\item \prac \textbf{[3 Points]} Use the Congruence-Closure algorithm to check if the following assignment for the equalities is satisfiable.
$$\varphi_{EUF} \quad := \quad f(b)=a \land e=b \land c=f(c) \land d \neq f(e) 
\land f(a)=f(d) \land a \neq f(c) \land d=f(a)$$