Consider the following premises. For all x_8, if x_8 sleeps, then x_8 is curious. For all x_8, x_8 is curious if and only if x_8 will go running. There is at least one x_8 for which x_8 will sleep if and only if x_8 will climb a mountain. For all x_8, x_8 will not go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will not climb a mountain.
 From the fact that for all x_8, x_8 is curious if and only if x_8 will go running, and that for all x_8, x_8 will not go running we can infer that for all x_8, x_8 is not curious via universal biconditional elimination. From the fact that for all x_8, if x_8 sleeps, then x_8 is curious, and that for all x_8, x_8 is not curious we can infer that for all x_8, x_8 will not sleep via universal modus tollens. Finally, from the fact that there is at least one x_8 for which x_8 will sleep if and only if x_8 will climb a mountain, and that for all x_8, x_8 will not sleep we can infer that there is at least one x_8 for which x_8 will not climb a mountain via existential biconditional elimination. Therefore, the answer is yes.