EPFL-LARA/lean-standard-prover-qwen3-8b-reasoning-grpo
Text Generation • 8B • Updated • 634
uuid stringlengths 14 90 | data_source stringclasses 5
values | question stringlengths 573 5.09M | answer stringlengths 1.2k 34k | question_feedback stringlengths 821 5.09M | answer_feedback stringlengths 1.32k 2.89M | source_question stringlengths 215 5.08M | source_answer stringlengths 128 25.7k | source_question_feedback stringlengths 339 5.08M | source_answer_feedback stringlengths 229 2.89M | proof_plan listlengths 1 6 | valid bool 1
class | proof_repair bool 2
classes | lean_code stringlengths 58 25.6k | token_count float64 9 3.89k ⌀ | tactic_count float64 0 567 ⌀ | lean_score float64 -58.32 -0.48 ⌀ | lean_rank float64 1 1 ⌀ |
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34015da3-ac2b-5a26-a366-f128b194ac96 | AI-MO/NuminaMath-LEAN | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- 359*. Solve the system of equations:
$$
\left\{\begin{array}{l}
x^{2}-y z=3 \\
y^{2}-x z=4 \\
z^{2}-x y=5
\end{array}\right.
$$ -/
theorem algebra_188165 {x y z : ℝ} (h1 : x^2 - y * z = 3) (h2 : y^2 - x * z = 4) (h3 : z... | [Problem Restatement]
We are given real numbers \(x,y,z\) satisfying
\[
x^2-yz=3,\qquad y^2-xz=4,\qquad z^2-xy=5.
\]
We must show that the only possible triples are
\[
(x,y,z)=\left(\frac{11}{6},-\frac16,-\frac{13}{6}\right)
\]
or
\[
(x,y,z)=\left(-\frac{11}{6},\frac16,\frac{13}{6}\right).
\]
[Useful Observation... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- 359*. Solve the system of equations:
$$
\left\{\begin{array}{l}
x^{2}-y z=3 \\
y^{2}-x z=4 \\
z^{2}-x y=5
\end{array}\right.
$$ -/
theorem algebra_188165 {x y z : ℝ} (h1 : x^2 - y * z = 3) (h2 : y^2 - x * z = 4) (h3 : z... | [Problem Restatement]
We are given real numbers \(x,y,z\) satisfying
\[
x^2-yz=3,\qquad y^2-xz=4,\qquad z^2-xy=5.
\]
We must show that the only possible triples are
\[
(x,y,z)=\left(\frac{11}{6},-\frac16,-\frac{13}{6}\right)
\]
or
\[
(x,y,z)=\left(-\frac{11}{6},\frac16,\frac{13}{6}\right).
\]
[Useful Observation... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- 359*. Solve the system of equations:
$$
\left\{\begin{array}{l}
x^{2}-y z=3 \\
y^{2}-x z=4 \\
z^{2}-x y=5
\end{array}\right.
$$ -/
theorem algebra_188165 {x y z : ℝ} (h1 : x^2 - y * z = 3) (h2 : y^2 - x * z = 4) (h3 : z... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
theorem algebra_188165 {x y z : ℝ} (h1 : x^2 - y * z = 3) (h2 : y^2 - x * z = 4) (h3 : z^2 - x * y = 5) :
(x, y, z) = (11 / 6, -1 / 6, -13 / 6) ∨ (x, y, z) = (-11 / 6, 1 / 6, 13 / 6) := by
have eq1 : (y - x) * (x + y + z) = 1 := by
nlinarith... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- 359*. Solve the system of equations:
$$
\left\{\begin{array}{l}
x^{2}-y z=3 \\
y^{2}-x z=4 \\
z^{2}-x y=5
\end{array}\right.
