\begin{logicproof}{2}
    p \lor q & \prem \\
    \lnot p \lor r & \prem \\
    \begin{subproof}
        p & \assum \\
        \begin{subproof}
            \lnot p & \assum \\
            \false & $\nege 3,4$ \\
            q \lor r & $\bote 5$
        \end{subproof}
        \begin{subproof}
            r & \assum \\
            q \lor r & $\ori{2} 7$
        \end{subproof}
        q \lor r & $\ore 2,4-6,7-8$
    \end{subproof}
    \begin{subproof}
        q & \assum \\
        q \lor r & $\ori{1} 10$
    \end{subproof}
    q \lor r & $\ore 1,3-9,10-11$
\end{logicproof}