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36 lines
1.1 KiB
36 lines
1.1 KiB
\begin{center}
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\begin{egraph}
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\node[base node] (a) {$a$};
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\node[base node] (b) [above right of=a] {$b$};
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\node[base node] (c) [below right of=b] {$c$};
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\node[base node] (d) [below of=c] {$d$};
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\node[base node] (e) [below left of=d] {$e$};
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\node[base node] (f) [left of=e] {$f$};
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\node[base node] (g) [above left of=f] {$g$};
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\path[]
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(a) edge [] node {} (b)
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(b) edge [] node {} (c)
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(c) edge [] node {} (d)
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(d) edge [] node {} (e)
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(e) edge [] node {} (a)
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(f) edge [] node {} (e)
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(g) edge [] node {} (f);
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\chord{b}{e};
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\chord{c}{e};
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\end{egraph}
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\end{center}
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\begin{align*}
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\varphi_{TC} =~\egraphFuncConstraint{a}{b}{e}~\land\\[0.75ex]
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\egraphFuncConstraint{b}{c}{e}~\land\\[0.75ex]
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\egraphFuncConstraint{c}{d}{e}
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\end{align*}
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\begin{align*}
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\hat\varphi_{E} \coloneqq
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\lnot e_{a=b} \land e_{b=c} \lor e_{c=d} \imp \lnot (\lnot e_{d=e} \lor e_{e=f}) \land \lnot(e_{f=g} \land \lnot e_{a=e})
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\end{align*}
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\begin{align*}
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\varphi_{prop} \coloneqq \varphi_{TC} \land \hat\varphi_{E}
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\end{align*}
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