Consider the following premises. forall x_15: P_15(x_15) -> Q_15(x_15). q_2 -> r_1. forall x_15: Q_15(x_15) -> P_15(x_15). Q_15(a_10) -> q_2. Can we infer ~(P_15(a_10) -> r_1) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.