Consider the following premises. For all x_10, x_10 will play squash. For all x_10, x_10 is a taxi driver. For all x_10, if x_10 plays squash, then x_10 is working. There is at least one x_10 for which if x_10 works, then x_10 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is sad.
 From the fact that for all x_10, x_10 will play squash, and that for all x_10, x_10 is a taxi driver we can infer that for all x_10, x_10 will play squash and x_10 is a taxi driver via universal conjunction. From the fact that for all x_10, x_10 will play squash and x_10 is a taxi driver we can infer that for all x_10, x_10 will play squash via universal simplification. From the fact that for all x_10, if x_10 plays squash, then x_10 is working, and that there is at least one x_10 for which if x_10 works, then x_10 is sad we can infer that there is at least one x_10 for which if x_10 plays squash, then x_10 is sad via existential transitivity. Finally, from the fact that there is at least one x_10 for which if x_10 plays squash, then x_10 is sad, and that for all x_10, x_10 will play squash we can infer that there is at least one x_10 for which x_10 is sad via existential modus ponens. Therefore, the answer is yes.