Consider the following premises. There is at least one x_17 for which if x_17 were curious, then x_17 is making tea. For all x_17, if x_17 plays squash, then x_17 is not driving a car. For all x_17, if x_17 makes tea, then x_17 is playing squash. For all x_17, if x_17 plays squash, then x_17 is curious. For all x_17, if x_17 were a writer, then x_17 is curious. For all x_17, x_17 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_17 for which x_17 is not a writer.
 From the fact that for all x_17, if x_17 plays squash, then x_17 is not driving a car, and that for all x_17, x_17 will drive a car we can infer that for all x_17, x_17 will not play squash via universal modus tollens. From the fact that there is at least one x_17 for which if x_17 were curious, then x_17 is making tea, and that for all x_17, if x_17 makes tea, then x_17 is playing squash we can infer that there is at least one x_17 for which if x_17 were curious, then x_17 is playing squash via existential transitivity. From the fact that there is at least one x_17 for which if x_17 were curious, then x_17 is playing squash, and that for all x_17, if x_17 plays squash, then x_17 is curious we can infer that there is at least one x_17 for which x_17 is curious if and only if x_17 will play squash via existential biconditional introduction. From the fact that there is at least one x_17 for which x_17 is curious if and only if x_17 will play squash, and that for all x_17, x_17 will not play squash we can infer that there is at least one x_17 for which x_17 is not curious via existential biconditional elimination. Finally, from the fact that for all x_17, if x_17 were a writer, then x_17 is curious, and that there is at least one x_17 for which x_17 is not curious we can infer that there is at least one x_17 for which x_17 is not a writer via existential modus tollens. Therefore, the answer is yes.