25.96bp) ellipse (11.0bp and 11.0bp);
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\draw (420.0bp,25.962bp) node {$\bot$};
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\end{scope}
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% Node: 3
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (275.0bp,12.96bp) ellipse (11.0bp and 11.0bp);
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\draw (275.0bp,12.962bp) node {$e$};
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\end{scope}
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% Node: 4
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (275.0bp,52.96bp) ellipse (11.0bp and 11.0bp);
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\draw (275.0bp,52.962bp) node {$c$};
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\end{scope}
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% Node: 6
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (186.0bp,37.96bp) ellipse (11.0bp and 11.0bp);
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\draw (186.0bp,37.962bp) node {$\lnot d$};
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\end{scope}
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%
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\end{tikzpicture}
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}
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\begin{prooftree}
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\AxiomC{$5. \; a \lor \lnot c \lor \lnot e$}
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\AxiomC{$1. \; \lnot b \lor d \lor e$}
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\BinaryInfC{$a \lor \lnot c \lor \lnot b \lor d$}
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\AxiomC{$3. \; c \lor d$}
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\BinaryInfC{$a \lor \lnot b \lor d$}
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\AxiomC{$7. \; \lnot b \lor \lnot d$}
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\BinaryInfC{$a \lor \lnot b$}
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\AxiomC{$8. \; a \lor b$}
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\BinaryInfC{$a$}
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\end{prooftree}
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