Consider the following premises. forall z_2: Q(z_2) or ~W_3(z_2). forall z_2: W_3(z_2) -> S_3(z_2). forall z_2: ~S_3(z_2). forall z_2: Q(z_2) -> W_3(z_2). Can we infer exists z_2: Q(z_2) from them?
 From forall z_2: W_3(z_2) -> S_3(z_2), forall z_2: ~S_3(z_2) we can infer forall z_2: ~W_3(z_2). From forall z_2: Q(z_2) or ~W_3(z_2) we can infer forall z_2: W_3(z_2) -> Q(z_2). From forall z_2: W_3(z_2) -> Q(z_2), forall z_2: Q(z_2) -> W_3(z_2) we can infer forall z_2: W_3(z_2) <-> Q(z_2). From forall z_2: W_3(z_2) <-> Q(z_2) we can infer forall z_2: Q(z_2) -> W_3(z_2). Finally, from forall z_2: Q(z_2) -> W_3(z_2), forall z_2: ~W_3(z_2) we can infer forall z_2: ~Q(z_2), which contradicts exists z_2: Q(z_2). Therefore, the answer is no.