Consider the following premises. forall z: W(z) -> P(z). forall z: W(z). forall z: T_3(z) -> P(z). forall z: T_1(z) -> T_3(z). Can we infer ~P(e_3) from them? If possible, name the inference rules being used at each step.
 From forall z: W(z) we can infer forall z: W(z) or T_1(z) via universal addition. From forall z: T_1(z) -> T_3(z), forall z: T_3(z) -> P(z) we can infer forall z: T_1(z) -> P(z) via universal transitivity. Finally, from forall z: W(z) -> P(z), forall z: T_1(z) -> P(z), forall z: W(z) or T_1(z) we can infer forall z: P(z) via universal disjunction elimination, which contradicts ~P(e_3). Therefore, the answer is no.