Consider the following premises. For all x_6, x_6 will climb a mountain. There is at least one x_6 for which if x_6 sleeps, then x_6 is climbing a mountain. For all x_6, if x_6 climbs a mountain, then x_6 is sleeping. Can we infer the following from them? There is at least one x_6 for which x_6 will sleep.
 From the fact that there is at least one x_6 for which if x_6 sleeps, then x_6 is climbing a mountain, and that for all x_6, if x_6 climbs a mountain, then x_6 is sleeping we can infer that there is at least one x_6 for which x_6 will sleep if and only if x_6 will climb a mountain. From the fact that there is at least one x_6 for which x_6 will sleep if and only if x_6 will climb a mountain we can infer that there is at least one x_6 for which if x_6 climbs a mountain, then x_6 is sleeping. Finally, from the fact that there is at least one x_6 for which if x_6 climbs a mountain, then x_6 is sleeping, and that for all x_6, x_6 will climb a mountain we can infer that there is at least one x_6 for which x_6 will sleep. Therefore, the answer is yes.