This sequent is provable.

\begin{logicproof}{1}
    \neg(p \land q) \imp r & \prem\\
    p \imp \neg q & \prem \\
    \begin{subproof}
        \neg r & \assum \\
        \neg\neg(p \land q) & $\MT 1$ \\
        p \land q & $\negnege 4$ \\
        p & $\ande{1} 5$ \\
        q & $\ande{2} 6$ \\
        \neg q & $\impe 2, 6$ \\
        \bot & $\bote 7, 8$
    \end{subproof}
    r & $\PBC 3-9$
\end{logicproof}