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formal-conjectures-gold

task_id stringlengths 18 77	harbor_task_name stringlengths 43 102	harbor_task_path stringlengths 24 83	theorem_name stringlengths 16 71	theorem_header stringlengths 29 509	source stringclasses 2 values	source_file stringlengths 39 54	benchmark_bucket stringclasses 1 value	oracle_status stringclasses 1 value	licence_status stringclasses 4 values	redistribution_status stringclasses 1 value	formal_conjectures_commit stringclasses 1 value	lean_toolchain stringclasses 1 value	mathlib_commit stringclasses 1 value	allow_internet bool 1 class	agent_timeout_sec float64 86.4k 86.4k	verifier_timeout_sec float64 7.2k 7.2k	environment_build_timeout_sec float64 14.4k 14.4k
arxiv-0911-2077-conjecture6-3-conjecture6-3	formal-conjectures-bench/arxiv-0911-2077-conjecture6-3-conjecture6-3	tasks/arxiv-0911-2077-conjecture6-3-conjecture6-3	Arxiv.arxiv.id0911_2077.conjecture6_3	theorem arxiv.id0911_2077.conjecture6_3 (p : ℝ) (h_p : p ∈ Set.Ioo 0 (1 / 2)) (k : ℕ) (hk : 0 < k) (σ : ℝ) (h_σ : σ = (p * (1 - p)).sqrt) : letI hp' : (⟨p, le_of_lt h_p.1⟩ : ℝ≥0) ≤ 1 := by have : p ≤ 1 := le_trans (le_of_lt (Set.mem_Ioo.mp h_p).right) (by linarith) exact this 1 - Φ ((1 / 2 ...	google-deepmind/formal-conjectures	FormalConjectures/Arxiv/0911.2077/Conjecture6_3.lean	gold_solution	bundled	MIT	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-100-erdos-100-piepmeyer	formal-conjectures-bench/erdosproblems-100-erdos-100-piepmeyer	tasks/erdosproblems-100-erdos-100-piepmeyer	Erdos100.erdos_100_piepmeyer	theorem erdos_100_piepmeyer : ∃ A : Finset ℝ², A.card = 9 ∧ DistancesSeparated A ∧ diam (A : Set ℝ²) < 5	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/100.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-1043-erdos-1043	formal-conjectures-bench/erdosproblems-1043-erdos-1043	tasks/erdosproblems-1043-erdos-1043	Erdos1043.erdos_1043	theorem erdos_1043 : answer(False) ↔ ∀ (f : ℂ[X]), f.Monic → f.degree ≥ 1 → ∃ (u : ℂ), ‖u‖ = 1 ∧ volume ((ℝ ∙ u).orthogonalProjection '' levelSet f) ≤ 2	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/1043.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-1051-erdos-1051	formal-conjectures-bench/erdosproblems-1051-erdos-1051	tasks/erdosproblems-1051-erdos-1051	Erdos1051.erdos_1051	theorem erdos_1051 : answer(True) ↔ ∀ (a : ℕ → ℤ), StrictMono a → GrowthCondition a → Irrational (ErdosSeries a)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/1051.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-1052-even-of-isunitaryperfect	formal-conjectures-bench/erdosproblems-1052-even-of-isunitaryperfect	tasks/erdosproblems-1052-even-of-isunitaryperfect	Erdos1052.even_of_isUnitaryPerfect	theorem even_of_isUnitaryPerfect (n : ℕ) (hn : IsUnitaryPerfect n) : Even n	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/1052.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-1074-ehsnumbers-infinite	formal-conjectures-bench/erdosproblems-1074-ehsnumbers-infinite	tasks/erdosproblems-1074-ehsnumbers-infinite	Erdos1074.erdos_1074.variants.EHSNumbers_infinite	theorem erdos_1074.variants.EHSNumbers_infinite : EHSNumbers.Infinite	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/1074.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-1080-erdos-1080	formal-conjectures-bench/erdosproblems-1080-erdos-1080	tasks/erdosproblems-1080-erdos-1080	Erdos1080.erdos_1080	theorem erdos_1080 : answer(False) ↔ ∃ c > (0 : ℝ), ∀ (V : Type) [Fintype V] [Nonempty V] (G : SimpleGraph V) (X Y : Set V), IsBipartition G X Y → X.ncard = ⌊(Fintype.card V : ℝ) ^ (2/3 : ℝ)⌋₊ → G.edgeSet.ncard ≥ c * Fintype.card V → ∃ (v : V) (walk : G.Walk v v), walk.IsCycle ∧ walk.length ...	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/1080.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-1082-ii	formal-conjectures-bench/erdosproblems-1082-ii	tasks/erdosproblems-1082-ii	Erdos1082.erdos_1082.parts.ii	theorem erdos_1082.parts.ii : answer(False) ↔ ∀ (A : Finset ℝ²) (hA : A.Nonempty) (hA_n3c : NonTrilinear (A : Set ℝ²)), ∃ (a : ℝ²) (ha : a ∈ A), A.card / 2 ≤ distinctDistancesFrom A a - 1	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/1082.