Consider the following premises. forall x_16: P_16(x_16) <-> R_3(x_16). forall x_16: P(x_16) -> ~U(x_16). forall x_16: P_16(x_16) -> P(x_16). exists x_16: U(x_16). Can we infer forall x_16: R_3(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) <-> R_3(x_16) we can infer forall x_16: R_3(x_16) -> P_16(x_16) via universal biconditional elimination. From forall x_16: R_3(x_16) -> P_16(x_16), forall x_16: P_16(x_16) -> P(x_16) we can infer forall x_16: R_3(x_16) -> P(x_16) via universal transitivity. From forall x_16: P(x_16) -> ~U(x_16), exists x_16: U(x_16) we can infer exists x_16: ~P(x_16) via existential modus tollens. Finally, from forall x_16: R_3(x_16) -> P(x_16), exists x_16: ~P(x_16) we can infer exists x_16: ~R_3(x_16) via existential modus tollens, which contradicts forall x_16: R_3(x_16). Therefore, the answer is no.