Consider the following premises. forall x_16: P_16(x_16) or ~S(x_16). P_16(g) -> r_4. S(g). Can we infer ~r_4 from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) or ~S(x_16) we can infer forall x_16: S(x_16) -> P_16(x_16) via universal rewriting. From forall x_16: S(x_16) -> P_16(x_16) we can infer S(g) -> P_16(g) via universal instantiation. From S(g) -> P_16(g), S(g) we can infer P_16(g) via modus ponens. Finally, from P_16(g) -> r_4, P_16(g) we can infer r_4 via modus ponens, which contradicts ~r_4. Therefore, the answer is no.