\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 $\mathcal{T}_{E}$.