Consider the following premises. For all x_25, x_25 will not drive a car. For all x_25, x_25 is a soldier if and only if x_25 will drive a car. There is at least one x_25 for which if x_25 were a server, then x_25 is a soldier. For all x_25, if x_25 plays tennis, then x_25 is not fast. For all x_25, x_25 is a server. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_25 for which x_25 will not play tennis.
 From the fact that for all x_25, x_25 is a soldier if and only if x_25 will drive a car, and that for all x_25, x_25 will not drive a car we can infer that for all x_25, x_25 is not a soldier via universal biconditional elimination. From the fact that there is at least one x_25 for which if x_25 were a server, then x_25 is a soldier, and that for all x_25, x_25 is a server we can infer that there is at least one x_25 for which x_25 is a soldier via existential modus ponens. From the fact that there is at least one x_25 for which x_25 is a soldier we can infer that there is at least one x_25 for which x_25 is a soldier or x_25 is fast via existential addition. From the fact that there is at least one x_25 for which x_25 is a soldier or x_25 is fast, and that for all x_25, x_25 is not a soldier we can infer that there is at least one x_25 for which x_25 is fast via existential disjunctive syllogism. Finally, from the fact that for all x_25, if x_25 plays tennis, then x_25 is not fast, and that there is at least one x_25 for which x_25 is fast we can infer that there is at least one x_25 for which x_25 will not play tennis via existential modus tollens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.