ACL2 is a mathematical logic, programming language, and mechanical theorem prover based on the applicative subset of Common Lisp. It is an "industrial-strength" version of the NQTHM or Boyer/Moore theorem prover, and has been used for the formal verification of commercial microprocessors, the Java Virtual Machine, interesting algorithms, and so forth.
The OpenAI site is centered around an Open Source project and community involving artificial intelligence. The project itself is the creation of a set of tools that are considered to be models of human intelligence or biomimicry. These tools are intended to be integrated into applications or used stand alone for research.