Let us look at the question first. The question is:
Given the following information for a database
A1. If x is on top of y, y supports x.
A2. If x is above y and they are touching each other, x is on top of y.
A3. A cup is above a book.
A4. A cup is touching a book.
(i) Translate the statements A1 through A4 into clausal form.
(ii) Show that the predicate supports(book, cup) is true using resolution.
Let us first convert A1 into clausal form.
top(x,y) ⟹ supports(y,x)
Now, let us convert A2.
above(x,y) & (touch(x,y) ∨ touch(y,x)) ⟹ top(x,y)
Now let us convert A3.
above(cup,book)
Let us now convert A4.
touch(book,cup)
Now, applying conjunction (AND) on statements A3 and A4, we get.
above(cup,book) & touch(book,cup) ⟹ top(cup,book)
Now, from this statement and A1, we get
top(cup,book) ⟹ supports(book,cup)