Datasets:
problem_id stringclasses 980
values | sample_idx int64 0 7 | round int64 0 0 | cap_tokens int64 16.4k 16.4k | prompt_ids listlengths 126 1.23k | completion_ids listlengths 349 16.4k | prompt_text stringclasses 980
values | completion_text stringlengths 1.04k 109k | finish_reason stringclasses 2
values | lean_code stringlengths 177 66.1k ⌀ | lean_code_error stringclasses 2
values | messages listlengths 1 1 | model_path stringclasses 1
value | model_rev stringclasses 1
value | sampling dict | context_clipped bool 1
class | parent null |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Goedel-Pset-619485 | 4 | 0 | 16,384 | [
151644,
872,
198,
12548,
279,
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220,
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488,
220,
16,
17,
8,
284,
220,
18,
15,
23,
28587,
4710,
820,
14822... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof and Analysis
First, we need to understand the problem correctly. The Lean theorem states that `11 * (7 + 9 + 12) = 308`.
#### Step 1: Evaluate the Sum Inside the Parentheses
The sum inside the parentheses is `7 + 9 + 12`. We can evaluate this step by step:
1. `7 + 9 = 16`
2. `16 + 12 = 28`
So, `7... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h_main : 11 * (7 + 9 + 12) = 308 := by
norm_num
<;> rfl
exact h_main | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 1845142802
} | false | null |
Goedel-Pset-619485 | 6 | 0 | 16,384 | [
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872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
2675,
19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
9672,
1932,
45384,
1371,
1862,
220,
15,
271,
2508,
6164,
77760,
8800,
23833,
6909,
2449,
40577,
... | [
14374,
62665,
36991,
323,
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271,
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311,
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353,
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220,
24,
488,
220,
16,
17,
8,
284,
220,
18,
15,
23,
28587,
4710,
16,
13,
3070,
16250,
2685,
279,
16378,
334,
510,
256,
576,
7493,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof and Analysis
We are to prove that `11 * (7 + 9 + 12) = 308`.
1. **Understand the Expression**:
The expression inside the parentheses is `7 + 9 + 12`, which sums to `28`.
Multiplying this by `11` gives `11 * 28 = 308`.
2. **Verification**:
- First, compute `7 + 9 + 12 = 28`.
- Next, co... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h₁ : 7 + 9 + 12 = 28 := by
norm_num
<;> simp [add_assoc]
<;> norm_num
<;> rfl
have h₂ : 11 * (7 + 9 + 12) = 308 := by
rw [... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 215054513
} | false | null |
Goedel-Pset-619485 | 0 | 0 | 16,384 | [
151644,
872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
2675,
19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
9672,
1932,
45384,
1371,
1862,
220,
15,
271,
2508,
6164,
77760,
8800,
23833,
6909,
2449,
40577,
... | [
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488,
220,
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17,
8,
284,
220,
18,
15,
23,
62338,
334,
28588,
610,
25,
1019,
16,
13,
5512,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof and Analysis
**Problem Statement:**
We need to prove that `11 * (7 + 9 + 12) = 308`.
**Approach:**
1. First, we calculate the sum inside the parentheses: `7 + 9 + 12 = 28`.
2. Then, we multiply the result by `11`: `11 * 28 = 308`.
3. The final result is `308`, which matches the right-hand side of t... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h₀ : 11 * (7 + 9 + 12) = 308 := by
norm_num
<;> decide
apply h₀ | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 1873636096
} | false | null |
Goedel-Pset-619485 | 5 | 0 | 16,384 | [
151644,
872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
2675,
19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
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1932,
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1371,
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220,
15,
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6164,
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8800,
23833,
6909,
2449,
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... | [
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62665,
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323,
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488,
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16,
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8,
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4710,
16,
13,
3070,
8304,
220,
16,
25,
61242,
1437,
279,
2629,
4766,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof and Analysis
We need to prove that `11 * (7 + 9 + 12) = 308`.
1. **Step 1: Simplify the sum inside the parentheses.**
- Compute `7 + 9 = 16`.
- Compute `16 + 12 = 28`.
- So, `7 + 9 + 12 = 28`.
2. **Step 2: Multiply by 11.**
- Compute `11 * 28 = 308`.
- This is the final result.
Ho... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h₁ : 9 + 12 = 21 := by
norm_num
<;> rfl
have h₂ : 7 + (9 + 12) = 28 := by
norm_num [h₁]
<;> rfl
have h₃ : 11 * (7 + 9 + 1... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 901082289
} | false | null |
Goedel-Pset-619485 | 2 | 0 | 16,384 | [
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872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
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19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
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1371,
1862,
220,
15,
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2508,
6164,
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8800,
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... | [
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16,
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8,
284,
220,
18,
15,
23,
62338,
16,
13,
3070,
47866,
279,
8... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof and Analysis
First, let's understand the problem: We need to prove that `11 * (7 + 9 + 12) = 308`.
1. **Calculate the Sum Inside the Parentheses**:
- Compute `7 + 9 + 12`.
- `7 + 9 = 16`
- `16 + 12 = 28`
- So, `7 + 9 + 12 = 28`.
2. **Multiply by 11**:
- Compute `11 * 28`.
- Break... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h1 : 7 + 9 + 12 = 28 := by
norm_num
<;> rfl
have h2 : 11 * (7 + 9 + 12) = 308 := by
rw [h1]
<;> norm_num
<;> rfl
exac... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 73773325
} | false | null |
Goedel-Pset-619485 | 1 | 0 | 16,384 | [
151644,
872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
2675,
19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
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1371,
1862,
220,
15,
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2508,
6164,
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23833,
6909,
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... | [
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323,
10146,
429,
432,
16819,
1565,
18,
15,
23,
28587,
4710,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof and Analysis
First, let's understand the problem: We need to compute `11 * (7 + 9 + 12)` and verify that it equals `308`.
