Consider the following premises. ~s. T(a_10) -> s. forall z: T(z) or P(z). s -> T(a_10). Can we infer P(a_10) from them?
 From forall z: T(z) or P(z) we can infer T(a_10) or P(a_10). From s -> T(a_10), T(a_10) -> s we can infer s <-> T(a_10). From s <-> T(a_10), ~s we can infer ~T(a_10). Finally, from T(a_10) or P(a_10), ~T(a_10) we can infer P(a_10). Therefore, the answer is yes.