$$ -/
theorem algebra_188165 {x y z : ℝ} (h1 : x^2 - y * z = 3) (h2 : y^2 - x * z = 4) (h3 : z... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
theorem algebra_188165 {x y z : ℝ} (h1 : x^2 - y * z = 3) (h2 : y^2 - x * z = 4) (h3 : z^2 - x * y = 5) :
(x, y, z) = (11 / 6, -1 / 6, -13 / 6) ∨ (x, y, z) = (-11 / 6, 1 / 6, 13 / 6) := by
/- <feedback>
... | [
"[Problem Restatement]\n\nWe are given real numbers \\(x,y,z\\) satisfying\n\n\\[\nx^2-yz=3,\\qquad y^2-xz=4,\\qquad z^2-xy=5.\n\\]\n\nWe must show that the only possible triples are\n\n\\[\n(x,y,z)=\\left(\\frac{11}{6},-\\frac16,-\\frac{13}{6}\\right)\n\\]\n\nor\n\n\\[\n(x,y,z)=\\left(-\\frac{11}{6},\\frac16,\\fra... | true | false | import Mathlib
theorem algebra_188165 {x y z : ℝ} (h1 : x^2 - y * z = 3) (h2 : y^2 - x * z = 4) (h3 : z^2 - x * y = 5) :
(x, y, z) = (11 / 6, -1 / 6, -13 / 6) ∨ (x, y, z) = (-11 / 6, 1 / 6, 13 / 6) := by
have eq1 : (y - x) * (x + y + z) = 1 := by
nlinarith
have eq2 : (z - y) * (x + y + z) = 1 := by
n... | 393 | 41 | -5.29527 | 1 |
66a82444-f91d-5440-8fe8-577e8b001f96 | AI-MO/NuminaMath-LEAN | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- Maria and Joe are jogging towards each other on a long straight path. Joe is running at $10$ mph and Maria at $8$ mph. When they are $3$ miles apart, a fly begins to fly back and forth between them at a constant rate of ... | [Problem Restatement]
Let \(t\) be a positive real number. Suppose
\[
10t+8t=3.
\]
Prove that
\[
15t=\frac52.
\]
[Useful Observations]
- The equation \(10t+8t=3\) immediately combines like terms to give \(18t=3\).
- Since \(18\neq 0\), we can divide by \(18\) and solve for \(t\).
- This gives \(t=\frac{3}{18}=\frac1... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- Maria and Joe are jogging towards each other on a long straight path. Joe is running at $10$ mph and Maria at $8$ mph. When they are $3$ miles apart, a fly begins to fly back and forth between them at a constant rate of ... | [Problem Restatement]
Let \(t\) be a positive real number. Suppose
\[
10t+8t=3.
\]
Prove that
\[
15t=\frac52.
\]
[Useful Observations]
- The equation \(10t+8t=3\) immediately combines like terms to give \(18t=3\).
- Since \(18\neq 0\), we can divide by \(18\) and solve for \(t\).
- This gives \(t=\frac{3}{18}=\frac1... | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- Maria and Joe are jogging towards each other on a long straight path. Joe is running at $10$ mph and Maria at $8$ mph. When they are $3$ miles apart, a fly begins to fly back and forth between them at a constant rate of ... | The complete typechecked Lean 4 proof is:
```lean4
import Mathlib
theorem calculus_59863 (t : ℝ) (ht : t > 0) (h : 10 * t + 8 * t = 3) :
15 * t = 5 / 2 := by
have eq1 : t = 1 / 6 := by
linarith
rw [eq1]
norm_num
```
<|endoftext|> | Solve the following problem with Lean 4 code and explanatory comments:
```lean4
import Mathlib
/- Maria and Joe are jogging towards each other on a long straight path. Joe is running at $10$ mph and Maria at $8$ mph. When they are $3$ miles apart, a fly begins to fly back and forth between them at a constant rate of ... | Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:
```lean4
import Mathlib
theorem calculus_59863 (t : ℝ) (ht : t > 0) (h : 10 * t + 8 * t = 3) :
15 * t = 5 / 2 := by
/- <feedback>
-- proof state:
t : ℝ
ht : t > 0
h : 10 * t + 8 * t = 3
⊢ 15 * t = 5 / 2
</feedback> -/
... | [
