Consider the following premises. For all x_10, x_10 will drink water if and only if x_10 is excited. For all x_10, x_10 is not excited. For all x_10, x_10 will play a game or x_10 will drink water. For all x_10, x_10 will not play a game or x_10 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is a poet or x_10 is bored.
 From the fact that for all x_10, x_10 will play a game or x_10 will drink water, and that for all x_10, x_10 will not play a game or x_10 is a poet we can infer that for all x_10, x_10 will drink water or x_10 is a poet via universal resolution. From the fact that for all x_10, x_10 will drink water if and only if x_10 is excited, and that for all x_10, x_10 is not excited we can infer that for all x_10, x_10 will not drink water via universal biconditional elimination. From the fact that for all x_10, x_10 will drink water or x_10 is a poet, and that for all x_10, x_10 will not drink water we can infer that for all x_10, x_10 is a poet via universal disjunctive syllogism. Finally, from the fact that for all x_10, x_10 is a poet we can infer that for all x_10, x_10 is a poet or x_10 is bored via universal addition. Therefore, the answer is yes.