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211 lines
7.9 KiB
211 lines
7.9 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|1|1|1}
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\dpllAssi{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, c$|\makecell{$\lnot a, b, c, $ \\ $\lnot d$}|\makecell{$\lnot a, b, c, $ \\ $\lnot d, \lnot e$}}
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\dpllClause{1}{$b, d$}{$b, d$|$b, d$|\done|\done|\done|\done}
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\dpllClause{2}{$b, c$}{$b, c$|$b, c$|\done|\done|\done|\done}
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\dpllClause{3}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot b, \lnot e$|$\lnot e$|$\lnot e$|$\lnot e$|\done}
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\dpllClause{4}{$\lnot a, \lnot c$}{$\lnot a, \lnot c$|\done|\done|\done|\done|\done}
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\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot d$|\done|\done}
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\dpllClause{6}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$c$|\done|\done|\done}
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\dpllClause{7}{$a, b$}{$a, b$|$b$|\done|\done|\done|\done}
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\dpllClause{8}{$\lnot b, d, e$}{$\lnot b, d, e$|$\lnot b, d, e$|$d, e$|$d, e$|$e$|\conflict}
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\dpllBCP{ - |$b$|$c$|$\lnot d$|$\lnot e$| - }
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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 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 -> 6
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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 {$$7$$};
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% Edge: 3 -> 2
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\draw [->] (237.0bp,68.631bp) .. controls (261.99bp,66.427bp) and (329.17bp,60.312bp) .. (385.0bp,53.5bp) .. controls (387.51bp,53.194bp) and (390.14bp,52.849bp) .. (402.9bp,51.044bp);
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% Edge: 4 -> 7
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\draw [->] (280.3bp,30.5bp) .. controls (293.47bp,30.5bp) and (316.58bp,30.5bp) .. (343.88bp,30.5bp);
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\draw (312.0bp,38.0bp) node {$$8$$};
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% Edge: 5 -> 4
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\draw [->] (194.3bp,30.5bp) .. controls (207.47bp,30.5bp) and (230.58bp,30.5bp) .. (257.88bp,30.5bp);
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\draw (226.0bp,38.0bp) node {$$5$$};
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% Edge: 6 -> 3
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\draw [->] (106.44bp,36.631bp) .. controls (111.81bp,40.268bp) and (119.03bp,44.701bp) .. (126.0bp,47.5bp) .. controls (152.19bp,58.026bp) and (184.4bp,63.996bp) .. (214.84bp,68.355bp);
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\draw (140.0bp,63.0bp) node {$$3$$};
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% Edge: 6 -> 5
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\draw [->] (108.3bp,30.5bp) .. controls (121.47bp,30.5bp) and (144.58bp,30.5bp) .. (171.88bp,30.5bp);
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\draw (140.0bp,38.0bp) node {$$6$$};
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% Edge: 6 -> 7
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\draw [->] (107.88bp,26.93bp) .. controls (121.91bp,22.069bp) and (148.52bp,13.617bp) .. (172.0bp,10.5bp) .. controls (219.58bp,4.1832bp) and (232.42bp,4.1832bp) .. (280.0bp,10.5bp) .. controls (298.9bp,13.009bp) and (319.81bp,18.971bp) .. (344.12bp,26.93bp);
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\draw (226.0bp,14.0bp) node {$$8$$};
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% Edge: 7 -> 2
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\draw [->] (365.67bp,33.723bp) .. controls (373.24bp,36.246bp) and (384.02bp,39.839bp) .. (403.09bp,46.197bp);
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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: 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 (97.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (97.0bp,30.5bp) node {$b$};
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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 (414.0bp,49.5bp) ellipse (11.0bp and 11.0bp);
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\draw (414.0bp,49.5bp) 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 (226.0bp,69.5bp) ellipse (11.0bp and 11.0bp);
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\draw (226.0bp,69.5bp) node {$\lnot e$};
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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 (269.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (269.0bp,30.5bp) node {$\lnot d$};
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\end{scope}
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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 (355.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (355.0bp,30.5bp) 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,30.5bp) ellipse (11.0bp and 11.0bp);
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\draw (183.0bp,30.5bp) node {$c$};
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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{$8. \; \lnot b \lor d \lor e$}
