\begin{logicproof}{2}
    p \implies (q \lor r) & \prem \\
    \lnot q \land \lnot r & \prem \\
    \begin{subproof}
        p & \assum \\
        q \lor r & $\impe 1,3$ \\
        \begin{subproof}
            q & \assum \\
            \lnot q & $\ande{1} 2$ \\
            \false & $\nege 5,6$
        \end{subproof}
        \begin{subproof}
            r & \assum \\
            \lnot r & $\ande{2} 2$ \\
            \false & $\nege 8,9$
        \end{subproof}
        \false & $\ore 4,5-7,8-10$
    \end{subproof}
    \lnot p & $\negi 3-11$
\end{logicproof}