\begin{logicproof}{2}
    \lnot q \lor p & \prem \\
    \begin{subproof}
        q & \assum \\
        \begin{subproof}
            \lnot q & \assum \\
            \false & $\nege 2,3$ \\
            p \lor r & $\bote 4$
        \end{subproof}
        \begin{subproof}
            p & \assum \\
            p \lor r & $\ori{1} 6$
        \end{subproof}
        p \lor r & $\ore 1,3-5,6-7$
    \end{subproof}
    q \implies (p \lor r) & $\impi 2-8$
\end{logicproof}
