name stringlengths 16 45 | instruction stringlengths 3.11k 1.41M | description stringlengths 140 209 | keywords listlengths 5 5 | schema_version stringclasses 1
value | config unknown | metadata unknown | files listlengths 15 15 | location stringlengths 10 39 |
|---|---|---|---|---|---|---|---|---|
openai-math/matching-affine-lift | # openai/math challenge `MatchingAffineLift` (family 126)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 126 of the release, *Exponential semidefinite complexity of perfect matchi... | Prove MatchingAffineLift (openai/math family 126: Exponential semidefinite complexity of perfect matching) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matching-affine-lift",
"version": "1.0.0",
"description": "Prove MatchingAffineLift (openai/math family 126: Exponential semidefinite complexity of perfect matching) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatchingAffineLift.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matching-affine-lift |
openai-math/matching-entropy-bounds | # openai/math challenge `MatchingEntropyBounds` (family 113)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 113 of the release, *Approximate counting and the perfect-matching entr... | Prove MatchingEntropyBounds (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matching-entropy-bounds",
"version": "1.0.0",
"description": "Prove MatchingEntropyBounds (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatchingEntropyBounds.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matching-entropy-bounds |
openai-math/matching-entropy | # openai/math challenge `MatchingEntropy` (family 113)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 113 of the release, *Approximate counting and the perfect-matching entropy co... | Prove MatchingEntropy (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matching-entropy",
"version": "1.0.0",
"description": "Prove MatchingEntropy (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"key... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatchingEntropy.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matching-entropy |
openai-math/matching-fpras | # openai/math challenge `MatchingFPRAS` (family 113)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 113 of the release, *Approximate counting and the perfect-matching entropy conj... | Prove MatchingFPRAS (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matching-fpras",
"version": "1.0.0",
"description": "Prove MatchingFPRAS (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keyword... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatchingFPRAS.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matching-fpras |
openai-math/matching-psd | # openai/math challenge `MatchingPSD` (family 126)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 126 of the release, *Exponential semidefinite complexity of perfect matching*
(Th... | Prove MatchingPSD (openai/math family 126: Exponential semidefinite complexity of perfect matching) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matching-psd",
"version": "1.0.0",
"description": "Prove MatchingPSD (openai/math family 126: Exponential semidefinite complexity of perfect matching) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatchingPSD.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matching-psd |
openai-math/matrix-fields | # openai/math challenge `MatrixFields` (family 107)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 107 of the release, *Matrix multiplication with exponent at most $9/4$*
(Theoret... | Prove MatrixFields (openai/math family 107: Matrix multiplication with exponent at most $9/4$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matrix-fields",
"version": "1.0.0",
"description": "Prove MatrixFields (openai/math family 107: Matrix multiplication with exponent at most $9/4$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatrixFields.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matrix-fields |
openai-math/matrix-removal | # openai/math challenge `MatrixRemoval` (family 190)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 190 of the release, *Polynomial removal fails for ordered binary matrices*
(Com... | Prove MatrixRemoval (openai/math family 190: Polynomial removal fails for ordered binary matrices) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matrix-removal",
"version": "1.0.0",
"description": "Prove MatrixRemoval (openai/math family 190: Polynomial removal fails for ordered binary matrices) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatrixRemoval.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matrix-removal |
openai-math/matroid-prophet | # openai/math challenge `MatroidProphet` (family 111)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 111 of the release, *One-sample matroid prophet inequalities against an almigh... | Prove MatroidProphet (openai/math family 111: One-sample matroid prophet inequalities against an almighty adversary) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matroid-prophet",
"version": "1.0.0",
"description": "Prove MatroidProphet (openai/math family 111: One-sample matroid prophet inequalities against an almighty adversary) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatroidProphet.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matroid-prophet |
openai-math/matroid-secretary | # openai/math challenge `MatroidSecretary` (family 111)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 111 of the release, *One-sample matroid prophet inequalities against an almi... | Prove MatroidSecretary (openai/math family 111: One-sample matroid prophet inequalities against an almighty adversary) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/matroid-secretary",
"version": "1.0.0",
"description": "Prove MatroidSecretary (openai/math family 111: One-sample matroid prophet inequalities against an almighty adversary) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MatroidSecretary.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/matroid-secretary |
openai-math/maximal-seshadri-constants | # openai/math challenge `MaximalSeshadriConstants` (family 039)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 039 of the release, *Nagata's conjecture and maximal Seshadri consta... | Prove MaximalSeshadriConstants (openai/math family 039: Nagata's conjecture and maximal Seshadri constants) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebraic-and-complex-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/maximal-seshadri-constants",
"version": "1.0.0",
"description": "Prove MaximalSeshadriConstants (openai/math family 039: Nagata's conjecture and maximal Seshadri constants) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MaximalSeshadriConstants.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/maximal-seshadri-constants |
openai-math/memory-precision | # openai/math challenge `MemoryPrecision` (family 140)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 140 of the release, *Memory–sample lower bounds for noiseless Gaussian regres... | Prove MemoryPrecision (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/memory-precision",
"version": "1.0.0",
"description": "Prove MemoryPrecision (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keyword... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MemoryPrecision.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/memory-precision |
openai-math/metric-entropy-duality | # openai/math challenge `MetricEntropyDuality` (family 329)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 329 of the release, *A counterexample to Pietsch's metric-entropy dualit... | Prove MetricEntropyDuality (openai/math family 329: A counterexample to Pietsch's metric-entropy duality conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/metric-entropy-duality",
"version": "1.0.0",
"description": "Prove MetricEntropyDuality (openai/math family 329: A counterexample to Pietsch's metric-entropy duality conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox."... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MetricEntropyDuality.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/metric-entropy-duality |
openai-math/metric-k-median | # openai/math challenge `MetricKMedian` (family 125)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 125 of the release, *The approximation threshold for metric $k$-median*
