DeepSeek-R1 Formal Mathematical Proof & Algorithm Verifier
Created for computer scientists, algorithm researchers, and quant traders requiring verifiable mathematical proofs with zero hand-waving.
Parametric Customizer & Compiler Live Tool
Adjust the variables below. The prompt code and API payload update dynamically in real time.
The mathematical theorem to verify.
You are a world-class theoretical computer scientist and formal proof architect. Prove or disprove the following theorem: 'Every graph with minimum degree d contains a cycle of length at least d + 1, and the longest path search bound is NP-complete.'. Execute your full reasoning derivation within <think> tokens following strict mathematical rigor: 1) State definitions, lemmas, and axiomatic basis, 2) Formulate the inductive base case or construct a formal contradiction, 3) Perform exhaustive step-by-step algebraic manipulation with self-checking verifications at each step, 4) Derive asymptotic tight bounds using Big-Theta notation, 5) Provide the complete formal proof in LaTeX notation alongside a Lean 4 or Coq formalization. No assumptions without proof.
Harness test-time compute for peer-review level proofs.
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πΈ Real Sample Outputs & Verified Results
Visual evidence and benchmark responses generated using this exact prompt formula.
π¬ Prompt Engineering Anatomy
Why this prompt consistently delivers high-tier results: technical parameter breakdown.
Maximal Substructure Proof Technique Selecting an extremal object (e.g. longest path) simplifies graph proofs by transforming global properties into endpoint local constraints.
π¬ Frequently Asked Questions
Troubleshooting common edge cases, model incompatibilities, and best practices.
Can DeepSeek-R1 generate verifiable Lean 4 theorem files?
Yes, DeepSeek-R1's reasoning tokens excel at generating syntactically valid Lean 4 tactics (intro, induction, simp, linarith).
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