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-1151-nonempty-fixed-point	formal-conjectures-bench/erdosproblems-1151-nonempty-fixed-point	tasks/erdosproblems-1151-nonempty-fixed-point	Erdos1151NonemptyFixedPoint.erdos_1151_nonempty_fixed_point	theorem erdos_1151_nonempty_fixed_point {x0 : ℝ} (hx0 : x0 ∈ SpaceI) {A : Set ℝ} (hA_closed : IsClosed A) (hA_nonempty : A.Nonempty) (hA_subset : A ⊆ SpaceI) : ∃ f : SpaceFun, clusterSet (fun m : ℕ => chebLagEval x0 f (m.succ)) = A	formal-conjectures-bench/local	benchmark_sources/erdos1151/NonemptyFixedPoint.lean	gold_solution	bundled	project-local	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-12-i	formal-conjectures-bench/erdosproblems-12-i	tasks/erdosproblems-12-i	Erdos12.erdos_12.parts.i	theorem erdos_12.parts.i : answer(True) ↔ ∃ (A : Set ℕ), IsGood A ∧ (0 : ℝ) < Filter.atTop.liminf (fun N => (A ∩ Icc 1 N).ncard / (N : ℝ).sqrt)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/12.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-12-ii	formal-conjectures-bench/erdosproblems-12-ii	tasks/erdosproblems-12-ii	Erdos12.erdos_12.parts.ii	theorem erdos_12.parts.ii : answer(False) ↔ ∃ c > (0 : ℝ), ∀ (A : Set ℕ), IsGood A → {N : ℕ\| (A ∩ Icc 1 N).ncard < (N : ℝ) ^ (1 - c)}.Infinite	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/12.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-12-isgood-example	formal-conjectures-bench/erdosproblems-12-isgood-example	tasks/erdosproblems-12-isgood-example	Erdos12.isGood_example	theorem isGood_example : IsGood {p ^ 2 \| (p : ℕ) (_ : p ≡ 3 [MOD 4]) (_ : p.Prime)}	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/12.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-125-erdos-125	formal-conjectures-bench/erdosproblems-125-erdos-125	tasks/erdosproblems-125-erdos-125	Erdos125.erdos_125	theorem erdos_125 : answer(False) ↔ (A + B).HasPosDensity	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/125.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-125-positive-lower-density	formal-conjectures-bench/erdosproblems-125-positive-lower-density	tasks/erdosproblems-125-positive-lower-density	Erdos125.erdos_125.variants.positive_lower_density	theorem erdos_125.variants.positive_lower_density : answer(False) ↔ 0 < (A + B).lowerDensity	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/125.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-138-difference	formal-conjectures-bench/erdosproblems-138-difference	tasks/erdosproblems-138-difference	Erdos138.erdos_138.variants.difference	theorem erdos_138.variants.difference : answer(True) ↔ atTop.Tendsto (fun k => (W (k + 1) - W k)) atTop	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/138.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-138-monoapnumber-two-one	formal-conjectures-bench/erdosproblems-138-monoapnumber-two-one	tasks/erdosproblems-138-monoapnumber-two-one	Erdos138.monoAPNumber_two_one	theorem monoAPNumber_two_one : W 1 = 1	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/138.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-138-monoapnumber-two-two	formal-conjectures-bench/erdosproblems-138-monoapnumber-two-two	tasks/erdosproblems-138-monoapnumber-two-two	Erdos138.monoAPNumber_two_two	theorem monoAPNumber_two_two : W 2 = 3	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/138.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-152-erdos-152	formal-conjectures-bench/erdosproblems-152-erdos-152	tasks/erdosproblems-152-erdos-152	Erdos152.erdos_152	theorem erdos_152 : answer(True) ↔ Tendsto f atTop atTop	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/152.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-152-square	formal-conjectures-bench/erdosproblems-152-square	tasks/erdosproblems-152-square	Erdos152.erdos_152.variants.square	theorem erdos_152.variants.square : answer(True) ↔ (fun n => f n : ℕ → ℝ) ≫ (fun n => n ^ 2 : ℕ → ℝ)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/152.