This sequent is provable.

\begin{logicproof}{1}
    p \land q & \prem \\
    r \imp s & \prem \\
    p & $\ande{1} 1$ \\
    p \lor (r \imp s) & $\ori{1} 3$ \\
    q & $\ande{2} 1$ \\
    q \lor ((t \lor r) \imp u) & $\ori{1} 5$ \\
    (p \lor (r \imp s)) \land (q \lor ((t \lor r) \imp u)) & $\andi 4,6$
\end{logicproof}