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22 lines
760 B
22 lines
760 B
This sequent is provable.
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\begin{logicproof}{1}
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\lnot \lnot k \imp (l \land m) & \prem \\
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\lnot \lnot \lnot l \imp m & \prem \\
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m \lor \lnot m & $\LEM$ \\
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\begin{subproof}
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m & \assum \\
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\lnot \lnot m & $\lnot \negi 4$ \\
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l \lor \lnot \lnot m & $\ori{2} 5$ \\
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\lnot k \lor (l \lor \lnot \lnot m) & $\ori{2} 6$
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\end{subproof}
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\begin{subproof}
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\lnot m & \assum \\
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\lnot \lnot \lnot \lnot l & $\MT 2,8$ \\
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\lnot \lnot l & $\negnege 9$ \\
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l & $\negnege 10$ \\
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l \lor \lnot \lnot m & $\ori{1} 11$ \\
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\lnot k \lor (l \lor \lnot \lnot m) & $\ori{2} 12$
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\end{subproof}
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\lnot k \lor (l \lor \lnot \lnot m) & $\ore 3, 4-7, 8-13$
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\end{logicproof}
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