Consider the following premises. For all x, x is an astronaut or x will play tennis. There is at least one x for which if x plays tennis, then x is a soldier. For all x, x is a soldier if and only if x is an astronaut. For all x, if x were an astronaut, then x is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is not a soldier.
 From the fact that for all x, x is a soldier if and only if x is an astronaut we can infer that for all x, if x were a soldier, then x is an astronaut via universal biconditional elimination. From the fact that for all x, if x were a soldier, then x is an astronaut, and that for all x, if x were an astronaut, then x is a soldier we can infer that for all x, x is a soldier if and only if x is an astronaut via universal biconditional introduction. From the fact that for all x, x is a soldier if and only if x is an astronaut we can infer that for all x, if x were an astronaut, then x is a soldier via universal biconditional elimination. Finally, from the fact that for all x, if x were an astronaut, then x is a soldier, that there is at least one x for which if x plays tennis, then x is a soldier, and that for all x, x is an astronaut or x will play tennis we can infer that there is at least one x for which x is a soldier via existential disjunction elimination, which contradicts that For all x, x is not a soldier. Therefore, the answer is no.