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234 lines
9.4 KiB
234 lines
9.4 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{ - |$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, \lnot c$|\makecell{$\lnot a, \lnot b, \lnot c, $ \\ $\lnot e$}|\makecell{$\lnot a, \lnot b, \lnot c, $ \\ $\lnot e, \lnot d$}}
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\dpllClause{1}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot b, \lnot e$|\done|\done|\done|\done}
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\dpllClause{2}{$a, d, e$}{$a, d, e$|$d, e$|$d, e$|$d, e$|$d$|\conflict}
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\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|$\lnot c$|\done|\done|\done}
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\dpllClause{4}{$c, \lnot d, e$}{$c, \lnot d, e$|$c, \lnot d, e$|$c, \lnot d, e$|$\lnot d, e$|$\lnot d$|\done}
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\dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|\done|\done|\done}
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\dpllClause{6}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done|\done}
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\dpllClause{7}{$a, b, \lnot e$}{$a, b, \lnot e$|$b, \lnot e$|$\lnot e$|$\lnot e$|\done|\done}
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\dpllBCP{ - | - |$\lnot c$|$\lnot e$|$\lnot d$| - }
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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 -> 5
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\draw [->] (21.98bp,107.68bp) .. controls (35.878bp,110.71bp) and (61.357bp,116.28bp) .. (89.136bp,122.35bp);
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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,124.0bp) node {$$3$$};
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% Edge: 1 -> 7
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\draw [->] (21.223bp,100.91bp) .. controls (26.631bp,98.299bp) and (33.631bp,95.049bp) .. (40.0bp,92.5bp) .. controls (53.069bp,87.269bp) and (68.1bp,82.187bp) .. (89.278bp,75.441bp);
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\draw (54.0bp,100.0bp) node {$$7$$};
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% Edge: 2 -> 4
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\draw [->] (22.153bp,30.975bp) .. controls (40.514bp,31.883bp) and (80.448bp,34.085bp) .. (114.0bp,37.5bp) .. controls (132.29bp,39.362bp) and (153.03bp,42.23bp) .. (177.97bp,45.931bp);
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\draw (100.0bp,45.0bp) node {$$2$$};
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% Edge: 2 -> 7
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\draw [->] (21.311bp,34.995bp) .. controls (35.439bp,41.815bp) and (62.567bp,54.912bp) .. (89.756bp,68.038bp);
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\draw (54.0bp,64.0bp) node {$$7$$};
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% Edge: 4 -> 3
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\draw [->] (199.67bp,50.723bp) .. controls (207.24bp,53.246bp) and (218.02bp,56.839bp) .. (237.09bp,63.197bp);
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% Edge: 5 -> 6
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\draw [->] (110.72bp,121.02bp) .. controls (122.5bp,116.74bp) and (142.92bp,109.08bp) .. (160.0bp,101.5bp) .. controls (163.18bp,100.09bp) and (166.52bp,98.509bp) .. (178.77bp,92.384bp);
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\draw (146.0bp,120.0bp) node {$$4$$};
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% Edge: 6 -> 3
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\draw [->] (199.67bp,83.938bp) .. controls (207.41bp,81.085bp) and (218.51bp,76.995bp) .. (237.47bp,70.01bp);
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% Edge: 7 -> 4
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\draw [->] (110.01bp,67.766bp) .. controls (116.08bp,64.741bp) and (124.35bp,60.943bp) .. (132.0bp,58.5bp) .. controls (143.63bp,54.787bp) and (157.03bp,52.1bp) .. (177.91bp,48.768bp);
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\draw (146.0bp,66.0bp) node {$$2$$};
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% Edge: 7 -> 6
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\draw [->] (110.98bp,74.221bp) .. controls (124.8bp,76.604bp) and (150.09bp,80.963bp) .. (177.87bp,85.753bp);
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\draw (146.0bp,90.0bp) 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,105.5bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,105.5bp) 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 (100.0bp,124.5bp) ellipse (11.0bp and 11.0bp);
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\draw (100.0bp,124.5bp) node {$\lnot c$};
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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 (100.0bp,72.5bp) ellipse (11.0bp and 11.0bp);
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\draw (100.0bp,72.5bp) node {$\lnot e$};
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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 (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: 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 (189.0bp,47.5bp) ellipse (11.0bp and 11.0bp);
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\draw (189.0bp,47.5bp) node {$d$};
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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 (248.0bp,66.5bp) ellipse (11.0bp and 11.0bp);
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\draw (248.0bp,66.5bp) node {$\bot$};
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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 (189.0bp,87.5bp) ellipse (11.0bp and 11.0bp);
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\draw (189.0bp,87.5bp) 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{$2. \; a \lor d \lor e$}
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\AxiomC{$4. \; c \lor \lnot d \lor e$}
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\BinaryInfC{$a \lor e \lor c$}
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\AxiomC{$7. \; a \lor b \lor \lnot e$}
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\BinaryInfC{$a \lor c \lor b$}
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\AxiomC{$3. \; b \lor \lnot c$}
