Consider the following premises. For all x_15, x_15 will play a game if and only if x_15 is a nurse. For all x_15, if x_15 were a sailor, then x_15 is an artist. For all x_15, if x_15 plays a game, then x_15 is a cashier. There is at least one x_15 for which if x_15 were a cashier, then x_15 is an artist. For all x_15, x_15 will not go running or x_15 is a sailor. For all x_15, x_15 will go running or x_15 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which x_15 is an artist.
 From the fact that for all x_15, x_15 will go running or x_15 is a nurse, and that for all x_15, x_15 will not go running or x_15 is a sailor we can infer that for all x_15, x_15 is a nurse or x_15 is a sailor via universal resolution. From the fact that for all x_15, x_15 will play a game if and only if x_15 is a nurse we can infer that for all x_15, if x_15 were a nurse, then x_15 is playing a game via universal biconditional elimination. From the fact that for all x_15, if x_15 were a nurse, then x_15 is playing a game, and that for all x_15, if x_15 plays a game, then x_15 is a cashier we can infer that for all x_15, if x_15 were a nurse, then x_15 is a cashier via universal transitivity. From the fact that for all x_15, if x_15 were a nurse, then x_15 is a cashier, and that there is at least one x_15 for which if x_15 were a cashier, then x_15 is an artist we can infer that there is at least one x_15 for which if x_15 were a nurse, then x_15 is an artist via existential transitivity. Finally, from the fact that there is at least one x_15 for which if x_15 were a nurse, then x_15 is an artist, that for all x_15, if x_15 were a sailor, then x_15 is an artist, and that for all x_15, x_15 is a nurse or x_15 is a sailor we can infer that there is at least one x_15 for which x_15 is an artist via existential disjunction elimination. Therefore, the answer is yes.