1. **Understand the Expression**:
The expression is `11 * (7 + 9 + 12)`.
- First, we compute the sum inside the parentheses: `7 + 9 + 12 = 28`.
- Then, multiply by `11... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h₁ : 7 + 9 + 12 = 28 := by
norm_num
<;> rfl
have h₂ : 11 * (7 + 9 + 12) = 308 := by
rw [h₁]
<;> norm_num
<;> rfl
exac... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 496699014
} | false | null |
Goedel-Pset-619485 | 7 | 0 | 16,384 | [
151644,
872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
2675,
19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
9672,
1932,
45384,
1371,
1862,
220,
15,
271,
2508,
6164,
77760,
8800,
23833,
6909,
2449,
40577,
... | [
14374,
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18,
15,
23,
28587,
4710,
16,
13,
5512,
11,
12564,
279,
2629,
4766,
279,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof
**Problem Analysis:**
We need to prove that `11 * (7 + 9 + 12) = 308`.
1. First, compute the sum inside the parentheses: `7 + 9 + 12 = 28`.
2. Multiply the sum by 11: `11 * 28 = 308`.
However, the Lean statement is `11 * (7 + 9 + 12) = 308`, where the operations are performed in `ℕ` (natural numb... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h₁ : 7 + 9 + 12 = 28 := by
norm_num
<;> rfl
have h₂ : 11 * (7 + 9 + 12) = 308 := by
rw [h₁]
<;> norm_num
<;> rfl
appl... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 196403911
} | false | null |
Goedel-Pset-938722 | 7 | 0 | 16,384 | [
151644,
872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
2675,
19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
9672,
1932,
45384,
1371,
1862,
220,
15,
271,
2508,
6164,
77760,
8800,
23833,
6909,
2449,
40577,
... | [
14374,
62665,
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701,
1221,
1124,
4080,
16,
366,
856,
366,
220,
19,
59,
568,
4710,... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-Solve the inequality
\[ -3x^2 + 9x + 12 > 0. \]-/
theorem lean_workbook_25084 (x : ℝ)
(h₀ : -3 * x^2 + 9 * x + 12 > 0) :
-1 < x ∧ x < 4 := by sorry`... | ### Detailed Proof and Analysis
First, we need to prove that if \(-3x^2 + 9x + 12 > 0\), then \(-1 < x < 4\).
#### Step 1: Understand the Inequality
The inequality \(-3x^2 + 9x + 12 > 0\) can be rewritten by dividing both sides by \(-3\) (and flipping the inequality because we are dividing by a negative number):
\[ ... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_25084 (x : ℝ)
(h₀ : -3 * x^2 + 9 * x + 12 > 0) :
-1 < x ∧ x < 4 := by
have h_main : -1 < x ∧ x < 4 := by
constructor
·
by_contra h
have h₁ : x ≤ -1 := by linarith
... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-Solve the inequality\n\\[ -3x^2 + 9x + 12 > 0. \\]-/ \ntheorem lean_workbook_25084 (x : ℝ)\n (h₀ : -3 * x^2 + 9 * x +... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 993324814
} | false | null |
Goedel-Pset-619485 | 3 | 0 | 16,384 | [
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Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the valu... | ### Detailed Proof and Analysis
First, let's understand the problem: we need to compute `11 * (7 + 9 + 12)` and verify that it equals `308`.
1. **Evaluate the Sum Inside the Parentheses**:
- The expression inside the parentheses is `7 + 9 + 12`.
- Compute `7 + 9 = 16`.
- Then `16 + 12 = 28`.
2. **Multiply ... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h₁ : 7 + 9 + 12 = 28 := by
norm_num
<;> rfl
<;> simp_all
<;> norm_num
<;> rfl
have h₂ : 11 * (7 + 9 + 12) = 308 := by
... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second l... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 297995302
} | false | null |
Goedel-Pset-1623413 | 1 | 0 | 16,384 | [
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510,... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_864 (x y z : ℝ)
(h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
(h₁ : x + y + z = 1) :
x + (y + z) = y + (z + x) ∧ y + (z + x) = z + (x + y) ∧ z... | ### Detailed Proof and Analysis
First, let's carefully understand the problem and the hypotheses. We have three real numbers \( x, y, z \) that are all positive, and their sum is 1:
\[ x + y + z = 1. \]
We need to prove that:
1. \( x + (y + z) = y + (z + x) \),
2. \( y + (z + x) = z + (x + y) \),
3. \( z + (x + y) = x... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_864 (x y z : ℝ)
(h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
(h₁ : x + y + z = 1) :
x + (y + z) = y + (z + x) ∧ y + (z + x) = z + (x + y) ∧ z + (x + y) = x + (y + z) := by
have h₂ : x + (y + z) = y +... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\ntheorem lean_workbook_plus_864 (x y z : ℝ)\n (h₀ : 0 < x ∧ 0 < y ∧ 0 < z)\n (h₁ : x + y + z = 1) :\n x + (y + z) = y + (... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 1784213585
} | false | null |
Goedel-Pset-1042382 | 3 | 0 | 16,384 | [
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... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- The probability of drawing at least one ball of each color when drawing 4 balls
from a bag containing 5 white, 4 red, and 3 yellow balls equals 6/11. -... | ### Detailed Proof and Analysis
First, we need to understand the problem correctly. The Lean theorem statement is a bit abstracted from the original problem, but we can see that:
1. `total_balls` is 12 (5 + 4 + 3), and `drawn_balls` is 4.
