Consider the following premises. forall y: S(y) <-> P_3(y). forall y: S(y) -> ~S_1(y). exists y: P_3(y) <-> W_1(y). forall y: S_1(y) and S_2(y). Can we infer forall y: W_1(y) from them? If possible, name the inference rules being used at each step.
 From forall y: S_1(y) and S_2(y) we can infer forall y: S_1(y) via universal simplification. From forall y: S(y) -> ~S_1(y), forall y: S_1(y) we can infer forall y: ~S(y) via universal modus tollens. From forall y: S(y) <-> P_3(y), forall y: ~S(y) we can infer forall y: ~P_3(y) via universal biconditional elimination. Finally, from exists y: P_3(y) <-> W_1(y), forall y: ~P_3(y) we can infer exists y: ~W_1(y) via existential biconditional elimination, which contradicts forall y: W_1(y). Therefore, the answer is no.