(Theore... | Prove MetricKMedian (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/metric-k-median",
"version": "1.0.0",
"description": "Prove MetricKMedian (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MetricKMedian.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/metric-k-median |
openai-math/midpoint-lenses | # openai/math challenge `MidpointLenses` (family 331)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 331 of the release, *Asymptotic midpoint uniform convexity without asymptotica... | Prove MidpointLenses (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/midpoint-lenses",
"version": "1.0.0",
"description": "Prove MidpointLenses (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separat... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MidpointLenses.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/midpoint-lenses |
openai-math/min-uncut | # openai/math challenge `MinUncut` (family 102)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 102 of the release, *The Unique Games Conjecture and optimal approximation threshold... | Prove MinUncut (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/min-uncut",
"version": "1.0.0",
"description": "Prove MinUncut (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MinUncut.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "M... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/min-uncut |
openai-math/nagata | # openai/math challenge `Nagata` (family 039)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 039 of the release, *Nagata's conjecture and maximal Seshadri constants*
(Algebraic an... | Prove Nagata (openai/math family 039: Nagata's conjecture and maximal Seshadri constants) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebraic-and-complex-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/nagata",
"version": "1.0.0",
"description": "Prove Nagata (openai/math family 039: Nagata's conjecture and maximal Seshadri constants) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"m... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Nagata.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Nag... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/nagata |
openai-math/naimark | # openai/math challenge `Naimark` (family 297)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 297 of the release, *A ZFC counterexample to Naimark's problem*
(Operator algebras). ... | Prove Naimark (openai/math family 297: A ZFC counterexample to Naimark's problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/naimark",
"version": "1.0.0",
"description": "Prove Naimark (openai/math family 297: A ZFC counterexample to Naimark's problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mathlib"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Naimark.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Na... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/naimark |
openai-math/navier-stokes-alternating | # openai/math challenge `NavierStokesAlternating` (family 376)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 376 of the release, *Universal computation in forced Navier–Stokes fl... | Prove NavierStokesAlternating (openai/math family 376: Universal computation in forced Navier–Stokes flows) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"partial-differential-equations"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/navier-stokes-alternating",
"version": "1.0.0",
"description": "Prove NavierStokesAlternating (openai/math family 376: Universal computation in forced Navier–Stokes flows) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/NavierStokesAlternating.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/navier-stokes-alternating |
openai-math/navier-stokes-velocity | # openai/math challenge `NavierStokesVelocity` (family 376)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 376 of the release, *Universal computation in forced Navier–Stokes flows... | Prove NavierStokesVelocity (openai/math family 376: Universal computation in forced Navier–Stokes flows) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"partial-differential-equations"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/navier-stokes-velocity",
"version": "1.0.0",
"description": "Prove NavierStokesVelocity (openai/math family 376: Universal computation in forced Navier–Stokes flows) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/NavierStokesVelocity.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/navier-stokes-velocity |
openai-math/nodal-length | # openai/math challenge `NodalLength` (family 350)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 350 of the release, *Yau's nodal conjecture: surfaces and counterexamples*
(Diffe... | Prove NodalLength (openai/math family 350: Yau's nodal conjecture: surfaces and counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"differential-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/nodal-length",
"version": "1.0.0",
"description": "Prove NodalLength (openai/math family 350: Yau's nodal conjecture: surfaces and counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lea... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/NodalLength.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/nodal-length |
openai-math/noiseless-regression | # openai/math challenge `NoiselessRegression` (family 140)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 140 of the release, *Memory–sample lower bounds for noiseless Gaussian re... | Prove NoiselessRegression (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/noiseless-regression",
"version": "1.0.0",
"description": "Prove NoiselessRegression (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/NoiselessRegression.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/noiseless-regression |
openai-math/odd-kaplansky | # openai/math challenge `OddKaplansky` (family 197)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 197 of the release, *Nonsofic groups and group-ring counterexamples*
(Algebra). ... | Prove OddKaplansky (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/odd-kaplansky",
"version": "1.0.0",
"description": "Prove OddKaplansky (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/OddKaplansky.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/odd-kaplansky |
openai-math/one-way-liveness | # openai/math challenge `OneWayLiveness` (family 129)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 129 of the release, *Exponential state costs for two-way automata*
(Theoretica... | Prove OneWayLiveness (openai/math family 129: Exponential state costs for two-way automata) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/one-way-liveness",
"version": "1.0.0",
"description": "Prove OneWayLiveness (openai/math family 129: Exponential state costs for two-way automata) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/OneWayLiveness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/one-way-liveness |
openai-math/optimal-max-cut | # openai/math challenge `OptimalMaxCut` (family 102)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 102 of the release, *The Unique Games Conjecture and optimal approximation thre... | Prove OptimalMaxCut (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/optimal-max-cut",
"version": "1.0.0",
"description": "Prove OptimalMaxCut (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/OptimalMaxCut.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/optimal-max-cut |
openai-math/ordinary-elliott | # openai/math challenge `OrdinaryElliott` (family 007)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 007 of the release, *Two-point Chowla and the corrected binary Elliott conjec... | Prove OrdinaryElliott (openai/math family 007: Two-point Chowla and the corrected binary Elliott conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/ordinary-elliott",
"version": "1.0.0",
"description": "Prove OrdinaryElliott (openai/math family 007: Two-point Chowla and the corrected binary Elliott conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keyword... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/OrdinaryElliott.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/ordinary-elliott |
openai-math/parity-lifts | # openai/math challenge `ParityLifts` (family 133)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 133 of the release, *The complexity of Weisfeiler–Leman refinement*
(Theoretical ... | Prove ParityLifts (openai/math family 133: The complexity of Weisfeiler–Leman refinement) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/parity-lifts",
