Consider the following premises. forall x_13: P_13(x_13) or Q_13(x_13). s_4 -> ~R_13(f). forall x_13: Q_13(x_13) -> R_13(x_13). forall x_13: P_13(x_13) -> R_13(x_13). Can we infer ~s_4 from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) -> R_13(x_13), forall x_13: Q_13(x_13) -> R_13(x_13), forall x_13: P_13(x_13) or Q_13(x_13) we can infer forall x_13: R_13(x_13) via universal disjunction elimination. From forall x_13: R_13(x_13) we can infer R_13(f) via universal instantiation. Finally, from s_4 -> ~R_13(f), R_13(f) we can infer ~s_4 via modus tollens. Therefore, the answer is yes.