EPFL-LARA/lean-standard-prover-qwen3-8b-reasoning-grpo
Text Generation • 8B • Updated • 564
Dataset Preview
The full dataset viewer is not available (click to read why). Only showing a preview of the rows.
Job manager crashed while running this job (missing heartbeats).
Error code: JobManagerCrashedError
Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
uuid string | data_source string | source_question string | source_answer string | source_answer_feedback string | question string | answer string | proof_plan string | valid bool | target_kind string | proof_repair bool | lean_code string | token_count float64 | tactic_count float64 | lean_score float64 | lean_rank float64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Goedel-Pset-678601 | Goedel-LM/Goedel-Pset-v1 | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- Theorem stating that among the elements in N₂O (dinitrogen monoxide),
nitrogen has a mass percentage closest to 63.64% -/
theorem nit... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem nitrogen_mass_percentage_in_n2o
(n_mass : ℝ := by
norm_num
<;> simp [Nat.cast_add, Nat.cast_mul, Nat.cast_ofNat]
<;> norm_num
<;> linarith
) :
T... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem nitrogen_mass_percentage_in_n2o
(n_mass : ℝ := by
norm_num
<;> simp [Nat.cast_add, Nat.cast_mul, Nat.cast_ofNat]
... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- Theorem stating that among the elements in N₂O (dinitrogen monoxide),
nitrogen has a mass percentage closest to 63.64% -/
theorem nit... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem nitrogen_mass_percentage_in_n2o
(n_mass : ℝ := by
norm_num
<;> simp [Nat.cast_add, Nat.cast_mul, Nat.cast_ofNat]
... | null | true | full_annotated_proof | false | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem nitrogen_mass_percentage_in_n2o
(n_mass : ℝ := by
norm_num
<;> simp [Nat.cast_add, Nat.cast_mul, Nat.cast_ofNat]
<;> norm_num
<;> linarith
) :
True := by
/-
The theorem states that among the e... | 336 | 59 | -7.064017 | 1 |
Goedel-Pset-224873 | Goedel-LM/Goedel-Pset-v1 | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- Given a regular hexagon with area 360, when randomly selecting three vertices,
the expected area of the intersection of the triangle... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem hexagon_intersection_area :
let hexagonArea : ℝ := 360
let triangleArea : ℝ := 12
let intersectionArea : ℝ := 12
-- The expected area of the intersectio... | null | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- Given a regular hexagon with area 360, when randomly selecting three vertices,
the expected area of the intersection of the triangle... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem hexagon_intersection_area :
let hexagonArea : ℝ := 360
let triangleArea : ℝ := 12
let intersectionArea : ℝ := 12
... | null | true | full_annotated_proof | false | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem hexagon_intersection_area :
let hexagonArea : ℝ := 360
let triangleArea : ℝ := 12
let intersectionArea : ℝ := 12
-- The expected area of the intersection is 12
True := by
let hexagonArea : ℝ := 360
... | 74 | 0 | -0.863498 | 1 |
Goedel-LM/SFT_dataset_v2=1567147 | Goedel-LM/SFT_dataset_v2 | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- Find all functions \( f: \mathbb{R} \rightarrow \mathbb{R} \) that satisfy the functional equations \( f(x) + f(y) = f(x + y) \) and \( P(... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem OMR_problem_52850 (f : ℝ → ℝ)
(h1 : ∀ x y : ℝ, f x + f y = f (x + y))
(h2 : ∀ P Q : Polynomial ℝ, P ≠ 0 → Q ≠ 0 → P.natDegree > 0 → Q.natDegree > 0 →
∀ ... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem OMR_problem_52850 (f : ℝ → ℝ)
(h1 : ∀ x y : ℝ, f x + f y = f (x + y))
(h2 : ∀ P Q : Polynomial ℝ, P ≠ 0 → Q ≠ 0 → P.natDegree > 0 → Q.natDegree > 0 →
∀ ... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- Find all functions \( f: \mathbb{R} \rightarrow \mathbb{R} \) that satisfy the functional equations \( f(x) + f(y) = f(x + y) \) and \( P(... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem OMR_problem_52850 (f : ℝ → ℝ)
(h1 : ∀ x y : ℝ, f x + f y = f (x + y))
(h2 : ∀ P Q : Polynomial ℝ, P ≠ 0 → Q ≠ 0 → P.nat... | ### Abstract Plan
1. **Step 1: Prove `f(0) = 0`**:
- Set `x = y = 0` in `h1` to get `2 f(0) = f(0)` ⇒ `f(0) = 0`.
2. **Step 2: Prove `f(x²) = x f(x)`**:
- Take `P = X`, `Q = X` in `h2` to get `x f(x) = f(x²)`.
