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