"[Problem Restatement]\n\nLet \\(t\\) be a positive real number. Suppose\n\\[\n10t+8t=3.\n\\]\nProve that\n\\[\n15t=\\frac52.\n\\]\n\n[Useful Observations]\n\n- The equation \\(10t+8t=3\\) immediately combines like terms to give \\(18t=3\\).\n- Since \\(18\\neq 0\\), we can divide by \\(18\\) and solve for \\(t\\).... | true | false | import Mathlib
theorem calculus_59863 (t : ℝ) (ht : t > 0) (h : 10 * t + 8 * t = 3) :
15 * t = 5 / 2 := by
have eq1 : t = 1 / 6 := by
linarith
rw [eq1]
norm_num | 47 | 4 | -1.17424 | 1 |
Goedel-LM/SFT_dataset_v2=842676 | 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
/-If \(27^3 = 9^x\), what is the value of \(3^{-x}\)? Express your answer as a common fraction.-/
theorem lean_workbook_plus_32164 (x : ℝ)... | [Error Analysis]
The rewrite failure occurs because, after `rw [Real.sqrt_eq_rpow]`, the goal is
```lean4
19683 ^ (1 / 2) = 3 ^ (9 / 2)
```
The attempted use of `← Real.rpow_nat_cast` was aimed at converting a natural-number power into a real power, but there is no expression of the required form `a ^ n` with a natu... | 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 \(27^3 = 9^x\), what is the value of \(3^{-x}\)? Express your answer as a common fraction.-/
theorem lean_workbook_plus_32164 (x : ℝ... | /- <feedback>
-- type: error, msg: tactic 'rewrite' failed, did not find instance of the pattern in the target expression
?x ^ ?n
x : ℝ
h₀ : 27 ^ 3 = 9 ^ x
h₁ : 0 < x
h_main : x = 9 / 2
h₇ :... | 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 \(27^3 = 9^x\), what is the value of \(3^{-x}\)? Express your answer as a common fraction.-/
theorem lean_workbook_plus_32164 (x : ℝ)... | The corrected Lean 4 proof is:
```lean4
import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_32164 (x : ℝ)
(h₀ : (27:ℝ)^3 = 9^x)
(h₁ : 0 < x) :
3^(-x) = 1 / Real.sqrt 19683 := by
have h_main : x = 9 / 2 := by
have h₂ : (27:ℝ)^3 = 9^x ... | 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 \(27^3 = 9^x\), what is the value of \(3^{-x}\)? Express your answer as a common fraction.-/
theorem lean_workbook_plus_32164 (x : ℝ... | /- <feedback>
-- type: error, msg: tactic 'rewrite' failed, did not find instance of the pattern in the target expression
?x ^ ?n
x : ℝ
h₀ : 27 ^ 3 = 9 ^ x
h₁ : 0 < x
h_main : x = 9 / 2
h₇ :... | [
"[Problem Restatement]\n\nLet \\(x>0\\) satisfy\n\\[\n27^3=9^x.\n\\]\nShow that\n\\[\n3^{-x}=\\frac1{\\sqrt{19683}}.\n\\]\n\n[Useful Observations]\n\n- Both \\(27\\) and \\(9\\) are powers of \\(3\\):\n \\[\n 27=3^3,\\qquad 9=3^2.\n \\]\n Rewriting the given equation in this common base should determine \\(x\\)... | true | true | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_plus_32164 (x : ℝ)
(h₀ : (27:ℝ)^3 = 9^x)
(h₁ : 0 < x) :
3^(-x) = 1 / Real.sqrt 19683 := by
have h_main : x = 9 / 2 := by
have h₂ : (27:ℝ)^3 = 9^x := h₀
have h₃ : (9:ℝ)^x = (3:ℝ)^(2*x)... | 373 | 55 | -6.684851 | 1 |
Goedel-Pset-779677 | formalmathatepfl/solved_problems_finetuning_iter1 | 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
/-A circle having common centre with the circumcircle of triangle $ABC$ meets the sides of the triangle at six points forming convex hexago... | [Problem Restatement]
We are given positive real numbers \(a,b,c,a_1,b_1,c_1,a_2,b_2,c_2\), together with many relations among their sums and products. The goal is to establish the six product identities
\[
\begin{aligned}
a_1b_1&=ca_2,\\
b_1c_1&=ab_2,\\
c_1a_1&=bc_2,\\
a_2b_2&=ca_1,\\
b_2c_2&=ab_1,\\
c_2a_2&=bc_1.
