Consider the following premises. There is at least one x_10 for which if x_10 plays a game, then x_10 is sad. For all x_10, x_10 will work if and only if x_10 is bored. For all x_10, x_10 will play a game. For all x_10, if x_10 works, then x_10 is sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is not sad.
 From the fact that for all x_10, x_10 will work if and only if x_10 is bored we can infer that for all x_10, if x_10 were bored, then x_10 is working via universal biconditional elimination. From the fact that for all x_10, if x_10 were bored, then x_10 is working, and that for all x_10, if x_10 works, then x_10 is sad we can infer that for all x_10, if x_10 were bored, then x_10 is sad via universal transitivity. From the fact that for all x_10, x_10 will play a game we can infer that for all x_10, x_10 will play a game or x_10 is bored via universal addition. Finally, from the fact that there is at least one x_10 for which if x_10 plays a game, then x_10 is sad, that for all x_10, if x_10 were bored, then x_10 is sad, and that for all x_10, x_10 will play a game or x_10 is bored we can infer that there is at least one x_10 for which x_10 is sad via existential disjunction elimination, which contradicts that For all x_10, x_10 is not sad. Therefore, the answer is no.