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: P versus NP problem | Statement: [SAT problem, relatedOpenProblem, P versus NP problem]

Target entity: P versus NP problem
Context triple: [SAT problem, relatedOpenProblem, P versus NP problem]

• A. P versus NP problem chosen
  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.
• B. Millennium Prize Problem
  The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
• C. 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.
• D. NP-completeness
  NP-completeness is a central concept in computational complexity theory that classifies decision problems believed to be among the hardest in NP, such that a polynomial-time solution to any one of them would yield polynomial-time solutions to all problems in NP.
• E. P, NP, and NP-Completeness: The Basics of Complexity Theory
  "P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: relatedOpenProblem
Context triple: [SAT problem, relatedOpenProblem, P versus NP problem]

• A. openProblemIn chosen
  Indicates that a particular problem or issue is currently active or unresolved within a specified context, domain, or environment.
• B. relatedConjecture
  Indicates that one conjecture is connected or associated with another conjecture, such as by similarity, dependency, or thematic relation.
• C. announcedMillenniumProblems
  Indicates that an entity formally proclaimed or made public the set of Millennium Problems.
• D. associatedConjecture
  Indicates that one entity is linked or connected to a particular conjecture, typically as its subject, source, or relevant context.
• E. numberOfMillenniumProblems
  Indicates the total count of Millennium Problems associated with a given subject or context.
• F. None of above.