A shelf contains six books on six different subjects: Art, Chemistry, Math, History, Physics, and Zoology. The positions of the books are numbered 1 through 6, from left to right.
The zoology book is not next to the math book.
The math book and the history book are exactly two spaces apart.
At most one other book separates the art book from the chemistry book.
The physics book cannot be on either end of the shelf.
If the history and the math books are both to the left of the chemistry book, then which one of the following must be false?