Construct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail. Use when you are stuck in reasoning and want to see where the assumptions take effect and gain intuition, when a proposed conjecture/claim feels fragile or unproved, or when you want to test whether the assumptions can hold while the claimed conclusion fails.
Actively falsify proposed conjectures or intermediate claims by finding examples that satisfy the assumptions but violate the claimed conclusion.
Read:
immediate_conclusions and toy_examplesrefuted: assumptions hold and the claim failsnot_refuted: no counterexample found yetinconclusive: search space unclear or partially exploredtoy_examplesAppend to counterexamples:
{
"target_claim": "...",
"candidate_counterexample": "...",
"status": "refuted|not_refuted|inconclusive",
"assumptions_satisfied": ["..."],
"failed_conclusion": "...",
"impact": "...",
"branch_id": "optional",
"subgoal_id": "optional"
}
If status="refuted", also append to failed_paths when it kills a branch.
If the search produced a concrete non-refuting example, also append a record to toy_examples:
{
"example": "...",
"why_relevant": "constructed while testing the claim ...",
"assumptions_satisfied": ["..."],
"conclusion_verified": true,
"where_assumptions_take_effect": "...",
"observed_pattern": "...",
"supports_branch_ids": ["optional"],
"subgoal_id": "optional"
}
Do this whenever the constructed example is useful enough to test future claims or clarify the current branch, even if it did not refute the target claim.
memory_appendmemory_searchbranch_updatesearch_arxiv_theorems to find standard counterexample patternsIf no meaningful counterexample space is identified, append:
events.event_type="counterexample_space_unclear"