Consider the following premises. r -> P_7(a_5). forall x_7: P_7(x_7) or ~S(x_7). r or S(a_5). Can we infer ~P_7(a_5) from them?
 From forall x_7: P_7(x_7) or ~S(x_7) we can infer forall x_7: S(x_7) -> P_7(x_7). From forall x_7: S(x_7) -> P_7(x_7) we can infer S(a_5) -> P_7(a_5). Finally, from r -> P_7(a_5), S(a_5) -> P_7(a_5), r or S(a_5) we can infer P_7(a_5), which contradicts ~P_7(a_5). Therefore, the answer is no.