Consider the following premises. w -> P_7(a_5). U_3(a_5) or w. forall x_7: P_7(x_7) or ~U_3(x_7). Can we infer ~P_7(a_5) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) or ~U_3(x_7) we can infer forall x_7: U_3(x_7) -> P_7(x_7) via universal rewriting. From forall x_7: U_3(x_7) -> P_7(x_7) we can infer U_3(a_5) -> P_7(a_5) via universal instantiation. Finally, from U_3(a_5) -> P_7(a_5), w -> P_7(a_5), U_3(a_5) or w we can infer P_7(a_5) via disjunction elimination, which contradicts ~P_7(a_5). Therefore, the answer is no.