Consider the following premises. For all x_8, x_8 is excited if and only if x_8 is curious. For all x_8, if x_8 were a sailor, then x_8 is excited. For all x_8, if x_8 climbs a mountain, then x_8 is a sailor. For all x_8, x_8 is not curious. 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 climb a mountain.
 From the fact that for all x_8, x_8 is excited if and only if 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 is not excited via universal biconditional elimination. From the fact that for all x_8, if x_8 were a sailor, then x_8 is excited, and that for all x_8, x_8 is not excited we can infer that for all x_8, x_8 is not a sailor via universal modus tollens. Finally, from the fact that for all x_8, if x_8 climbs a mountain, then x_8 is a sailor, and that for all x_8, x_8 is not a sailor we can infer that for all x_8, x_8 will not climb a mountain via universal modus tollens, which contradicts that There is at least one x_8 for which x_8 will climb a mountain. Therefore, the answer is no.