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208 lines
7.5 KiB
208 lines
7.5 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|0|1|1|1}
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\dpllAssi{ - |$a$|$a, \lnot b$|$a, \lnot b, d$|\makecell{$a, \lnot b, d, $ \\ $\lnot e$}}
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\dpllClause{1}{$b, d$}{$b, d$|$b, d$|$d$|\done|\done}
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\dpllClause{2}{$\lnot d, e$}{$\lnot d, e$|$\lnot d, e$|$\lnot d, e$|$e$|\conflict}
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\dpllClause{3}{$a, d$}{$a, d$|\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}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|\done|\done}
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\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$\lnot c$}
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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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\dpllBCP{ - | - |$d$|$\lnot e$| - }
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\dpllPL{$a$| - | - | - | - }
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\dpllDeci{ - |$\lnot b$| - | - | - }
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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 [->] (22.3bp,31.0bp) .. controls (35.47bp,31.0bp) and (58.583bp,31.0bp) .. (85.878bp,31.0bp);
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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,38.5bp) node {$$1$$};
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% Edge: 3 -> 4
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\draw [->] (107.97bp,33.373bp) .. controls (121.23bp,36.53bp) and (144.98bp,42.186bp) .. (172.05bp,48.63bp);
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\draw (140.0bp,50.5bp) node {$$2$$};
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% Edge: 3 -> 5
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\draw [->] (107.11bp,26.371bp) .. controls (112.48bp,23.828bp) and (119.48bp,20.828bp) .. (126.0bp,19.0bp) .. controls (137.65bp,15.733bp) and (151.06bp,13.758bp) .. (171.92bp,11.639bp);
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\draw (140.0bp,26.5bp) node {$$7$$};
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% Edge: 4 -> 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: 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 {$\lnot b$};
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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,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,31.0bp) node {$d$};
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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: 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 (183.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,51.0bp) node {$e$};
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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 (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{$2. \; \lnot d \lor e$}
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\AxiomC{$7. \; \lnot d \lor \lnot e$}
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\BinaryInfC{$\lnot d$}
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\AxiomC{$1. \; b \lor d$}
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\BinaryInfC{$b$}
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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{6|7|8|9|10}
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\dpllDecL{0|0|0|0|0}
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\dpllAssi{$a$|$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $d$}|\makecell{$a, b, c, $ \\ $d, \lnot e$}}
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\dpllClause{1}{$b, d$}{$b, d$|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot d, e$}{$\lnot d, e$|$\lnot d, e$|$\lnot d, e$|$e$|\done}
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\dpllClause{3}{$a, d$}{\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}{$b$}{$b$|\done|\done|\done|\done}
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\dpllBCP{$b$|$c$|$d$|$\lnot e$| - }
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\dpllPL{ - | - | - | - | - }
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\dpllDeci{ - | - | - | - |UNSAT}
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\end{dplltabular}
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}
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Conflict in step 10\\
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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: 0 -> 7
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\draw [->] (1.0536bp,30.0bp) .. controls (2.5071bp,30.0bp) and (33.188bp,30.0bp) .. (64.696bp,30.0bp);
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (33.0bp,37.5bp) node {$$8$$};
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% Edge: 2 -> 1
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\draw [->] (343.41bp,84.098bp) .. controls (351.75bp,78.249bp) and (364.75bp,69.126bp) .. (383.55bp,55.926bp);
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% Edge: 3 -> 4
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\draw [->] (172.97bp,32.373bp) .. controls (186.23bp,35.53bp) and (209.98bp,41.186bp) .. (237.05bp,47.63bp);
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\draw (205.0bp,49.5bp) node {$$5$$};
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% Edge: 3 -> 5
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\draw [->] (172.07bp,25.196bp) .. controls (177.42bp,22.594bp) and (184.42bp,19.594bp) .. (191.0bp,18.0bp) .. controls (217.72bp,11.525bp) and (249.6bp,10.402bp) .. (280.0bp,10.619bp);
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\draw (205.0bp,25.5bp) node {$$6$$};
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% Edge: 4 -> 2
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\draw [->] (257.63bp,55.72bp) .. controls (263.06bp,59.202bp) and (270.3bp,63.616bp) .. (277.0bp,67.0bp) .. controls (288.94bp,73.032bp) and (302.86bp,78.753bp) .. (323.28bp,86.537bp);
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\draw (291.0bp,86.5bp) node {$$2$$};
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% Edge: 4 -> 6
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\draw [->] (259.3bp,50.0bp) .. controls (272.47bp,50.0bp) and (295.58bp,50.0bp) .. (322.88bp,50.0bp);
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\draw (291.0bp,57.5bp) node {$$7$$};
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% Edge: 5 -> 1
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\draw [->] (301.83bp,14.333bp) .. controls (312.52bp,18.001bp) and (330.07bp,24.154bp) .. (345.0bp,30.0bp) .. controls (354.39bp,33.678bp) and (364.72bp,38.037bp) .. (382.7bp,45.855bp);
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% Edge: 6 -> 1
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\draw [->] (345.19bp,50.0bp) .. controls (352.57bp,50.0bp) and (362.78bp,50.0bp) .. (381.9bp,50.0bp);
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% Edge: 7 -> 3
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\draw [->] (87.3bp,30.0bp) .. controls (100.47bp,30.0bp) and (123.58bp,30.0bp) .. (150.88bp,30.0bp);
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\draw (119.0bp,37.5bp) node {$$4$$};
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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 (76.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (76.0bp,30.0bp) node {$b$};
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\end{scope}
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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 (393.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
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\draw (393.0bp,50.0bp) node {$\bot$};
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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 (334.0bp,90.0bp) ellipse (11.0bp and 11.0bp);
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\draw (334.0bp,90.0bp) node {$e$};
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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 (162.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (162.0bp,30.0bp) 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 (248.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
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\draw (248.0bp,50.0bp) 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 (291.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (291.0bp,11.0bp) 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 (334.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
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\draw (334.0bp,50.0bp) 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{$2. \; \lnot d \lor e$}
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\AxiomC{$7. \; \lnot d \lor \lnot e$}
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\BinaryInfC{$\lnot d$}
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\AxiomC{$5. \; \lnot c \lor d$}
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\BinaryInfC{$\lnot c$}
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\AxiomC{$6. \; \lnot c \lor e$}
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\BinaryInfC{$\lnot c \lor e$}
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\AxiomC{$4. \; \lnot b \lor c$}
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\BinaryInfC{$e \lor \lnot b$}
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\AxiomC{$8. \; b$}
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\BinaryInfC{$e$}
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\end{prooftree}
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