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