Consider the following premises. For all x_6, if x_6 were a poet, then x_6 is a cashier. For all x_6, x_6 is a poet or x_6 is not a carpenter. There is at least one x_6 for which x_6 is not a cashier. Can we infer the following from them? For all x_6, x_6 is a poet or x_6 is not a carpenter.
That is one of the premises. Therefore, the answer is yes.