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: [Jacques Herbrand, theoremNamedAfter, Herbrand's theorem]

Target entity: Herbrand's theorem
Context triple: [Jacques Herbrand, theoremNamedAfter, 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 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.
• C. 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.
• D. Herbrand expansion
  Herbrand expansion is a method in mathematical logic that transforms first-order formulas into equivalent (often infinite) propositional combinations by systematically instantiating quantified variables with terms from the Herbrand universe.
• E. Recherches sur la théorie de la démonstration
  Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: theoremNamedAfter
Context triple: [Jacques Herbrand, theoremNamedAfter, Herbrand's theorem]

• A. hasTheoremNamedAfter chosen
  Indicates that a theorem is named in honor of or after a particular person or entity.
• B. hasAwardNamedAfter
  Indicates that an entity has an award that is named in honor of another entity.
• C. hasLawNamedAfter
  Indicates that a law or piece of legislation is named in honor of, or directly after, a particular entity.
• D. isNamedFor
  Indicates that one entity bears its name in honor of, or derived from, another entity.
• E. hasAsteroidNamedAfter
  Indicates that an asteroid has been officially named in honor of a particular entity.
• F. None of above.