Translate the following inference to logic notation: If James climbs a mountain, then Thomas is running. For all x, x_16 is happy if and only if x_16 will go running. If it is overcast, then Thomas is not running. Thomas is happy or James is climbing a mountain. Therefore it is not overcast.
p -> P(a). forall x: Q(x) <-> P(x). q -> ~P(a). Q(a) or p. Therefore ~q.