I'm currently trying to prove this.
$(p \to q) \land (q \to r) \land (r \to p) \iff p \land q \land r ~\lor~ \lnot p \land\lnot q \land\lnot r$
After this step, I've gotten stuck. Normally I can do these just fine, but this one seems much less obvious than the ones I've been given previously.
$\iff (\lnot p \lor q) \land (\lnot q \lor r) \land (\lnot r \lor p)$ Law of Implication (3x)