  We present a versatile automated theorem proving framework capable of
automated discovery, simplification and proofs of inner and outer bounds in
network information theory, deduction of properties of information-theoretic
quantities (e.g. Wyner and G\'acs-K\"orner common information), and discovery
of non-Shannon-type inequalities, under a unified framework. Our implementation
successfully generated proofs for 32 out of 56 theorems in Chapters 1-14 of the
book Network Information Theory by El Gamal and Kim. Our framework is based on
the concept of existential information inequalities, which provides an
axiomatic framework for a wide range of problems in information theory.
