Convert the following sentences into first order logic statements. This is a more complex system than the previous question; try to be general and think ahead to make the system practical. You likely want to check out what you want to do with this system (see the rest of the question!) as you do this. Then put these in clause form . You must SHOW YOUR WORK if you want any part marks to be considered. 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.

1) Spiderman, The Green Goblin, Wolverine, and Mary Jane are persons.

2) The Green Goblin has special powers and he also cheats.

3) The Green Goblin is not a fan of Mary Jane.

4) Spiderman is a mutant, and so is Wolverine.

5) Wolverine is a fan of Captain Picard.

6) All persons with special powers are mutants.

7) All people who do not cheat are good.

8) Some mutants are not X-Men.

9) Mary Jane loves all good persons who are not X-Men.

10) There is no such thing as an X-Man who is not a fan of Captain Picard, and there is no such thing as an X-Man who cheats.

11) All X-Men are mutants.

12) All mutants who are fans of Captain Picard are X-Men.

13) Spiderman does not cheat and is not a fan of Captain Picard.

Now, using the above system, perform the following proofs using resolution refutation (show your work by stating the numbers of each pair of clauses you are resolving and the necessary substitutions to unify these, numbering each new deduction as you go):

i) Prove that Mary Jane loves Spiderman.

ii) Prove that Wolverine does not cheat.