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\item \applyEagerEUF{
\begin{align*}
\phi_{EUF} \quad := \quad f(x)=f(y) \land f(y)=y \lor f(g(x))=f(f(y)) \land g(x)=x \\ \lor f(x) \neq f(y) \land y \neq g(f(y)) \land x \neq g(x)
\end{align*}
}