2. The first goal is to show that the number of ways to draw any 4 balls out of... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem probability_one_of_each_color :
let total_balls : ℕ := 12
let white_balls : ℕ := 5
let red_balls : ℕ := 4
let yellow_balls : ℕ := 3
let drawn_balls : ℕ := 4
(choose total_balls drawn_balls) = 495 ∧
... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n/-- The probability of drawing at least one ball of each color when drawing 4 balls\n from a bag containing 5 white, 4 re... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 1881009388
} | false | null |
Goedel-Pset-938722 | 2 | 0 | 16,384 | [
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646,
387,
58524,
438,
510... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-Solve the inequality
\[ -3x^2 + 9x + 12 > 0. \]-/
theorem lean_workbook_25084 (x : ℝ)
(h₀ : -3 * x^2 + 9 * x + 12 > 0) :
-1 < x ∧ x < 4 := by sorry`... | ### Detailed Proof and Analysis
First, let's recall the inequality we need to solve:
\[ -3x^2 + 9x + 12 > 0. \]
This can be rewritten as:
\[ 3x^2 - 9x - 12 < 0. \]
However, we will work directly with the original inequality for simplicity.
#### Step 1: Find the roots of the quadratic equation
The quadratic equation \... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_25084 (x : ℝ)
(h₀ : -3 * x^2 + 9 * x + 12 > 0) :
-1 < x ∧ x < 4 := by
have h₁ : -1 < x := by
by_contra h
have h₂ : x ≤ -1 := by linarith
have h₃ : -3 * x ^ 2 + 9 * x... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n\n /-Solve the inequality\n\\[ -3x^2 + 9x + 12 > 0. \\]-/ \ntheorem lean_workbook_25084 (x : ℝ)\n (h₀ : -3 * x^2 + 9 * x +... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 402391689
} | false | null |
Goedel-Pset-1042382 | 6 | 0 | 16,384 | [
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510,
16,
13,... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- The probability of drawing at least one ball of each color when drawing 4 balls
from a bag containing 5 white, 4 red, and 3 yellow balls equals 6/11. -... | ### Detailed Proof and Analysis
First, we need to compute the binomial coefficients involved in the problem and verify the given arithmetic statements.
#### Understanding the Problem
The problem consists of two parts:
1. Prove that `choose 12 4 = 495`.
2. Prove that the sum `choose 5 2 * choose 4 1 * choose 3 1 + cho... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem probability_one_of_each_color :
let total_balls : ℕ := 12
let white_balls : ℕ := 5
let red_balls : ℕ := 4
let yellow_balls : ℕ := 3
let drawn_balls : ℕ := 4
(choose total_balls drawn_balls) = 495 ∧
... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n/-- The probability of drawing at least one ball of each color when drawing 4 balls\n from a bag containing 5 white, 4 re... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 1288884693
} | false | null |
Goedel-Pset-1623413 | 4 | 0 | 16,384 | [
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311,
12118,
429,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_864 (x y z : ℝ)
(h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
(h₁ : x + y + z = 1) :
x + (y + z) = y + (z + x) ∧ y + (z + x) = z + (x + y) ∧ z... | ### Detailed Proof
#### Understanding the Problem
We are given three positive real numbers \( x, y, z \) such that \( x + y + z = 1 \). We need to prove that the following three equations hold:
1. \( x + (y + z) = y + (z + x) \)
2. \( y + (z + x) = z + (x + y) \)
3. \( z + (x + y) = x + (y + z) \)
However, since \( ... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_864 (x y z : ℝ)
(h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
(h₁ : x + y + z = 1) :
x + (y + z) = y + (z + x) ∧ y + (z + x) = z + (x + y) ∧ z + (x + y) = x + (y + z) := by
have h₂ : x + (y + z) = 1 :... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\ntheorem lean_workbook_plus_864 (x y z : ℝ)\n (h₀ : 0 < x ∧ 0 < y ∧ 0 < z)\n (h₁ : x + y + z = 1) :\n x + (y + z) = y + (... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 283817749
} | false | null |
Goedel-Pset-1042382 | 7 | 0 | 16,384 | [
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315,
220,
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17,
374,
220,
19,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- The probability of drawing at least one ball of each color when drawing 4 balls
from a bag containing 5 white, 4 red, and 3 yellow balls equals 6/11. -... | ### Detailed Proof
#### Problem Analysis
We are given a problem that asks to prove two combinatorial identities:
1. The number of ways to choose 4 balls out of 12 is 495.
2. The sum of certain products of binomial coefficients is 270, where the binomial coefficients are derived from the number of white, red, and yello... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem probability_one_of_each_color :
let total_balls : ℕ := 12
let white_balls : ℕ := 5
let red_balls : ℕ := 4
let yellow_balls : ℕ := 3
let drawn_balls : ℕ := 4
(choose total_balls drawn_balls) = 495 ∧
... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n/-- The probability of drawing at least one ball of each color when drawing 4 balls\n from a bag containing 5 white, 4 re... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 1511817582
} | false | null |
Goedel-Pset-1623413 | 3 | 0 | 16,384 | [
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488,
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488,
856,
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284,
11... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_864 (x y z : ℝ)
(h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
(h₁ : x + y + z = 1) :
x + (y + z) = y + (z + x) ∧ y + (z + x) = z + (x + y) ∧ z... | ### Detailed Proof and Analysis
First, we need to prove three statements:
1. `x + (y + z) = y + (z + x)`
2. `y + (z + x) = z + (x + y)`
3. `z + (x + y) = x + (y + z)`
We are given that `x, y, z > 0` and `x + y + z = 1`. However, the assumptions `x, y, z > 0` and `x + y + z = 1` are irrelevant to the actual goal, as t... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_864 (x y z : ℝ)
(h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
(h₁ : x + y + z = 1) :
x + (y + z) = y + (z + x) ∧ y + (z + x) = z + (x + y) ∧ z + (x + y) = x + (y + z) := by
have h₂ : x + (y + z) = y +... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\ntheorem lean_workbook_plus_864 (x y z : ℝ)\n (h₀ : 0 < x ∧ 0 < y ∧ 0 < z)\n (h₁ : x + y + z = 1) :\n x + (y + z) = y + (... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 650167729
} | false | null |
Goedel-Pset-1042382 | 5 | 0 | 16,384 | [
151644,
872,
198,
12548,
279,
2701,
62106,
220,
19,
2038,
1447,
73594,
2675,
19,
198,
474,
4149,
2740,
198,
474,
362,
288,
453,
271,
746,
9672,
1932,
45384,
1371,
1862,
220,
15,
271,
2508,
6164,
77760,
8800,
23833,
6909,
2449,
40577,
... | [
14374,
62665,
36991,
323,
18320,
271,
5338,
11,
19091,
429,
279,
3491,
374,
311,
12564,
9544,
20855,
36829,
323,
10146,
1378,
8186,
510,
16,
13,
1565,
27052,
220,
16,
17,
220,
19,
284,
220,
19,
24,
20,
3989,
17,
13,
362,
2629,
315,
... | <|im_start|>user
Complete the following Lean 4 code:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- The probability of drawing at least one ball of each color when drawing 4 balls
from a bag containing 5 white, 4 red, and 3 yellow balls equals 6/11. -... | ### Detailed Proof and Analysis
First, recall that the problem is to compute binomial coefficients and verify two claims:
