Consider the following premises. forall z: W_1(z) -> P(z). exists z: P(z) -> W(z). forall z: ~W_1(z). forall z: W(z) -> P(z). forall z: P(z) -> W_1(z). Can we infer forall z: W(z) from them?
 From exists z: P(z) -> W(z), forall z: W(z) -> P(z) we can infer exists z: P(z) <-> W(z). From forall z: P(z) -> W_1(z), forall z: W_1(z) -> P(z) we can infer forall z: P(z) <-> W_1(z). From forall z: P(z) <-> W_1(z), forall z: ~W_1(z) we can infer forall z: ~P(z). Finally, from exists z: P(z) <-> W(z), forall z: ~P(z) we can infer exists z: ~W(z), which contradicts forall z: W(z). Therefore, the answer is no.