Consider the following premises. For all x_8, x_8 will not play a game. There is at least one x_8 for which if x_8 were a cashier, then x_8 is a poet. For all x_8, if x_8 were a cashier, then x_8 is playing a game. For all x_8, if x_8 were a poet, then x_8 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is a poet.
 From the fact that for all x_8, if x_8 were a cashier, then x_8 is playing a game, and that for all x_8, x_8 will not play a game we can infer that for all x_8, x_8 is not a cashier via universal modus tollens. From the fact that for all x_8, if x_8 were a poet, then x_8 is a cashier, and that there is at least one x_8 for which if x_8 were a cashier, then x_8 is a poet we can infer that there is at least one x_8 for which x_8 is a poet if and only if x_8 is a cashier via existential biconditional introduction. From the fact that there is at least one x_8 for which x_8 is a poet if and only if x_8 is a cashier we can infer that there is at least one x_8 for which if x_8 were a poet, then x_8 is a cashier via existential biconditional elimination. Finally, from the fact that there is at least one x_8 for which if x_8 were a poet, then x_8 is a cashier, and that for all x_8, x_8 is not a cashier we can infer that there is at least one x_8 for which x_8 is not a poet via existential modus tollens, which contradicts that For all x_8, x_8 is a poet. Therefore, the answer is no.