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123 lines
5.0 KiB
123 lines
5.0 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|1|2|2|2}
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\dpllAssi{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, \lnot c$|\makecell{$\lnot a, b, \lnot c, $ \\ $\lnot e$}|\makecell{$\lnot a, b, \lnot c, $ \\ $\lnot e, \lnot d$}}
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\dpllClause{1}{$\lnot a, \lnot b$}{$\lnot a, \lnot b$|\done|\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}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|\done|\done|\done|\done}
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\dpllClause{4}{$c, \lnot d, e$}{$c, \lnot d, e$|$c, \lnot d, e$|$c, \lnot d, e$|$\lnot d, e$|$\lnot d$|\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}{$\lnot a, b$}{$\lnot a, b$|\done|\done|\done|\done|\done}
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\dpllClause{7}{$a, c, \lnot e$}{$a, c, \lnot e$|$c, \lnot e$|$c, \lnot e$|$\lnot e$|\done|\done}
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\dpllBCP{ - | - | - |$\lnot e$|$\lnot d$| - }
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\dpllPL{ - |$b$| - | - | - | - }
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\dpllDeci{$\lnot a$| - |$\lnot c$| - | - | - }
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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 -> 5
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\draw [->] (22.199bp,102.59bp) .. controls (46.427bp,104.91bp) and (109.22bp,109.27bp) .. (160.0bp,98.5bp) .. controls (163.17bp,97.828bp) and (166.44bp,96.837bp) .. (178.9bp,91.96bp);
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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,112.0bp) node {$$4$$};
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% Edge: 1 -> 6
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\draw [->] (21.231bp,96.616bp) .. controls (26.641bp,93.822bp) and (33.641bp,90.322bp) .. (40.0bp,87.5bp) .. controls (53.079bp,81.696bp) and (68.11bp,75.848bp) .. (89.282bp,67.976bp);
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\draw (54.0bp,95.0bp) node {$$7$$};
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% Edge: 2 -> 4
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\draw [->] (22.182bp,29.536bp) .. controls (40.588bp,27.986bp) and (80.592bp,25.495bp) .. (114.0bp,29.5bp) .. controls (132.62bp,31.732bp) and (153.33bp,37.017bp) .. (178.08bp,44.285bp);
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\draw (100.0bp,37.0bp) node {$$2$$};
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% Edge: 2 -> 6
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\draw [->] (21.645bp,33.374bp) .. controls (32.91bp,36.821bp) and (52.04bp,42.96bp) .. (68.0bp,49.5bp) .. controls (72.232bp,51.234bp) and (76.703bp,53.271bp) .. (89.911bp,59.734bp);
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\draw (54.0bp,57.0bp) 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 -> 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: 6 -> 4
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\draw [->] (109.85bp,58.993bp) .. controls (115.85bp,55.569bp) and (124.11bp,51.458bp) .. (132.0bp,49.5bp) .. controls (143.63bp,46.614bp) and (157.04bp,46.043bp) .. (177.91bp,46.626bp);
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\draw (146.0bp,57.0bp) node {$$2$$};
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% Edge: 6 -> 5
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\draw [->] (110.98bp,67.138bp) .. controls (124.94bp,70.83bp) and (150.6bp,77.612bp) .. (178.14bp,84.892bp);
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\draw (146.0bp,87.0bp) 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,101.5bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,101.5bp) 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 (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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% 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 (100.0bp,64.5bp) ellipse (11.0bp and 11.0bp);
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\draw (100.0bp,64.5bp) 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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%
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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{$7. \; a \lor c \lor \lnot e$}
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\BinaryInfC{$a \lor c$}
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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{7|8|9}
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\dpllDecL{1|1|1}
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\dpllAssi{$\lnot a, b$|$\lnot a, b, c$|\makecell{$\lnot a, b, c, $ \\ $e$}}
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\dpllClause{1}{$\lnot a, \lnot b$}{\done|\done|\done}
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\dpllClause{2}{$a, d, e$}{$d, e$|$d, e$|\done}
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\dpllClause{3}{$b, \lnot c$}{\done|\done|\done}
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\dpllClause{4}{$c, \lnot d, e$}{$c, \lnot d, e$|\done|\done}
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\dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$e$|\done}
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\dpllClause{6}{$\lnot a, b$}{\done|\done|\done}
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\dpllClause{7}{$a, c, \lnot e$}{$c, \lnot e$|\done|\done}
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\dpllClause{8}{$a, c$}{$c$|\done|\done}
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\dpllBCP{$c$|$e$| - }
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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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