\item \self Consider the following formula in the conjunctive fragment of $\mathcal{T}_{EUF}$. Let $a \neq b$ be a shorthand notation for $\lnot(a=b)$.
    \begin{align*}
        f(b) = a \land c \neq d \land f(e) = b \land d \neq f(b) \land f(a) = f(e) \; \land \\
         b \neq f(b) \land a \neq e \land f(a) = e \land a = c \land f(b) \neq e \land d = f(c)
    \end{align*}
    Use the \textit{Congruence Closure} algorithm to determine whether this formula is satisfiable.