"version": "1.0.0",
"description": "Prove ParityLifts (openai/math family 133: The complexity of Weisfeiler–Leman refinement) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ParityLifts.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/parity-lifts |
openai-math/partial-permutation | # openai/math challenge `PartialPermutation` (family 238)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 238 of the release, *Optimal logarithmic mixing of the Thorp shuffle*
(Pro... | Prove PartialPermutation (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/partial-permutation",
"version": "1.0.0",
"description": "Prove PartialPermutation (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PartialPermutation.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/partial-permutation |
openai-math/partition-consistency | # openai/math challenge `PartitionConsistency` (family 244)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 244 of the release, *The partition principle does not imply choice*
(Mat... | Prove PartitionConsistency (openai/math family 244: The partition principle does not imply choice) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-logic"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/partition-consistency",
"version": "1.0.0",
"description": "Prove PartitionConsistency (openai/math family 244: The partition principle does not imply choice) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PartitionConsistency.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/partition-consistency |
openai-math/partition-principle | # openai/math challenge `PartitionPrinciple` (family 244)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 244 of the release, *The partition principle does not imply choice*
(Mathe... | Prove PartitionPrinciple (openai/math family 244: The partition principle does not imply choice) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-logic"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/partition-principle",
"version": "1.0.0",
"description": "Prove PartitionPrinciple (openai/math family 244: The partition principle does not imply choice) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PartitionPrinciple.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/partition-principle |
openai-math/perceptron-free-energy | # openai/math challenge `PerceptronFreeEnergy` (family 222)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 222 of the release, *Perceptron free energies and microscopic jamming*
(... | Prove PerceptronFreeEnergy (openai/math family 222: Perceptron free energies and microscopic jamming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/perceptron-free-energy",
"version": "1.0.0",
"description": "Prove PerceptronFreeEnergy (openai/math family 222: Perceptron free energies and microscopic jamming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PerceptronFreeEnergy.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/perceptron-free-energy |
openai-math/perfect-completeness | # openai/math challenge `PerfectCompleteness` (family 105)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 105 of the release, *The 2-to-1 Games Conjecture with perfect completenes... | Prove PerfectCompleteness (openai/math family 105: The 2-to-1 Games Conjecture with perfect completeness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/perfect-completeness",
"version": "1.0.0",
"description": "Prove PerfectCompleteness (openai/math family 105: The 2-to-1 Games Conjecture with perfect completeness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PerfectCompleteness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/perfect-completeness |
openai-math/periodic-group | # openai/math challenge `PeriodicGroup` (family 247)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 247 of the release, *An infinite finitely presented residually finite $2$-group... | Prove PeriodicGroup (openai/math family 247: An infinite finitely presented residually finite $2$-group) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/periodic-group",
"version": "1.0.0",
"description": "Prove PeriodicGroup (openai/math family 247: An infinite finitely presented residually finite $2$-group) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PeriodicGroup.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/periodic-group |
openai-math/periodic-tiling-three | # openai/math challenge `PeriodicTilingThree` (family 155)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 155 of the release, *A counterexample to periodic tiling in dimension thr... | Prove PeriodicTilingThree (openai/math family 155: A counterexample to periodic tiling in dimension three) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/periodic-tiling-three",
"version": "1.0.0",
"description": "Prove PeriodicTilingThree (openai/math family 155: A counterexample to periodic tiling in dimension three) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keyw... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PeriodicTilingThree.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/periodic-tiling-three |
openai-math/permanent-cubic | # openai/math challenge `PermanentCubic` (family 108)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 108 of the release, *A cubic permanent–determinant lower bound*
(Theoretical c... | Prove PermanentCubic (openai/math family 108: A cubic permanent–determinant lower bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/permanent-cubic",
"version": "1.0.0",
"description": "Prove PermanentCubic (openai/math family 108: A cubic permanent–determinant lower bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PermanentCubic.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/permanent-cubic |
openai-math/petty-projection-volume | # openai/math challenge `PettyProjectionVolume` (family 088)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 088 of the release, *Petty's projection-volume conjecture and simplex c... | Prove PettyProjectionVolume (openai/math family 088: Petty's projection-volume conjecture and simplex counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/petty-projection-volume",
"version": "1.0.0",
"description": "Prove PettyProjectionVolume (openai/math family 088: Petty's projection-volume conjecture and simplex counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PettyProjectionVolume.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/petty-projection-volume |
openai-math/pi-exponent | # openai/math challenge `PiExponent` (family 017)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 017 of the release, *The irrationality exponent of $\pi$ is $2$*
(Number theory). ... | Prove PiExponent (openai/math family 017: The irrationality exponent of $\pi$ is $2$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/pi-exponent",
"version": "1.0.0",
"description": "Prove PiExponent (openai/math family 017: The irrationality exponent of $\\pi$ is $2$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PiExponent.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/pi-exponent |
openai-math/pinched-kahler | # openai/math challenge `PinchedKahler` (family 359)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 359 of the release, *Negative Kahler curvature without bounded holomorphic coor... | Prove PinchedKahler (openai/math family 359: Negative Kahler curvature without bounded holomorphic coordinates) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"differential-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/pinched-kahler",
"version": "1.0.0",
"description": "Prove PinchedKahler (openai/math family 359: Negative Kahler curvature without bounded holomorphic coordinates) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PinchedKahler.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/pinched-kahler |
openai-math/pinned-distances | # openai/math challenge `PinnedDistances` (family 167)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 167 of the release, *Pinned distances and a power saving for planar unit dist... | Prove PinnedDistances (openai/math family 167: Pinned distances and a power saving for planar unit distances) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/pinned-distances",
"version": "1.0.0",
