Consider the following premises. If it is sunny, then John is an office clerk. Jessica is making tea and Jessica is a scientist. If Sarah were bored, then John is an office clerk. Jessica is not making tea or it is sunny. Can we infer the following from them? If we can, name the inference rule being used: John is not an office clerk.
 From the fact that Jessica is making tea and Jessica is a scientist we can infer that Jessica is making tea via simplification. From the fact that Jessica is making tea we can infer that Jessica is making tea or Sarah is bored via addition. From the fact that Jessica is making tea or Sarah is bored, and that Jessica is not making tea or it is sunny we can infer that Sarah is bored or it is sunny via resolution. Finally, from the fact that if Sarah were bored, then John is an office clerk, that if it is sunny, then John is an office clerk, and that Sarah is bored or it is sunny we can infer that John is an office clerk via disjunction elimination, which contradicts that John is not an office clerk. Therefore, the answer is no.