Consider the following premises. For all x_11, x_11 is a writer. There is at least one x_11 for which x_11 will not drink water. For all x_11, if x_11 drinks water, then x_11 is a writer. For all x_11, if x_11 were a writer, then x_11 is drinking water. Can we infer the following from them? For all x_11, x_11 will not write a letter.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.