"description": "Prove PinnedDistances (openai/math family 167: Pinned distances and a power saving for planar unit distances) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PinnedDistances.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/pinned-distances |
openai-math/planar-anderson-spectrum | # openai/math challenge `PlanarAndersonSpectrum` (family 261)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 261 of the release, *Localization and delocalization in the Anderson m... | Prove PlanarAndersonSpectrum (openai/math family 261: Localization and delocalization in the Anderson model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/planar-anderson-spectrum",
"version": "1.0.0",
"description": "Prove PlanarAndersonSpectrum (openai/math family 261: Localization and delocalization in the Anderson model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PlanarAndersonSpectrum.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/planar-anderson-spectrum |
openai-math/planar-falconer | # openai/math challenge `PlanarFalconer` (family 073)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 073 of the release, *The Falconer distance conjecture*
(Real and complex analy... | Prove PlanarFalconer (openai/math family 073: The Falconer distance conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"real-and-complex-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/planar-falconer",
"version": "1.0.0",
"description": "Prove PlanarFalconer (openai/math family 073: The Falconer distance conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"ma... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PlanarFalconer.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/planar-falconer |
openai-math/planar-first-passage | # openai/math challenge `PlanarFirstPassage` (family 212)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 212 of the release, *No bigeodesics and smooth limit shapes in planar firs... | Prove PlanarFirstPassage (openai/math family 212: No bigeodesics and smooth limit shapes in planar first-passage percolation) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/planar-first-passage",
"version": "1.0.0",
"description": "Prove PlanarFirstPassage (openai/math family 212: No bigeodesics and smooth limit shapes in planar first-passage percolation) in Lean 4 with Mathlib; graded by Comparator in a separate sa... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PlanarFirstPassage.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/planar-first-passage |
openai-math/planar-l1 | # openai/math challenge `PlanarL1` (family 089)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 089 of the release, *Bounded-distortion $L_1$ embeddings of planar and bounded-treew... | Prove PlanarL1 (openai/math family 089: Bounded-distortion $L_1$ embeddings of planar and bounded-treewidth graphs) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/planar-l1",
"version": "1.0.0",
"description": "Prove PlanarL1 (openai/math family 089: Bounded-distortion $L_1$ embeddings of planar and bounded-treewidth graphs) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keyword... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PlanarL1.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "P... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/planar-l1 |
openai-math/planar-unit-distances | # openai/math challenge `PlanarUnitDistances` (family 167)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 167 of the release, *Pinned distances and a power saving for planar unit ... | Prove PlanarUnitDistances (openai/math family 167: Pinned distances and a power saving for planar unit distances) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/planar-unit-distances",
"version": "1.0.0",
"description": "Prove PlanarUnitDistances (openai/math family 167: Pinned distances and a power saving for planar unit distances) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PlanarUnitDistances.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/planar-unit-distances |
openai-math/plane-coloring | # openai/math challenge `PlaneColoring` (family 158)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 158 of the release, *The Euclidean plane cannot be colored with five colors*
(C... | Prove PlaneColoring (openai/math family 158: The Euclidean plane cannot be colored with five colors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/plane-coloring",
"version": "1.0.0",
"description": "Prove PlaneColoring (openai/math family 158: The Euclidean plane cannot be colored with five colors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PlaneColoring.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/plane-coloring |
openai-math/posterior-replicas | # openai/math challenge `PosteriorReplicas` (family 140)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 140 of the release, *Memory–sample lower bounds for noiseless Gaussian regr... | Prove PosteriorReplicas (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/posterior-replicas",
"version": "1.0.0",
"description": "Prove PosteriorReplicas (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"key... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PosteriorReplicas.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/posterior-replicas |
openai-math/power-free-values | # openai/math challenge `PowerFreeValues` (family 020)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 020 of the release, *Squarefree quartics and power-free polynomial values*
(N... | Prove PowerFreeValues (openai/math family 020: Squarefree quartics and power-free polynomial values) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/power-free-values",
"version": "1.0.0",
"description": "Prove PowerFreeValues (openai/math family 020: Squarefree quartics and power-free polynomial values) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PowerFreeValues.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/power-free-values |
openai-math/prime-gaps | # openai/math challenge `PrimeGaps` (family 026)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 026 of the release, *Positive lower density of large prime gaps*
(Number theory). T... | Prove PrimeGaps (openai/math family 026: Positive lower density of large prime gaps) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/prime-gaps",
"version": "1.0.0",
"description": "Prove PrimeGaps (openai/math family 026: Positive lower density of large prime gaps) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"ma... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/PrimeGaps.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/prime-gaps |
openai-math/product-brown | # openai/math challenge `ProductBrown` (family 293)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 293 of the release, *A counterexample to the hyperinvariant-subspace problem*
(O... | Prove ProductBrown (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/product-brown",
"version": "1.0.0",
"description": "Prove ProductBrown (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ProductBrown.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/product-brown |
openai-math/projection-counterexample | # openai/math challenge `ProjectionCounterexample` (family 088)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 088 of the release, *Petty's projection-volume conjecture and simple... | Prove ProjectionCounterexample (openai/math family 088: Petty's projection-volume conjecture and simplex counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/projection-counterexample",
"version": "1.0.0",
"description": "Prove ProjectionCounterexample (openai/math family 088: Petty's projection-volume conjecture and simplex counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate s... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ProjectionCounterexample.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/projection-counterexample |
openai-math/projection-moments | # openai/math challenge `ProjectionMoments` (family 140)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 140 of the release, *Memory–sample lower bounds for noiseless Gaussian regr... | Prove ProjectionMoments (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/projection-moments",
"version": "1.0.0",
"description": "Prove ProjectionMoments (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"key... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ProjectionMoments.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/projection-moments |
