This sequent is provable.

\begin{logicproof}{1}
  (p \land q) \imp (r \lor s) & \prem\\
  r \land p \land q & \prem\\
  p \land q & $\ande{2} 1$\\
  r \lor s & $\impe 1,3$ \\
	  \begin{subproof}
	  q & \assum\\
    r & $\ande{1} 2$
	  \end{subproof}
  q \imp r & $\impi 5-6$ \\
	  \begin{subproof}
	  s & \assum\\
    q & $\ande{2} 3$
	  \end{subproof}
  s \imp q & $\impi 8-9$ \\
  (q \imp r) \land (s \imp q) & $\andi 7, 10$
\end{logicproof}
