Consider the following premises. For all x_15, x_15 will sleep and x_15 is a carpenter. For all x_15, if x_15 sleeps, then x_15 is a nurse. For all x_15, if x_15 were a nurse, then x_15 is an artist. For all x_15, if x_15 works, then x_15 is not an artist. For all x_15, if x_15 were a sailor, then x_15 is working. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 is not a sailor.
 From the fact that for all x_15, x_15 will sleep and x_15 is a carpenter we can infer that for all x_15, x_15 will sleep via universal simplification. From the fact that for all x_15, if x_15 sleeps, then x_15 is a nurse, and that for all x_15, if x_15 were a nurse, then x_15 is an artist we can infer that for all x_15, if x_15 sleeps, then x_15 is an artist via universal transitivity. From the fact that for all x_15, if x_15 sleeps, then x_15 is an artist, and that for all x_15, x_15 will sleep we can infer that for all x_15, x_15 is an artist via universal modus ponens. From the fact that for all x_15, if x_15 works, then x_15 is not an artist, and that for all x_15, x_15 is an artist we can infer that for all x_15, x_15 will not work via universal modus tollens. Finally, from the fact that for all x_15, if x_15 were a sailor, then x_15 is working, and that for all x_15, x_15 will not work we can infer that for all x_15, x_15 is not a sailor via universal modus tollens. Therefore, the answer is yes.