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222 lines
8.1 KiB
222 lines
8.1 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{ - |$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, c$|\makecell{$\lnot a, \lnot b, c, $ \\ $d$}|\makecell{$\lnot a, \lnot b, c, $ \\ $d, \lnot e$}}
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\dpllClause{1}{$\lnot a, \lnot d$}{$\lnot a, \lnot d$|\done|\done|\done|\done|\done}
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\dpllClause{2}{$a, b, c$}{$a, b, c$|$b, c$|$c$|\done|\done|\done}
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\dpllClause{3}{$\lnot a, b$}{$\lnot a, b$|\done|\done|\done|\done|\done}
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\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|\done|\done|\done|\done}
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\dpllClause{5}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\done|\done}
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\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$e$|$e$|\conflict}
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\dpllClause{7}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done}
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\dpllBCP{ - | - |$c$|$d$|$\lnot e$| - }
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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 [->] (21.966bp,68.127bp) .. controls (35.227bp,64.97bp) and (58.98bp,59.314bp) .. (86.047bp,52.87bp);
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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,70.0bp) node {$$2$$};
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% Edge: 2 -> 4
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\draw [->] (22.172bp,29.583bp) .. controls (33.596bp,28.885bp) and (52.558bp,28.73bp) .. (68.0bp,33.5bp) .. controls (71.81bp,34.677bp) and (75.634bp,36.485bp) .. (87.704bp,43.958bp);
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\draw (54.0bp,41.0bp) node {$$2$$};
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% Edge: 4 -> 5
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\draw [->] (107.97bp,52.873bp) .. controls (121.23bp,56.03bp) and (144.98bp,61.686bp) .. (172.05bp,68.13bp);
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\draw (140.0bp,70.0bp) node {$$5$$};
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% Edge: 4 -> 6
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\draw [->] (107.07bp,45.696bp) .. controls (112.42bp,43.094bp) and (119.42bp,40.094bp) .. (126.0bp,38.5bp) .. controls (152.72bp,32.025bp) and (184.6bp,30.902bp) .. (215.0bp,31.119bp);
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\draw (140.0bp,46.0bp) node {$$6$$};
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% Edge: 5 -> 7
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\draw [->] (194.3bp,70.5bp) .. controls (207.47bp,70.5bp) and (230.58bp,70.5bp) .. (257.88bp,70.5bp);
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\draw (226.0bp,78.0bp) node {$$7$$};
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% Edge: 6 -> 3
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\draw [->] (236.95bp,32.694bp) .. controls (253.12bp,34.634bp) and (285.4bp,38.508bp) .. (316.79bp,42.275bp);
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% Edge: 7 -> 3
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\draw [->] (279.16bp,66.162bp) .. controls (287.01bp,62.445bp) and (298.56bp,56.972bp) .. (317.68bp,47.917bp);
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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,70.5bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,70.5bp) 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,50.5bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,50.5bp) 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 (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 (328.0bp,43.5bp) ellipse (11.0bp and 11.0bp);
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\draw (328.0bp,43.5bp) 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,70.5bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,70.5bp) 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 (226.0bp,31.5bp) ellipse (11.0bp and 11.0bp);
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\draw (226.0bp,31.5bp) node {$e$};
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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 (269.0bp,70.5bp) ellipse (11.0bp and 11.0bp);
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\draw (269.0bp,70.5bp) node {$\lnot e$};
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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{$7. \; \lnot d \lor \lnot e$}
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\AxiomC{$5. \; \lnot c \lor d$}
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\BinaryInfC{$\lnot e \lor \lnot c$}
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\AxiomC{$6. \; \lnot c \lor e$}
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\BinaryInfC{$\lnot c$}
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\AxiomC{$2. \; a \lor b \lor c$}
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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{$\lnot a$|$\lnot a, b$|$\lnot a, b, c$|\makecell{$\lnot a, b, c, $ \\ $d$}|\makecell{$\lnot a, b, c, $ \\ $d, \lnot e$}}
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\dpllClause{1}{$\lnot a, \lnot d$}{\done|\done|\done|\done|\done}
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\dpllClause{2}{$a, b, c$}{$b, c$|\done|\done|\done|\done}
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\dpllClause{3}{$\lnot a, b$}{\done|\done|\done|\done|\done}
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\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$c$|\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}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$e$|$e$|\conflict}
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\dpllClause{7}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done}
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\dpllClause{8}{$a, b$}{$b$|\done|\done|\done|\done}
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\dpllBCP{$b$|$c$|$d$|$\lnot e$| - }
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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 -> 7
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\draw [->] (22.3bp,30.5bp) .. controls (35.47bp,30.5bp) and (58.583bp,30.5bp) .. (85.878bp,30.5bp);
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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,38.0bp) node {$$8$$};
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% Edge: 3 -> 4
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\draw [->] (193.97bp,32.873bp) .. controls (207.23bp,36.03bp) and (230.98bp,41.686bp) .. (258.05bp,48.13bp);
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\draw (226.0bp,50.0bp) node {$$5$$};
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% Edge: 3 -> 5
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\draw [->] (193.07bp,25.696bp) .. controls (198.42bp,23.094bp) and (205.42bp,20.094bp) .. (212.0bp,18.5bp) .. controls (238.72bp,12.025bp) and (270.6bp,10.902bp) .. (301.0bp,11.119bp);
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\draw (226.0bp,26.0bp) node {$$6$$};
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% Edge: 4 -> 6
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\draw [->] (280.3bp,50.5bp) .. controls (293.47bp,50.5bp) and (316.58bp,50.5bp) .. (343.88bp,50.5bp);
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\draw (312.0bp,58.0bp) node {$$7$$};
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% Edge: 5 -> 2
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\draw [->] (322.95bp,12.694bp) .. controls (339.12bp,14.634bp) and (371.4bp,18.508bp) .. (402.79bp,22.275bp);
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% Edge: 6 -> 2
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\draw [->] (365.16bp,46.162bp) .. controls (373.01bp,42.445bp) and (384.56bp,36.972bp) .. (403.68bp,27.917bp);
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% Edge: 7 -> 3
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\draw [->] (108.3bp,30.5bp) .. controls (121.47bp,30.5bp) and (144.58bp,30.5bp) .. (171.88bp,30.5bp);
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\draw (140.0bp,38.0bp) node {$$4$$};
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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: 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,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,30.5bp) 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 (414.0bp,23.5bp) ellipse (11.0bp and 11.0bp);
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\draw (414.0bp,23.5bp) 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,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,30.5bp) node {$c$};
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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 (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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% 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 (312.0bp,11.5bp) ellipse (11.0bp and 11.0bp);
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\draw (312.0bp,11.5bp) node {$e$};
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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 (355.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
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\draw (355.0bp,50.5bp) node {$\lnot e$};
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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{$7. \; \lnot d \lor \lnot e$}
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\AxiomC{$5. \; \lnot c \lor d$}
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\BinaryInfC{$\lnot e \lor \lnot c$}
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\AxiomC{$6. \; \lnot c \lor e$}
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\BinaryInfC{$\lnot c$}
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\AxiomC{$4. \; \lnot b \lor c$}
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\BinaryInfC{$\lnot b$}
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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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