1. `choose 12 4 = 495`
2. A sum of products of binomial coefficients equals `270`.
#### 1. Verification of `choose 12 4 = 495`
The binomial coefficient `choose 12 4` is calculated as:
\[
\binom{1... | stop | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem probability_one_of_each_color :
let total_balls : ℕ := 12
let white_balls : ℕ := 5
let red_balls : ℕ := 4
let yellow_balls : ℕ := 3
let drawn_balls : ℕ := 4
(choose total_balls drawn_balls) = 495 ∧
... | null | [
{
"role": "user",
"content": "Complete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology Rat\n\n/-- The probability of drawing at least one ball of each color when drawing 4 balls\n from a bag containing 5 white, 4 re... | /apps/development/rlhf/hf_cache/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a | dfd02e6271a58375dfbf3ece0175277cf6b6a89a | {
"temperature": 1,
"top_p": 0.95,
"top_k": 0,
"n": 1,
"max_tokens": 16384,
"seed": 1404214551
} | false | null |
ProofForge e2e attested generations
This dataset holds 7,803 Lean 4 proof attempts that Goedel-LM/Goedel-Prover-V2-8B wrote for 980 statements from the Goedel-Pset-v1 training pool. A frozen Lean verifier labelled every attempt, so each row comes with its verdict. Every stored prompt was re-tokenized and compared token by token with the prompt the model actually received. All 7,803 matched. The ProofForge end-to-end smoke run of 2026-10-26 built its SFT and DPO data from these rows.
Part of the ProofForge experiment archive. This card describes the data only. The checkpoints trained on it have their own cards (section 10).
1. TL;DR
| What it is | Single-round, verifier-labelled proof samples (prompt, full completion, extracted Lean code, token ids, sampling settings, verdict) |
| Generator | Goedel-LM/Goedel-Prover-V2-8B @ dfd02e6271a58375dfbf3ece0175277cf6b6a89a (Qwen3-8B architecture), round 0 |
| Sampling | temperature 1.0, top-p 0.95, top-k off, n = 8 per statement, 16,384-token completion cap, vLLM 0.26.0, TP = 4 |
| Statements | 980 Goedel-Pset-v1 training-pool statements (from viai957/lean-prover-data:problems/train_pool.jsonl) |
| Size | 7,803 generations (305 MB JSONL) + 7,803 verdicts (5.3 MB JSONL); 38.1 M completion tokens |
| Labels | pf_strict policy, Lean v4.9.0-rc1, Mathlib d1d1e4b7, 180 s budget, kernel re-check, axiom whitelist {propext, Quot.sound, Classical.choice} |
| Label mix | 4,007 valid (51.4%) / 3,533 rejected (45.3%) / 263 masked (3.4%) |
| Coverage | 571 of 980 statements (58.3%) have at least 1 valid proof; 373 have 8/8 valid (375 have every sample valid) |
| Base-model pass@k on this pool | pass@1 51.2% [48.3, 54.1], pass@8 58.6% [55.5, 61.7] (95% CI). Masked rows count as failures. This is a training pool, not a benchmark. |
| Prompt attestation | 7,803 checked, 0 mismatches |
| Contamination | 0 hits on all 16 protected sets on file (miniF2F test and valid, ProofNet, PutnamBench, MOBench and 11 others) |
| Compute | Generation: 49,712 s (13.8 h) wall on 4x NVIDIA L4, 797 tok/s end to end. Verification: 102,528 worker-seconds (8 Lean workers). |
| Downstream use | e2e SFT (320 valid proofs, 80 steps) and DPO (69 pairs, 20 steps) LoRA smoke runs on Goedel-Prover-V2-8B |
| Status | Superseded on 2026-10-29: the project moved to Nemotron-3-Nano and Lean v4.35 |
2. Dataset details and mechanism
- Curated by: viai957 (ProofForge project).
- Language: English natural-language problem text and proof plans, plus Lean 4 code.
- Licence: Apache-2.0 (section 10).
- Rounds: round 0 only. No correction or self-repair rounds are included.
flowchart LR
A["viai957/lean-prover-data<br/>problems/train_pool.jsonl<br/>2,000 Goedel-Pset-v1 statements"] --> B["vLLM 0.26 · TP=4 · 4x L4<br/>Goedel-Prover-V2-8B @dfd02e6<br/>T=1.0, top-p 0.95, n=8, cap 16,384"]
B --> C["gen_r0.jsonl<br/>8,082 samples<br/>(session ended early: crash)"]
C --> D["Lean verifier pf_strict<br/>v4.9.0-rc1 · Mathlib d1d1e4b7<br/>180 s · kernel recheck · axiom whitelist"]
D --> E["ver_r0.jsonl<br/>7,987 verdicts"]
C --> F{"attest_shim.py<br/>drop not-in-pool (184)<br/>drop no-verdict (95)<br/>re-tokenize prompt"}
E --> F
F --> G["gens.attested.jsonl<br/>7,803 rows · 0 prompt mismatches"]
E --> H["verdicts.pf_strict.jsonl<br/>7,803 rows"]
G --> I["e2e SFT mix (320)"]
G --> J["e2e DPO mix (96 → 69 pairs)"]
H --> I
H --> J
The verifier's verdict has three values. valid means Lean accepted the proof, the kernel re-check passed and only whitelisted axioms were used. rejected means the attempt failed deterministically: a compile error, no extractable code, or sorry or another banned construct. masked means the verifier did not reach a verdict (timeout, out of memory, or a crash). A masked row is neither positive nor negative, and ProofForge never uses one as a negative.
