Consider the following premises. forall z_2: T(z_2) or W(z_2). forall z_2: ~R(z_2). forall z_2: R(z_2) or P(z_2). forall z_2: T(z_2) -> S(z_2). forall z_2: W(z_2) -> S(z_2). Can we infer ~P(a_2) from them?
That contradicts the premises. Therefore the answer is no.