Herbrand's theorem

Herbrand's theorem is a fundamental result in logic stating that if a statement is logically valid (true in all interpretations), then there exists a finite set of specific, concrete examples (called Herbrand instances) that can be used to verify its validity. In simpler terms, instead of checking all possible scenarios, the theorem assures us that a finite, manageable set of cases can be examined to confirm whether a complex logical statement is universally true. This principle is foundational in automated theorem proving and formal logic, helping computers systematically determine the validity of logical formulas.