This sequent is not provable.

$\mathcal{M} : p = T, q = T, r = T, s = F$ \\
$\mathcal{M} \models \neg (p \land q) \lor \neg (r \land s)$ \\
$\mathcal{M} \nmodels (\neg p \land \neg r) \lor (\neg q \land \neg s)$