Consider the following premises. For all x_6, x_6 is an artist or x_6 will work. For all x_6, if x_6 were an artist, then x_6 is a lawyer. For all x_6, if x_6 works, then x_6 is a lawyer. There is at least one x_6 for which x_6 is not a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will sleep.
 From the fact that for all x_6, if x_6 were an artist, then x_6 is a lawyer, that for all x_6, if x_6 works, then x_6 is a lawyer, and that for all x_6, x_6 is an artist or x_6 will work we can infer that for all x_6, x_6 is a lawyer via universal disjunction elimination. From the fact that for all x_6, x_6 is a lawyer we can infer that for all x_6, x_6 is a lawyer or x_6 will sleep via universal addition. Finally, from the fact that for all x_6, x_6 is a lawyer or x_6 will sleep, and that there is at least one x_6 for which x_6 is not a lawyer we can infer that there is at least one x_6 for which x_6 will sleep via existential disjunctive syllogism. Therefore, the answer is yes.