Consider the following premises. David is making tea or William is a soldier. If John plays tennis, then it is late. If David makes tea, then Joseph is a cashier. If William were a soldier, then Joseph is a cashier. John is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: It is not late.
 From the fact that if David makes tea, then Joseph is a cashier, that if William were a soldier, then Joseph is a cashier, and that David is making tea or William is a soldier we can infer that Joseph is a cashier via disjunction elimination. Finally, from the fact that if John plays tennis, then it is late, and that John is playing tennis we can infer that it is late via modus ponens, which contradicts that It is not late. Therefore, the answer is no.