Consider the following premises. forall x_18: Q_18(x_18) -> P_18(x_18). forall x_18: Q_18(x_18). forall x_18: P_18(x_18) -> Q_18(x_18). Can we infer ~r from them? If possible, name the inference rules being used at each step.
We cannot infer that from the premises. Therefore the answer is no.