Consider the following premises. For all x_10, x_10 will sleep. For all x_10, if x_10 were a mechanic, then x_10 is a lawyer. For all x_10, if x_10 were a server, then x_10 is a lawyer. There is at least one x_10 for which x_10 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: Some lawyers will sleep.
 From the fact that there is at least one x_10 for which x_10 is a mechanic we can infer that there is at least one x_10 for which x_10 is a mechanic or x_10 is a server via existential addition. From the fact that for all x_10, if x_10 were a mechanic, then x_10 is a lawyer, that for all x_10, if x_10 were a server, then x_10 is a lawyer, and that there is at least one x_10 for which x_10 is a mechanic or x_10 is a server we can infer that there is at least one x_10 for which x_10 is a lawyer via existential disjunction elimination. Finally, from the fact that there is at least one x_10 for which x_10 is a lawyer, and that for all x_10, x_10 will sleep we can infer that some lawyers will sleep via existential conjunction. Therefore, the answer is yes.