dataset_index stringlengths 11 55 | formal_statement stringlengths 203 1.04k | informal_statement stringlengths 46 762 | dataset_source stringclasses 1
value | premise_list listlengths 128 128 | checkpoint stringclasses 1
value | checkpoint_name stringclasses 1
value |
|---|---|---|---|---|---|---|
mathd_algebra_478 | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
/-- The volume of a cone is given by the formula $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. The area of the base of a cone is 30 square units, and its height is 6.5 units. What is the number of cubic units in its volume? Show that it is 65.-/
theorem mathd_algebra_478 (b h v : ℝ) (h₀ : 0 < b ∧ 0 < h ∧ 0 < v) (h₁ : v = 1 / 3 * (b * h))
(h₂ : b = 30) (h₃ : h = 13 / 2) : v = 65 := by
| /-- The volume of a cone is given by the formula $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. The area of the base of a cone is 30 square units, and its height is 6.5 units. What is the number of cubic units in its volume? Show that it is 65.-/
| AI-MO/minif2f_test | [
{
"rank": 1,
"score": 0.5112922787666321,
"node_id": 246678,
"name": "Mathlib.Meta.NormNum.isNat_eq_false",
"guess_type": "theorem",
"kind": "theorem",
"module": "Mathlib.Tactic.NormNum.Eq",
"source_path": "/mathlib4-4.22.0/Mathlib/Tactic/NormNum/Eq.lean",
"line": 18,
"column... | /Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-modernbert-ft/checkpoint_epoch_80.pt | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
numbertheory_4x3m7y3neq2003 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | /-- Show that there are no integers $x$ and $y$ such that $4x^3 - 7y^3 = 2003$.-/
| AI-MO/minif2f_test | [{"rank":1,"score":0.6394791603088379,"node_id":246506,"name":"Mathlib.Meta.NormNum.isNat_intCast","(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
aime_1983_p1 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- Let $x$, $y$ and $z$ all exceed $1$ and let $w$ be a positive number such that $\\log_x w = 24$(...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.5456372499465942,"node_id":139864,"name":"GCongr.natCast_le_natCast","guess_typ(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
amc12_2001_p5 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- What is the product of all positive odd integers less than $10000$?\n\n$\\text{(A)}\\ \\dfrac{1(...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.58953458070755,"node_id":195595,"name":"Nat.mem_divisors","guess_type":"theorem(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
mathd_algebra_141 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- A rectangular patio has an area of $180$ square feet and a perimeter of $54$ feet. What is the (...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.6301696300506592,"node_id":12924,"name":"sq","guess_type":"theorem_derived","ki(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
mathd_numbertheory_3 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- What is the units digit of the sum of the squares of the first nine positive integers? Show tha(...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.62775719165802,"node_id":195653,"name":"Nat.mem_divisors_self","guess_type":"th(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
imo_1969_p2 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- Let $a_1, a_2,\\cdots, a_n$ be real constants, $x$ a real variable, and $f(x)=\\cos(a_1+x)+\\fr(...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.6350749731063843,"node_id":246678,"name":"Mathlib.Meta.NormNum.isNat_eq_false",(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
mathd_algebra_209 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- Suppose that $h(x)=f^{-1}(x)$. If $h(2)=10$, $h(10)=1$ and $h(1)=2$, what is $f(f(10))$? Show t(...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.6072186827659607,"node_id":239714,"name":"Nat.card_congr","guess_type":"theorem(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
mathd_numbertheory_1124 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- The four-digit number $\\underline{374n}$ is divisible by 18. Find the units digit $n$. Show th(...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.619723916053772,"node_id":246490,"name":"Mathlib.Meta.NormNum.isNat_dvd_true","(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
imo_1983_p6 | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | "/-- Let $a$, $b$ and $c$ be the lengths of the sides of a triangle. Prove that\n\n$a^2 b(a-b) + b^2(...TRUNCATED) | AI-MO/minif2f_test | [{"rank":1,"score":0.6434430480003357,"node_id":199481,"name":"euler_four_squares","guess_type":"the(...TRUNCATED) | "/Volumes/Workspace1/rlgt_v21_chekcpoints/20260108_233520_mode0_k64_pp_none_src_ckpt_alibaba-gte-mod(...TRUNCATED) | 20260104_210141_epoch38_alibaba-gte-modernbert-ft |
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