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-189-erdos-189	formal-conjectures-bench/erdosproblems-189-erdos-189	tasks/erdosproblems-189-erdos-189	Erdos189.erdos_189	theorem erdos_189 : answer(False) ↔ Erdos189For (fun a b c d ↦ line[ℝ, a, b].direction ⟂ line[ℝ, b, c].direction ∧ line[ℝ, b, c].direction ⟂ line[ℝ, c, d].direction ∧ line[ℝ, c, d].direction ⟂ line[ℝ, d, a].direction) (fun a b c d ↦ dist a b * dist b c)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/189.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-198-concrete	formal-conjectures-bench/erdosproblems-198-concrete	tasks/erdosproblems-198-concrete	Erdos198.erdos_198.variants.concrete	theorem erdos_198.variants.concrete : ∃ (A : Set ℕ), A = {n ! + n \| n} ∧ IsSidon A ∧ (∀ Y, IsAPOfLength Y ⊤ → (A ∩ Y).Nonempty)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/198.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-198-erdos-198	formal-conjectures-bench/erdosproblems-198-erdos-198	tasks/erdosproblems-198-erdos-198	Erdos198.erdos_198	theorem erdos_198 : (∀ A : Set ℕ, IsSidon A → (∃ Y, IsAPOfLength Y ⊤ ∧ Y ⊆ Aᶜ)) ↔ answer(False)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/198.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-229-erdos-229	formal-conjectures-bench/erdosproblems-229-erdos-229	tasks/erdosproblems-229-erdos-229	Erdos229.erdos_229	theorem erdos_229 : letI := Polynomial.algebraPi ℂ ℂ ℂ answer(True) ↔ ∀ (S : ℕ → Set ℂ), (∀ n, derivedSet (S n) = ∅) → ∃ (f : ℂ → ℂ), Transcendental (Polynomial ℂ) f ∧ Differentiable ℂ f ∧ ∀ n ≥ 1, ∃ k, ∀ z ∈ S n, iteratedDeriv k f z = 0	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/229.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-233-lower-bound	formal-conjectures-bench/erdosproblems-233-lower-bound	tasks/erdosproblems-233-lower-bound	Erdos233.erdos_233.variants.lower_bound	theorem erdos_233.variants.lower_bound : (fun (N : ℕ) => N * (log N)^2) =O[atTop] (fun N => ((∑ n ∈ Finset.range N, (primeGap n) ^ 2) : ℝ))	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/233.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-259-erdos-259	formal-conjectures-bench/erdosproblems-259-erdos-259	tasks/erdosproblems-259-erdos-259	Erdos259.erdos_259	theorem erdos_259 : Irrational (∑' n : ℕ, (μ n) ^ 2 * n / (2 ^ n))	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/259.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-26-erdos-26	formal-conjectures-bench/erdosproblems-26-erdos-26	tasks/erdosproblems-26-erdos-26	Erdos26.erdos_26	theorem erdos_26 : answer(False) ↔ ∀ A : ℕ → ℕ, StrictMono A → IsThick A → ∃ k, IsBehrend (A · + k)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/26.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-26-tenenbaum	formal-conjectures-bench/erdosproblems-26-tenenbaum	tasks/erdosproblems-26-tenenbaum	Erdos26.erdos_26.variants.tenenbaum	theorem erdos_26.variants.tenenbaum : answer(False) ↔ ∀ᵉ (A : ℕ → ℕ), StrictMono A → IsThick A → (∀ ε > (0 : ℝ), ∃ k, IsWeaklyBehrend (A · + k) ε)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/26.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-263-ii	formal-conjectures-bench/erdosproblems-263-ii	tasks/erdosproblems-263-ii	Erdos263.erdos_263.parts.ii	theorem erdos_263.parts.ii : answer(False) ↔ ∀ a : ℕ → ℕ, IsIrrationalitySequence a → atTop.Tendsto (fun n : ℕ => (a n : ℝ) ^ (1 / (n : ℝ))) atTop	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/263.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-267-specialization-pow-two	formal-conjectures-bench/erdosproblems-267-specialization-pow-two	tasks/erdosproblems-267-specialization-pow-two	Erdos267.erdos_267.variants.specialization_pow_two	theorem erdos_267.variants.specialization_pow_two : Irrational <\| ∑' k, 1 / (Nat.fib <\| 2^k)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/267.