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20 lines
558 B
20 lines
558 B
This sequent is provable.
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\begin{logicproof}{2}
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p \lor \lnot p & $\LEM$ \\
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\begin{subproof}
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p & \assum \\
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\lnot (p \land q) \lor p & $\ori{2} 2$
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\end{subproof}
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\begin{subproof}
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\lnot p & \assum \\
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\begin{subproof}
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p \land q & \assum \\
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p & $\ande{1} 5$ \\
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\bot & $\nege 6,4$
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\end{subproof}
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\lnot (p \land q) & $\negi 5-7$\\
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\lnot (p \land q) \lor p & $\ori{1} 8$
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\end{subproof}
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\lnot (p \land q) \lor p & $\ore 1, 2-3, 4-9$
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\end{logicproof}
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