Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Herbrand’s theorem | Statement: [First-Order Logic and Automated Theorem Proving, topic, Herbrand’s theorem]

Target entity: Herbrand’s theorem
Context triple: [First-Order Logic and Automated Theorem Proving, topic, Herbrand’s theorem]

• A. Herbrand's theorem chosen
  Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
• B. Herbrand semantics
  Herbrand semantics is a formal framework in logic and automated theorem proving that interprets first-order formulas over the Herbrand universe of ground terms to define truth and satisfiability.
• C. Herbrand universe
  The Herbrand universe is a fundamental concept in mathematical logic and automated theorem proving, consisting of all ground (variable-free) terms that can be built from the function symbols and constants of a given first-order language.
• D. Herbrand conjunction (for universal formulas)
  A Herbrand conjunction (for universal formulas) is a finite conjunction of ground instances of a universally quantified formula, used in Herbrand’s theorem and automated reasoning to represent universal information over a Herbrand universe.
• E. Herbrand disjunction
  Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.