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-style proof calculi | Statement: [Herbrand disjunction, occursIn, Herbrand-style proof calculi]

Target entity: Herbrand-style proof calculi
Context triple: [Herbrand disjunction, occursIn, Herbrand-style proof calculi]

• 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. Hilbert-style deductive systems
  Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel set theory.
• C. First-Order Logic and Automated Theorem Proving
  "First-Order Logic and Automated Theorem Proving" is a foundational textbook that systematically introduces first-order logic while presenting key methods and algorithms used in automated theorem proving.
• D. 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.
• E. "The Complexity of Theorem-Proving Procedures"
  "The Complexity of Theorem-Proving Procedures" is Stephen Cook’s landmark 1971 paper that introduced the concept of NP-completeness and proved the Boolean satisfiability problem (SAT) to be NP-complete, laying the foundation for modern computational complexity theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.