Consider the following premises. forall x_13: P_13(x_13) or Q_13(x_13). U(a_5) or r_2. forall x_13: Q_13(x_13) -> S_2(x_13). forall x_13: U(x_13) -> ~S_2(x_13). forall x_13: P_13(x_13) -> S_2(x_13). Can we infer ~r from them?
We cannot infer that from the premises. Therefore the answer is no.