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-275-erdos-275	formal-conjectures-bench/erdosproblems-275-erdos-275	tasks/erdosproblems-275-erdos-275	Erdos275.erdos_275	theorem erdos_275 (r : ℕ) (a : Fin r → ℤ) (n : Fin r → ℕ) (H : ∃ k : ℤ, ∀ x ∈ Ico k (k + 2 ^ r), ∃ i, x ≡ a i [ZMOD n i]) (x : ℤ) : ∃ i, x ≡ a i [ZMOD n i]	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/275.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-316-erdos-316	formal-conjectures-bench/erdosproblems-316-erdos-316	tasks/erdosproblems-316-erdos-316	Erdos316.erdos_316	theorem erdos_316 : answer(False) ↔ ∀ A : Finset ℕ, 0 ∉ A → 1 ∉ A → ∑ n ∈ A, (1 / n : ℚ) < 2 → ∃ (A₁ A₂ : Finset ℕ), Disjoint A₁ A₂ ∧ A = A₁ ∪ A₂ ∧ ∑ n ∈ A₁, (1 / n : ℚ) < 1 ∧ ∑ n ∈ A₂, (1 / n : ℚ) < 1	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/316.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-330-upper-density	formal-conjectures-bench/erdosproblems-330-upper-density	tasks/erdosproblems-330-upper-density	Erdos330UpperDensity.erdos_330_upper_density	theorem erdos_330_upper_density : MainTarget	formal-conjectures-bench/local	benchmark_sources/erdos330/UpperDensity.lean	gold_solution	bundled	project-local	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-331-erdos-331	formal-conjectures-bench/erdosproblems-331-erdos-331	tasks/erdosproblems-331-erdos-331	Erdos331.erdos_331	theorem erdos_331 : answer(False) ↔ ∀ A B : Set ℕ, (fun (n : ℕ) ↦ (n : ℝ) ^ (1 / 2 : ℝ)) =O[atTop] (fun (n : ℕ) ↦ (count A n : ℝ)) → (fun (n : ℕ) ↦ (n : ℝ) ^ (1 / 2 : ℝ)) =O[atTop] (fun (n : ℕ) ↦ (count B n : ℝ)) → { s : ℕ × ℕ × ℕ × ℕ \| let ⟨a₁, a₂, b₁, b₂⟩ := s a₁ ∈ A ∧ a₂ ∈ A ∧ b₁ ...	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/331.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-350-erdos-350	formal-conjectures-bench/erdosproblems-350-erdos-350	tasks/erdosproblems-350-erdos-350	Erdos350.erdos_350	theorem erdos_350 (A : Finset ℕ) (hA : DecidableDistinctSubsetSums A) : ∑ n ∈ A, (1 / n : ℝ) < 2	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/350.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-355-erdos-355	formal-conjectures-bench/erdosproblems-355-erdos-355	tasks/erdosproblems-355-erdos-355	Erdos355.erdos_355	theorem erdos_355 : answer(True) ↔ ∃ A : ℕ → ℕ, IsLacunary A ∧ ∃ u v : ℝ, u < v ∧ ∀ q : ℚ, ↑q ∈ Set.Ioo u v → q ∈ {∑ a ∈ A', (1 / a : ℚ) \| (A' : Finset ℕ) (_ : ↑A' ⊆ Set.range A)}	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/355.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-370-erdos-370	formal-conjectures-bench/erdosproblems-370-erdos-370	tasks/erdosproblems-370-erdos-370	Erdos370.erdos_370	theorem erdos_370 : answer(True) ↔ { n \| Nat.maxPrimeFac n < √n ∧ Nat.maxPrimeFac (n + 1) < √(n + 1) }.Infinite	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/370.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-379-erdos-379	formal-conjectures-bench/erdosproblems-379-erdos-379	tasks/erdosproblems-379-erdos-379	Erdos379.erdos_379	theorem erdos_379 : atTop.limsup (fun n => (S n : ℕ∞)) = ⊤	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/379.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-397-erdos-397	formal-conjectures-bench/erdosproblems-397-erdos-397	tasks/erdosproblems-397-erdos-397	Erdos397.erdos_397	theorem erdos_397 : answer(False) ↔ {(M, N) : Finset ℕ × Finset ℕ \| Disjoint M N ∧ ∏ i ∈ M, centralBinom i = ∏ j ∈ N, centralBinom j}.Finite	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/397.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-399-erdos-399	formal-conjectures-bench/erdosproblems-399-erdos-399	tasks/erdosproblems-399-erdos-399	Erdos399.erdos_399	theorem erdos_399 : answer(False) ↔ ¬ ∃ (n x y k : ℕ), 1 < x * y ∧ 2 < k ∧ (n ! = x ^ k + y ^ k ∨ n ! + y ^ k = x ^ k)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/399.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-645-erdos-645	formal-conjectures-bench/erdosproblems-645-erdos-645	tasks/erdosproblems-645-erdos-645	Erdos645.erdos_645	theorem erdos_645 (c : ℕ → Bool) : ∃ x d, 0 < x ∧ x < d ∧ (∃ C, c x = C ∧ c (x + d) = C ∧ c (x + 2 * d) = C)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/645.