Consider the following premises. exists x: R(x) <-> R_1(x). forall x: R_1(x) -> ~Q(x). forall x: Q(x). forall x: U_3(x). Can we infer forall x: R(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q(x), forall x: U_3(x) we can infer forall x: Q(x) and U_3(x) via universal conjunction. From forall x: Q(x) and U_3(x) we can infer forall x: Q(x) via universal simplification. From forall x: R_1(x) -> ~Q(x), forall x: Q(x) we can infer forall x: ~R_1(x) via universal modus tollens. Finally, from exists x: R(x) <-> R_1(x), forall x: ~R_1(x) we can infer exists x: ~R(x) via existential biconditional elimination, which contradicts forall x: R(x). Therefore, the answer is no.