E is a purely equational theorem prover for full first-order logic.
That means it is a program that you can stuff a mathematical specification
(in first-order format) and a hypothesis into, and which will then run
forever, using up all of your machines' resources.
Very occasionally it will find a proof for the hypothesis and tell you so.
E's inference core is based on a modified version of the superposition
calculus for equational clausal logic. Both clausification and reasoning on
the clausal form can be documented in checkable proof objects.
E was the best-performing open source software prover in the 2008
CADE ATP System Competition (CASC) in the FOF, CNF, and UEQ divisions.