Consider the following premises. If Elisabeth were a soldier, then John is drinking water. For all x_8, x_8 is a soldier or x_8 is a cashier. John is drinking water or Elisabeth is not a cashier. Can we infer the following from them? If we can, name the inference rule being used: John is not drinking water.
 From the fact that for all x_8, x_8 is a soldier or x_8 is a cashier we can infer that Elisabeth is a soldier or Elisabeth is a cashier via universal instantiation. From the fact that John is drinking water or Elisabeth is not a cashier we can infer that if Elisabeth were a cashier, then John is drinking water via rewriting. Finally, from the fact that if Elisabeth were a soldier, then John is drinking water, that if Elisabeth were a cashier, then John is drinking water, and that Elisabeth is a soldier or Elisabeth is a cashier we can infer that John is drinking water via disjunction elimination, which contradicts that John is not drinking water. Therefore, the answer is no.