Consider the following premises. forall x_15: Q_15(x_15) -> P_15(x_15). exists x_15: P_15(x_15) -> Q_15(x_15). forall x_15: Q_15(x_15) -> R_1(x_15). forall x_15: P_15(x_15) or ~Q_12(x_15). Can we infer forall x_15: ~(Q_12(x_15) -> R_1(x_15)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.