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-707-erdos-707	formal-conjectures-bench/erdosproblems-707-erdos-707	tasks/erdosproblems-707-erdos-707	Erdos707.erdos_707	theorem erdos_707 : (∀ (A : Set ℕ) (h : A.Finite), IsSidon A → ∃ᵉ (B : Set ℕ) (n > 0), A ⊆ B ∧ IsPerfectDifferenceSet B n) ↔ False	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/707.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-741-i	formal-conjectures-bench/erdosproblems-741-i	tasks/erdosproblems-741-i	Erdos741.erdos_741.parts.i	theorem erdos_741.parts.i : answer(False) ↔ ∀ A : Set ℕ, HasPosDensity (A + A) → ∃ A₁ A₂, A = A₁ ∪ A₂ ∧ Disjoint A₁ A₂ ∧ HasPosDensity (A₁ + A₁) ∧ HasPosDensity (A₂ + A₂)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/741.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-741-ii	formal-conjectures-bench/erdosproblems-741-ii	tasks/erdosproblems-741-ii	Erdos741.erdos_741.parts.ii	theorem erdos_741.parts.ii : answer(True) ↔ ∃ A : Set ℕ, IsAddBasisOfOrder (A ∪ {0}) 2 ∧ ∀ A₁ A₂, A = A₁ ∪ A₂ → Disjoint A₁ A₂ → ¬ (IsSyndetic (A₁ + A₁) ∧ IsSyndetic (A₂ + A₂))	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/741.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-741-upper	formal-conjectures-bench/erdosproblems-741-upper	tasks/erdosproblems-741-upper	Erdos741.erdos_741.variants.upper	theorem erdos_741.variants.upper : answer(True) ↔ ∀ A : Set ℕ, 0 < upperDensity (A + A) → ∃ A₁ A₂, A = A₁ ∪ A₂ ∧ Disjoint A₁ A₂ ∧ 0 < upperDensity (A₁ + A₁) ∧ 0 < upperDensity (A₂ + A₂)	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/741.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-828-phi-dvd-self-iff-pow2-pow3	formal-conjectures-bench/erdosproblems-828-phi-dvd-self-iff-pow2-pow3	tasks/erdosproblems-828-phi-dvd-self-iff-pow2-pow3	Erdos828.erdos_828.variants.phi_dvd_self_iff_pow2_pow3	theorem erdos_828.variants.phi_dvd_self_iff_pow2_pow3 {n : ℕ} : φ n ∣ n ↔ n ≤ 1 ∨ ∃ᵉ (a > 0) (b), n = 2 ^ a * 3 ^ b	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/828.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-846-erdos-846	formal-conjectures-bench/erdosproblems-846-erdos-846	tasks/erdosproblems-846-erdos-846	Erdos846.erdos_846	theorem erdos_846 : answer(False) ↔ ∀ᵉ (A : Set ℝ²) (ε > 0), A.Infinite → NonTrilinearFor A ε → WeaklyNonTrilinear A	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/846.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-897-i	formal-conjectures-bench/erdosproblems-897-i	tasks/erdosproblems-897-i	Erdos897.erdos_897.parts.i	theorem erdos_897.parts.i : answer(False) ↔ ∀ (f : ℕ → ℝ), (∀ᵉ (a > 0) (b > 0), a.Coprime b → f (a * b) = f a + f b) → ((Filter.atTop ⊓ Filter.principal {(p, k) : ℕ × ℕ \| p.Prime}).limsup (fun (p, k) => (f (p^k) / (p^k : ℝ).log : EReal)) = ⊤) → Filter.atTop.limsup (fun (n : ℕ) => ((f (n+1) - f n) / (n...	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/897.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-897-ii	formal-conjectures-bench/erdosproblems-897-ii	tasks/erdosproblems-897-ii	Erdos897.erdos_897.parts.ii	theorem erdos_897.parts.ii : answer(False) ↔ ∀ (f : ℕ → ℝ), (∀ᵉ (a > 0) (b > 0), a.Coprime b → f (a * b) = f a + f b) → ((Filter.atTop ⊓ Filter.principal {(p, k) : ℕ × ℕ \| p.Prime}).limsup (fun (p, k) => (f (p^k) / (p^k : ℝ).log : EReal)) = ⊤) → Filter.atTop.limsup (fun (n : ℕ) => (f (n+1) / f n : ERe...	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/897.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
erdosproblems-978-allow-fixed-divisors	formal-conjectures-bench/erdosproblems-978-allow-fixed-divisors	tasks/erdosproblems-978-allow-fixed-divisors	Erdos978.erdos_978.variants.allow_fixed_divisors	theorem erdos_978.variants.allow_fixed_divisors : answer(False) ↔ ∀ {f : ℤ[X]}, Irreducible f → f.natDegree > 3 → (¬ ∃ l : ℕ, f.natDegree = 2 ^ l) → 0 < f.leadingCoeff → (¬ ∃ p : ℕ, p.Prime ∧ ∀ n : ℕ, (p : ℤ) ^ (f.natDegree - 1) ∣ f.eval (n : ℤ)) → {n : ℕ \| Powerfree (f.natDegree - 2) (f.eval (n : ℤ))}....	google-deepmind/formal-conjectures	FormalConjectures/ErdosProblems/978.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
