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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}