Consider the following premises. For all x_7, if x_7 sleeps, then x_7 is a taxi driver. For all x_7, x_7 is not a server or x_7 is a cashier. For all x_7, if x_7 were a taxi driver, then x_7 is writing a letter. For all x_7, if x_7 were a cashier, then x_7 is writing a letter. For all x_7, x_7 is a server or x_7 will sleep. Can we infer the following from them? If we can, name the inference rule being used: Karen is not writing a letter.
 From the fact that for all x_7, if x_7 sleeps, then x_7 is a taxi driver, and that for all x_7, if x_7 were a taxi driver, then x_7 is writing a letter we can infer that for all x_7, if x_7 sleeps, then x_7 is writing a letter via universal transitivity. From the fact that for all x_7, x_7 is a server or x_7 will sleep, and that for all x_7, x_7 is not a server or x_7 is a cashier we can infer that for all x_7, x_7 will sleep or x_7 is a cashier via universal resolution. Finally, from the fact that for all x_7, if x_7 sleeps, then x_7 is writing a letter, that for all x_7, if x_7 were a cashier, then x_7 is writing a letter, and that for all x_7, x_7 will sleep or x_7 is a cashier we can infer that for all x_7, x_7 will write a letter via universal disjunction elimination, which contradicts that Karen is not writing a letter. Therefore, the answer is no.