Consider the following premises. forall y: W(y) <-> S(y). forall y: ~T_4(y). exists y: P_3(y) <-> W(y). forall y: P_3(y) -> T_4(y). Can we infer forall y: S(y) from them? If possible, name the inference rules being used at each step.
 From forall y: P_3(y) -> T_4(y), forall y: ~T_4(y) we can infer forall y: ~P_3(y) via universal modus tollens. From exists y: P_3(y) <-> W(y), forall y: ~P_3(y) we can infer exists y: ~W(y) via existential biconditional elimination. Finally, from forall y: W(y) <-> S(y), exists y: ~W(y) we can infer exists y: ~S(y) via existential biconditional elimination, which contradicts forall y: S(y). Therefore, the answer is no.