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120 lines
4.6 KiB
120 lines
4.6 KiB
\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{5}
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\dpllStep{1|2|3|4|5}
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\dpllDecL{0|1|1|1|1}
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\dpllAssi{ - |$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, c$|\makecell{$\lnot a, \lnot b, c, $ \\ $\lnot d$}}
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\dpllClause{1}{$a, \lnot b, c$}{$a, \lnot b, c$|$\lnot b, c$|\done|\done|\done}
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\dpllClause{2}{$b, \lnot c, d$}{$b, \lnot c, d$|$b, \lnot c, d$|$\lnot c, d$|$d$|\conflict}
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\dpllClause{3}{$a, \lnot b$}{$a, \lnot b$|$\lnot b$|\done|\done|\done}
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\dpllClause{4}{$a, c$}{$a, c$|$c$|$c$|\done|\done}
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\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot d$|\done}
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\dpllClause{6}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done}
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\dpllBCP{ - |$\lnot b$|$c$|$\lnot d$| - }
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\dpllPL{ - | - | - | - | - }
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\dpllDeci{$\lnot a$| - | - | - | - }
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\end{dplltabular}
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}
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Conflict in step 5\\
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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 [->] (21.966bp,69.373bp) .. controls (35.227bp,72.53bp) and (58.98bp,78.186bp) .. (86.047bp,84.63bp);
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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,87.5bp) node {$$3$$};
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% Edge: 1 -> 5
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\draw [->] (21.417bp,62.714bp) .. controls (26.77bp,60.427bp) and (33.652bp,57.735bp) .. (40.0bp,56.0bp) .. controls (51.702bp,52.801bp) and (65.111bp,50.597bp) .. (85.949bp,47.957bp);
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\draw (54.0bp,63.5bp) node {$$4$$};
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% Edge: 3 -> 2
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\draw [->] (193.67bp,47.438bp) .. controls (201.41bp,44.585bp) and (212.51bp,40.495bp) .. (231.47bp,33.51bp);
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% Edge: 4 -> 3
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\draw [->] (107.62bp,83.519bp) .. controls (118.86bp,79.383bp) and (137.97bp,72.139bp) .. (154.0bp,65.0bp) .. controls (157.18bp,63.585bp) and (160.52bp,62.002bp) .. (172.77bp,55.877bp);
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\draw (140.0bp,84.5bp) node {$$2$$};
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% Edge: 5 -> 3
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\draw [->] (108.3bp,47.49bp) .. controls (121.47bp,48.118bp) and (144.58bp,49.218bp) .. (171.88bp,50.518bp);
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\draw (140.0bp,57.5bp) node {$$2$$};
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% Edge: 5 -> 6
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\draw [->] (106.56bp,41.131bp) .. controls (111.96bp,37.593bp) and (119.2bp,33.173bp) .. (126.0bp,30.0bp) .. controls (137.72bp,24.533bp) and (151.47bp,19.844bp) .. (172.24bp,13.608bp);
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\draw (140.0bp,37.5bp) node {$$5$$};
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% Edge: 6 -> 2
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\draw [->] (193.67bp,14.223bp) .. controls (201.24bp,16.746bp) and (212.02bp,20.339bp) .. (231.09bp,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,67.0bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,67.0bp) node {$\lnot a$};
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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,87.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,87.0bp) node {$\lnot b$};
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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 (97.0bp,47.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,47.0bp) node {$c$};
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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 (242.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (242.0bp,30.0bp) 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 (183.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,51.0bp) node {$d$};
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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,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,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{$2. \; b \lor \lnot c \lor d$}
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\AxiomC{$5. \; \lnot c \lor \lnot d$}
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\BinaryInfC{$b \lor \lnot c$}
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\AxiomC{$3. \; a \lor \lnot b$}
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\BinaryInfC{$\lnot c \lor a$}
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\AxiomC{$4. \; a \lor c$}
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\BinaryInfC{$a$}
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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{6|7|8|9|10}
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\dpllDecL{0|0|0|0|0}
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\dpllAssi{ - |$a$|$a, c$|$a, c, \lnot d$|\makecell{$a, c, \lnot d, $ \\ $b$}}
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\dpllClause{1}{$a, \lnot b, c$}{$a, \lnot b, c$|\done|\done|\done|\done}
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\dpllClause{2}{$b, \lnot c, d$}{$b, \lnot c, d$|$b, \lnot c, d$|$b, d$|$b$|\done}
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\dpllClause{3}{$a, \lnot b$}{$a, \lnot b$|\done|\done|\done|\done}
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\dpllClause{4}{$a, c$}{$a, c$|\done|\done|\done|\done}
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\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot d$|\done|\done}
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\dpllClause{6}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
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\dpllClause{7}{$a$}{$a$|\done|\done|\done|\done}
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\dpllBCP{$a$|$c$|$\lnot d$|$b$| - }
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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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