Consider the following premises. For all y_3, if y_3 were a scientist, then y_3 is playing squash. There is at least one y_3 for which if y_3 were a scientist, then y_3 is playing squash. For all y_3, y_3 will not work. For all y_3, if y_3 were a scientist, then y_3 is working. For all y_3, if y_3 plays squash, then y_3 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_3 for which y_3 will not play squash.
 From the fact that for all y_3, if y_3 were a scientist, then y_3 is playing squash, and that for all y_3, if y_3 plays squash, then y_3 is a scientist we can infer that for all y_3, y_3 is a scientist if and only if y_3 will play squash via universal biconditional introduction. From the fact that for all y_3, if y_3 were a scientist, then y_3 is working, and that for all y_3, y_3 will not work we can infer that for all y_3, y_3 is not a scientist via universal modus tollens. From the fact that for all y_3, y_3 is a scientist if and only if y_3 will play squash we can infer that for all y_3, if y_3 plays squash, then y_3 is a scientist via universal biconditional elimination. From the fact that there is at least one y_3 for which if y_3 were a scientist, then y_3 is playing squash, and that for all y_3, if y_3 plays squash, then y_3 is a scientist we can infer that there is at least one y_3 for which y_3 is a scientist if and only if y_3 will play squash via existential biconditional introduction. Finally, from the fact that there is at least one y_3 for which y_3 is a scientist if and only if y_3 will play squash, and that for all y_3, y_3 is not a scientist we can infer that there is at least one y_3 for which y_3 will not play squash via existential biconditional elimination. Therefore, the answer is yes.