Assumption Negation

Tactics

• contradiction-derivation
• counterexample-heuristics

Method

1. Extract the core claim or assumption from the artifact
2. Formally negate it (produce ~P from P)
3. Derive logical consequences of ~P through deductive chains
4. Evaluate whether derivation reaches genuine contradiction
5. If contradiction found: original claim survives this test
6. If no contradiction: claim may be contingent, not necessary

Budget

Size	Negation chains	Max derivation depth
S	3	5 steps
M	6	8 steps
L	10	12 steps

Orchestration

1. Dispatch claim-negation to produce formal negation
2. For each negation, dispatch deductive-chain to derive consequences
3. Dispatch contradiction-detection to evaluate results
4. If no contradiction, dispatch claim-refinement for weakened version

Subagents

• claim-negation
• deductive-chain
• contradiction-detection
• claim-refinement

Available Tactics

Optional, no fixed order; the final leaf is always a sop.

Tactic	When to use
contradiction-derivation	Negate a claim, derive logical consequences step by step, detect whether a genuine contradiction or absurdity emerges.
counterexample-heuristics	Generate counterexamples (monsters), attempt monster-barring, incorporate surviving counterexamples as lemma refinements (Lakatos method).

Available SOPs

Optional, no fixed order; the final leaf is always a sop.

SOP	When to use
claim-negation	Formally negate the core claim, producing the logical complement for reductio testing.
claim-refinement	Propose a refined claim that survives counterexamples while preserving maximum explanatory power (Lakatos lemma-incorporation).
contradiction-detection	Evaluate whether a derivation chain has reached a genuine contradiction, absurdity, or inconclusive state.
deductive-chain	Derive logical consequences step by step from a given premise, building a traceable derivation chain.