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133 lines
5.2 KiB
133 lines
5.2 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|1|1|1|1}
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\dpllAssi{ - |$\lnot u$|$\lnot u, \lnot v$|$\lnot u, \lnot v, \lnot x$|\makecell{$\lnot u, \lnot v, \lnot x, $ \\ $\lnot y$}|\makecell{$\lnot u, \lnot v, \lnot x, $ \\ $\lnot y, \lnot z$}}
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\dpllClause{1}{$u, \lnot v$}{$u, \lnot v$|$\lnot v$|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot u, w$}{$\lnot u, w$|\done|\done|\done|\done|\done}
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\dpllClause{3}{$v, \lnot x$}{$v, \lnot x$|$v, \lnot x$|$\lnot x$|\done|\done|\done}
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\dpllClause{4}{$w, \lnot y$}{$w, \lnot y$|$w, \lnot y$|$w, \lnot y$|$w, \lnot y$|\done|\done}
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\dpllClause{5}{$v, \lnot y$}{$v, \lnot y$|$v, \lnot y$|$\lnot y$|$\lnot y$|\done|\done}
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\dpllClause{6}{$\lnot w, z$}{$\lnot w, z$|$\lnot w, z$|$\lnot w, z$|$\lnot w, z$|$\lnot w, z$|$\lnot w$}
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\dpllClause{7}{$z, x$}{$z, x$|$z, x$|$z, x$|$z$|$z$|\conflict}
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\dpllClause{8}{$y, \lnot z$}{$y, \lnot z$|$y, \lnot z$|$y, \lnot z$|$y, \lnot z$|$\lnot z$|\done}
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\dpllBCP{ - |$\lnot v$|$\lnot x$|$\lnot y$|$\lnot z$| - }
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\dpllPL{ - | - | - | - | - | - }
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\dpllDeci{$\lnot u$| - | - | - | - | - }
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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 -> 3
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\draw [->] (22.3bp,31.0bp) .. controls (35.47bp,31.0bp) and (58.583bp,31.0bp) .. (85.878bp,31.0bp);
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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,38.5bp) node {$$1$$};
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% Edge: 3 -> 4
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\draw [->] (107.97bp,33.373bp) .. controls (121.23bp,36.53bp) and (144.98bp,42.186bp) .. (172.05bp,48.63bp);
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\draw (140.0bp,50.5bp) node {$$3$$};
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% Edge: 3 -> 5
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\draw [->] (107.11bp,26.371bp) .. controls (112.48bp,23.828bp) and (119.48bp,20.828bp) .. (126.0bp,19.0bp) .. controls (137.65bp,15.733bp) and (151.06bp,13.758bp) .. (171.92bp,11.639bp);
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\draw (140.0bp,26.5bp) node {$$5$$};
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% Edge: 4 -> 6
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\draw [->] (194.3bp,51.0bp) .. controls (207.47bp,51.0bp) and (230.58bp,51.0bp) .. (257.88bp,51.0bp);
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\draw (226.0bp,58.5bp) node {$$7$$};
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% Edge: 5 -> 7
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\draw [->] (194.3bp,11.0bp) .. controls (207.47bp,11.0bp) and (230.58bp,11.0bp) .. (257.88bp,11.0bp);
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\draw (226.0bp,18.5bp) node {$$8$$};
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% Edge: 6 -> 2
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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: 7 -> 2
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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,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,31.0bp) node {$\lnot u$};
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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 (97.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,31.0bp) node {$\lnot v$};
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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 (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: 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 (183.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,51.0bp) node {$\lnot x$};
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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 (183.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,11.0bp) node {$\lnot y$};
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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 (269.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (269.0bp,51.0bp) node {$z$};
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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 {$\lnot z$};
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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{$8. \; y \lor \lnot z$}
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\AxiomC{$7. \; z \lor x$}
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\BinaryInfC{$y \lor x$}
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\AxiomC{$3. \; v \lor \lnot x$}
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\BinaryInfC{$y \lor v$}
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\AxiomC{$5. \; v \lor \lnot y$}
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\BinaryInfC{$v$}
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\AxiomC{$1. \; u \lor \lnot v$}
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\BinaryInfC{$u$}
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\end{prooftree}
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\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{6}
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\dpllStep{7|8|9|10|11|12}
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\dpllDecL{0|0|0|0|0|0}
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\dpllAssi{ - |$u$|$u, w$|$u, w, z$|\makecell{$u, w, z, $ \\ $y$}|\makecell{$u, w, z, $ \\ $y, v$}}
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\dpllClause{1}{$u, \lnot v$}{$u, \lnot v$|\done|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot u, w$}{$\lnot u, w$|$w$|\done|\done|\done|\done}
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\dpllClause{3}{$v, \lnot x$}{$v, \lnot x$|$v, \lnot x$|$v, \lnot x$|$v, \lnot x$|$v, \lnot x$|\done}
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\dpllClause{4}{$w, \lnot y$}{$w, \lnot y$|$w, \lnot y$|\done|\done|\done|\done}
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\dpllClause{5}{$v, \lnot y$}{$v, \lnot y$|$v, \lnot y$|$v, \lnot y$|$v, \lnot y$|$v$|\done}
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\dpllClause{6}{$\lnot w, z$}{$\lnot w, z$|$\lnot w, z$|$z$|\done|\done|\done}
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\dpllClause{7}{$z, x$}{$z, x$|$z, x$|$z, x$|\done|\done|\done}
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\dpllClause{8}{$y, \lnot z$}{$y, \lnot z$|$y, \lnot z$|$y, \lnot z$|$y$|\done|\done}
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\dpllClause{9}{$u$}{$u$|\done|\done|\done|\done|\done}
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\dpllBCP{$u$|$w$|$z$|$y$|$v$| - }
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\dpllPL{ - | - | - | - | - | - }
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\dpllDeci{ - | - | - | - | - |SAT}
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\end{dplltabular}
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}
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