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20 lines
472 B
20 lines
472 B
This sequent is provable.
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\begin{logicproof}{1}
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(p \imp q) \land (q \imp r) & \prem\\
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\neg r \lor q & \prem\\
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p \imp q & $\ande 1$ \\
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q \imp r & $\ande 1$ \\
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\begin{subproof}
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\neg r & \assum\\
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\neg q & $\MT 4, 5$ \\
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\neg p & $\MT 3, 6$ \\
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\neg p \lor r & $\ori 7$
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\end{subproof}
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\begin{subproof}
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q & \assum \\
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r & $\impe 9, 4$ \\
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\neg p \lor r & $\ori 10$
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\end{subproof}
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\neg p \lor r & $\ore 2, 5-8, 9-10$
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\end{logicproof}
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