LRAT-Catcher uses reflection to import LRAT certificates into Lean 4 as theorems, scaling to large combinatorial problems and enabling verified cube-and-conquer compositions, demonstrated on Schur S(4)=44 and Ramsey R(4,4)=18.
In: McIlraith, S.A., Weinberger, K.Q
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Small symmetries create strict hierarchies in resolution with exponential separations from standard resolution, constant-depth Frege, and between SRCI and SRII.
A SAT-plus-LLM method discovers infinite families of doubly saturated Ramsey-good graphs, answering Grinstead and Roberts' 1982 question.
citing papers explorer
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LRAT-Catcher: Importing SAT Solver Certificates into Lean4 by Reflection
LRAT-Catcher uses reflection to import LRAT certificates into Lean 4 as theorems, scaling to large combinatorial problems and enabling verified cube-and-conquer compositions, demonstrated on Schur S(4)=44 and Ramsey R(4,4)=18.
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The Power of Small Symmetries
Small symmetries create strict hierarchies in resolution with exponential separations from standard resolution, constant-depth Frege, and between SRCI and SRII.
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Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery
A SAT-plus-LLM method discovers infinite families of doubly saturated Ramsey-good graphs, answering Grinstead and Roberts' 1982 question.