Consider the following sequence of statements, which relate to Batmans perception of Superman as a potential threat to humanity and his decision to fight against him. For Superman to be defeated, it has to be that he is facing an opponent alone and his opponent is carrying Kryptonite. Acquiring Kryptonite, however, means that Batman has to coordinate with Lex Luthor and acquire it from him. If, however, Batman coordinates with Lex Luthor, this upsets Wonder Woman, who will intervene and fight on the side of Superman.

a. Convert the above statements into a knowledge base using the symbols of propositional logic.

b. Transform your knowledge base into 3-CNF.

c. Using your knowledge base, prove that Batman cannot defeat Superman through an application of the resolution inference rule (this is the required methodology for the proof).