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\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}