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222 lines
8.4 KiB
222 lines
8.4 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{ - |$\lnot a$|$\lnot a, \lnot c$|$\lnot a, \lnot c, b$|\makecell{$\lnot a, \lnot c, b, $ \\ $\lnot d$}}
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\dpllClause{1}{$\lnot b, c, d$}{$\lnot b, c, d$|$\lnot b, c, d$|$\lnot b, d$|$d$|\conflict}
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\dpllClause{2}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot d$|\done}
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\dpllClause{3}{$a, \lnot c$}{$a, \lnot c$|$\lnot c$|\done|\done|\done}
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\dpllClause{4}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|\done|\done|\done}
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\dpllClause{5}{$b, c$}{$b, c$|$b, c$|$b$|\done|\done}
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\dpllClause{6}{$\lnot a, \lnot e$}{$\lnot a, \lnot e$|\done|\done|\done|\done}
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\dpllBCP{ - |$\lnot c$|$b$|$\lnot d$| - }
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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 -> 5
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\draw [->] (22.3bp,56.0bp) .. controls (35.47bp,56.0bp) and (58.583bp,56.0bp) .. (85.878bp,56.0bp);
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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,63.5bp) node {$$3$$};
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% Edge: 3 -> 2
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\draw [->] (285.67bp,47.438bp) .. controls (293.41bp,44.585bp) and (304.51bp,40.495bp) .. (323.47bp,33.51bp);
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% Edge: 4 -> 2
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\draw [->] (285.67bp,14.223bp) .. controls (293.24bp,16.746bp) and (304.02bp,20.339bp) .. (323.09bp,26.697bp);
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% Edge: 5 -> 3
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\draw [->] (107.41bp,59.835bp) .. controls (112.76bp,61.808bp) and (119.64bp,64.004bp) .. (126.0bp,65.0bp) .. controls (149.1bp,68.621bp) and (199.96bp,74.429bp) .. (246.0bp,64.0bp) .. controls (249.24bp,63.266bp) and (252.55bp,62.125bp) .. (265.02bp,56.363bp);
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\draw (186.0bp,76.5bp) node {$$1$$};
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% Edge: 5 -> 6
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\draw [->] (107.98bp,53.247bp) .. controls (121.94bp,49.395bp) and (147.6bp,42.318bp) .. (175.14bp,34.721bp);
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\draw (140.0bp,56.5bp) node {$$5$$};
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% Edge: 6 -> 3
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\draw [->] (196.98bp,34.18bp) .. controls (210.88bp,37.215bp) and (236.36bp,42.779bp) .. (264.14bp,48.846bp);
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\draw (232.0bp,52.5bp) node {$$1$$};
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% Edge: 6 -> 4
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\draw [->] (196.37bp,28.221bp) .. controls (202.46bp,25.881bp) and (210.6bp,22.959bp) .. (218.0bp,21.0bp) .. controls (229.76bp,17.886bp) and (243.17bp,15.453bp) .. (263.98bp,12.283bp);
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\draw (232.0bp,28.5bp) node {$$2$$};
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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,56.0bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,56.0bp) node {$\lnot a$};
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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 (97.0bp,56.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,56.0bp) node {$\lnot c$};
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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 (334.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (334.0bp,30.0bp) 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 (275.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (275.0bp,51.0bp) node {$d$};
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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 (275.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (275.0bp,11.0bp) 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 (186.0bp,32.0bp) ellipse (11.0bp and 11.0bp);
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\draw (186.0bp,32.0bp) node {$b$};
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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{$1. \; \lnot b \lor c \lor d$}
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\AxiomC{$2. \; \lnot b \lor \lnot d$}
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\BinaryInfC{$\lnot b \lor c$}
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\AxiomC{$5. \; b \lor c$}
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\BinaryInfC{$c$}
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\AxiomC{$3. \; a \lor \lnot c$}
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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}{6}
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\dpllStep{6|7|8|9|10|11}
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\dpllDecL{0|0|0|0|0|0}
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\dpllAssi{ - |$a$|$a, \lnot e$|$a, \lnot e, \lnot c$|\makecell{$a, \lnot e, \lnot c, $ \\ $b$}|\makecell{$a, \lnot e, \lnot c, $ \\ $b, \lnot d$}}
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\dpllClause{1}{$\lnot b, c, d$}{$\lnot b, c, d$|$\lnot b, c, d$|$\lnot b, c, d$|$\lnot b, d$|$d$|\conflict}
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\dpllClause{2}{$\lnot b, \lnot d$}{$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot b, \lnot d$|$\lnot d$|\done}
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\dpllClause{3}{$a, \lnot c$}{$a, \lnot c$|\done|\done|\done|\done|\done}
