Proof Strategy Selection Chain

validated scientific chain v1.0.0 cc-by-sa

Block ID: 849fb405-ea2e-417d-bfa1-de71d35ed89f

Community-contributed block. PromptDNA makes no guarantee of output quality or fitness for purpose. User assumes all responsibility for use.

Template

Prove or disprove the mathematical statement in {statement}, choosing strategy before charging ahead. (1) Parse the statement into precise logical form: identify the quantifiers, the hypothesis, and the conclusion, and restate any ambiguous term with its formal definition — most failed proofs attack a misread statement. (2) Test the statement's plausibility on small or extreme cases first: a single counterexample settles a universal claim in the negative and saves a doomed proof attempt, while confirming cases build the intuition a proof will formalize. (3) Choose the technique the statement's structure invites: direct proof for straightforward implications, contrapositive when the negated conclusion is easier to work with, contradiction when assuming falsehood yields leverage, induction for statements over the naturals, construction for existence claims. State why the chosen technique fits. (4) Execute the proof in explicit steps, justifying each inference by a definition, hypothesis, or established result — no step by intimidation. (5) Check the boundaries and the base case (for induction) and any division or existence assumption for hidden gaps. (6) Review the finished argument for whether every hypothesis was actually used — an unused hypothesis signals either a stronger theorem or a flaw.

Prove or disprove the mathematical statement in {statement}, choosing strategy before charging ahead. (1) Parse the statement into precise logical form: identify the quantifiers, the hypothesis, and the conclusion, and restate any ambiguous term with its formal definition — most failed proofs attack a misread statement. (2) Test the statement's plausibility on small or extreme cases first: a single counterexample settles a universal claim in the negative and saves a doomed proof attempt, while confirming cases build the intuition a proof will formalize. (3) Choose the technique the statement's structure invites: direct proof for straightforward implications, contrapositive when the negated conclusion is easier to work with, contradiction when assuming falsehood yields leverage, induction for statements over the naturals, construction for existence claims. State why the chosen technique fits. (4) Execute the proof in explicit steps, justifying each inference by a definition, hypothesis, or established result — no step by intimidation. (5) Check the boundaries and the base case (for induction) and any division or existence assumption for hidden gaps. (6) Review the finished argument for whether every hypothesis was actually used — an unused hypothesis signals either a stronger theorem or a flaw.

Variables

Name	Type	Required	Trust level
statement		yes

mathematical-proofproof-techniquelogicchain-of-thought

Ratings

0.0

Overall (0)

0.0

Accuracy

0.0

Consistency

0.0

Clarity

0.0

Efficiency

Benchmarks

Not yet self-validated against any benchmark. Automated, evaluative only - not a factor in whether this block was published.

Submitted by James P FounderMod via mcp · 2026-07-18