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184 lines
7.7 KiB
184 lines
7.7 KiB
\begin{cofactors}
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$f$ \= $= (((p \lor q) \land (r \lor \lnot s)) \land (\lnot p \lor t))$\\
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\>$f_{p}$ \= $= ((r \lor \lnot s) \land t)$\\
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\>\>$f_{pr}$ \= $= t$\\
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\>\>\>$f_{prt}$ \= $= \true$\\
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\>\>\>$f_{pr\lnot t}$ \= $= \false$\\
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\>\>$f_{p\lnot r}$ \= $= (\lnot s \land t)$\\
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\>\>\>$f_{p\lnot rs}$ \= $= \false$\\
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\>\>\>$f_{p\lnot r\lnot s}$ \= $= f_{pr}$\\
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\>$f_{\lnot p}$ \= $= (q \land (r \lor \lnot s))$\\
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\>\>$f_{\lnot pq}$ \= $= (r \lor \lnot s)$\\
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\>\>\>$f_{\lnot pqr}$ \= $= \true$\\
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\>\>\>$f_{\lnot pq\lnot r}$ \= $= \lnot s$\\
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\>\>\>\>$f_{\lnot pq\lnot rs}$ \= $= \false$\\
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\>\>\>\>$f_{\lnot pq\lnot r\lnot s}$ \= $= \true$\\
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\>\>$f_{\lnot p\lnot q}$ \= $= \false$\\
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\end{cofactors}
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The final ROBDD:
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\begin{center}
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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: f_E -> p0
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\draw [] (107.57bp,268.99bp) .. controls (107.57bp,258.92bp) and (107.57bp,243.47bp) .. (107.57bp,233.3bp);
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% Edge: f_p -> r1
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\draw [] (188.57bp,210.99bp) .. controls (188.57bp,200.92bp) and (188.57bp,185.47bp) .. (188.57bp,175.3bp);
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% Edge: f_pr -> t2
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\draw [] (231.63bp,94.988bp) .. controls (221.85bp,84.04bp) and (206.4bp,66.729bp) .. (197.5bp,56.763bp);
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% Edge: f_p!r -> s3
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\draw [] (140.07bp,152.99bp) .. controls (142.62bp,142.8bp) and (146.55bp,127.09bp) .. (149.09bp,116.93bp);
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (144.24bp,136.33bp) node {\Large$\bullet$};
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% Edge: f_!p -> q4
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\draw [] (23.569bp,210.99bp) .. controls (23.569bp,200.92bp) and (23.569bp,185.47bp) .. (23.569bp,175.3bp);
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% Edge: f_!pq -> r5
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\draw [] (70.099bp,152.99bp) .. controls (65.493bp,142.67bp) and (58.363bp,126.7bp) .. (53.833bp,116.55bp);
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% Edge: f_!pq!r -> s6
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\draw [] (98.781bp,94.988bp) .. controls (96.961bp,84.795bp) and (94.156bp,69.087bp) .. (92.341bp,58.925bp);
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\draw (95.857bp,78.614bp) node {\Large$\bullet$};
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% Edge: p0 -> q4
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\draw [] (98.896bp,215.22bp) .. controls (82.799bp,204.49bp) and (48.476bp,181.6bp) .. (32.321bp,170.83bp);
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\draw (48.962bp,181.93bp) node {\Large$\circ$};
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% Edge: p0 -> r1
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\draw [] (116.24bp,215.01bp) .. controls (131.75bp,204.29bp) and (164.08bp,181.93bp) .. (179.72bp,171.12bp);
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% Edge: q4 -> r5
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\draw [] (27.862bp,153.75bp) .. controls (32.651bp,143.44bp) and (40.356bp,126.84bp) .. (45.182bp,116.45bp);
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% Edge: q4 -> 6
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\draw [] (22.854bp,152.99bp) .. controls (21.739bp,137.38bp) and (19.701bp,108.85bp) .. (19.575bp,107.09bp);
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\draw (21.0bp,127.04bp) node {\Large$\bullet$};
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% Edge: r5 -> s6
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\draw [] (55.619bp,96.737bp) .. controls (63.37bp,86.149bp) and (76.731bp,67.901bp) .. (84.494bp,57.297bp);
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\draw (72.68bp,73.434bp) node {\Large$\bullet$};
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% Edge: r5 -> 3
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\draw [] (49.569bp,94.988bp) .. controls (49.569bp,79.384bp) and (49.569bp,50.854bp) .. (49.569bp,49.086bp);
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% Edge: s6 -> 4
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\draw [] (88.35bp,36.791bp) .. controls (85.496bp,23.663bp) and (80.869bp,2.3815bp) .. (80.583bp,1.0642bp);
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% Edge: s6 -> 5
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\draw [] (92.566bp,36.791bp) .. controls (95.135bp,23.663bp) and (99.299bp,2.3815bp) .. (99.556bp,1.0642bp);
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\draw (95.716bp,20.692bp) node {\Large$\bullet$};
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% Edge: r1 -> s3
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\draw [] (182.79bp,154.25bp) .. controls (175.8bp,143.67bp) and (164.11bp,125.98bp) .. (157.19bp,115.51bp);
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\draw (168.21bp,132.19bp) node {\Large$\bullet$};
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% Edge: r1 -> t2
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\draw [] (188.75bp,152.88bp) .. controls (189.12bp,131.3bp) and (190.01bp,80.962bp) .. (190.39bp,59.258bp);
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% Edge: s3 -> t2
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\draw [] (157.66bp,96.25bp) .. controls (165.03bp,85.668bp) and (177.35bp,67.976bp) .. (184.65bp,57.505bp);
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\draw (173.22bp,73.917bp) node {\Large$\bullet$};