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\dpllClause{4}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c$|\done|\done|\done}
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\dpllClause{5}{$b, c$}{$b, c$|$b, c$|$b, c$|$b$|\done|\done}
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\dpllClause{6}{$\lnot a, \lnot e$}{$\lnot a, \lnot e$|$\lnot e$|\done|\done|\done|\done}
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\dpllClause{7}{$a$}{$a$|\done|\done|\done|\done|\done}
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\dpllBCP{$a$|$\lnot e$|$\lnot c$|$b$|$\lnot d$| - }
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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 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: 0 -> 7
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\draw [->] (1.0536bp,56.0bp) .. controls (2.5071bp,56.0bp) and (33.188bp,56.0bp) .. (64.696bp,56.0bp);
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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,63.5bp) node {$$7$$};
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% Edge: 2 -> 1
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\draw [->] (436.67bp,47.438bp) .. controls (444.41bp,44.585bp) and (455.51bp,40.495bp) .. (474.47bp,33.51bp);
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% Edge: 3 -> 1
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\draw [->] (436.67bp,14.223bp) .. controls (444.24bp,16.746bp) and (455.02bp,20.339bp) .. (474.09bp,26.697bp);
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% Edge: 4 -> 2
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\draw [->] (258.41bp,59.835bp) .. controls (263.76bp,61.808bp) and (270.64bp,64.004bp) .. (277.0bp,65.0bp) .. controls (300.93bp,68.751bp) and (353.64bp,72.391bp) .. (397.0bp,63.0bp) .. controls (400.2bp,62.306bp) and (403.5bp,61.244bp) .. (415.96bp,55.925bp);
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\draw (337.0bp,75.5bp) node {$$1$$};
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% Edge: 4 -> 5
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\draw [->] (258.98bp,53.247bp) .. controls (272.94bp,49.395bp) and (298.6bp,42.318bp) .. (326.14bp,34.721bp);
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\draw (291.0bp,55.5bp) node {$$5$$};
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% Edge: 5 -> 2
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\draw [->] (347.98bp,34.18bp) .. controls (361.88bp,37.215bp) and (387.36bp,42.779bp) .. (415.14bp,48.846bp);
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\draw (383.0bp,51.5bp) node {$$1$$};
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% Edge: 5 -> 3
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\draw [->] (347.33bp,27.798bp) .. controls (353.39bp,25.214bp) and (361.54bp,22.021bp) .. (369.0bp,20.0bp) .. controls (380.71bp,16.83bp) and (394.12bp,14.627bp) .. (414.95bp,11.971bp);
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\draw (383.0bp,27.5bp) node {$$2$$};
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% Edge: 6 -> 4
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\draw [->] (173.3bp,56.0bp) .. controls (186.47bp,56.0bp) and (209.58bp,56.0bp) .. (236.88bp,56.0bp);
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\draw (205.0bp,63.5bp) node {$$4$$};
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% Edge: 7 -> 6
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\draw [->] (87.3bp,56.0bp) .. controls (100.47bp,56.0bp) and (123.58bp,56.0bp) .. (150.88bp,56.0bp);
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\draw (119.0bp,63.5bp) node {$$6$$};
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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,56.0bp) ellipse (11.0bp and 11.0bp);
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\draw (76.0bp,56.0bp) node {$a$};
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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 (485.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (485.0bp,30.0bp) 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 (426.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (426.0bp,51.0bp) 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 (426.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (426.0bp,11.0bp) node {$\lnot d$};
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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,56.0bp) ellipse (11.0bp and 11.0bp);
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\draw (248.0bp,56.0bp) node {$\lnot c$};
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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 (337.0bp,32.0bp) ellipse (11.0bp and 11.0bp);
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\draw (337.0bp,32.0bp) node {$b$};
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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 (162.0bp,56.0bp) ellipse (11.0bp and 11.0bp);
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\draw (162.0bp,56.0bp) 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{$1. \; \lnot b \lor c \lor d$}
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\AxiomC{$2. \; \lnot b \lor \lnot d$}
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\BinaryInfC{$\lnot b \lor c$}
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\AxiomC{$5. \; b \lor c$}
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\BinaryInfC{$c$}
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\AxiomC{$4. \; \lnot c \lor e$}
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\BinaryInfC{$e$}
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\AxiomC{$6. \; \lnot a \lor \lnot e$}
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\BinaryInfC{$\lnot a$}
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\AxiomC{$7. \; a$}
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\BinaryInfC{$\bot$}
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\end{prooftree}
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