Counterexample Heuristics

---
name: counterexample-heuristics
description: "Generate counterexamples (monsters), attempt monster-barring, incorporate surviving counterexamples as lemma refinements (Lakatos method)."
type: tactic
used-by: [adversarial-stress-testing]
strategies: [lakatos-heuristics, assumption-negation, critical-case-design]
---

# Counterexample Heuristics

## Orchestration Steps

1. Receive claim/theorem from strategy
2. Dispatch `counterexample-generation` to produce candidate monsters
3. For each counterexample:
   a. Dispatch `monster-barring-attempt` — can it be excluded legitimately?
   b. If barring succeeds: record as excluded, note narrowed scope
   c. If barring fails: counterexample is genuine
4. For genuine counterexamples, dispatch `claim-refinement`:
   - Incorporate as lemma (add condition to claim)
   - Or weaken claim scope
5. Report: original claim, counterexamples found, refined claim

## Subagents

- counterexample-generation
- monster-barring-attempt
- claim-refinement

## Termination Conditions

- All generated counterexamples resolved (barred or incorporated)
- Claim refined to survive all counterexamples (success)
- Claim collapses entirely under counterexamples (falsified)
- Budget exhausted (report current state)