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119 lines
4.3 KiB
119 lines
4.3 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{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, c$|\makecell{$\lnot a, b, c, $ \\ $\lnot d$}}
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\dpllClause{1}{$a, b$}{$a, b$|$b$|\done|\done|\done}
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\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done}
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\dpllClause{3}{$a, \lnot d$}{$a, \lnot d$|$\lnot d$|$\lnot d$|$\lnot d$|\done}
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\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$c$|\done|\done}
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\dpllClause{5}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\conflict}
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\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$e$|$e$}
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\dpllClause{7}{$d, \lnot e$}{$d, \lnot e$|$d, \lnot e$|$d, \lnot e$|$d, \lnot e$|$\lnot e$}
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\dpllBCP{ - |$b$|$c$|$\lnot d$| - }
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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 -> 3
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\draw [->] (21.966bp,32.873bp) .. controls (35.227bp,36.03bp) and (58.98bp,41.686bp) .. (86.047bp,48.13bp);
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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,50.0bp) node {$$1$$};
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% Edge: 1 -> 4
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\draw [->] (21.066bp,25.696bp) .. controls (26.421bp,23.094bp) and (33.421bp,20.094bp) .. (40.0bp,18.5bp) .. controls (66.721bp,12.025bp) and (98.595bp,10.902bp) .. (129.0bp,11.119bp);
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\draw (54.0bp,26.0bp) node {$$3$$};
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% Edge: 3 -> 5
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\draw [->] (108.3bp,50.5bp) .. controls (121.47bp,50.5bp) and (144.58bp,50.5bp) .. (171.88bp,50.5bp);
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\draw (140.0bp,58.0bp) node {$$4$$};
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% Edge: 4 -> 2
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\draw [->] (151.0bp,12.145bp) .. controls (180.46bp,14.046bp) and (267.31bp,19.649bp) .. (316.95bp,22.852bp);
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% Edge: 5 -> 6
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\draw [->] (194.3bp,50.5bp) .. controls (207.47bp,50.5bp) and (230.58bp,50.5bp) .. (257.88bp,50.5bp);
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\draw (226.0bp,58.0bp) node {$$5$$};
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% Edge: 6 -> 2
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\draw [->] (279.16bp,46.162bp) .. controls (287.01bp,42.445bp) and (298.56bp,36.972bp) .. (317.68bp,27.917bp);
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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,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,30.5bp) node {$\lnot a$};
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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,50.5bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,50.5bp) node {$b$};
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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 (140.0bp,11.5bp) ellipse (11.0bp and 11.0bp);
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\draw (140.0bp,11.5bp) node {$\lnot d$};
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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,23.5bp) ellipse (11.0bp and 11.0bp);
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\draw (328.0bp,23.5bp) 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 (183.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,50.5bp) 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 (269.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
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\draw (269.0bp,50.5bp) node {$d$};
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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{$5. \; \lnot c \lor d$}
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\AxiomC{$4. \; \lnot b \lor c$}
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\BinaryInfC{$d \lor \lnot b$}
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\AxiomC{$1. \; a \lor b$}
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\BinaryInfC{$d \lor a$}
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\AxiomC{$3. \; a \lor \lnot d$}
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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{ - |$a$|$a, c$|$a, c, d$|\makecell{$a, c, d, $ \\ $e$}}
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\dpllClause{1}{$a, b$}{$a, b$|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
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\dpllClause{3}{$a, \lnot d$}{$a, \lnot d$|\done|\done|\done|\done}
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\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|\done|\done|\done}
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\dpllClause{5}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$d$|\done|\done}
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\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$e$|$e$|\done}
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\dpllClause{7}{$d, \lnot e$}{$d, \lnot e$|$d, \lnot e$|$d, \lnot e$|\done|\done}
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\dpllClause{8}{$a$}{$a$|\done|\done|\done|\done}
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\dpllBCP{$a$|$c$|$d$|$e$| - }
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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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