Consider the following premises. forall x_10: P_10(x_10) -> T(x_10). w -> P_10(a_5). forall x_10: T(x_10) -> P_10(x_10). T(a_5) or w. Can we infer ~P_10(a_5) from them?
 From forall x_10: P_10(x_10) -> T(x_10), forall x_10: T(x_10) -> P_10(x_10) we can infer forall x_10: P_10(x_10) <-> T(x_10). From forall x_10: P_10(x_10) <-> T(x_10) we can infer forall x_10: T(x_10) -> P_10(x_10). From forall x_10: T(x_10) -> P_10(x_10) we can infer T(a_5) -> P_10(a_5). Finally, from T(a_5) -> P_10(a_5), w -> P_10(a_5), T(a_5) or w we can infer P_10(a_5), which contradicts ~P_10(a_5). Therefore, the answer is no.