This sequent is provable.

\begin{logicproof}{2}
    p \imp (q \land r) & \prem \\
    q \imp s & \prem \\
    \begin{subproof}
        p & \assum \\
        q \land r & $\impe 1,3$ \\
        q & $\ande{1} 4$ \\
        s & $\impe 2,5$ \\
        r & $\ande{2} 4$ \\
        s \land r & $\andi 6,7$
    \end{subproof}
    p \imp (s \land r) & $\impi 3-8$
\end{logicproof}