Direct Proving

What it does

When your agent uses it

• A decomposition plan is created

Example prompts

• “/direct-proving”

Workflow steps

12 steps, taken from the first numbered list in SKILL.md.

1. 1Take one decomposition plan at a time.
2. 2For each subgoal, actively use the searched results, toy examples, and counterexamples that are most relevant to that subgoal.
3. 3When a similar theorem has been found, try to adapt its proof idea, construction, or reduction to the current subgoal instead of treating…
4. 4If the adapted theorem is only a partial result with extra hypotheses, first analyze why its method needs those hypotheses and where it…
5. 5First attempt to prove all subgoals in that plan directly.
6. 6Try to carry the whole plan through before switching into failure diagnosis mode.
7. 7For each subgoal, record whether it is
8. 8If a subgoal is blocked or you get stuck on it, FIRST invoke $construct-counterexamples for that subgoal — test whether it is false, too…
9. 9If a proof adaptation attempt fails, identify why the migration fails. Be concrete: for example, note which hypothesis is missing, which…
10. 10If a subgoal is solved with a self-contained partial result that the rest of the plan will USE downstream, partial-verify that result with…
11. 11If all subgoals are solved directly AND the partial results that compose into a full proof have each been partial-verified as needed, mark…
12. 12When a direction remains viable and supports sustained progress, work on it

What it can do on your machine

Read from SKILL.md and the folder at commit 6d92e8d. It shows what the files ask for, not the result of running them.

• Tool permissions

  Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.

  From allowed-tools in the SKILL.md frontmatter.

• Runs code

  No scripts in the folder and no shell commands in SKILL.md (its code samples are json).

  From the folder's file list and the shell code blocks in SKILL.md.

• Network

  No URLs in SKILL.md.

  From URLs in SKILL.md, links to its own repository left out.

• Credentials

  Names no API keys, tokens, secrets or passwords.

  From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Direct Proving loads about 1.3k tokens when it runs. Until then it costs about 54 tokens; SKILL.md has 643 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it

~54

When it runs · the whole SKILL.md, loaded when a task matches

~1.3k

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from frenzymath/Danus at commit 6d92e8d, republished under its Apache-2.0 licence (© frenzymath). 643 words, ~1,291 tokens.

name

direct-proving

description

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.

{
  "plan_id": "...",
  "attempt_type": "direct",
  "subgoal": "...",
  "attempt_summary": "...",
  "status": "solved|partial|stuck",
  "used_examples": ["..."],
  "used_counterexamples": ["..."],
  "counterexample_search_for_stuck_subgoal": {
    "performed": true,
    "summary": "...",
    "result": "refuted|not_refuted|inconclusive|not_needed"
  },
  "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"
}

© frenzymath, Apache-2.0. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

SKILL.md and 1 other file in agents/skills/worker/direct-proving of frenzymath/Danus.

• SKILL.md
• agents/openai.yaml

Open the folder on GitHubat commit 6d92e8d