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Inconsistent system

Given two inconsistent statements (0 and 1) we can infer anything, e. g. both H and ¬H, where H can be anything, e.g. "Americans landed on the moon".
0P ∧ Qpremise
1¬Qpremise
2Hassumption
3Qsimplification [0]
4FALSEcontradiction [1, 3]
5¬HReductio ad absurdum [2, 4]
6¬Hassumption
7Qsimplification [0]
8FALSEcontradiction [1, 7]
9HReductio ad absurdum [6, 8]
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