Consider the following premises. For all x_18, if x_18 writes a letter, then x_18 is climbing a mountain. For all x_18, x_18 will write a letter. For all x_18, if x_18 climbs a mountain, then x_18 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Robert is not climbing a mountain.
 From the fact that for all x_18, if x_18 climbs a mountain, then x_18 is writing a letter, and that for all x_18, if x_18 writes a letter, then x_18 is climbing a mountain we can infer that for all x_18, x_18 will climb a mountain if and only if x_18 will write a letter via universal biconditional introduction. From the fact that for all x_18, x_18 will climb a mountain if and only if x_18 will write a letter we can infer that for all x_18, if x_18 writes a letter, then x_18 is climbing a mountain via universal biconditional elimination. Finally, from the fact that for all x_18, if x_18 writes a letter, then x_18 is climbing a mountain, and that for all x_18, x_18 will write a letter we can infer that for all x_18, x_18 will climb a mountain via universal modus ponens, which contradicts that Robert is not climbing a mountain. Therefore, the answer is no.