openai-math/projection-volume | # openai/math challenge `ProjectionVolume` (family 088)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 088 of the release, *Petty's projection-volume conjecture and simplex counte... | Prove ProjectionVolume (openai/math family 088: Petty's projection-volume conjecture and simplex counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/projection-volume",
"version": "1.0.0",
"description": "Prove ProjectionVolume (openai/math family 088: Petty's projection-volume conjecture and simplex counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"k... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ProjectionVolume.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/projection-volume |
openai-math/qac-parity | # openai/math challenge `QACParity` (family 274)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 274 of the release, *Moore's parity conjecture for $\mathrm{QAC}^0$*
(Mathematical ... | Prove QACParity (openai/math family 274: Moore's parity conjecture for $\mathrm{QAC}^0$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/qac-parity",
"version": "1.0.0",
"description": "Prove QACParity (openai/math family 274: Moore's parity conjecture for $\\mathrm{QAC}^0$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/QACParity.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/qac-parity |
openai-math/quadric-bundles | # openai/math challenge `QuadricBundles` (family 050)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 050 of the release, *A counterexample to Griffiths' positivity conjecture*
(Al... | Prove QuadricBundles (openai/math family 050: A counterexample to Griffiths' positivity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebraic-and-complex-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/quadric-bundles",
"version": "1.0.0",
"description": "Prove QuadricBundles (openai/math family 050: A counterexample to Griffiths' positivity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/QuadricBundles.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/quadric-bundles |
openai-math/quantitative-van-der-waerden | # openai/math challenge `QuantitativeVanDerWaerden` (family 160)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 160 of the release, *Superexponential van der Waerden numbers*
(Com... | Prove QuantitativeVanDerWaerden (openai/math family 160: Superexponential van der Waerden numbers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/quantitative-van-der-waerden",
"version": "1.0.0",
"description": "Prove QuantitativeVanDerWaerden (openai/math family 160: Superexponential van der Waerden numbers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/QuantitativeVanDerWaerden.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/quantitative-van-der-waerden |
openai-math/quintic-lienard | # openai/math challenge `QuinticLienard` (family 143)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 143 of the release, *Uniform limit-cycle bounds in Hilbert's sixteenth problem... | Prove QuinticLienard (openai/math family 143: Uniform limit-cycle bounds in Hilbert's sixteenth problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"dynamical-systems-and-ergodic-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/quintic-lienard",
"version": "1.0.0",
"description": "Prove QuinticLienard (openai/math family 143: Uniform limit-cycle bounds in Hilbert's sixteenth problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/QuinticLienard.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/quintic-lienard |
openai-math/radial-density-interval | # openai/math challenge `RadialDensityInterval` (family 228)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 228 of the release, *Continuum phase transitions for radial pair potent... | Prove RadialDensityInterval (openai/math family 228: Continuum phase transitions for radial pair potentials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/radial-density-interval",
"version": "1.0.0",
"description": "Prove RadialDensityInterval (openai/math family 228: Continuum phase transitions for radial pair potentials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RadialDensityInterval.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/radial-density-interval |
openai-math/radial-transition | # openai/math challenge `RadialTransition` (family 228)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 228 of the release, *Continuum phase transitions for radial pair potentials*... | Prove RadialTransition (openai/math family 228: Continuum phase transitions for radial pair potentials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/radial-transition",
"version": "1.0.0",
"description": "Prove RadialTransition (openai/math family 228: Continuum phase transitions for radial pair potentials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RadialTransition.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/radial-transition |
openai-math/ramsey-five | # openai/math challenge `RamseyFive` (family 170)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 170 of the release, *Sharp logarithmic exponents for off-diagonal Ramsey numbers*
... | Prove RamseyFive (openai/math family 170: Sharp logarithmic exponents for off-diagonal Ramsey numbers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/ramsey-five",
"version": "1.0.0",
"description": "Prove RamseyFive (openai/math family 170: Sharp logarithmic exponents for off-diagonal Ramsey numbers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RamseyFive.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/ramsey-five |
openai-math/randomized-mean-payoff | # openai/math challenge `RandomizedMeanPayoff` (family 104)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 104 of the release, *Quasipolynomial algorithms for mean-payoff, stochas... | Prove RandomizedMeanPayoff (openai/math family 104: Quasipolynomial algorithms for mean-payoff, stochastic and parity games) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/randomized-mean-payoff",
"version": "1.0.0",
"description": "Prove RandomizedMeanPayoff (openai/math family 104: Quasipolynomial algorithms for mean-payoff, stochastic and parity games) in Lean 4 with Mathlib; graded by Comparator in a separate s... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RandomizedMeanPayoff.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/randomized-mean-payoff |
openai-math/rational-hitting | # openai/math challenge `RationalHitting` (family 116)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 116 of the release, *Uniform identity testing for noncommutative formulas*
(T... | Prove RationalHitting (openai/math family 116: Uniform identity testing for noncommutative formulas) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/rational-hitting",
"version": "1.0.0",
"description": "Prove RationalHitting (openai/math family 116: Uniform identity testing for noncommutative formulas) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RationalHitting.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/rational-hitting |
openai-math/real-l1-renorming | # openai/math challenge `RealL1Renorming` (family 330)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 330 of the release, *A negative answer to Kalton's Lipschitz-free approximati... | Prove RealL1Renorming (openai/math family 330: A negative answer to Kalton's Lipschitz-free approximation question) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/real-l1-renorming",
"version": "1.0.0",
"description": "Prove RealL1Renorming (openai/math family 330: A negative answer to Kalton's Lipschitz-free approximation question) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RealL1Renorming.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/real-l1-renorming |
openai-math/recursive-potentials | # openai/math challenge `RecursivePotentials` (family 331)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 331 of the release, *Asymptotic midpoint uniform convexity without asympt... | Prove RecursivePotentials (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/recursive-potentials",
"version": "1.0.0",
"description": "Prove RecursivePotentials (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RecursivePotentials.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/recursive-potentials |
