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166 lines
5.4 KiB
166 lines
5.4 KiB
\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{4}
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\dpllStep{1|2|3|4}
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\dpllDecL{0|1|1|1}
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\dpllAssi{ - |$a$|$a, \lnot c$|$a, \lnot c, b$}
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\dpllClause{1}{$a, b$}{$a, b$|\done|\done|\done}
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\dpllClause{2}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$\lnot b$|\conflict}
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\dpllClause{3}{$\lnot a, \lnot c$}{$\lnot a, \lnot c$|$\lnot c$|\done|\done}
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\dpllClause{4}{$b, c$}{$b, c$|$b, c$|$b$|\done}
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\dpllClause{5}{$a, \lnot b$}{$a, \lnot b$|\done|\done|\done}
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\dpllBCP{ - |$\lnot c$|$b$| - }
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\dpllPL{ - | - | - | - }
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\dpllDeci{$a$| - | - | - }
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\end{dplltabular}
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}
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Conflict in step 4\\
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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 [->] (22.3bp,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 {$$3$$};
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% Edge: 3 -> 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: 4 -> 3
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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: 4 -> 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 {$$4$$};
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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 {$a$};
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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 (97.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,31.0bp) 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 (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: 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,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,51.0bp) 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 (183.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,11.0bp) 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{$2. \; \lnot b \lor c$}
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\AxiomC{$4. \; b \lor c$}
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\BinaryInfC{$c$}
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\AxiomC{$3. \; \lnot a \lor \lnot c$}
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\BinaryInfC{$\lnot a$}
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\end{prooftree}
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\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{3}
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\dpllStep{5|6|7}
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\dpllDecL{0|0|0}
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\dpllAssi{ - |$\lnot a$|$\lnot a, b$}
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\dpllClause{1}{$a, b$}{$a, b$|$b$|\done}
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\dpllClause{2}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$c$}
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\dpllClause{3}{$\lnot a, \lnot c$}{$\lnot a, \lnot c$|\done|\done}
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\dpllClause{4}{$b, c$}{$b, c$|$b, c$|\done}
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\dpllClause{5}{$a, \lnot b$}{$a, \lnot b$|$\lnot b$|\conflict}
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\dpllClause{6}{$\lnot a$}{$\lnot a$|\done|\done}
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\dpllBCP{$\lnot a$|$b$| - }
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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 7\\
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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 -> 4
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\draw [->] (1.0536bp,31.0bp) .. controls (2.5071bp,31.0bp) and (33.188bp,31.0bp) .. (64.696bp,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 (33.0bp,38.5bp) node {$$6$$};
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% Edge: 2 -> 1
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\draw [->] (172.67bp,47.438bp) .. controls (180.41bp,44.585bp) and (191.51bp,40.495bp) .. (210.47bp,33.51bp);
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% Edge: 3 -> 1
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\draw [->] (172.67bp,14.223bp) .. controls (180.24bp,16.746bp) and (191.02bp,20.339bp) .. (210.09bp,26.697bp);
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% Edge: 4 -> 2
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\draw [->] (86.966bp,33.373bp) .. controls (100.23bp,36.53bp) and (123.98bp,42.186bp) .. (151.05bp,48.63bp);
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\draw (119.0bp,50.5bp) node {$$1$$};
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% Edge: 4 -> 3
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\draw [->] (86.111bp,26.371bp) .. controls (91.482bp,23.828bp) and (98.482bp,20.828bp) .. (105.0bp,19.0bp) .. controls (116.65bp,15.733bp) and (130.06bp,13.758bp) .. (150.92bp,11.639bp);
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\draw (119.0bp,26.5bp) node {$$5$$};
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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 (76.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (76.0bp,31.0bp) node {$\lnot a$};
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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 (221.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (221.0bp,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 (162.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (162.0bp,51.0bp) node {$b$};
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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 (162.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (162.0bp,11.0bp) node {$\lnot b$};
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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{$1. \; a \lor b$}
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\AxiomC{$5. \; a \lor \lnot b$}
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\BinaryInfC{$a$}
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\AxiomC{$6. \; \lnot a$}
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\BinaryInfC{$\bot$}
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\end{prooftree}
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