Consider the following premises. forall z: S_3(z) <-> S_1(z). forall z: T(z) -> S_3(z). forall z: W(z) -> T(z). Can we infer exists z: ~(W(z) -> S_1(z)) from them? If possible, name the inference rules being used at each step.
 From forall z: W(z) -> T(z), forall z: T(z) -> S_3(z) we can infer forall z: W(z) -> S_3(z) via universal transitivity. From forall z: S_3(z) <-> S_1(z) we can infer forall z: S_3(z) -> S_1(z) via universal biconditional elimination. Finally, from forall z: W(z) -> S_3(z), forall z: S_3(z) -> S_1(z) we can infer forall z: W(z) -> S_1(z) via universal transitivity, which contradicts exists z: ~(W(z) -> S_1(z)). Therefore, the answer is no.