\... | 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
/-A circle having common centre with the circumcircle of triangle $ABC$ meets the sides of the triangle at six points forming convex hexago... | [Problem Restatement]
We are given positive real numbers \(a,b,c,a_1,b_1,c_1,a_2,b_2,c_2\), together with many relations among their sums and products. The goal is to establish the six product identities
\[
\begin{aligned}
a_1b_1&=ca_2,\\
b_1c_1&=ab_2,\\
c_1a_1&=bc_2,\\
a_2b_2&=ca_1,\\
b_2c_2&=ab_1,\\
c_2a_2&=bc_1.
\... | 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
/-A circle having common centre with the circumcircle of triangle $ABC$ meets the sides of the triangle at six points forming convex hexago... | 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_47862 (a b c : ℝ)
(h₀ : 0 < a ∧ 0 < b ∧ 0 < c)
(h₁ : a + b > c)
(h₂ : a + c > b)
(h₃ : b + c > a)
(h₄ : 0 < a₁ ∧ 0 < b₁ ∧ 0 < c₁)
(... | 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
/-A circle having common centre with the circumcircle of triangle $ABC$ meets the sides of the triangle at six points forming convex hexago... | 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_47862 (a b c : ℝ)
(h₀ : 0 < a ∧ 0 < b ∧ 0 < c)
(h₁ : a + b > c)
(h₂ : a + c > b)
(h₃ : b + c > ... | [
"[Problem Restatement]\n\nWe are given positive real numbers \\(a,b,c,a_1,b_1,c_1,a_2,b_2,c_2\\), together with many relations among their sums and products. The goal is to establish the six product identities\n\n\\[\n\\begin{aligned}\na_1b_1&=ca_2,\\\\\nb_1c_1&=ab_2,\\\\\nc_1a_1&=bc_2,\\\\\na_2b_2&=ca_1,\\\\\nb_2c... | true | false | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_47862 (a b c : ℝ)
(h₀ : 0 < a ∧ 0 < b ∧ 0 < c)
(h₁ : a + b > c)
(h₂ : a + c > b)
(h₃ : b + c > a)
(h₄ : 0 < a₁ ∧ 0 < b₁ ∧ 0 < c₁)
(h₅ : a₁ + b₁ > c₁)
(h₆ : a₁ + c₁ > b₁)
(h₇ : b₁ ... | 540 | 7 | -1.958684 | 1 |
Goedel-Pset-1049080_repair_2_1260990 | Goedel-LM/Goedel-Pset-v1 | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Error Analysis]\n\nThe denominator-clearing step was valid, but the final `nlinarith` call tried t(...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(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "The corrected Lean 4 proof is:\n\n```lean4\nimport Mathlib\nimport Aesop\nset_option maxHeartbeats (...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(...TRUNCATED) | ["[Problem Restatement]\n\nLet \\(AD,BD,CD,BC,AB,AC\\) be positive real numbers, with\n\n\\[\nBD+CD=(...TRUNCATED) | true | true | "import Mathlib\nimport Aesop\nset_option maxHeartbeats 0\nopen BigOperators Real Nat Topology Rat\n(...TRUNCATED) | 423 | 18 | -3.009947 | 1 |
Goedel-LM/SFT_dataset_v2=576045 | Goedel-LM/SFT_dataset_v2 | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Error Analysis]\n\nThe attempted normalization of the functional equation was mathematically valid(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | " /- <feedback>\n -- type: error, msg: type mismatch\n h₁ x y\n has (...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "The corrected Lean 4 proof is:\n\n```lean4\nimport Mathlib\nimport Aesop\nset_option maxHeartbeats (...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | " /- <feedback>\n -- type: error, msg: type mismatch\n h₁ x y\n has (...TRUNCATED) | ["[Problem Restatement]\n\nLet \\(f:\\mathbb R\\to\\mathbb R\\) be continuous and satisfy\n\n\\[\nf((...TRUNCATED) | true | true | "import Mathlib\nimport Aesop\nset_option maxHeartbeats 0\nopen BigOperators Real Nat Topology Rat\n(...TRUNCATED) | 700 | 73 | -8.610502 | 1 |
08ca323e-4cf9-5443-8851-528502f72d1b | AI-MO/NuminaMath-LEAN | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nLet \\(f:\\mathbb R\\to\\mathbb R\\) satisfy\n\\[\nf(f(x))=6x-2005\n\\]\nf(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nLet \\(f:\\mathbb R\\to\\mathbb R\\) satisfy\n\\[\nf(f(x))=6x-2005\n\\]\nf(...TRUNCATED) | "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\n/-\nThe function $f(x)$ sati(...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) | ["[Problem Restatement]\n\nLet \\(f:\\mathbb R\\to\\mathbb R\\) satisfy\n\\[\nf(f(x))=6x-2005\n\\]\n(...TRUNCATED) | true | false | "import Mathlib\n/-\nThe function $f(x)$ satisfies\n\n\\[f(f(x)) = 6x - 2005\\]for all real numbers (...TRUNCATED) | 219 | 14 | -2.478726 | 1 |
