\item \lect Consider the following formula in the conjunctive fragment of $\mathcal{T}_{EUF}$.
    \begin{align*}
         \varphi_{EUF} \quad := \quad  x=f(y) \wedge x \neq y \wedge y \neq u \wedge y = f(u) \wedge z \neq f(u) \wedge \\ u = v  \wedge v= z \wedge v = f(y) \wedge v \neq f(z) \wedge f(x) \neq f(z)
    \end{align*}
    Use the \textit{Congruence Closure} algorithm to determine whether this formula is satisfiable.