Consider the following premises. For all x_9, x_9 is not a carpenter. For all x_9, x_9 will write a letter and x_9 will make tea. For all x_9, x_9 is a carpenter or x_9 will work. Can we infer the following from them? If we can, name the inference rule being used: Charles is writing a letter.
 From the fact that for all x_9, x_9 is a carpenter or x_9 will work, and that for all x_9, x_9 is not a carpenter we can infer that for all x_9, x_9 will work via universal disjunctive syllogism. From the fact that for all x_9, x_9 will write a letter and x_9 will make tea we can infer that for all x_9, x_9 will write a letter via universal simplification. From the fact that for all x_9, x_9 will write a letter, and that for all x_9, x_9 will work we can infer that for all x_9, x_9 will write a letter and x_9 will work via universal conjunction. From the fact that for all x_9, x_9 will write a letter and x_9 will work we can infer that Charles is writing a letter and Charles is working via universal instantiation. Finally, from the fact that Charles is writing a letter and Charles is working we can infer that Charles is writing a letter via simplification. Therefore, the answer is yes.