3. Data
3.1 Sources
| source | role | licence | size used |
|---|---|---|---|
Goedel-LM/Goedel-Pset-v1 via viai957/lean-prover-data problems/train_pool.jsonl |
formal statements (Lean 4) and informal problem text | none declared on the HF card (Goedel-Prover code repo is MIT); informal problems from NuminaMath, Apache-2.0 | 980 of the 2,000-statement pool |
| Goedel-LM/Goedel-Prover-V2-8B | generator | Apache-2.0 | revision dfd02e6271a58375dfbf3ece0175277cf6b6a89a |
Why 980 statements and not 2,000: the generation session (lean_gen.py, session 1791951209-4193267) ran from 2026-10-14 09:43 to 23:32 IST. It ended in a crash after writing 8,082 samples, with 160 requests still in flight. The archived data covers the statements that were finished at that point. 969 of the 980 statements have all 8 samples. The rest have 1 to 7 (table 3.4).
3.2 Filtering and decontamination
| step | rows in | rows out | evidence |
|---|---|---|---|
raw generations (gen_r0.jsonl) |
8,082 | generation manifest samples_written |
|
| drop rows whose problem is not in the ProofForge e2e pool | 8,082 | 7,898 | attestation manifest drop_not_in_pool: 184 |
| drop rows without a verifier verdict | 7,898 | 7,803 | attestation manifest drop_no_verdict: 95 |
prompt attestation (re-render with tokenizer, compare prompt_ids) |
7,803 | 7,803 | rows_checked: 7803, rows_mismatched: 0 |
Figure 0. Row counts from raw generation to the e2e SFT and DPO mixes (log scale). Sources: generation manifest, attestation manifest, ProofForge/data/e2e/2026.10.26/proofs.json, docs/evidence/p4_e2e_2026-10-26/preference_set.MANIFEST.json.
The ProofForge e2e pool was built from the 2,000-statement source pool. 8 statements were dropped for informal-text overlap with a protected set, 6 by the decontamination gate (miniF2F test and valid, MOBench), 1 by an excluded-id rule, and 24 by a float-numeral filter, leaving 1,961 statements (pool/problemset.json). This is why 184 generated rows fell outside the pool.
On 2026-11-03 every row was re-scanned with proofforge/data/blocklist.py against all 16 protected sets on file: clever, dafnybench, fate-h, fate-m, fate-x, flteval, minif2f-test, minif2f-valid, mobench, proofnet, putnambench, reform-dafnycomp, swebench-verified, verina, verinalite and verinaplus. Result: 0 hard hits and 0 weak overlaps in 7,803 rows (artifacts/hf_archive/blocklist_scan.json). One pool statement (Goedel-Pset-1349070) overlaps PutnamBench putnam_1987_b5 by natural-language window. No row in this dataset uses it.
3.3 Schema
generations config (data/gens.attested.jsonl, one generation per row)
| field | type | description |
|---|---|---|
problem_id |
str | Goedel-Pset id, e.g. Goedel-Pset-619485 |
sample_idx |
int | 0..7, sample index within the statement |
round |
int | always 0 |
cap_tokens |
int | always 16,384 |
prompt_ids, completion_ids |
list[int] | exact token ids (Qwen3 tokenizer of the generator) |
prompt_text, completion_text |
str | decoded prompt (chat-templated) and completion |
messages |
list[dict] | the single user turn before templating |
lean_code |
str | Lean code extracted from the last code block of the completion |
lean_code_error |
str or null | extraction error; null on 7,630 rows, no_code_block 153, proof_theorem_not_found 20. This is separate from the verifier's no_code tag (443 rows, exactly the finish_reason == length rows) |
finish_reason |
str | stop (7,360) or length (443) |
model_path, model_rev |
str | generator snapshot and revision |
sampling |
dict | temperature, top_p, top_k, n, max_tokens, per-request seed |
context_clipped |
bool | always false |
parent |
null | reserved for correction rounds (none here) |
verdicts config (data/verdicts.pf_strict.jsonl), joined to generations on key = [problem_id, sample_idx, round, cap_tokens]
| field | description |
|---|---|
verdict |
valid / rejected / masked |
kind |
finer class: valid, invalid, timeout, infra, crash |
accepted |
bool, true iff verdict == valid |
reasons |
list of tags, e.g. compile_error, no_code, banned:sorry, timeout, memory |
axioms |
axioms the accepted proof depends on |
budget_s, timeout_class |
180.0, train180 |
kernel_recheck |
true on all rows |
policy, verifier_hash, pins_config_hash, F |
verifier identity (single value on all rows) |
code_sha256, row_id, stage |
content hash of the checked code, row id, and the verifier stage the row reached (e.g. skipped, compile, repl, audit) |
Example (abridged), generations row Goedel-Pset-619485, sample 4:
prompt_text: <|im_start|>user\nComplete the following Lean 4 code:\n\n```lean4\nimport Mathlib\nimport Aesop\n
set_option maxHeartbeats 0\nopen BigOperators Real Nat Topology Rat\n
/-The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the
second largest factor of \( n \). What is the value of \( 11C \)?-/
theorem lean_workbook_51472 :\n 11 * (7 + 9 + 12) = 308 := by sorry```\n\nBefore producing the Lean 4 code ...
provide a detailed proof plan ...
lean_code (tail):
theorem lean_workbook_51472 :
11 * (7 + 9 + 12) = 308 := by
have h_main : 11 * (7 + 9 + 12) = 308 := by
norm_num
<;> rfl
exact h_main
finish_reason: stop prompt tokens: 190 completion tokens: 556
The matching verdict: {"verdict": "valid", "kind": "valid", "accepted": true, "axioms": ["propext"], "budget_s": 180.0, "kernel_recheck": true, "policy": "pf_strict"}.
