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.