Consider the following premises. For all x_9, if x_9 were fast, then x_9 is a scientist. For all x_9, if x_9 were bored, then x_9 is a scientist. For all x_9, x_9 is bored or x_9 is fast. For all x_9, x_9 is a cashier and x_9 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is not a cashier.
 From the fact that for all x_9, if x_9 were bored, then x_9 is a scientist, that for all x_9, if x_9 were fast, then x_9 is a scientist, and that for all x_9, x_9 is bored or x_9 is fast we can infer that for all x_9, x_9 is a scientist via universal disjunction elimination. From the fact that for all x_9, x_9 is a cashier and x_9 will listen to a song we can infer that for all x_9, x_9 is a cashier via universal simplification. From the fact that for all x_9, x_9 is a cashier, and that for all x_9, x_9 is a scientist we can infer that for all x_9, x_9 is a cashier and x_9 is a scientist via universal conjunction. Finally, from the fact that for all x_9, x_9 is a cashier and x_9 is a scientist we can infer that for all x_9, x_9 is a cashier via universal simplification, which contradicts that There is at least one x_9 for which x_9 is not a cashier. Therefore, the answer is no.