Consider the following premises. R(i_2). forall x_16: P_16(x_16) or ~R(x_16). forall x_16: P_16(x_16) <-> Q_16(x_16). Can we infer ~Q_16(i_2) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) <-> Q_16(x_16) we can infer forall x_16: P_16(x_16) -> Q_16(x_16) via universal biconditional elimination. From forall x_16: P_16(x_16) or ~R(x_16) we can infer forall x_16: R(x_16) -> P_16(x_16) via universal rewriting. From forall x_16: R(x_16) -> P_16(x_16), forall x_16: P_16(x_16) -> Q_16(x_16) we can infer forall x_16: R(x_16) -> Q_16(x_16) via universal transitivity. From forall x_16: R(x_16) -> Q_16(x_16) we can infer R(i_2) -> Q_16(i_2) via universal instantiation. Finally, from R(i_2) -> Q_16(i_2), R(i_2) we can infer Q_16(i_2) via modus ponens, which contradicts ~Q_16(i_2). Therefore, the answer is no.