As of 2007 , most of the ( state - of - the - art ) theorem provers for first - order logic are based on superposition ( e.g. the E equational theorem prover ) .
Only a few implement the pure calculus .
As of 2007 , most of the ( state - of - the - art ) theorem provers for first - order logic are based on superposition ( e.g. the E equational theorem prover ) , although only a few implement the pure calculus .