A rejected verdict: {"key": ["Goedel-Pset-1599045", 0, 0, 16384], "verdict": "rejected", "kind": "invalid", "reasons": ["compile_error"], "axioms": null}.
3.4 Splits and statistics
There is a single train split per config, because every statement comes from the Goedel-Pset-v1 training pool. Do not use this data as an evaluation set.
| statistic | value |
|---|---|
| rows (each config) | 7,803 |
| statements | 980 |
| samples per statement | 8 for 969 statements; 7 (2), 6 (4), 4 (2), 2 (2), 1 (1) |
| verdicts | valid 4,007 · rejected 3,533 · masked 263 |
kind |
valid 4,007 · invalid 3,533 · timeout 223 · infra (memory) 29 · crash 11 |
| reason tags | compile_error 3,007 · no_code 443 · timeout 223 · banned:sorry 83 · memory 29 · crash 11 · banned:meta_api:Lean 1 · target_missing 1 (one row, Goedel-Pset-1482028 sample 4, carries three tags: banned:sorry, banned:meta_api:Lean, target_missing) |
| axioms in accepted proofs | propext 3,827 · Quot.sound 3,460 · Classical.choice 3,196 (of 4,007) |
finish_reason |
stop 7,360 · length 443. All 443 cap hits are rejected / no_code. None is masked. |
| prompt tokens | mean 262, median 245, p10 168, p90 359, max 1,230 |
| completion tokens | mean 4,883, median 3,160, p10 945, p90 11,734, max 16,384; total 38,099,556 |
| completion tokens, valid | mean 2,090, median 1,615, p90 3,899 |
| completion tokens, rejected | mean 7,766, median 6,772, p90 16,384 |
| completion tokens, masked | mean 8,699, median 8,600, p90 13,707 |
| verify time per row, valid | median 1.24 s, p90 7.48 s, max 174.6 s |
| verify time per row, rejected | median 2.71 s, p90 34.0 s |
| verify time per row, masked | median 180.3 s (timeouts at the 180 s budget) |
Figure 1. Left: verifier kind per row; verdict in brackets. Right: reason tags on non-valid rows (log scale). Source: data/verdicts.pf_strict.jsonl (local copy ProofForge/data/e2e/2026.10.26/sidecars/sidecars/0ee6fcb0.../pf_strict/verdicts.jsonl, sha256 d86ce61d...).
Figure 2. Number of valid proofs per statement. 409 statements have none, 373 have 8/8 valid, and 198 fall in between (1 to 7). The middle band is where group-relative RL gets a learning signal. Source: verdicts joined to generations.
Figure 3. Completion length (len(completion_ids)) by verdict. Valid proofs are short (median 1,615 tokens). The spike at the 16,384-token cap is the 443 truncated, rejected rows. Source: data/gens.attested.jsonl + verdicts.
Figure 4. Lean verification wall time per row, as an ECDF. Masked timeouts (223 of 263) sit at the 180 s budget; the 40 memory and crash rows end earlier (from 16 s). 443 rejected rows (12.5%) have a recorded time of 0 s, meaning they never reached Lean. The count equals the number of no_code tags; values below 0.01 s are drawn at 0.01 s. Source: verify_s in align/.tmp/p2/r1/pool/ver_r0.jsonl (the upstream verifier file; this field is not in the published verdicts file), joined on key.
Figure 5. Unbiased pass@k estimator (Chen et al., 2021) averaged over statements with n ≥ k samples. Masked rows count as failures. Error bars are 95% normal-approximation CIs over statements. Source: verdicts joined to generations. This measures the base model on its own training pool, not on a benchmark.
4. Procedure
4.1 Generation
Each statement was rendered with Goedel-Prover-V2's prompt (prompt_format: goedel): the Lean header, the informal problem as a comment, the formal statement ending in := by sorry, and a request for a proof plan before the code. The model's chat template was applied. Then n = 8 independent samples were drawn per statement:
Engine: align/extras/vllm_rollout/lean_gen.py, vLLM 0.26.0, torch 2.11.0+cu130, tensor parallel 4, max_model_len 40,960, max_num_seqs 128, gpu_memory_utilization 0.82, KV cache 405,120 tokens, seed 0 (per-request seeds are stored in sampling.seed). The tokenizer round-trip was checked on 4 rows at start-up.
4.2 Verification (labelling)
Verifier config: statement_mode: strict, allow_helper_defs: false, lexical_gate: true, max_code_chars: 200000, proof_timeout_s: 180, 8 workers. Pins: Lean leanprover/lean4:v4.9.0-rc1, Mathlib d1d1e4b72c6e009edd97cabe1d661b021fe8eeae, REPL v4.9.0-rc1 @ 7df77c0a. Verifier hash f1dd9e78..., pins hash 00c37786....
4.3 Attestation
proofforge/e2e/attest_shim.py (commit 72e9dfa) re-renders each row's round-0 prompt in align/.venv-rollout (transformers 5.19.0). It then asserts prompt_ids == tokenizer.encode(rendered_prompt) and drops rows that cannot be joined. Output: prompt_render_sha256 = 83d0bbb9..., file sha256 1951f443... (identical to the HF LFS object).
