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