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\item \lect
Perform the graph-based reduction on the following formula to compute an equsatisfiable formula in propositional logic.
Given the formula
\begin{equation*}
\varphi_{EUF} \quad := \quad f(x,y)=f(y,z) \; \lor \; (z=f(y,z) \land f(x,x) \neq f(x,y))
\end{equation*}
Apply the \emph{Ackermann} reduction algorithm to compute an equisatisfiable formula in $\mathcal{T}_{E}$.