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206 lines
7.3 KiB
206 lines
7.3 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{ - |$\lnot a$|$\lnot a, \lnot d$|$\lnot a, \lnot d, b$|\makecell{$\lnot a, \lnot d, b, $ \\ $\lnot c$}}
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\dpllClause{1}{$b, d$}{$b, d$|$b, d$|$b$|\done|\done}
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\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done}
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\dpllClause{3}{$a, \lnot d$}{$a, \lnot d$|$\lnot d$|\done|\done|\done}
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\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$\lnot b, c$|$c$|\conflict}
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\dpllClause{5}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c$|$\lnot c$|\done}
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\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|\done}
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\dpllClause{7}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|\done|\done|\done}
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\dpllBCP{ - |$\lnot d$|$b$|$\lnot c$| - }
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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 -> 4
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\draw [->] (22.3bp,30.5bp) .. controls (35.47bp,30.5bp) and (58.583bp,30.5bp) .. (85.878bp,30.5bp);
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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,38.0bp) node {$$3$$};
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% Edge: 3 -> 5
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\draw [->] (194.3bp,50.5bp) .. controls (207.47bp,50.5bp) and (230.58bp,50.5bp) .. (257.88bp,50.5bp);
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\draw (226.0bp,58.0bp) node {$$4$$};
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% Edge: 4 -> 3
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\draw [->] (107.97bp,32.873bp) .. controls (121.23bp,36.03bp) and (144.98bp,41.686bp) .. (172.05bp,48.13bp);
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\draw (140.0bp,50.0bp) node {$$1$$};
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% Edge: 4 -> 6
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\draw [->] (107.07bp,25.696bp) .. controls (112.42bp,23.094bp) and (119.42bp,20.094bp) .. (126.0bp,18.5bp) .. controls (152.72bp,12.025bp) and (184.6bp,10.902bp) .. (215.0bp,11.119bp);
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\draw (140.0bp,26.0bp) node {$$5$$};
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% Edge: 5 -> 2
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\draw [->] (279.16bp,46.162bp) .. controls (287.01bp,42.445bp) and (298.56bp,36.972bp) .. (317.68bp,27.917bp);
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% Edge: 6 -> 2
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\draw [->] (236.95bp,12.694bp) .. controls (253.12bp,14.634bp) and (285.4bp,18.508bp) .. (316.79bp,22.275bp);
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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,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 (97.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,30.5bp) 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 (328.0bp,23.5bp) ellipse (11.0bp and 11.0bp);
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\draw (328.0bp,23.5bp) 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,50.5bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,50.5bp) node {$b$};
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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 (269.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
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\draw (269.0bp,50.5bp) node {$c$};
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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 (226.0bp,11.5bp) ellipse (11.0bp and 11.0bp);
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\draw (226.0bp,11.5bp) node {$\lnot c$};
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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{$4. \; \lnot b \lor c$}
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\AxiomC{$1. \; b \lor d$}
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\BinaryInfC{$c \lor d$}
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\AxiomC{$5. \; \lnot c \lor d$}
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\BinaryInfC{$d$}
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\AxiomC{$3. \; a \lor \lnot d$}
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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}{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{ - |$a$|$a, c$|$a, c, d$|\makecell{$a, c, d, $ \\ $\lnot e$}}
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\dpllClause{1}{$b, d$}{$b, d$|$b, d$|$b, d$|\done|\done}
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\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
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\dpllClause{3}{$a, \lnot d$}{$a, \lnot d$|\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}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$d$|\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}{$a$}{$a$|\done|\done|\done|\done}
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\dpllBCP{$a$|$c$|$d$|$\lnot e$| - }
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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 -> 6
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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 -> 3
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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: 2 -> 4
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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: 3 -> 5
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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: 4 -> 1
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\draw [->] (301.95bp,12.194bp) .. controls (318.12bp,14.134bp) and (350.4bp,18.008bp) .. (381.79bp,21.775bp);
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% Edge: 5 -> 1
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\draw [->] (344.16bp,45.662bp) .. controls (352.01bp,41.945bp) and (363.56bp,36.472bp) .. (382.68bp,27.417bp);
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% Edge: 6 -> 2
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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 {$$2$$};
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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 (76.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (76.0bp,30.0bp) 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 (393.0bp,23.0bp) ellipse (11.0bp and 11.0bp);
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\draw (393.0bp,23.0bp) 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,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: 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,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: 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 (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: 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 (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{$7. \; \lnot d \lor \lnot e$}
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\AxiomC{$5. \; \lnot c \lor d$}
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\BinaryInfC{$\lnot e \lor \lnot c$}
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\AxiomC{$6. \; \lnot c \lor e$}
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\BinaryInfC{$\lnot c$}
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\AxiomC{$2. \; \lnot a \lor c$}
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\BinaryInfC{$\lnot a$}
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\AxiomC{$8. \; a$}
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\BinaryInfC{$\bot$}
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\end{prooftree}
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