Consider the following premises. forall x_4: ~Q(x_4) or R(x_4). exists x_4: ~P_4(x_4) or W_3(x_4). forall x_4: P_4(x_4). Can we infer exists x_4: W_3(x_4) or R(x_4) from them?
 From forall x_4: P_4(x_4) we can infer forall x_4: P_4(x_4) or Q(x_4). From forall x_4: P_4(x_4) or Q(x_4), exists x_4: ~P_4(x_4) or W_3(x_4) we can infer exists x_4: Q(x_4) or W_3(x_4). Finally, from exists x_4: Q(x_4) or W_3(x_4), forall x_4: ~Q(x_4) or R(x_4) we can infer exists x_4: W_3(x_4) or R(x_4). Therefore, the answer is yes.