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This sequent is provable.
\begin{logicproof}{3}
\begin{subproof}
(p \imp q) \imp p & \assum \\
\begin{subproof}
\lnot p & \assum \\
\lnot (p \imp q) & $\MT 1,2$ \\
\begin{subproof}
p & \assum \\
\bot & $\nege 2,4$ \\
q & $\bote 5$
\end{subproof}
p \imp q & $\impi 4-6$ \\
\bot & $\nege 3,7$
\end{subproof}
p & $\PBC 2-8$
\end{subproof}
((p \imp q) \imp p) \imp p & $\impi 1-9$
\end{logicproof}