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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{$\lnot a$|$\lnot a, b$|$\lnot a, b, \lnot e$|\makecell{$\lnot a, b, \lnot e, $ \\ $\lnot c$}|\makecell{$\lnot a, b, \lnot e, $ \\ $\lnot c, \lnot d$}}
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\dpllClause{1}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot e$|\done|\done|\done}
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\dpllClause{2}{$a, d, e$}{$d, e$|$d, e$|$d$|$d$|\conflict}
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\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|\done|\done|\done|\done}
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\dpllClause{4}{$c, \lnot d, e$}{$c, \lnot d, e$|$c, \lnot d, e$|$c, \lnot d$|$\lnot d$|\done}
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\dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c$|\done|\done}
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\dpllClause{6}{$\lnot a, c$}{\done|\done|\done|\done|\done}
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\dpllClause{7}{$a, b, \lnot e$}{$b, \lnot e$|\done|\done|\done|\done}
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\dpllClause{8}{$a, b$}{$b$|\done|\done|\done|\done}
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\dpllBCP{$b$|$\lnot e$|$\lnot c$|$\lnot d$| - }
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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 -> 4
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\draw [->] (22.088bp,105.34bp) .. controls (27.406bp,105.99bp) and (34.044bp,106.68bp) .. (40.0bp,107.0bp) .. controls (128.76bp,111.74bp) and (151.4bp,114.1bp) .. (240.0bp,107.0bp) .. controls (243.53bp,106.72bp) and (247.27bp,106.26bp) .. (261.0bp,104.03bp);
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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,119.5bp) node {$$2$$};
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% Edge: 1 -> 7
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\draw [->] (21.216bp,99.701bp) .. controls (26.622bp,97.268bp) and (33.622bp,94.268bp) .. (40.0bp,92.0bp) .. controls (51.861bp,87.783bp) and (65.43bp,83.883bp) .. (85.966bp,78.457bp);
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\draw (54.0bp,99.5bp) node {$$8$$};
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% Edge: 3 -> 4
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\draw [->] (193.64bp,73.547bp) .. controls (207.62bp,78.689bp) and (233.81bp,88.321bp) .. (261.31bp,98.437bp);
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\draw (226.0bp,97.5bp) node {$$2$$};
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% Edge: 3 -> 5
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\draw [->] (194.22bp,69.303bp) .. controls (222.41bp,67.381bp) and (301.66bp,61.978bp) .. (349.75bp,58.699bp);
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\draw (272.0bp,72.5bp) node {$$4$$};
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% Edge: 3 -> 6
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\draw [->] (188.34bp,60.121bp) .. controls (192.93bp,50.793bp) and (201.03bp,37.066bp) .. (212.0bp,29.0bp) .. controls (223.36bp,20.648bp) and (238.65bp,16.125bp) .. (260.91bp,12.018bp);
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\draw (226.0bp,36.5bp) node {$$5$$};
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% Edge: 4 -> 2
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\draw [->] (283.04bp,100.42bp) .. controls (306.89bp,96.661bp) and (367.37bp,87.133bp) .. (408.89bp,80.592bp);
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% Edge: 5 -> 2
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\draw [->] (371.67bp,61.562bp) .. controls (379.41bp,64.415bp) and (390.51bp,68.505bp) .. (409.47bp,75.49bp);
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% Edge: 6 -> 5
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\draw [->] (283.25bp,12.51bp) .. controls (295.55bp,14.674bp) and (316.47bp,19.492bp) .. (332.0bp,29.0bp) .. controls (337.58bp,32.419bp) and (342.82bp,37.21bp) .. (353.76bp,49.494bp);
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\draw (318.0bp,36.5bp) node {$$4$$};
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% Edge: 7 -> 3
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\draw [->] (108.3bp,75.264bp) .. controls (121.47bp,74.324bp) and (144.58bp,72.673bp) .. (171.88bp,70.723bp);
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\draw (140.0bp,81.5bp) node {$$1$$};
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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,104.0bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,104.0bp) 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 (272.0bp,102.0bp) ellipse (11.0bp and 11.0bp);
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\draw (272.0bp,102.0bp) 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 (97.0bp,76.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,76.0bp) 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,79.0bp) ellipse (11.0bp and 11.0bp);
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\draw (420.0bp,79.0bp) 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,70.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,70.0bp) node {$\lnot e$};
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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,58.0bp) ellipse (11.0bp and 11.0bp);
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\draw (361.0bp,58.0bp) node {$\lnot d$};
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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 (272.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (272.0bp,11.0bp) node {$\lnot c$};
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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{$4. \; c \lor \lnot d \lor e$}
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\AxiomC{$2. \; a \lor d \lor e$}
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\BinaryInfC{$c \lor e \lor a$}
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\AxiomC{$5. \; \lnot c \lor e$}
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\BinaryInfC{$e \lor a$}
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\AxiomC{$1. \; \lnot b \lor \lnot e$}
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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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