Consider the following premises. forall y: ~U_4(y). forall y: R_3(y) <-> U_4(y). forall y: U_4(y) -> R_3(y). exists y: S(y) -> R_3(y). Can we infer forall y: S(y) from them? If possible, name the inference rules being used at each step.
 From forall y: R_3(y) <-> U_4(y) we can infer forall y: R_3(y) -> U_4(y) via universal biconditional elimination. From forall y: R_3(y) -> U_4(y), forall y: U_4(y) -> R_3(y) we can infer forall y: R_3(y) <-> U_4(y) via universal biconditional introduction. From forall y: R_3(y) <-> U_4(y), forall y: ~U_4(y) we can infer forall y: ~R_3(y) via universal biconditional elimination. Finally, from exists y: S(y) -> R_3(y), forall y: ~R_3(y) we can infer exists y: ~S(y) via existential modus tollens, which contradicts forall y: S(y). Therefore, the answer is no.