Consider the following premises. For all x_5, x_5 is an artist. For all x_5, x_5 will go running if and only if x_5 is an artist. For all x_5, x_5 will not go running. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a soldier.
 From the fact that for all x_5, x_5 will go running if and only if x_5 is an artist, and that for all x_5, x_5 will not go running we can infer that for all x_5, x_5 is not an artist via universal biconditional elimination. From the fact that for all x_5, x_5 is an artist we can infer that for all x_5, x_5 is an artist or x_5 is a soldier via universal addition. Finally, from the fact that for all x_5, x_5 is an artist or x_5 is a soldier, and that for all x_5, x_5 is not an artist we can infer that for all x_5, x_5 is a soldier via universal disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.