Consider the following premises. Susan is a soldier if and only if Karen is playing a game. Susan is a soldier or Karen is a doctor. For all x_13, x_13 is a doctor if and only if x_13 will play a game. Can we infer the following from them? If we can, name the inference rule being used: Karen is not playing a game.
 From the fact that for all x_13, x_13 is a doctor if and only if x_13 will play a game we can infer that for all x_13, if x_13 were a doctor, then x_13 is playing a game via universal biconditional elimination. From the fact that for all x_13, if x_13 were a doctor, then x_13 is playing a game we can infer that if Karen were a doctor, then Karen is playing a game via universal instantiation. From the fact that Susan is a soldier if and only if Karen is playing a game we can infer that if Susan were a soldier, then Karen is playing a game via biconditional elimination. Finally, from the fact that if Susan were a soldier, then Karen is playing a game, that if Karen were a doctor, then Karen is playing a game, and that Susan is a soldier or Karen is a doctor we can infer that Karen is playing a game via disjunction elimination, which contradicts that Karen is not playing a game. Therefore, the answer is no.