greensopenproblems-57-green-57	formal-conjectures-bench/greensopenproblems-57-green-57	tasks/greensopenproblems-57-green-57	Green57.green_57	theorem green_57 : answer(False) ↔ ∀ (G : Type) [AddCommGroup G] [Fintype G] [DecidableEq G], Φ G = Φ' G	google-deepmind/formal-conjectures	FormalConjectures/GreensOpenProblems/57.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
greensopenproblems-57-z3	formal-conjectures-bench/greensopenproblems-57-z3	tasks/greensopenproblems-57-z3	Green57.green_57.variants.z3	theorem green_57.variants.z3 : answer(False) ↔ (Φ (ZMod 3) = Φ' (ZMod 3))	google-deepmind/formal-conjectures	FormalConjectures/GreensOpenProblems/57.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
greensopenproblems-57-z3-functional	formal-conjectures-bench/greensopenproblems-57-z3-functional	tasks/greensopenproblems-57-z3-functional	Green57.green_57.variants.z3_functional	theorem green_57.variants.z3_functional : let a : ZMod 3 → ℂ := ![(-1 : ℂ), -3, 3] answer(True) ↔ supportFn (ZMod 3) a (Φ' (ZMod 3)) < supportFn (ZMod 3) a (Φ (ZMod 3))	google-deepmind/formal-conjectures	FormalConjectures/GreensOpenProblems/57.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
greensopenproblems-94-green-94-outer-measure	formal-conjectures-bench/greensopenproblems-94-green-94-outer-measure	tasks/greensopenproblems-94-green-94-outer-measure	Green94.green_94_outer_measure	theorem green_94_outer_measure : answer(False) ↔ ∀ A : Set ℝ, volume A > 0 → ∃ a b : ℝ, a ≠ 0 ∧ ∀ n : ℕ, a * (1 / 2^n) + b ∈ A	google-deepmind/formal-conjectures	FormalConjectures/GreensOpenProblems/94.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
mathoverflow-10799-mathoverflow-10799	formal-conjectures-bench/mathoverflow-10799-mathoverflow-10799	tasks/mathoverflow-10799-mathoverflow-10799	Mathoverflow10799.mathoverflow_10799	theorem mathoverflow_10799 : answer(False) ↔ ∀ (n : ℕ) (_ : 2 ≤ n) (F : Finset (Finset (Fin n))) (_ : IsMonotoneIncreasing F) (s t : ℝ) (_ : 0 < s) (_ : s ≤ t) (_ : t < 1) (_ : t / s > 1000 * Real.log n), ∃ p, s ≤ p ∧ p ≤ t ∧ IsOptimal p F	google-deepmind/formal-conjectures	FormalConjectures/Mathoverflow/10799.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
mathoverflow-486451-exists-semiring-unique-left-right-maximal-ne	formal-conjectures-bench/mathoverflow-486451-exists-semiring-unique-left-right-maximal-ne	tasks/mathoverflow-486451-exists-semiring-unique-left-right-maximal-ne	Mathoverflow486451.exists_semiring_unique_left_right_maximal_ne	theorem exists_semiring_unique_left_right_maximal_ne : answer(True) ↔ ∃ (R : Type) (_ : Semiring R) (hI : ∃! I : Ideal R, I.IsMaximal) (hJ : ∃! J : Ideal Rᵐᵒᵖ, J.IsMaximal), (hI.choose : Set R) ≠ MulOpposite.op ⁻¹' hJ.choose	google-deepmind/formal-conjectures	FormalConjectures/Mathoverflow/486451.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
openquantumproblems-13-mutuallyunbiasedbases-dim6-bounds	formal-conjectures-bench/openquantumproblems-13-mutuallyunbiasedbases-dim6-bounds	tasks/openquantumproblems-13-mutuallyunbiasedbases-dim6-bounds	OpenQuantumProblem13.mutuallyUnbiasedBases_dim6_bounds	theorem mutuallyUnbiasedBases_dim6_bounds : HasMUBs 6 3 ∧ ∀ m : ℕ, HasMUBs 6 m → m ≤ 7	google-deepmind/formal-conjectures	FormalConjectures/OpenQuantumProblems/13.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
openquantumproblems-35-ame-11-5-open	formal-conjectures-bench/openquantumproblems-35-ame-11-5-open	tasks/openquantumproblems-35-ame-11-5-open	OpenQuantumProblem35.ame_11_5_open	theorem ame_11_5_open : answer(True) ↔ ExistsAME 11 5	google-deepmind/formal-conjectures	FormalConjectures/OpenQuantumProblems/35.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-casasalvero-positive-char-counterexample	formal-conjectures-bench/paper-casasalvero-positive-char-counterexample	tasks/paper-casasalvero-positive-char-counterexample	CasasAlvero.casas_alvero.positive_char_counterexample	theorem casas_alvero.positive_char_counterexample {p : ℕ} (hp : p.Prime) : ∃ (K : Type*) (_ : Field K) (_ : CharP K p), let P := X ^ (p + 1) - X ^ p Monic P ∧ HasCasasAlveroProp P ∧ ¬∃ α : K, P = (X - C α) ^ P.natDegree	google-deepmind/formal-conjectures	FormalConjectures/Paper/CasasAlvero.