A more recent test is the use of what is called a consistency tree. It plays off the same idea we have seen in indirect derivations, that in a valid argument it would lead to a contradiction to have all true premises and a (hypothesized) false conclusion. Go to my pages for consistency trees and consistency trees with quantifiers, and take the time to try the exercises that are there before going on to the assignment.
Computer science majors should look over these sections as well: normal forms and Horn formulas.