Consider the following premises. For all x_9, x_9 is a taxi driver if and only if x_9 is a poet. For all x_9, x_9 will not play a game. There is at least one x_9 for which x_9 will play a game if and only if x_9 is a taxi driver. 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 poet.
 From the fact that there is at least one x_9 for which x_9 will play a game if and only if x_9 is a taxi driver, and that for all x_9, x_9 will not play a game we can infer that there is at least one x_9 for which x_9 is not a taxi driver via existential biconditional elimination. From the fact that for all x_9, x_9 is a taxi driver if and only if x_9 is a poet we can infer that for all x_9, if x_9 were a poet, then x_9 is a taxi driver via universal biconditional elimination. Finally, from the fact that for all x_9, if x_9 were a poet, then x_9 is a taxi driver, and that there is at least one x_9 for which x_9 is not a taxi driver we can infer that there is at least one x_9 for which x_9 is not a poet via existential modus tollens. Therefore, the answer is yes.