Question 1. 12 Marks. Consider the following English statements, which form a logical system:

1) The Rock and Captain Janeway are humans.

2) Seven of Nine is Borg.

3) If you are not Borg, then Resistance is Futile.

4) Someone can smell what The Rock is cooking.

5) Anytime someone fights someone else, and that first someone wins, then the other someone does not win.

6) The Rock fought Seven of Nine, and The Rock won.

7) If a human fights a Borg, and the Borg does not win, then the human is lucky.

8) Some humans are lucky.

9) Someone fought the Law and the Law won.

Convert these English statements to first order logic statements every statement should result in a single first order logic statement (5 marks). Then convert the statements to clause form (4 marks - you must SHOW YOUR WORK if you want any part marks to be considered) and using resolution refutation, prove that The Rock is Lucky (3 marks). Each clause form statement should state the number of the original FOL statement that it came from, and each should also be numbered so the marker can follow your reasoning in the resolution proof. Each new resolution should show the two parent clauses used to derive the resolution, along with any substitutions for unification.