This sequent is not provable, counter example: \\
$\mathcal{M} : p = F, q = F, r = F, s = F$ \\
$\mathcal{M} \models (p \land q) \implies (\lnot r \land \lnot s), \lnot r \land \lnot s$ \\
$\mathcal{M} \nmodels p$