3. **Step 3: Prove `x f(c) = f(x c)` for all rational `c`**:
- Take `P = X`, `Q = X + c` (`c ≠ 0`)... | true | full_annotated_proof | false | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem OMR_problem_52850 (f : ℝ → ℝ)
(h1 : ∀ x y : ℝ, f x + f y = f (x + y))
(h2 : ∀ P Q : Polynomial ℝ, P ≠ 0 → Q ≠ 0 → P.natDegree > 0 → Q.natDegree > 0 →
∀ x : ℝ, P.eval x * f (Q.eval x) = f (P.eval x * Q.eva... | 1,229 | 128 | -14.222954 | 1 |
Goedel-LM/SFT_dataset_v2=109863 | Goedel-LM/SFT_dataset_v2 | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem extracted_97f28b30_negation : ¬ ( ∀ (x y : ℝ) (hx : (0 : ℝ) < x) (hy : (0 : ℝ) < y) (h : x ^ (2 : ℕ) + y ^ (2 : ℕ) ≤ (1 : ℝ)) (h₃ : (0 :... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem extracted_97f28b30_negation : ¬ ( ∀ (x y : ℝ) (hx : (0 : ℝ) < x) (hy : (0 : ℝ) < y) (h : x ^ (2 : ℕ) + y ^ (2 : ℕ) ≤ (1 : ℝ)) (h₃ : (0 : ℝ) < x) (h₄ : (0 : ℝ) < y) ... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem extracted_97f28b30_negation : ¬ ( ∀ (x y : ℝ) (hx : (0 : ℝ) < x) (hy : (0 : ℝ) < y) (h : x ^ (2 : ℕ) + y ^ (2 : ℕ) ≤ (1 : ℝ)) (h₃ : (0 : ℝ) < x) (h₄ : (0 : ℝ) < y) ... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem extracted_97f28b30_negation : ¬ ( ∀ (x y : ℝ) (hx : (0 : ℝ) < x) (hy : (0 : ℝ) < y) (h : x ^ (2 : ℕ) + y ^ (2 : ℕ) ≤ (1 : ℝ)) (h₃ : (0 :... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem extracted_97f28b30_negation : ¬ ( ∀ (x y : ℝ) (hx : (0 : ℝ) < x) (hy : (0 : ℝ) < y) (h : x ^ (2 : ℕ) + y ^ (2 : ℕ) ≤ (1 : ℝ)... | #### Step 1: Abstract Plan
1. **Find a specific counterexample**: Choose `x = y = √2 / 2`.
- Check that all conditions are satisfied for this choice.
- Compute `2 * x = √2`, so `2 * x > √2` is false (as `√2 > √2` is false).
2. **Prove that the counterexample works**:
- `x = y = √2 / 2 > 0`.
- `x² + y² = 1... | true | full_annotated_proof | false | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem extracted_97f28b30_negation : ¬ ( ∀ (x y : ℝ) (hx : (0 : ℝ) < x) (hy : (0 : ℝ) < y) (h : x ^ (2 : ℕ) + y ^ (2 : ℕ) ≤ (1 : ℝ)) (h₃ : (0 : ℝ) < x) (h₄ : (0 : ℝ) < y) (h₅ : x ^ (2 : ℕ) + y ^ (2 : ℕ) ≤ (1 : ℝ)) (h₇ : x ≤... | 497 | 18 | -3.04212 | 1 |
Goedel-Pset-761934_repair_1_757817 | Goedel-LM/Goedel-Pset-v1 | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- If someone starts with 36 cookies, eats 10, and ends with 12,
then they must have given away 14 cookies -/
theorem cookies_given_awa... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem cookies_given_away
(initial : ℕ := by
/-
Given that someone starts with 36 cookies, eats 10, and ends with 12, we need to determine how many cookies t... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem cookies_given_away
(initial : ℕ := by
/- <feedback>
-- type: error, msg: elaboration function for 'by' has ... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- If someone starts with 36 cookies, eats 10, and ends with 12,
then they must have given away 14 cookies -/
theorem cookies_given_awa... | /- <feedback>
-- type: error, msg: elaboration function for 'by' has not been implemented
failed to pretty print term (use 'set_option pp.rawOnError true' for raw representation)
-- type: error, msg: declaration body is missing
</feedback> -/
```
Here is the corrected Lean 4 proof annotated with ... | null | true | proof_repair | true | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem cookies_given_away
(initial : ℕ := by
/-
Given that someone starts with 36 cookies, eats 10, and ends with 12, we need to show that they must have given away 14 cookies. This can be verified by checking ... | 175 | 7 | -1.734097 | 1 |
Goedel-LM/SFT_dataset_v2=348513 | Goedel-LM/SFT_dataset_v2 | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_59277_17 (a b c k : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hk : 0 ≤ k) : (a^2 + k * b * c) * (b^2 + k * c * a) ... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_59277_17 (a b c k : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hk : 0 ≤ k) : (a^2 + k * b * c) * (b^2 + k * c * a) * (c^2 + k * a * b) ≥ a * b *... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_59277_17 (a b c k : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hk : 0 ≤ k) : (a^2 + k * b * c) * (b^2 + k * c * a) * (c^2 + k * a * b) ≥ a * b *... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_59277_17 (a b c k : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hk : 0 ≤ k) : (a^2 + k * b * c) * (b^2 + k * c * a) ... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_59277_17 (a b c k : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hk : 0 ≤ k) : (a^2 + k * b * c) * (b^2 + ... | ### Abstract Plan
1. **Re-examining the Problem**:
- The original inequality involves a product of terms on the left and a product of terms on the right. We need to ensure that all the terms are non-negative and that the products are also non-negative.
