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107 lines
4.1 KiB
107 lines
4.1 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|0|0|1|1|1}
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\dpllAssi{ - |$a$|$a, b$|$a, b, \lnot c$|\makecell{$a, b, \lnot c, $ \\ $\lnot d$}|\makecell{$a, b, \lnot c, $ \\ $\lnot d, \lnot e$}}
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\dpllClause{1}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c, \lnot d$|\done|\done|\done}
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\dpllClause{2}{$c, e$}{$c, e$|$c, e$|$c, e$|$e$|$e$|\conflict}
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\dpllClause{3}{$\lnot d, c$}{$\lnot d, c$|$\lnot d, c$|$\lnot d, c$|$\lnot d$|\done|\done}
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\dpllClause{4}{$d, \lnot e$}{$d, \lnot e$|$d, \lnot e$|$d, \lnot e$|$d, \lnot e$|$\lnot e$|\done}
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\dpllClause{5}{$b, \lnot d$}{$b, \lnot d$|$b, \lnot d$|\done|\done|\done|\done}
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\dpllClause{6}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|\done|\done}
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\dpllClause{7}{$a, c$}{$a, c$|\done|\done|\done|\done|\done}
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\dpllBCP{ - | - | - |$\lnot d$|$\lnot e$| - }
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\dpllPL{$a$|$b$| - | - | - | - }
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\dpllDeci{ - | - |$\lnot c$| - | - | - }
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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 [->] (21.965bp,32.491bp) .. controls (42.831bp,35.613bp) and (91.46bp,42.888bp) .. (129.08bp,48.516bp);
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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,46.5bp) node {$$2$$};
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% Edge: 1 -> 4
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\draw [->] (20.22bp,24.026bp) .. controls (25.504bp,19.994bp) and (32.72bp,15.28bp) .. (40.0bp,13.0bp) .. controls (51.438bp,9.4177bp) and (64.837bp,8.8202bp) .. (85.817bp,9.7781bp);
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\draw (54.0bp,20.5bp) node {$$3$$};
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% Edge: 3 -> 2
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\draw [->] (150.95bp,48.009bp) .. controls (167.28bp,44.745bp) and (200.03bp,38.194bp) .. (231.09bp,31.983bp);
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% Edge: 4 -> 5
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\draw [->] (108.3bp,11.0bp) .. controls (121.47bp,11.0bp) and (144.58bp,11.0bp) .. (171.88bp,11.0bp);
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\draw (140.0bp,18.5bp) node {$$4$$};
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% Edge: 5 -> 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,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,31.0bp) node {$\lnot c$};
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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 (140.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
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\draw (140.0bp,50.0bp) node {$e$};
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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,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,11.0bp) 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 (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: 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 {$\lnot e$};
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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{$4. \; d \lor \lnot e$}
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\AxiomC{$2. \; c \lor e$}
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\BinaryInfC{$d \lor c$}
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\AxiomC{$3. \; \lnot d \lor c$}
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\BinaryInfC{$c$}
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\end{prooftree}
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\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{4}
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\dpllStep{7|8|9|10}
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\dpllDecL{0|0|0|0}
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\dpllAssi{$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $\lnot d$}|\makecell{$a, b, c, $ \\ $\lnot d, \lnot e$}}
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\dpllClause{1}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot d$|\done|\done}
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\dpllClause{2}{$c, e$}{$c, e$|\done|\done|\done}
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\dpllClause{3}{$\lnot d, c$}{$\lnot d, c$|\done|\done|\done}
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\dpllClause{4}{$d, \lnot e$}{$d, \lnot e$|$d, \lnot e$|$\lnot e$|\done}
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\dpllClause{5}{$b, \lnot d$}{\done|\done|\done|\done}
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\dpllClause{6}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|\done|\done}
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\dpllClause{7}{$a, c$}{\done|\done|\done|\done}
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\dpllClause{8}{$c$}{$c$|\done|\done|\done}
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\dpllBCP{$c$|$\lnot d$|$\lnot e$| - }
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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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