Consider the following premises. For all x_6, x_6 is sad. There is at least one x_6 for which x_6 is excited if and only if x_6 will play a game. For all x_6, if x_6 plays squash, then x_6 is not sad. For all x_6, x_6 will play squash if and only if x_6 will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is excited.
 From the fact that for all x_6, if x_6 plays squash, then x_6 is not sad, and that for all x_6, x_6 is sad we can infer that for all x_6, x_6 will not play squash via universal modus tollens. From the fact that for all x_6, x_6 will play squash if and only if x_6 will play a game, and that for all x_6, x_6 will not play squash we can infer that for all x_6, x_6 will not play a game via universal biconditional elimination. Finally, from the fact that there is at least one x_6 for which x_6 is excited if and only if x_6 will play a game, and that for all x_6, x_6 will not play a game we can infer that there is at least one x_6 for which x_6 is not excited via existential biconditional elimination, which contradicts that For all x_6, x_6 is excited. Therefore, the answer is no.