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\AxiomC{$5. \; \lnot c \lor \lnot d$}
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\BinaryInfC{$\lnot b \lor e \lor \lnot c$}
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\AxiomC{$3. \; \lnot b \lor \lnot e$}
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\BinaryInfC{$\lnot b \lor \lnot c$}
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\AxiomC{$6. \; \lnot b \lor c$}
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\BinaryInfC{$\lnot b$}
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\AxiomC{$7. \; a \lor b$}
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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}{4}
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\dpllStep{7|8|9|10}
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\dpllDecL{0|0|0|0}
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\dpllAssi{ - |$a$|$a, \lnot c$|$a, \lnot c, \lnot b$}
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\dpllClause{1}{$b, d$}{$b, d$|$b, d$|$b, d$|$d$}
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\dpllClause{2}{$b, c$}{$b, c$|$b, c$|$b$|\conflict}
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\dpllClause{3}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot b, \lnot e$|$\lnot b, \lnot e$|\done}
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\dpllClause{4}{$\lnot a, \lnot c$}{$\lnot a, \lnot c$|$\lnot c$|\done|\done}
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\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|\done|\done}
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\dpllClause{6}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$\lnot b$|\done}
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\dpllClause{7}{$a, b$}{$a, b$|\done|\done|\done}
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\dpllClause{8}{$\lnot b, d, e$}{$\lnot b, d, e$|$\lnot b, d, e$|$\lnot b, d, e$|\done}
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\dpllClause{9}{$a$}{$a$|\done|\done|\done}
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\dpllBCP{$a$|$\lnot c$|$\lnot b$| - }
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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 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 -> 5
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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 {$$9$$};
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% Edge: 2 -> 1
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\draw [->] (258.67bp,47.438bp) .. controls (266.41bp,44.585bp) and (277.51bp,40.495bp) .. (296.47bp,33.51bp);
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% Edge: 3 -> 2
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\draw [->] (172.97bp,33.373bp) .. controls (186.23bp,36.53bp) and (209.98bp,42.186bp) .. (237.05bp,48.63bp);
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\draw (205.0bp,50.5bp) node {$$2$$};
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% Edge: 3 -> 4
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\draw [->] (172.11bp,26.371bp) .. controls (177.48bp,23.828bp) and (184.48bp,20.828bp) .. (191.0bp,19.0bp) .. controls (202.65bp,15.733bp) and (216.06bp,13.758bp) .. (236.92bp,11.639bp);
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\draw (205.0bp,26.5bp) node {$$6$$};
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% Edge: 4 -> 1
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\draw [->] (258.67bp,14.223bp) .. controls (266.24bp,16.746bp) and (277.02bp,20.339bp) .. (296.09bp,26.697bp);
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% Edge: 5 -> 3
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\draw [->] (87.3bp,31.0bp) .. controls (100.47bp,31.0bp) and (123.58bp,31.0bp) .. (150.88bp,31.0bp);
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\draw (119.0bp,38.5bp) node {$$4$$};
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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 (76.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (76.0bp,31.0bp) 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 (307.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
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\draw (307.0bp,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 (248.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
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\draw (248.0bp,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,31.0bp) ellipse (11.0bp and 11.0bp);
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\draw (162.0bp,31.0bp) node {$\lnot c$};
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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,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (248.0bp,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{$2. \; b \lor c$}
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\AxiomC{$6. \; \lnot b \lor c$}
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\BinaryInfC{$c$}
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\AxiomC{$4. \; \lnot a \lor \lnot c$}
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\BinaryInfC{$\lnot a$}
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\AxiomC{$9. \; a$}
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\BinaryInfC{$\bot$}
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\end{prooftree}
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