Consider the following premises. For all x_5, if x_5 were an astronaut, then x_5 is climbing a mountain. For all x_5, x_5 will not climb a mountain. For all x_5, x_5 is an astronaut or x_5 is not a poet. Can we infer the following from them? For all x_5, x_5 is not a poet.
 From the fact that for all x_5, if x_5 were an astronaut, then x_5 is climbing a mountain, and that for all x_5, x_5 will not climb a mountain we can infer that for all x_5, x_5 is not an astronaut. From the fact that for all x_5, x_5 is an astronaut or x_5 is not a poet we can infer that for all x_5, if x_5 were a poet, then x_5 is an astronaut. Finally, from the fact that for all x_5, if x_5 were a poet, then x_5 is an astronaut, and that for all x_5, x_5 is not an astronaut we can infer that for all x_5, x_5 is not a poet. Therefore, the answer is yes.