The power set is a combination of all possible subsets. This approach uses conjunctions and disjunctions to combine the power set of statements within a rank into longer but fewer statements. It then uses this power set to determine if a query is entailed by the knowledge base.

This approach lowered the overall statements that are stored. This changed the space complexity from O(n^2) to O(n). This allowed for more statements to be handled within a single rank.

This approach is similar to the ternary search however, it uses the Fibonacci sequence to create the search ranges. The search ranges are divided into three parts to locate the element in the data structure.

This approach is the same time complexity as the ternary search, O(log3n). The approach determines the rank to be removed and uses the power set approach on the rank to check the query against the statements.

This approach uses the console-application to allow the user to enter a single text file that contains multiple query statements simultaneously instead of each query being done one at a time.

The approach divides the queries into three sets of threads and performs the Fibonacci search approach with each set. This allows for a speedup of up to three times faster than doing each query sequentially.