This sequent is not provable.

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