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-claudescycles-cube-hamiltonian-arc-decomposition	formal-conjectures-bench/paper-claudescycles-cube-hamiltonian-arc-decomposition	tasks/paper-claudescycles-cube-hamiltonian-arc-decomposition	ClaudesCycles.cube_hamiltonian_arc_decomposition	theorem cube_hamiltonian_arc_decomposition {m : ℕ} [NeZero m] (hm : Odd m) (hm' : 1 < m) : HasHamiltonianArcDecomposition m	google-deepmind/formal-conjectures	FormalConjectures/Paper/ClaudesCycles.lean	gold_solution	bundled	no-explicit-license	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem-no-solution-even-ge4-d-eq-n-explicit	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem-no-solution-even-ge4-d-eq-n-explicit	tasks/paper-monochromaticquantumgraph-eqsystem-no-solution-even-ge4-d-eq-n-explicit	MonochromaticQuantumGraph.eqSystem_no_solution_even_ge4_d_eq_n_explicit	theorem eqSystem_no_solution_even_ge4_d_eq_n_explicit : answer(True) ↔ ∀ N : Nat, N ≥ 4 → Even N → ¬ ∃ W : WeightsN N N ℂ, EqSystemN N N W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem10-no-solution-d10	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem10-no-solution-d10	tasks/paper-monochromaticquantumgraph-eqsystem10-no-solution-d10	MonochromaticQuantumGraph.eqSystem10_no_solution_d10	theorem eqSystem10_no_solution_d10 : answer(True) ↔ ¬ ∃ W : WeightsN 10 10 ℂ, EqSystemN 10 10 W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem4-no-solution-d4	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem4-no-solution-d4	tasks/paper-monochromaticquantumgraph-eqsystem4-no-solution-d4	MonochromaticQuantumGraph.eqSystem4_no_solution_d4	theorem eqSystem4_no_solution_d4 : answer(True) ↔ ¬ ∃ W : WeightsN 4 4 ℂ, EqSystemN 4 4 W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4	tasks/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4	MonochromaticQuantumGraph.eqSystem4_no_solution_ge4	theorem eqSystem4_no_solution_ge4 : answer(True) ↔ ∀ D : Nat, D ≥ 4 → ¬ ∃ W : WeightsN 4 D ℂ, EqSystemN 4 D W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-int	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-int	tasks/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-int	MonochromaticQuantumGraph.eqSystem4_no_solution_ge4_int	theorem eqSystem4_no_solution_ge4_int : answer(True) ↔ ∀ D : Nat, D ≥ 4 → ¬ ∃ W : WeightsN 4 D ℤ, EqSystemN 4 D W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-real	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-real	tasks/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-real	MonochromaticQuantumGraph.eqSystem4_no_solution_ge4_real	theorem eqSystem4_no_solution_ge4_real : answer(True) ↔ ∀ D : Nat, D ≥ 4 → ¬ ∃ W : WeightsN 4 D ℝ, EqSystemN 4 D W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-trinary-int	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-trinary-int	tasks/paper-monochromaticquantumgraph-eqsystem4-no-solution-ge4-trinary-int	MonochromaticQuantumGraph.eqSystem4_no_solution_ge4_trinary_int	theorem eqSystem4_no_solution_ge4_trinary_int : answer(True) ↔ ∀ D : Nat, D ≥ 4 → ¬ ∃ W : WeightsN 4 D ℤ, (∀ e, W e = (-1 : ℤ) ∨ W e = 0 ∨ W e = 1) ∧ EqSystemN 4 D W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem6-no-solution-d6	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem6-no-solution-d6	tasks/paper-monochromaticquantumgraph-eqsystem6-no-solution-d6	MonochromaticQuantumGraph.eqSystem6_no_solution_d6	theorem eqSystem6_no_solution_d6 : answer(True) ↔ ¬ ∃ W : WeightsN 6 6 ℂ, EqSystemN 6 6 W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
paper-monochromaticquantumgraph-eqsystem8-no-solution-d10	formal-conjectures-bench/paper-monochromaticquantumgraph-eqsystem8-no-solution-d10	tasks/paper-monochromaticquantumgraph-eqsystem8-no-solution-d10	MonochromaticQuantumGraph.eqSystem8_no_solution_d10	theorem eqSystem8_no_solution_d10 : answer(True) ↔ ¬ ∃ W : WeightsN 8 10 ℂ, EqSystemN 8 10 W	google-deepmind/formal-conjectures	FormalConjectures/Paper/MonochromaticQuantumGraph.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