4.4 Downstream training that consumed this data (e2e smoke, 2026-10-26)
These runs exist to show that the data plumbing works end to end. They are not attempts to improve the model. All of them used LoRA r = 64, α = 128, dropout 0, targets q/k/v/o/gate/up/down, on a frozen bf16 base, with 4x L4 FSDP (dp_shard 4), one sequence per GPU per micro-step, and AdamW (β = 0.9, 0.999, wd 0). The schedule was 3% linear warmup then cosine to 0, with grad clip 1.0.
SFT mix. Of the 4,007 valid rows, 27 were dropped because the proof rewrote the theorem statement (drop_statement_not_faithful). From the remaining 3,980, 320 rows (234 statements) were drawn as a seeded subset (seed 20261025). Objective: token-level cross-entropy on completion tokens only, with prompt tokens masked by labels_from_prompt_len. The sum is normalized by the global count of supervised tokens $N$ in the step's window across all ranks:
DPO mix. 347 eligible (valid, rejected) pairs of the same statement, 96 selected (83 statements), and 69 left after dropping 27 whose prompt plus the longer completion exceeded 8,192 tokens. Pairs are dropped, never truncated. The reference log-probs were precomputed once (ref_logps.json) from the SFT adapter, which also initializes the policy. Loss per pair, with β = 0.1:
| hyperparameter | SFT | DPO |
|---|---|---|
| rows / pairs | 320 rows | 69 pairs |
| steps | 80 (1 epoch, 4 rows per step) | 20 (80 pair-slots, about 1.16 epochs) |
| peak LR | 2e-5 | 2e-5 |
| warmup / schedule | 3% / cosine to 0 | 3% / cosine to 0 |
| β | n/a | 0.1 |
| max length | seq_target 18,432 |
8,192 (prompt + max(chosen, rejected)) |
| micro-batch × world × accum | 1 × 4 × 1 | 1 × 4 × 1 |
| grad clip | 1.0 | 1.0 |
| precision / attention | bf16 / SDPA (flash-attn not installed) | bf16 / SDPA |
| supervised units | 656,910 tokens | 80 pairs |
| wall time | 1,243.4 s | 881.8 s |
| code commit | 50453074 |
186238f8 |
| trainable tensors moved | 504/504, base unchanged | 504/504, base unchanged |
The RLVR stage of the same smoke run (CISPO, 2 iterations × 8 prompts × group size 4) drew its 16 prompts from the e2e pool, not from these generations. It is documented on the checkpoints card.
5. Training curves (downstream, from real logs)
Figure 6. e2e SFT on 320 valid proofs from this dataset. loss_local is rank 0's contribution to the global token-normalized loss, so it is roughly 1/4 of the mean CE. It moves between 0.011 and 0.146 with no trend (step 1: 0.0305, step 80: 0.0333), which fits training on the model's own samples. Pre-clip grad norm stays between 0.041 and 0.092, below the 1.0 clip. Source: ProofForge/runs/pf-e2e-sft-20261026/metrics.jsonl.
Figure 7. e2e DPO on 69 pairs. loss_local is rank 0's per-pair loss divided by the 4 pairs in the window. At step 1 it equals ln 2 / 4 = 0.1733 (logged 0.17329), confirming that the policy equals the reference at initialization. Step 20: 0.139. Pre-clip grad norm is 7.0 to 14.6, so every step was clipped to 1.0. Source: ProofForge/runs/pf-e2e-dpo-20261026/metrics.jsonl.
Reward, KL and accuracy curves: not measured for these SFT and DPO runs. The loop logs loss, LR, grad norm and elapsed time only.
6. Evaluation
| measurement | n | value | source |
|---|---|---|---|
| prompt attestation mismatches | 7,803 | 0 | attestation manifest |
| protected-set hard hits (16 sets) | 7,803 | 0 | blocklist_scan.json |
| statements with ≥ 1 valid proof | 980 | 571 (58.3%) | verdicts |
| base-model pass@1 on this pool | 980 statements | 51.2% [48.3, 54.1] | verdicts, unbiased estimator |
| base-model pass@4 on this pool | 977 statements | 57.0% [54.0, 60.1] | verdicts |
| base-model pass@8 on this pool | 969 statements | 58.6% [55.5, 61.7] | verdicts |
| sample-level valid rate | 7,803 | 51.4% | verdicts |
| SFT / DPO checkpoint benchmark scores | not measured in the e2e smoke run (the evidence gate checks plumbing, not accuracy) | p4_e2e_2026-10-26/evidence.log |
Baseline, for context only (different set, not this data). The same base model and sampling settings at a 16k cap reached miniF2F-test pass@8 = 78.7% (192/244) and pass@1 = 62.1% [57.0, 67.3] (P2 baseline, 2026-10-13). On this pool pass@8 is lower (58.6%) than on miniF2F-test (78.7%) under the same sampling and 180 s verifier, though the two use different problem sets and subsets (969 vs 244 statements). Source: p2_runs/r1_baseline/ver_minif2f_c16384.jsonl (rlhf workspace).
Hill climbing: not applicable. This is a single round-0 sampling pass, with no iterations to plot.
7. Discussion, negative results and lessons
- Correction to the earlier card. The previous README said the 263 masked rows were "timeouts and truncations". The verdict file says otherwise: masked = 223 timeouts + 29 out-of-memory + 11 REPL crashes. The 443 cap-truncated completions are labelled
rejected(no_code), so a pairing step that takes rejected rows as negatives can use them. The e2e protocol runs withmask_truncated_completions: false. If you do not want truncation to count as failure, filter onfinish_reason == "length". - The 180 s budget hides some solvable rows. Goedel-Prover-V2's own compile harness uses 300 s. Some of the 223 timeouts may be valid proofs, so pass@k here is a lower bound under the stricter budget.
