Example of Resolution
“If the butler had a motive and the butler was alone with the victim then the butler is guilty. If the butler needed money, then the butler had a motive. The butler needed money. The butler was alone with the victim.”
Prove that the butler was guilty.
Premises: c1: ~ P V ~ Q V R
c2: ~ S V P If the butler needed money, then the butler had a motive.
c3: S The butler needed money.
c4: Q The butler was alone with the victim.
Assume to the contrary that the butler was not guilty: c5: ~ R
Show a contradiction by resolving to obtain the null clause [].
c1 and c4 resolve to give c6: ~ P V R
c6 and c2 resolve to give c7: ~ S V R
c7 and c5 resolve to give c8: ~ S
c8 and c3 resolve to give c6: [] Q.E.D. (Quod Erat Demonstrandum)