Consider the following premises. forall z: U(z) -> P(z). forall z: P(z) or ~W_1(z). forall z: Q(z) or P_2(z). forall z: ~Q(z) or U(z). exists z: P_2(z) -> W_1(z). Can we infer forall z: ~P(z) from them?
 From forall z: Q(z) or P_2(z), forall z: ~Q(z) or U(z) we can infer forall z: P_2(z) or U(z). From forall z: P(z) or ~W_1(z) we can infer forall z: W_1(z) -> P(z). From exists z: P_2(z) -> W_1(z), forall z: W_1(z) -> P(z) we can infer exists z: P_2(z) -> P(z). Finally, from exists z: P_2(z) -> P(z), forall z: U(z) -> P(z), forall z: P_2(z) or U(z) we can infer exists z: P(z), which contradicts forall z: ~P(z). Therefore, the answer is no.