Consider the following premises. There is at least one x_1 for which x_1 will climb a mountain. For all x_1, if x_1 sleeps, then x_1 is a sailor. For all x_1, if x_1 climbs a mountain, then x_1 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 is not a sailor.
 From the fact that there is at least one x_1 for which x_1 will climb a mountain we can infer that there is at least one x_1 for which x_1 will climb a mountain or x_1 will sleep via existential addition. Finally, from the fact that for all x_1, if x_1 climbs a mountain, then x_1 is a sailor, that for all x_1, if x_1 sleeps, then x_1 is a sailor, and that there is at least one x_1 for which x_1 will climb a mountain or x_1 will sleep we can infer that there is at least one x_1 for which x_1 is a sailor via existential disjunction elimination, which contradicts that For all x_1, x_1 is not a sailor. Therefore, the answer is no.