Consider the following premises. forall x_2: W(x_2) <-> P_1(x_2). exists x_2: S(x_2) <-> W(x_2). forall x_2: Q(x_2) <-> P_1(x_2). forall x_2: ~Q(x_2). Can we infer forall x_2: S(x_2) from them?
 From forall x_2: Q(x_2) <-> P_1(x_2), forall x_2: ~Q(x_2) we can infer forall x_2: ~P_1(x_2). From forall x_2: W(x_2) <-> P_1(x_2), forall x_2: ~P_1(x_2) we can infer forall x_2: ~W(x_2). Finally, from exists x_2: S(x_2) <-> W(x_2), forall x_2: ~W(x_2) we can infer exists x_2: ~S(x_2), which contradicts forall x_2: S(x_2). Therefore, the answer is no.