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: 3-SAT is NP-hard | Statement: [NP-hardness, exampleProblem, 3-SAT is NP-hard]

Target entity: 3-SAT is NP-hard
Context triple: [NP-hardness, exampleProblem, 3-SAT is NP-hard]

• A. 3-SAT chosen
  3-SAT is a classic Boolean satisfiability problem where each clause has exactly three literals and which serves as a fundamental NP-complete benchmark in computational complexity theory.
• B. Max-3-SAT
  Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
• C. “Inapproximability results for SAT and other problems”
  “Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
• D. Cook–Levin theorem
  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.
• E. NP-hardness
  NP-hardness is a classification in computational complexity theory for problems at least as hard as the hardest problems in NP, such that every problem in NP can be reduced to them in polynomial time.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.