Consider the following premises. For all x_1, if x_1 sleeps, then x_1 is climbing a mountain. For all x_1, x_1 will sleep or x_1 will not climb a mountain. Jennifer is not sleeping. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not climbing a mountain.
 From the fact that for all x_1, x_1 will sleep or x_1 will not climb a mountain we can infer that for all x_1, if x_1 climbs a mountain, then x_1 is sleeping via universal rewriting. From the fact that for all x_1, if x_1 sleeps, then x_1 is climbing a mountain, and that for all x_1, if x_1 climbs a mountain, then x_1 is sleeping we can infer that for all x_1, x_1 will sleep if and only if x_1 will climb a mountain via universal biconditional introduction. From the fact that for all x_1, x_1 will sleep if and only if x_1 will climb a mountain we can infer that Jennifer is sleeping if and only if Jennifer is climbing a mountain via universal instantiation. Finally, from the fact that Jennifer is sleeping if and only if Jennifer is climbing a mountain, and that Jennifer is not sleeping we can infer that Jennifer is not climbing a mountain via biconditional elimination. Therefore, the answer is yes.