messages listlengths 7 78 | reward float64 0 1 | session_id stringlengths 36 36 | model stringclasses 1
value | n_turns int64 3 39 | n_tool_calls int64 3 38 | n_oracle_runs int64 0 9 | last_oracle_score float64 0 1 ⌀ | ever_scored_1 bool 2
classes | source stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|
[
{
"content": "You are agent9 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order):\n1. program.md — task description and construction\n2. mathlib_hints.md — exact Mathlib lemma names and tactic patterns\n\nAfter those two reads, your IMMEDIATE next action must be Edit on workspace/agent9/Erd... | 1 | 08dc7947-3463-4c75-b486-cc5cd7b50181 | claude-opus-4-8 | 16 | 15 | 3 | 1 | true | rrma-erdos-741ii-g1 |
[
{
"content": "You are agent12 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order):\n1. program.md — task description and construction\n2. mathlib_hints.md — exact Mathlib lemma names and tactic patterns\n\nAfter those two reads, your IMMEDIATE next action must be Edit on workspace/agent12/E... | 1 | 09b99749-c228-4f9c-bb87-b5977bb7954f | claude-opus-4-8 | 9 | 8 | 1 | 1 | true | rrma-erdos-741ii-g1 |
[
{
"content": "You are agent4 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order):\n1. program.md — task description and construction\n2. mathlib_hints.md — exact Mathlib lemma names and tactic patterns\n\nAfter those two reads, your IMMEDIATE next action must be Edit on workspace/agent4/Erd... | 1 | 0d8e3fe6-77e0-49e5-83a2-b905c247d673 | claude-opus-4-8 | 16 | 15 | 3 | 1 | true | rrma-erdos-741ii-g1 |
[
{
"content": "You are agent1 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order):\n1. program.md — task description and construction\n2. mathlib_hints.md — exact Mathlib lemma names and tactic patterns\n\nAfter those two reads, your IMMEDIATE next action must be Edit on workspace/agent1/Erd... | 1 | 11e08619-5a0f-41d0-bd75-9a88eb581fa1 | claude-opus-4-8 | 10 | 9 | 1 | 1 | true | rrma-erdos-741ii-g1 |
[
{
"content": "You are agent11 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order):\n1. program.md — task description and construction\n2. mathlib_hints.md — exact Mathlib lemma names and tactic patterns\n\nAfter those two reads, your IMMEDIATE next action must be Edit on workspace/agent11/E... | 1 | 345857e5-9de1-4432-929f-3fee59ae4cde | claude-opus-4-8 | 19 | 18 | 5 | 1 | true | rrma-erdos-741ii-g1 |
[{"content":"You are agent9 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order)(...TRUNCATED) | 1 | 3f046149-4b17-40bf-a6f7-c4091c2fff3f | claude-opus-4-8 | 15 | 14 | 2 | 1 | true | rrma-erdos-741ii-g1 |
[{"content":"You are agent0 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order)(...TRUNCATED) | 0 | 3f3bbdea-4893-476b-bd1d-f12262e2cf1c | claude-opus-4-8 | 3 | 3 | 0 | null | false | rrma-erdos-741ii-g1 |
[{"content":"You are agent3 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order)(...TRUNCATED) | 1 | 4424f4c8-6710-49d3-8ac8-cc7a83a7f143 | claude-opus-4-8 | 25 | 24 | 3 | 1 | true | rrma-erdos-741ii-g1 |
[{"content":"You are agent1 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order)(...TRUNCATED) | 1 | 4af03bb0-b8fb-469d-b02a-3f73d1b6e10b | claude-opus-4-8 | 25 | 24 | 9 | 1 | true | rrma-erdos-741ii-g1 |
[{"content":"You are agent3 for a Lean 4 proof domain.\n\nREQUIRED first reads (ONCE, in this order)(...TRUNCATED) | 1 | 4c8e0d30-5aed-4f0e-bcd8-4ca749524b37 | claude-opus-4-8 | 19 | 18 | 5 | 1 | true | rrma-erdos-741ii-g1 |
Erdős #741(ii) — Lean 4 Opus Agent Traces
39 Claude Opus agent sessions attempting Erdős problem #741(ii) in Lean 4 (G1 rung: build the proof from an NL construction description).
v2 (2026-06-10) — label correction. The original upload labeled all 39 traces
reward=1.0; the labeler matched the textSCORE=1.0anywhere in the conversation, including the worker prompt. Rewards are now anchored to genuine oracle output (line-anchoredSCORE=adjacent toSORRY_COUNT:/BUILD_EXIT:/STATUS:inside a tool result), withreward = 1.0iff the session's last oracle score is 1.0. Corrected: 31 of 39 proved; of the other 8, 6 never ran the oracle (session cap / API errors) and 2 ran it but never reached 1.0. Chat structure normalized (strict role alternation, empty<thinking>removed).
Task
Prove that there exists a set of integers that is both an additive basis (every n≥4 is a sum of two elements) and unsplittable (every partition has a non-syndetic half). Construction: tower on powers of 5.
Traces
Each row is one complete agent session:
- messages: list of
{role, content}turns (user prompt + tool calls + oracle feedback + fixes) - reward: 1.0 = session's final genuine oracle run scored 1.0 (Lean compiled, 0 sorry), else 0.0 — 31/39
- n_oracle_runs, last_oracle_score, ever_scored_1: oracle audit fields
- model: claude-opus-4-8
- n_turns, n_tool_calls: session stats
- Tool calls inlined as
<tool_call>/<tool_result>markers - Thinking blocks preserved as
<thinking>
Signal
Hard verifiable reward — Lean compiler accepts or rejects, no fuzzy grading. Traces show the edit→compile→diagnose→fix loop that amortizes formal-language friction.
Usage
from datasets import load_dataset
ds = load_dataset("vincentoh/erdos741ii-lean4-opus-traces", split="train")
proved = ds.filter(lambda x: x["reward"] == 1.0) # 31 traces
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