Consider the following premises. forall y_2: ~S(y_2). p_1 -> ~W_4(e). forall y_2: P_2(y_2) or S(y_2). forall y_2: ~P_2(y_2). Can we infer ~p_1 from them?
 From forall y_2: P_2(y_2) or S(y_2), forall y_2: ~P_2(y_2) we can infer forall y_2: S(y_2). From forall y_2: S(y_2) we can infer forall y_2: S(y_2) or W_4(y_2). From forall y_2: S(y_2) or W_4(y_2), forall y_2: ~S(y_2) we can infer forall y_2: W_4(y_2). From forall y_2: W_4(y_2) we can infer W_4(e). Finally, from p_1 -> ~W_4(e), W_4(e) we can infer ~p_1. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.