Triple

T9809588
Position Surface form Disambiguated ID Type / Status
Subject Herbrand's theorem E238234 entity
Predicate hasVersion P455 FINISHED
Object Herbrand's theorem for unsatisfiability E238234 NE FINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
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).
Input
Phrase: Herbrand's theorem for unsatisfiability | Statement: [Herbrand's theorem, hasVersion, Herbrand's theorem for unsatisfiability]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Herbrand's theorem for unsatisfiability
Context triple: [Herbrand's theorem, hasVersion, Herbrand's theorem for unsatisfiability]
  • 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. 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.
  • C. 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.
  • 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. "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.

Provenance (3 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69ca84defac48190abc1148804f184c1 completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb220310c8190a16ca0b746f0ef7a completed April 2, 2026, 12:02 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1cc5b4dd8819088c86946b4eb8a39 completed April 5, 2026, 2:43 a.m.
Created at: March 30, 2026, 8:29 p.m.