This sequent is not provable.

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