Consider the following premises. forall z_1: U(z_1) <-> S(z_1). forall z_1: S_1(z_1) -> S(z_1). forall z_1: S_1(z_1) <-> S(z_1). forall z_1: U(z_1) -> ~W_1(z_1). exists z_1: W_1(z_1). Can we infer forall z_1: S_1(z_1) from them? If possible, name the inference rules being used at each step.
 From forall z_1: U(z_1) -> ~W_1(z_1), exists z_1: W_1(z_1) we can infer exists z_1: ~U(z_1) via existential modus tollens. From forall z_1: U(z_1) <-> S(z_1), exists z_1: ~U(z_1) we can infer exists z_1: ~S(z_1) via existential biconditional elimination. From forall z_1: S_1(z_1) <-> S(z_1) we can infer forall z_1: S(z_1) -> S_1(z_1) via universal biconditional elimination. From forall z_1: S_1(z_1) -> S(z_1), forall z_1: S(z_1) -> S_1(z_1) we can infer forall z_1: S_1(z_1) <-> S(z_1) via universal biconditional introduction. Finally, from forall z_1: S_1(z_1) <-> S(z_1), exists z_1: ~S(z_1) we can infer exists z_1: ~S_1(z_1) via existential biconditional elimination, which contradicts forall z_1: S_1(z_1). Therefore, the answer is no.