Goedel-LM/SFT_dataset_v2=1380215 | Goedel-LM/SFT_dataset_v2 | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nWe are given a sequence of real numbers \\(a_0,a_1,a_2,\\dots\\) such that(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nWe are given a sequence of real numbers \\(a_0,a_1,a_2,\\dots\\) such that(...TRUNCATED) | "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\nset_option max(...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) | ["[Problem Restatement]\n\nWe are given a sequence of real numbers \\(a_0,a_1,a_2,\\dots\\) such tha(...TRUNCATED) | true | false | "import Mathlib\nimport Aesop\nset_option maxHeartbeats 0\nopen BigOperators Real Nat Topology Rat\n(...TRUNCATED) | 912 | 83 | -9.663347 | 1 |
ce8e9007-4dcf-5796-9a1e-5284d13495d1.lean | uw-math-ai/APRIL | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nWe must count the number of 5-tuples \\((a,b,c,d,e)\\) such that\n\n\\[\na(...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nWe must count the number of 5-tuples \\((a,b,c,d,e)\\) such that\n\n\\[\na(...TRUNCATED) | "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\n\nset_option maxRecDepth 200(...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) | ["[Problem Restatement]\n\nWe must count the number of 5-tuples \\((a,b,c,d,e)\\) such that\n\n\\[\n(...TRUNCATED) | true | false | "import Mathlib\n\nset_option maxRecDepth 2000\n\n\ntheorem combinatorics_608153 :\n (((Finset.Icc (...TRUNCATED) | 268 | 12 | -2.318942 | 1 |
f4bb4297-5a83-5d4a-b3f8-6c723c225b01.lean | uw-math-ai/APRIL | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nLet \\(p\\) and \\(q\\) be two different prime numbers and let \\(m\\) be (...TRUNCATED) | "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\(...TRUNCATED) | "[Problem Restatement]\n\nLet \\(p\\) and \\(q\\) be two different prime numbers and let \\(m\\) be (...TRUNCATED) | "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\n\nopen Finset\n\n\ntheorem n(...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) | ["[Problem Restatement]\n\nLet \\(p\\) and \\(q\\) be two different prime numbers and let \\(m\\) be(...TRUNCATED) | true | false | "import Mathlib\n\nopen Finset\n\n\ntheorem number_theory_636168 (p q m : ℕ) (ppr : p.Prime) (qpr (...TRUNCATED) | 316 | 50 | -6.15178 | 1 |
End of preview. Expand in Data Studio
Informal-reasoning SFT corpus
The additional reasoning data for WM8 + reasoning and S8 + reasoning in Formal Theorem Proving with Lean World Models. Kimi-K2.7-Code supplies an informal plan for each proof attempt, including reasoning updates for repair histories.
| Split | Rows | Contents |
|---|---|---|
train |
111,880 | Reasoning-augmented direct proofs and repair histories |
test |
66,593 | Unsolved-problem prompts |
Load
from datasets import load_dataset
examples = load_dataset("EPFL-LARA/lean-world-model-reasoning-sft", split="train", streaming=True)
row = next(iter(examples))
standard_prompt, standard_target = row["question"], row["answer"]
world_model_prompt = row["question_feedback"]
world_model_target = row["answer_feedback"]
Use question / answer for the standard prover and question_feedback /
answer_feedback for the world-model prover. proof_plan stores the ordered
reasoning segments; source_* preserves the original prompt and proof
material. Supervise the answer while retaining the prompt as context.
This release contains the paper's default train and test configuration.
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Models trained or fine-tuned on EPFL-LARA/lean-world-model-reasoning-sft
