Consider the following premises. forall x_14: Q_14(x_14) -> P_14(x_14). forall x_14: Q_11(x_14). forall x_14: P_14(x_14) -> ~Q_11(x_14). Q_14(a_5) or r_3. forall x_14: P_14(x_14) -> Q_14(x_14). Can we infer ~r_3 from them?
 From forall x_14: P_14(x_14) -> Q_14(x_14), forall x_14: Q_14(x_14) -> P_14(x_14) we can infer forall x_14: P_14(x_14) <-> Q_14(x_14). From forall x_14: P_14(x_14) -> ~Q_11(x_14), forall x_14: Q_11(x_14) we can infer forall x_14: ~P_14(x_14). From forall x_14: P_14(x_14) <-> Q_14(x_14), forall x_14: ~P_14(x_14) we can infer forall x_14: ~Q_14(x_14). From forall x_14: ~Q_14(x_14) we can infer ~Q_14(a_5). Finally, from Q_14(a_5) or r_3, ~Q_14(a_5) we can infer r_3, which contradicts ~r_3. Therefore, the answer is no.