openai-math/reflexive-fixed-points | # openai/math challenge `ReflexiveFixedPoints` (family 328)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 328 of the release, *Fixed points of nonexpansive maps in reflexive Bana... | Prove ReflexiveFixedPoints (openai/math family 328: Fixed points of nonexpansive maps in reflexive Banach spaces) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/reflexive-fixed-points",
"version": "1.0.0",
"description": "Prove ReflexiveFixedPoints (openai/math family 328: Fixed points of nonexpansive maps in reflexive Banach spaces) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ReflexiveFixedPoints.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/reflexive-fixed-points |
openai-math/regular-parity | # openai/math challenge `RegularParity` (family 274)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 274 of the release, *Moore's parity conjecture for $\mathrm{QAC}^0$*
(Mathemati... | Prove RegularParity (openai/math family 274: Moore's parity conjecture for $\mathrm{QAC}^0$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/regular-parity",
"version": "1.0.0",
"description": "Prove RegularParity (openai/math family 274: Moore's parity conjecture for $\\mathrm{QAC}^0$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RegularParity.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/regular-parity |
openai-math/relative-generation | # openai/math challenge `RelativeGeneration` (family 296)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 296 of the release, *The generator problem for finite factors*
(Operator a... | Prove RelativeGeneration (openai/math family 296: The generator problem for finite factors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/relative-generation",
"version": "1.0.0",
"description": "Prove RelativeGeneration (openai/math family 296: The generator problem for finite factors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RelativeGeneration.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/relative-generation |
openai-math/rokhlin | # openai/math challenge `Rokhlin` (family 145)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 145 of the release, *Rokhlin's multiple-mixing problem*
(Dynamical systems and ergodi... | Prove Rokhlin (openai/math family 145: Rokhlin's multiple-mixing problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"dynamical-systems-and-ergodic-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/rokhlin",
"version": "1.0.0",
"description": "Prove Rokhlin (openai/math family 145: Rokhlin's multiple-mixing problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mathlib",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Rokhlin.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Ro... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/rokhlin |
openai-math/ruled-covering | # openai/math challenge `RuledCovering` (family 100)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 100 of the release, *A counterexample to Bang's cylinder-covering bound*
(Conve... | Prove RuledCovering (openai/math family 100: A counterexample to Bang's cylinder-covering bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/ruled-covering",
"version": "1.0.0",
"description": "Prove RuledCovering (openai/math family 100: A counterexample to Bang's cylinder-covering bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RuledCovering.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/ruled-covering |
openai-math/ryser-covering | # openai/math challenge `RyserCovering` (family 162)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 162 of the release, *Counterexamples to Ryser's covering and Gyarfas's tree-cov... | Prove RyserCovering (openai/math family 162: Counterexamples to Ryser's covering and Gyarfas's tree-cover conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/ryser-covering",
"version": "1.0.0",
"description": "Prove RyserCovering (openai/math family 162: Counterexamples to Ryser's covering and Gyarfas's tree-cover conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RyserCovering.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/ryser-covering |
openai-math/ryser-odd-extensions | # openai/math challenge `RyserOddExtensions` (family 162)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 162 of the release, *Counterexamples to Ryser's covering and Gyarfas's tre... | Prove RyserOddExtensions (openai/math family 162: Counterexamples to Ryser's covering and Gyarfas's tree-cover conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/ryser-odd-extensions",
"version": "1.0.0",
"description": "Prove RyserOddExtensions (openai/math family 162: Counterexamples to Ryser's covering and Gyarfas's tree-cover conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sand... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/RyserOddExtensions.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/ryser-odd-extensions |
openai-math/sat-computability | # openai/math challenge `SATComputability` (family 235)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 235 of the release, *Random-SAT thresholds, sharp variance and computability... | Prove SATComputability (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sat-computability",
"version": "1.0.0",
"description": "Prove SATComputability (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords":... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SATComputability.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sat-computability |
openai-math/sat-sharpness | # openai/math challenge `SATSharpness` (family 235)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 235 of the release, *Random-SAT thresholds, sharp variance and computability*
(P... | Prove SATSharpness (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sat-sharpness",
"version": "1.0.0",
"description": "Prove SATSharpness (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SATSharpness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sat-sharpness |
openai-math/sat-variance | # openai/math challenge `SATVariance` (family 235)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 235 of the release, *Random-SAT thresholds, sharp variance and computability*
(Pr... | Prove SATVariance (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sat-variance",
"version": "1.0.0",
"description": "Prove SATVariance (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SATVariance.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sat-variance |
openai-math/saxl | # openai/math challenge `Saxl` (family 205)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 205 of the release, *Saxl's conjecture and universal tensor squares*
(Algebra). The fami... | Prove Saxl (openai/math family 205: Saxl's conjecture and universal tensor squares) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/saxl",
"version": "1.0.0",
"description": "Prove Saxl (openai/math family 205: Saxl's conjecture and universal tensor squares) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mathlib",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Saxl.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Saxl"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/saxl |
openai-math/second-kahn-kalai | # openai/math challenge `SecondKahnKalai` (family 176)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 176 of the release, *The second Kahn–Kalai conjecture*
(Combinatorics). The f... | Prove SecondKahnKalai (openai/math family 176: The second Kahn–Kalai conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/second-kahn-kalai",
"version": "1.0.0",
"description": "Prove SecondKahnKalai (openai/math family 176: The second Kahn–Kalai conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SecondKahnKalai.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/second-kahn-kalai |
openai-math/self-similar-corollaries | # openai/math challenge `SelfSimilarCorollaries` (family 148)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 148 of the release, *The dimension formula for self-similar measures o... | Prove SelfSimilarCorollaries (openai/math family 148: The dimension formula for self-similar measures on the line) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"dynamical-systems-and-ergodic-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/self-similar-corollaries",
"version": "1.0.0",
"description": "Prove SelfSimilarCorollaries (openai/math family 148: The dimension formula for self-similar measures on the line) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox."... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SelfSimilarCorollaries.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/self-similar-corollaries |
