Consider the following premises. For all y_1, if y_1 were curious, then y_1 is an artist. There is at least one y_1 for which y_1 is a taxi driver if and only if y_1 is curious. For all y_1, if y_1 were fast, then y_1 is curious. For all y_1, y_1 is not fast. For all y_1, if y_1 were an artist, then y_1 is fast. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which y_1 is not a taxi driver.
 From the fact that for all y_1, if y_1 were curious, then y_1 is an artist, and that for all y_1, if y_1 were an artist, then y_1 is fast we can infer that for all y_1, if y_1 were curious, then y_1 is fast via universal transitivity. From the fact that for all y_1, if y_1 were fast, then y_1 is curious, and that for all y_1, if y_1 were curious, then y_1 is fast we can infer that for all y_1, y_1 is fast if and only if y_1 is curious via universal biconditional introduction. From the fact that for all y_1, y_1 is fast if and only if y_1 is curious, and that for all y_1, y_1 is not fast we can infer that for all y_1, y_1 is not curious via universal biconditional elimination. Finally, from the fact that there is at least one y_1 for which y_1 is a taxi driver if and only if y_1 is curious, and that for all y_1, y_1 is not curious we can infer that there is at least one y_1 for which y_1 is not a taxi driver via existential biconditional elimination. Therefore, the answer is yes.