Consider the following premises. T_3(f). forall x_16: P_16(x_16) <-> Q_16(x_16). forall x_16: P_16(x_16) or ~T_3(x_16). Can we infer ~Q_16(f) 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 ~T_3(x_16) we can infer forall x_16: T_3(x_16) -> P_16(x_16) via universal rewriting. From forall x_16: T_3(x_16) -> P_16(x_16), forall x_16: P_16(x_16) -> Q_16(x_16) we can infer forall x_16: T_3(x_16) -> Q_16(x_16) via universal transitivity. From forall x_16: T_3(x_16) -> Q_16(x_16) we can infer T_3(f) -> Q_16(f) via universal instantiation. Finally, from T_3(f) -> Q_16(f), T_3(f) we can infer Q_16(f) via modus ponens, which contradicts ~Q_16(f). Therefore, the answer is no.