openai-math/self-similar | # openai/math challenge `SelfSimilar` (family 148)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 148 of the release, *The dimension formula for self-similar measures on the line*... | Prove SelfSimilar (openai/math family 148: The dimension formula for self-similar measures on the line) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"dynamical-systems-and-ergodic-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/self-similar",
"version": "1.0.0",
"description": "Prove SelfSimilar (openai/math family 148: The dimension formula for self-similar measures on the line) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SelfSimilar.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/self-similar |
openai-math/sensitivity-separation | # openai/math challenge `SensitivitySeparation` (family 132)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 132 of the release, *A counterexample to the quadratic sensitivity conj... | Prove SensitivitySeparation (openai/math family 132: A counterexample to the quadratic sensitivity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sensitivity-separation",
"version": "1.0.0",
"description": "Prove SensitivitySeparation (openai/math family 132: A counterexample to the quadratic sensitivity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SensitivitySeparation.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sensitivity-separation |
openai-math/separable-quotient-negative | # openai/math challenge `SeparableQuotientNegative` (family 323)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 323 of the release, *Relative independence of the separable quotien... | Prove SeparableQuotientNegative (openai/math family 323: Relative independence of the separable quotient problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/separable-quotient-negative",
"version": "1.0.0",
"description": "Prove SeparableQuotientNegative (openai/math family 323: Relative independence of the separable quotient problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SeparableQuotientNegative.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/separable-quotient-negative |
openai-math/seymour-second-neighborhood | # openai/math challenge `SeymourSecondNeighborhood` (family 173)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 173 of the release, *Seymour's second-neighborhood conjecture*
(Com... | Prove SeymourSecondNeighborhood (openai/math family 173: Seymour's second-neighborhood conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/seymour-second-neighborhood",
"version": "1.0.0",
"description": "Prove SeymourSecondNeighborhood (openai/math family 173: Seymour's second-neighborhood conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SeymourSecondNeighborhood.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/seymour-second-neighborhood |
openai-math/sharp-cat0-filling | # openai/math challenge `SharpCAT0Filling` (family 337)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 337 of the release, *Cartan–Hadamard isoperimetry and CAT$(0)$ fillings*
(Di... | Prove SharpCAT0Filling (openai/math family 337: Cartan–Hadamard isoperimetry and CAT$(0)$ fillings) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"differential-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sharp-cat0-filling",
"version": "1.0.0",
"description": "Prove SharpCAT0Filling (openai/math family 337: Cartan–Hadamard isoperimetry and CAT$(0)$ fillings) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SharpCAT0Filling.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sharp-cat0-filling |
openai-math/sharp-log-ramsey | # openai/math challenge `SharpLogRamsey` (family 170)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 170 of the release, *Sharp logarithmic exponents for off-diagonal Ramsey numbe... | Prove SharpLogRamsey (openai/math family 170: Sharp logarithmic exponents for off-diagonal Ramsey numbers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sharp-log-ramsey",
"version": "1.0.0",
"description": "Prove SharpLogRamsey (openai/math family 170: Sharp logarithmic exponents for off-diagonal Ramsey numbers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SharpLogRamsey.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sharp-log-ramsey |
openai-math/sharp-threshold | # openai/math challenge `SharpThreshold` (family 186)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 186 of the release, *The Friedgut–Kalai graph and hypergraph threshold conject... | Prove SharpThreshold (openai/math family 186: The Friedgut–Kalai graph and hypergraph threshold conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sharp-threshold",
"version": "1.0.0",
"description": "Prove SharpThreshold (openai/math family 186: The Friedgut–Kalai graph and hypergraph threshold conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SharpThreshold.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sharp-threshold |
openai-math/short-egyptian-fractions | # openai/math challenge `ShortEgyptianFractions` (family 025)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 025 of the release, *Erd\H{o}s’s short Egyptian-fraction conjecture*
(... | Prove ShortEgyptianFractions (openai/math family 025: Erd\H{o}s’s short Egyptian-fraction conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/short-egyptian-fractions",
"version": "1.0.0",
"description": "Prove ShortEgyptianFractions (openai/math family 025: Erd\\H{o}s’s short Egyptian-fraction conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ShortEgyptianFractions.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/short-egyptian-fractions |
openai-math/sidorenko-counterexample | # openai/math challenge `SidorenkoCounterexample` (family 161)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 161 of the release, *Counterexamples to Sidorenko's conjecture and th... | Prove SidorenkoCounterexample (openai/math family 161: Counterexamples to Sidorenko's conjecture and the forcing conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sidorenko-counterexample",
"version": "1.0.0",
"description": "Prove SidorenkoCounterexample (openai/math family 161: Counterexamples to Sidorenko's conjecture and the forcing conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SidorenkoCounterexample.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sidorenko-counterexample |
openai-math/signed-finite-band | # openai/math challenge `SignedFiniteBand` (family 085)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 085 of the release, *Endpoint regularity of the planar centered maximal func... | Prove SignedFiniteBand (openai/math family 085: Endpoint regularity of the planar centered maximal function) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"real-and-complex-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/signed-finite-band",
"version": "1.0.0",
"description": "Prove SignedFiniteBand (openai/math family 085: Endpoint regularity of the planar centered maximal function) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SignedFiniteBand.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/signed-finite-band |
openai-math/signed-sweep-moment | # openai/math challenge `SignedSweepMoment` (family 238)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 238 of the release, *Optimal logarithmic mixing of the Thorp shuffle*
(Prob... | Prove SignedSweepMoment (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/signed-sweep-moment",
"version": "1.0.0",
"description": "Prove SignedSweepMoment (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SignedSweepMoment.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/signed-sweep-moment |
openai-math/simple-amenable | # openai/math challenge `SimpleAmenable` (family 253)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 253 of the release, *An infinite finitely presented simple amenable group*
(Gr... | Prove SimpleAmenable (openai/math family 253: An infinite finitely presented simple amenable group) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/simple-amenable",
"version": "1.0.0",
"description": "Prove SimpleAmenable (openai/math family 253: An infinite finitely presented simple amenable group) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SimpleAmenable.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/simple-amenable |
