This sequent is provable.

\begin{logicproof}{2}
    \lnot q \lor \lnot p & \prem \\
    \begin{subproof}
        q \land p & \assum \\
        \begin{subproof}
            \lnot q & \assum \\
            q & $\ande{1} 2$ \\
            \bot & $\nege 3,4$
        \end{subproof}
        \begin{subproof}
            \lnot p & \assum \\
            p & $\ande{2} 2$ \\
            \bot & $\nege 6,7$
        \end{subproof}
        \bot & $\ore 1, 3-5, 6-8$
    \end{subproof}
    \lnot (q \land p) & $\negi 2-9$
\end{logicproof}