Exercise $3$: resolution proof $(60$ points$).$ Consider the following statements in English:

Any two people who have a friend in common like the same things.

Mary is a friend of Susan.

Joan is not a friend of Susan.

Alice is a friend of Susan.

Alice likes icecream.

Anybody who likes icecream has friends.

Does Mary like icecream? Do a proof using resolution. Specifically:

$1.(24$ points$)$ Write each statement as a first$-$order logic sentence.

$2.(10$ points$)$ Transform them into conjunctive normal form $($CNF$).$

$3.(26$ points$)$ Give a proof using resolution, showing it in graphical form as in fig. $9\mathrm{.}10.$ For each step, indicate the clause$($s$)$ that are resolved and the literals that unify.

See AIMA $9\mathrm{.}5.$