openai-math/simple-overgroups | # openai/math challenge `SimpleOvergroups` (family 250)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 250 of the release, *The Boone–Higman conjecture and higher finiteness*
(Gro... | Prove SimpleOvergroups (openai/math family 250: The Boone–Higman conjecture and higher finiteness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/simple-overgroups",
"version": "1.0.0",
"description": "Prove SimpleOvergroups (openai/math family 250: The Boone–Higman conjecture and higher finiteness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SimpleOvergroups.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/simple-overgroups |
openai-math/single-fold | # openai/math challenge `SingleFold` (family 242)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 242 of the release, *Single-fold Diophantine representations*
(Mathematical logic)... | Prove SingleFold (openai/math family 242: Single-fold Diophantine representations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-logic"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/single-fold",
"version": "1.0.0",
"description": "Prove SingleFold (openai/math family 242: Single-fold Diophantine representations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mat... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SingleFold.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/single-fold |
openai-math/single-lattice-covering | # openai/math challenge `SingleLatticeCovering` (family 092)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 092 of the release, *The optimal order of convex-body covering density*... | Prove SingleLatticeCovering (openai/math family 092: The optimal order of convex-body covering density) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/single-lattice-covering",
"version": "1.0.0",
"description": "Prove SingleLatticeCovering (openai/math family 092: The optimal order of convex-body covering density) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SingleLatticeCovering.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/single-lattice-covering |
openai-math/singleton-loop-matching | # openai/math challenge `SingletonLoopMatching` (family 113)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 113 of the release, *Approximate counting and the perfect-matching entr... | Prove SingletonLoopMatching (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/singleton-loop-matching",
"version": "1.0.0",
"description": "Prove SingletonLoopMatching (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SingletonLoopMatching.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/singleton-loop-matching |
openai-math/sk-barriers | # openai/math challenge `SKBarriers` (family 227)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 227 of the release, *The dynamical phase transition in the Sherrington–Kirkpatrick... | Prove SKBarriers (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sk-barriers",
"version": "1.0.0",
"description": "Prove SKBarriers (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords":... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SKBarriers.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sk-barriers |
openai-math/sk-full-support | # openai/math challenge `SKFullSupport` (family 281)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 281 of the release, *QAOA optimality for the SK model*
(Mathematical physics). ... | Prove SKFullSupport (openai/math family 281: QAOA optimality for the SK model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sk-full-support",
"version": "1.0.0",
"description": "Prove SKFullSupport (openai/math family 281: QAOA optimality for the SK model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mat... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SKFullSupport.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sk-full-support |
openai-math/sk-high-temperature | # openai/math challenge `SKHighTemperature` (family 227)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 227 of the release, *The dynamical phase transition in the Sherrington–Kirk... | Prove SKHighTemperature (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sk-high-temperature",
"version": "1.0.0",
"description": "Prove SKHighTemperature (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SKHighTemperature.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sk-high-temperature |
openai-math/sk-ratio | # openai/math challenge `SKRatio` (family 227)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 227 of the release, *The dynamical phase transition in the Sherrington–Kirkpatrick mo... | Prove SKRatio (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sk-ratio",
"version": "1.0.0",
"description": "Prove SKRatio (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SKRatio.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "SK... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sk-ratio |
openai-math/sk-value | # openai/math challenge `SKValue` (family 281)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 281 of the release, *QAOA optimality for the SK model*
(Mathematical physics). The fa... | Prove SKValue (openai/math family 281: QAOA optimality for the SK model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sk-value",
"version": "1.0.0",
"description": "Prove SKValue (openai/math family 281: QAOA optimality for the SK model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mathlib",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SKValue.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "SK... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sk-value |
openai-math/sle-lower-positivity | # openai/math challenge `SLELowerPositivity` (family 230)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 230 of the release, *Exact Hausdorff measure for SLE*
(Probability and sta... | Prove SLELowerPositivity (openai/math family 230: Exact Hausdorff measure for SLE) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/sle-lower-positivity",
"version": "1.0.0",
"description": "Prove SLELowerPositivity (openai/math family 230: Exact Hausdorff measure for SLE) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SLELowerPositivity.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/sle-lower-positivity |
openai-math/smooth-initial-form | # openai/math challenge `SmoothInitialForm` (family 108)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 108 of the release, *A cubic permanent–determinant lower bound*
(Theoretica... | Prove SmoothInitialForm (openai/math family 108: A cubic permanent–determinant lower bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/smooth-initial-form",
"version": "1.0.0",
"description": "Prove SmoothInitialForm (openai/math family 108: A cubic permanent–determinant lower bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SmoothInitialForm.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/smooth-initial-form |
openai-math/smooth-obstruction | # openai/math challenge `SmoothObstruction` (family 152)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 152 of the release, *Zero entropy does not guarantee a smooth positive-volu... | Prove SmoothObstruction (openai/math family 152: Zero entropy does not guarantee a smooth positive-volume model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"dynamical-systems-and-ergodic-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/smooth-obstruction",
"version": "1.0.0",
"description": "Prove SmoothObstruction (openai/math family 152: Zero entropy does not guarantee a smooth positive-volume model) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"k... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SmoothObstruction.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/smooth-obstruction |
openai-math/smooth-yau | # openai/math challenge `SmoothYau` (family 350)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 350 of the release, *Yau's nodal conjecture: surfaces and counterexamples*
(Differe... | Prove SmoothYau (openai/math family 350: Yau's nodal conjecture: surfaces and counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"differential-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/smooth-yau",
"version": "1.0.0",
"description": "Prove SmoothYau (openai/math family 350: Yau's nodal conjecture: surfaces and counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SmoothYau.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/smooth-yau |
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