Consider the following premises. forall y: W(y) <-> R(y). forall y: W(y) <-> R_2(y). forall y: U_4(y). forall y: R_2(y) -> ~U_4(y). Can we infer exists y: R(y) from them? If possible, name the inference rules being used at each step.
 From forall y: R_2(y) -> ~U_4(y), forall y: U_4(y) we can infer forall y: ~R_2(y) via universal modus tollens. From forall y: W(y) <-> R_2(y), forall y: ~R_2(y) we can infer forall y: ~W(y) via universal biconditional elimination. Finally, from forall y: W(y) <-> R(y), forall y: ~W(y) we can infer forall y: ~R(y) via universal biconditional elimination, which contradicts exists y: R(y). Therefore, the answer is no.