Consider the following premises. For all z, z will sleep or z will not play a game. There is at least one z for which z will climb a mountain if and only if z will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all z, the fact that z climbs a mountain does not imply that z is sleeping.
 From the fact that there is at least one z for which z will climb a mountain if and only if z will play a game we can infer that there is at least one z for which if z climbs a mountain, then z is playing a game via existential biconditional elimination. Finally, from the fact that for all z, z will sleep or z will not play a game we can infer that for all z, if z plays a game, then z is sleeping via universal rewriting, which contradicts that For all z, the fact that z climbs a mountain does not imply that z is sleeping. Therefore, the answer is no.