Screen a decomposition plan by first trying to prove all of its subgoals directly, then identifying the key stuck points if the plan does not fully go through. Use when a decomposition plan is created.
Use this skill to screen decomposition plans by first trying to carry the whole plan through, and if it does not fully go through, then identify the key stuck points.
Read:
subgoalsimmediate_conclusions, toy_examples, counterexamples, and failed_pathsAppend one record per attempted subgoal to proof_steps:
{
"plan_id": "...",
"attempt_type": "direct",
"subgoal": "...",
"attempt_summary": "...",
"status": "solved|partial|stuck",
"used_examples": ["..."],
"used_counterexamples": ["..."],
"key_stuck_points": ["..."],
"used_results": ["..."],
"adapted_from": ["relevant statements or proofs whose ideas were migrated"],
"migration_failures": ["why a proof adaptation or migration failed"],
"branch_id": "optional"
}
Update the corresponding decomposition-plan record in subgoals to screening, screened, or solved.
memory_searchmemory_appendbranch_updatesearch_arxiv_theoremsIf a decomposition plan does not solve the problem directly after attempting all of its subgoals, append a failed_paths record that summarizes the plan-local stuck points and any important proof-migration failures.