- Given that `a, b, c, k ≥ 0`, we can use the fact that `a *... | true | full_annotated_proof | false | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_59277_17 (a b c k : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hk : 0 ≤ k) : (a^2 + k * b * c) * (b^2 + k * c * a) * (c^2 + k * a * b) ≥ a * b * c * (a + k * b) * (b + k * c) * (c + k * a) * (Real... | 765 | 27 | -4.028236 | 1 |
april-feedback-0d6675c8ddc6b16f5add6308b3d45472-repair-dcbf916f2e32dc44847025c8d2520a9d | uw-math-ai/APRIL | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "Here is the complete Lean 4 proof:\n\n```lean4\nimport Mathlib\nopen Finset Set Nat List\nnoncomput(...TRUNCATED) | "Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:\n\n```lean4\nimpo(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | " /- <feedback>\n -- type: error, msg: no goals to be solved\n </feedback(...TRUNCATED) | null | true | proof_repair | true | "import Mathlib\nopen Finset Set Nat List\nnoncomputable section\n\n-- Define property: a set has in(...TRUNCATED) | 879 | 72 | -8.555984 | 1 |
Goedel-Pset-317581 | Goedel-LM/Goedel-Pset-v1 | "Solve the following problem with Lean 4 code and explanatory comments:\n\n\nLean 4 code that states(...TRUNCATED) | "The complete typechecked Lean 4 proof is:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option m(...TRUNCATED) | "Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:\n\n```lean4\nimpo(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | " /- <feedback>\n -- type: error, msg: linarith failed to find a contradiction\n case fst\n ⊢ (...TRUNCATED) | null | true | proof_repair | true | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | 134 | 0 | -0.981055 | 1 |
Goedel-Pset-90989_repair_2_164181 | Goedel-LM/Goedel-Pset-v1 | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | " The complete typechecked Lean 4 proof is:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option (...TRUNCATED) | "Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:\n\n```lean4\nimpo(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | " /- <feedback>\n -- type: error, msg: failed to synthesize\n Decidable ({x | (1 ≤ x ∧ x (...TRUNCATED) | null | true | proof_repair | true | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | 1,162 | 123 | -13.711752 | 2 |
Goedel-Pset-1573448 | formalmathatepfl/solved_problems_finetuning_iter1 | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "The complete typechecked Lean 4 proof is:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option m(...TRUNCATED) | "The complete typechecked Lean 4 proof is:\n\n```lean4\nimport Mathlib\nimport Aesop\n\nset_option m(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:\n\n```lean4\nimpo(...TRUNCATED) | null | true | full_annotated_proof | false | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | 84 | 8 | -1.68853 | 1 |
End of preview.
Supervised fine-tuning corpus
The feedback-annotated SFT collection for Formal Theorem Proving with Lean World Models, containing direct proofs and proof-repair histories.
| Split | Rows | Contents |
|---|---|---|
train |
2,763,895 | Supervised prompt/answer pairs |
test |
623,741 | Unsolved-problem source catalog |
Load
from datasets import load_dataset
examples = load_dataset("EPFL-LARA/lean-world-model-sft", split="train", streaming=True)
row = next(iter(examples))
prompt, target = row["question"], row["answer"]
question contains the theorem prompt and any previous failed attempts.
answer contains the annotated proof or repair target. proof_repair and
target_kind identify the example type; lean_code stores the proof code.
The source_* columns retain source material and provenance.
Use the prompt as context and supervise the answer. The test split is a
problem catalog. This release contains only train and test.
Paper collection · CPT corpus · Reasoning SFT
The GRPO problem source is Goedel-Prover-V2 RL; prepared prompts and model-specific filtering are available in the existing RL dataset.
- Downloads last month
- -