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Propose a refined claim that survives counterexamples while preserving maximum explanatory power (Lakatos lemma-incorporation).
Passed 18 of 22 test cases with the skill, and 13 of 22 without it.
and 6 more in the full report
6 fixed12 passed either way3 still failing1 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 6 test cases the skill fixed. Same model, same prompt, with and without the skill.
An analyst asserts: 'For all positive integers n, the polynomial f(n) = n^2 + n + 41 produces a prime number.' A colleague points out n = 41, where f(41) = 41 * 43, which is composite. Instead of abandoning the formula or claiming n = 41 is an exception that should be ignored, refine the claim's domain. State the modified constraint and the refinement technique.
| Checked | Without skill | With skill |
|---|---|---|
| The domain of n is restricted to positive integers strictly less than 41 | Missed | Passed |
| The refinement method is identified as scope narrowing | Missed | Passed |
The instructions your model reads when the skill loads.
Subagent that refines claims to survive counterexamples using lemma incorporation, scope narrowing, or claim splitting.
Optional, no fixed order; the final leaf is always a sop.
| SOP | When to use |
|---|---|
| spawn-agent | Spawn a customized CC subagent with full MCP tool access. Used by SOPs that declare execution: subagent. |
test cases passed, vs 13 / 22 without
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