Consider the following premises. For all x_5, if x_5 writes a letter, then x_5 is not a police officer. For all x_5, if x_5 writes a letter, then x_5 is climbing a mountain. For all x_5, x_5 is a police officer. There is at least one x_5 for which if x_5 climbs a mountain, then x_5 is writing a letter. Can we infer the following from them? There is at least one x_5 for which x_5 will not climb a mountain.
 From the fact that there is at least one x_5 for which if x_5 climbs a mountain, then x_5 is writing a letter, and that for all x_5, if x_5 writes a letter, then x_5 is climbing a mountain we can infer that there is at least one x_5 for which x_5 will climb a mountain if and only if x_5 will write a letter. From the fact that for all x_5, if x_5 writes a letter, then x_5 is not a police officer, and that for all x_5, x_5 is a police officer we can infer that for all x_5, x_5 will not write a letter. Finally, from the fact that there is at least one x_5 for which x_5 will climb a mountain if and only if x_5 will write a letter, and that for all x_5, x_5 will not write a letter we can infer that there is at least one x_5 for which x_5 will not climb a mountain. Therefore, the answer is yes.