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: Cook–Levin theorem | Statement: [NP-completeness, firstNPCompleteProof, Cook–Levin theorem]

Target entity: Cook–Levin theorem
Context triple: [NP-completeness, firstNPCompleteProof, Cook–Levin theorem]

• A. Cook–Levin theorem chosen
  The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
• B. Valiant–Vazirani theorem
  The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
• C. PCP theorem
  The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
• D. P versus NP problem
  The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
• E. Rice's theorem
  Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: firstNPCompleteProof
Context triple: [NP-completeness, firstNPCompleteProof, Cook–Levin theorem]

• A. wasFirstProvedBy chosen
  Indicates that a particular statement, theorem, or result was originally and for the first time demonstrated or established as true by a specified agent.
• B. provedUndecidableUsing
  Indicates that the undecidability of one problem, theory, or statement was established by applying or reducing it to another specific method, result, or formal system.
• C. firstSolvedBy
  Indicates that a particular problem, task, or challenge was initially solved or completed by a specific entity before any others.
• D. statusOfFermatProof
  Indicates the current state or condition of the proof related to Fermat’s Last Theorem (e.g., whether it is proposed, verified, refuted, or incomplete).
• E. firstWinningWork
  Indicates the relationship where a particular work is the first one for which an entity (such as a person or group) received a win, award, or notable victory.
• F. None of above.