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\item \ifassignmentsheet \points{5} \fi
Use the lazy encoding approach to check whether the formula $\varphi$ in $\EUF$ is satisfiable.
\begin{align*}
\varphi =&(\clause{(f(x)=x); (f(x)=y); (x=y)}) \land (\clause{\lnot (f(x)=x); (f(x)=y)})~\land \\
&(\clause{\lnot (f(x)=y); (x=y)}) \land (\clause{(x=y); (z=f(x))})~\land \\
&(\clause{\lnot (x=y); (f(x)=y)}) \land (\clause{\lnot (z=f(x)); \lnot (f(x)=y)})
\end{align*}