Consider the following premises. For all x_10, x_10 will climb a mountain or x_10 is not a sailor. For all x_10, x_10 will read a book or x_10 will sleep. For all x_10, x_10 will not read a book or x_10 is a sailor. For all x_10, if x_10 sleeps, then x_10 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which neither x_10 will climb a mountain nor x_10 will work.
 From the fact that for all x_10, x_10 will read a book or x_10 will sleep, and that for all x_10, x_10 will not read a book or x_10 is a sailor we can infer that for all x_10, x_10 will sleep or x_10 is a sailor via universal resolution. From the fact that for all x_10, x_10 will climb a mountain or x_10 is not a sailor we can infer that for all x_10, if x_10 were a sailor, then x_10 is climbing a mountain via universal rewriting. From the fact that for all x_10, if x_10 sleeps, then x_10 is climbing a mountain, that for all x_10, if x_10 were a sailor, then x_10 is climbing a mountain, and that for all x_10, x_10 will sleep or x_10 is a sailor we can infer that for all x_10, x_10 will climb a mountain via universal disjunction elimination. Finally, from the fact that for all x_10, x_10 will climb a mountain we can infer that for all x_10, x_10 will climb a mountain or x_10 will work via universal addition, which contradicts that There is at least one x_10 for which neither x_10 will climb a mountain nor x_10 will work. Therefore, the answer is no.