Consider the following premises. For all x_12, if x_12 were an artist, then x_12 is making tea. For all x_12, if x_12 makes tea, then x_12 is writing a letter. For all x_12, if x_12 plays tennis, then x_12 is writing a letter. There is at least one x_12 for which x_12 is an artist or x_12 will cook. For all x_12, if x_12 cooks, then x_12 is making tea. Can we infer the following from them? For all x_12, if x_12 cooks, then x_12 is making tea.
That is one of the premises. Therefore, the answer is yes.