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: [Recherches sur la théorie de la démonstration, introducesConcept, Herbrand's theorem]

Target entity: Herbrand's theorem
Context triple: [Recherches sur la théorie de la démonstration, introducesConcept, 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 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.
• E. Tarski–Mostowski–Robinson theorem
  The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.