- Statement fidelity. 27 valid proofs changed the theorem statement and were excluded from training mixes (
drop_statement_not_faithful). The verdict file still marks themvalid. Re-check the statement before you use valid rows as positives. - Formal vs informal mismatch in Goedel-Pset. Some formal statements are much weaker than the informal problem they come from. In the example in section 3.3, the informal problem asks for $11C$, while the formal theorem only checks
11 * (7 + 9 + 12) = 308. Avalidverdict certifies the formal statement only. - Truncated generation run. The session crashed with 160 requests in flight, leaving 980 of 2,000 statements covered. Statement coverage is therefore set by generation order, not by random sampling.
- Downstream merge parity failed. The SFT adapter trained on this data failed the bf16 merged-vs-unmerged parity check: max |Δlogit| 9.37 against a limit of 0.05, greedy agreement 99.457% against 99.5%. Use the adapters unmerged. This concerns the checkpoints, not the data.
8. Intended use, limitations and risks
Intended: SFT on verified proofs, preference pairs (valid vs rejected for the same statement), RL difficulty filtering (figure 2), verifier and extraction research, and reproducing the ProofForge e2e smoke run.
Out of scope: evaluating any prover (these are training-pool statements), and claiming correctness under other Lean or Mathlib versions.
Limitations.
- One model, one round, one temperature. It says nothing about other provers.
- Labels are tied to Lean v4.9.0-rc1 and Mathlib
d1d1e4b7. A proof valid here may fail on newer Mathlib. - The blocklist catches copies and light rewrites, not heavy paraphrases of benchmark problems.
- Completions contain model-written natural-language reasoning, which can be wrong even when the Lean proof is valid.
Risks. Low. The data contains no personal data and is mathematical content only. Training on unfiltered rejected rows as positives would teach wrong proofs, so always join on key and filter on verdict.
9. Reproducibility
# load
python -c "from datasets import load_dataset as L; \
g=L('viai957/proofforge-goedel8b-e2e-attested-generations','generations',split='train'); \
v=L('viai957/proofforge-goedel8b-e2e-attested-generations','verdicts',split='train'); print(len(g),len(v))"
# regenerate (align repo; 4 GPUs). Recorded argv of session 1791951209-4193267, wrapped in hostguard.
# The run passed --model as the local HF snapshot dir of Goedel-LM/Goedel-Prover-V2-8B rev dfd02e62...;
# equivalently use --model Goedel-LM/Goedel-Prover-V2-8B --model-rev dfd02e6271a58375dfbf3ece0175277cf6b6a89a
python scripts/hostguard.py run --cores 16 --mem-gb 60 --label p2-lean-gen -- \
python extras/vllm_rollout/lean_gen.py \
--model <HF_HOME>/hub/models--Goedel-LM--Goedel-Prover-V2-8B/snapshots/dfd02e6271a58375dfbf3ece0175277cf6b6a89a \
--problems .tmp/p2/r1/problems/train_pool.jsonl --out .tmp/p2/r1/pool/gen_r0.jsonl \
--n 8 --cap-tokens 16384 --round 0 --tp 4 --seed 0 --max-num-seqs 128 --gpu-mem-util 0.82
# e2e proofs/sft/pairs/dpo stages (ProofForge)
python scripts/pf_e2e.py plan # renders stage configs from configs/e2e/e2e_smoke.yaml + probed HwCaps
| artifact | identity |
|---|---|
data/gens.attested.jsonl |
sha256 1951f443fe7a606c627de4b3b9d3cb4f0588bf59ef8699a0f2463a772459efa4 |
data/verdicts.pf_strict.jsonl |
sha256 d86ce61d72785898942645c5973275af2928a6c4f86d865ccd30bbcdeec9e18f |
upstream gen_r0.jsonl / ver_r0.jsonl |
sha256 2b4b5f3d... / 5eeb800c... (in viai957/lean-prover-data @ 4058f681, r1/pool/) |
| source pool | train_pool.jsonl sha256 9e8a9fbc...; e2e pool identity 88e380b1... |
| attestation code | ProofForge 72e9dfa (proofforge/e2e/attest_shim.py) |
| SFT mix / DPO mix config | 055990de... / 9e845630... (configs/e2e/e2e_smoke.yaml) |
| e2e SFT / DPO / pairs commits | 50453074 / 186238f8 / c5e6c61c |
| HF archive upload | commit c97a34bd5e43, tool tools/pf_hf_archive.py, scan tools/pf_hf_archive_scan.py |
The figures were produced from the files above by _tools/stats.py and _tools/plots.py. Every number in this card is mapped to its source in evidence.json.
10. Related repos, licence, citation
- viai957/proofforge-goedel8b-e2e-smoke-checkpoints: SFT, DPO and RLVR training state from the e2e run that consumed this data.
- viai957/proofforge-goedel8b-sft-lora-e2e-smoke: final e2e SFT adapter.
- viai957/lean-prover-data: source pool and the raw
gen_r0/ver_r0files. - viai957/Goedel-Prover-V2-8B-EI-campaign1-r1 (also r2, r3): later expert-iteration models on the same base.
- ProofForge experiment archive collection.
Licence. Apache-2.0 for the generations, which are outputs of the Apache-2.0 Goedel-Prover-V2-8B. The statements come from Goedel-Pset-v1 (no licence declared on its HF card; the Goedel-Prover code repository is MIT), whose informal problems come from NuminaMath (Apache-2.0). Please credit both.
@misc{proofforge_e2e_attested_generations_2026,
title = {ProofForge e2e attested generations: verifier-labelled Goedel-Prover-V2-8B samples on Goedel-Pset-v1},
author = {viai957},
year = {2026},
howpublished = {\url{https://huggingface.co/datasets/viai957/proofforge-goedel8b-e2e-attested-generations}}
}
@article{lin2025goedelproverv2,
title = {Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction},
author = {Lin, Yong and others},
journal = {arXiv preprint arXiv:2508.03613},
year = {2025}
}
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