\item \self Consider the following formula in $\mathcal{T}_{EUF}$. 
    \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}
    
    Use Ackermann's reduction to compute an equisatisfiable formula in $\mathcal{T}_{E}$.
    
    Then perform the graph-based reduction on the outcome of Ackermann's reduction to construct an equisatisfiable propositional formula $\phi_{prop}$.