Consider the following premises. For all x_13, if x_13 sleeps, then x_13 is a scientist. For all x_13, x_13 will sleep if and only if x_13 is sad. For all x_13, if x_13 were a scientist, then x_13 is sleeping. For all x_13, x_13 is not a scientist. For all x_13, if x_13 were a sailor, then x_13 is sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 is not a sailor.
 From the fact that for all x_13, if x_13 sleeps, then x_13 is a scientist, and that for all x_13, if x_13 were a scientist, then x_13 is sleeping we can infer that for all x_13, x_13 will sleep if and only if x_13 is a scientist via universal biconditional introduction. From the fact that for all x_13, x_13 will sleep if and only if x_13 is a scientist we can infer that for all x_13, if x_13 sleeps, then x_13 is a scientist via universal biconditional elimination. From the fact that for all x_13, if x_13 sleeps, then x_13 is a scientist, and that for all x_13, x_13 is not a scientist we can infer that for all x_13, x_13 will not sleep via universal modus tollens. From the fact that for all x_13, x_13 will sleep if and only if x_13 is sad, and that for all x_13, x_13 will not sleep we can infer that for all x_13, x_13 is not sad via universal biconditional elimination. Finally, from the fact that for all x_13, if x_13 were a sailor, then x_13 is sad, and that for all x_13, x_13 is not sad we can infer that for all x_13, x_13 is not a sailor via universal modus tollens. Therefore, the answer is yes.