Consider the following premises. There is at least one x_6 for which if x_6 plays a game, then x_6 is climbing a mountain. For all x_6, if x_6 were a doctor, then x_6 is playing a game. For all x_6, x_6 is an astronaut or x_6 is a doctor. For all x_6, x_6 is not an astronaut. Can we infer the following from them? There is at least one x_6 for which x_6 will climb a mountain.
 From the fact that for all x_6, if x_6 were a doctor, then x_6 is playing a game, and that there is at least one x_6 for which if x_6 plays a game, then x_6 is climbing a mountain we can infer that there is at least one x_6 for which if x_6 were a doctor, then x_6 is climbing a mountain. From the fact that for all x_6, x_6 is an astronaut or x_6 is a doctor, and that for all x_6, x_6 is not an astronaut we can infer that for all x_6, x_6 is a doctor. Finally, from the fact that there is at least one x_6 for which if x_6 were a doctor, then x_6 is climbing a mountain, and that for all x_6, x_6 is a doctor we can infer that there is at least one x_6 for which x_6 will climb a mountain. Therefore, the answer is yes.