Consider the following premises. For all x_8, x_8 will cook or x_8 is a sailor. For all x_8, x_8 will cook if and only if x_8 will climb a mountain. For all x_8, x_8 will not work. For all x_8, x_8 will climb a mountain if and only if x_8 will work. 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 is not a sailor.
 From the fact that for all x_8, x_8 will climb a mountain if and only if x_8 will work, and that for all x_8, x_8 will not work we can infer that for all x_8, x_8 will not climb a mountain via universal biconditional elimination. From the fact that for all x_8, x_8 will cook if and only if x_8 will climb a mountain, and that for all x_8, x_8 will not climb a mountain we can infer that for all x_8, x_8 will not cook via universal biconditional elimination. Finally, from the fact that for all x_8, x_8 will cook or x_8 is a sailor, and that for all x_8, x_8 will not cook we can infer that for all x_8, x_8 is a sailor via universal disjunctive syllogism, which contradicts that There is at least one x_8 for which x_8 is not a sailor. Therefore, the answer is no.