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% Edge: s3 -> 2
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\draw [] (151.57bp,94.988bp) .. controls (151.57bp,79.384bp) and (151.57bp,50.854bp) .. (151.57bp,49.086bp);
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% Edge: t2 -> 0
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\draw [] (188.35bp,36.791bp) .. controls (185.5bp,23.663bp) and (180.87bp,2.3815bp) .. (180.58bp,1.0642bp);
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% Edge: t2 -> 1
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\draw [] (192.57bp,36.791bp) .. controls (195.13bp,23.663bp) and (199.3bp,2.3815bp) .. (199.56bp,1.0642bp);
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\draw (195.72bp,20.692bp) node {\Large$\bullet$};
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% Node: f_E
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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 (129.07bp,291.0bp) -- (86.07bp,291.0bp) -- (86.07bp,269.0bp) -- (129.07bp,269.0bp) -- cycle;
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\draw (107.57bp,280.0bp) node {$f$};
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\end{scope}
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% Node: p0
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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 (107.57bp,222.0bp) ellipse (11.0bp and 11.0bp);
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\draw (107.57bp,222.0bp) node {$p$};
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\end{scope}
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% Node: f_p
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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 (210.07bp,233.0bp) -- (167.07bp,233.0bp) -- (167.07bp,211.0bp) -- (210.07bp,211.0bp) -- cycle;
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\draw (188.57bp,222.0bp) node {$f_{p}$};
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\end{scope}
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% Node: r1
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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 (188.57bp,164.0bp) ellipse (11.0bp and 11.0bp);
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\draw (188.57bp,164.0bp) node {$r$};
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\end{scope}
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% Node: f_pr
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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 (262.07bp,117.0bp) -- (219.07bp,117.0bp) -- (219.07bp,95.0bp) -- (262.07bp,95.0bp) -- cycle;
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\draw (240.57bp,106.0bp) node {$f_{pr}$};
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\end{scope}
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% Node: t2
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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 (190.57bp,48.0bp) ellipse (11.0bp and 11.0bp);
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\draw (190.57bp,48.0bp) node {$t$};
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\end{scope}
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% Node: f_p!r
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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 (159.07bp,175.0bp) -- (116.07bp,175.0bp) -- (116.07bp,153.0bp) -- (159.07bp,153.0bp) -- cycle;
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\draw (137.57bp,164.0bp) node {$f_{p\lnot r}$};
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\end{scope}
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% Node: s3
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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 (151.57bp,106.0bp) ellipse (11.0bp and 11.0bp);
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\draw (151.57bp,106.0bp) node {$s$};
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\end{scope}
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% Node: f_!p
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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 (45.07bp,233.0bp) -- (2.07bp,233.0bp) -- (2.07bp,211.0bp) -- (45.07bp,211.0bp) -- cycle;
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\draw (23.569bp,222.0bp) node {$f_{\lnot p}$};
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\end{scope}
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% Node: q4
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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 (23.57bp,164.0bp) ellipse (11.0bp and 11.0bp);
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\draw (23.569bp,164.0bp) node {$q$};
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\end{scope}
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% Node: f_!pq
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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 (96.07bp,175.0bp) -- (53.07bp,175.0bp) -- (53.07bp,153.0bp) -- (96.07bp,153.0bp) -- cycle;
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\draw (74.569bp,164.0bp) node {$f_{\lnot pq}$};
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\end{scope}
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% Node: r5
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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 (49.57bp,106.0bp) ellipse (11.0bp and 11.0bp);
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\draw (49.569bp,106.0bp) node {$r$};
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\end{scope}
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% Node: f_!pq!r
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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 (122.07bp,117.0bp) -- (79.07bp,117.0bp) -- (79.07bp,95.0bp) -- (122.07bp,95.0bp) -- cycle;
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\draw (100.57bp,106.0bp) node {$f_{\lnot pq\lnot r}$};
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\end{scope}
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% Node: s6
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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 (90.57bp,48.0bp) ellipse (11.0bp and 11.0bp);
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\draw (90.569bp,48.0bp) node {$s$};
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\end{scope}
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%
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\end{tikzpicture}
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}
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\end{center}
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