Consider the following premises. For all x_5, x_5 will go running or x_5 is a cashier. For all x_5, if x_5 were a cashier, then x_5 is working. For all x_5, if x_5 goes running, then x_5 is taking a plane. For all x_5, if x_5 takes a plane, then x_5 is working. For all x_5, x_5 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will work and x_5 is a bartender.
 From the fact that for all x_5, if x_5 goes running, then x_5 is taking a plane, and that for all x_5, if x_5 takes a plane, then x_5 is working we can infer that for all x_5, if x_5 goes running, then x_5 is working via universal transitivity. From the fact that for all x_5, if x_5 goes running, then x_5 is working, that for all x_5, if x_5 were a cashier, then x_5 is working, and that for all x_5, x_5 will go running or x_5 is a cashier we can infer that for all x_5, x_5 will work via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 will work, and that for all x_5, x_5 is a bartender we can infer that for all x_5, x_5 will work and x_5 is a bartender via universal conjunction. Therefore, the answer is yes.