E is a theorem prover for full first-order logic with equality. It accepts a problem specification, typically consisting of a number of first-order clauses or formulas, and a conjecture, again either in clausal or full first-order form. The system will then try to find a formal proof for the conjecture, assuming the axioms.
If a proof is found, the system can provide a detailed list of proof steps that can be individually verified. If the conjecture is existential (i.e. it is of the form "there exists an X with property P"), more recent versions can also provide possible answers (values for X).
Development of E started as part of the E-SETHEO project at TUM. The first public release was in in 1998, and the system has been continuously improved ever since. I believe that E now is one of the most powerful and friendly reasoning systems for first-order logic. The prover has successfully participated in many competitions.