wikipedia-agohgiuga-isweakgiuga-iff-prime-dvd	formal-conjectures-bench/wikipedia-agohgiuga-isweakgiuga-iff-prime-dvd	tasks/wikipedia-agohgiuga-isweakgiuga-iff-prime-dvd	AgohGiuga.isWeakGiuga_iff_prime_dvd	theorem isWeakGiuga_iff_prime_dvd {n : ℕ} (hn : n.Composite) : IsWeakGiuga n ↔ ∀ p ∈ n.primeFactors, p ∣ (n / p - 1)	google-deepmind/formal-conjectures	FormalConjectures/Wikipedia/AgohGiuga.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
wikipedia-eulerbrick-cuboidone	formal-conjectures-bench/wikipedia-eulerbrick-cuboidone	tasks/wikipedia-eulerbrick-cuboidone	EulerBrick.cuboidOne	theorem cuboidOne : CuboidOne	google-deepmind/formal-conjectures	FormalConjectures/Wikipedia/EulerBrick.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
wikipedia-legendreconjecture-bounded-gap-legendre	formal-conjectures-bench/wikipedia-legendreconjecture-bounded-gap-legendre	tasks/wikipedia-legendreconjecture-bounded-gap-legendre	LegendreConjecture.bounded_gap_legendre	theorem bounded_gap_legendre (H : ∃ c > 0, ∀ᶠ n in atTop, (n + 1).nth Nat.Prime - n.nth Nat.Prime < (n.nth Nat.Prime : ℝ) ^ (1 / (2 : ℝ) - c)) : ∀ᶠ n in atTop, ∃ p ∈ Set.Ioo (n ^ 2) ((n + 1) ^ 2), Nat.Prime p	google-deepmind/formal-conjectures	FormalConjectures/Wikipedia/LegendreConjecture.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
wikipedia-perfectnumbers-euler-form	formal-conjectures-bench/wikipedia-perfectnumbers-euler-form	tasks/wikipedia-perfectnumbers-euler-form	PerfectNumbers.odd_perfect_number.euler_form	theorem odd_perfect_number.euler_form (n : ℕ) (hn : Odd n) (hp : Perfect n) : ∃ (p m α : ℕ), p.Prime ∧ p ≡ 1 [ZMOD 4] ∧ α ≡ 1 [ZMOD 4] ∧ ¬ p ∣ m ∧ n = p^α * m^2	google-deepmind/formal-conjectures	FormalConjectures/Wikipedia/PerfectNumbers.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
wikipedia-wolstenholmeprime-wolstenholme-prime-16483	formal-conjectures-bench/wikipedia-wolstenholmeprime-wolstenholme-prime-16483	tasks/wikipedia-wolstenholmeprime-wolstenholme-prime-16483	WolstenholmePrime.wolstenholme_prime_16483	theorem wolstenholme_prime_16483 : IsWolstenholmePrime 16843	google-deepmind/formal-conjectures	FormalConjectures/Wikipedia/WolstenholmePrime.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400
wikipedia-wolstenholmeprime-wolstenholme-theorem	formal-conjectures-bench/wikipedia-wolstenholmeprime-wolstenholme-theorem	tasks/wikipedia-wolstenholmeprime-wolstenholme-theorem	WolstenholmePrime.wolstenholme_theorem	theorem wolstenholme_theorem (p : ℕ) (h : p > 3) (hp : Nat.Prime p) : (2 * p - 1).choose (p - 1) ≡ 1 [MOD p ^ 3]	google-deepmind/formal-conjectures	FormalConjectures/Wikipedia/WolstenholmePrime.lean	gold_solution	bundled	Apache-2.0	bundled	233a10e857ef78e79fd9fe661d37db724089170a	leanprover/lean4:v4.27.0	a3a10db0e9d66acbebf76c5e6a135066525ac900	false	86,400	7,200	14,400

FormalConjectures-Bench Gold

FormalConjectures-Bench Gold v1.1.0 is a set of 74 offline Lean 4 theorem-proving tasks with bundled oracle solutions. The executable benchmark is distributed as a Harbor dataset; this Hugging Face dataset is the metadata and discovery mirror.

The benchmark is intended for evaluation or RL. Benchmark target files and oracle solutions should not be included in training corpora.

Running

Install Harbor and run the registry-backed dataset:

uv tool install harbor

harbor run \
  --dataset formal-conjectures-gold@1.1.0 \
  --registry-url https://raw.githubusercontent.com/AllenGrahamHart/FormalConjectures-Bench/v1.1.0/registry.json \
  --agent terminus-2 \
  --model <provider/model>

Run a single task:

harbor run \
  --dataset formal-conjectures-gold@1.1.0 \
  --registry-url https://raw.githubusercontent.com/AllenGrahamHart/FormalConjectures-Bench/v1.1.0/registry.json \
  --task-name erdosproblems-399-erdos-399 \
  --agent terminus-2 \
  --model <provider/model>

The release defaults are intentionally generous: 24 hours for agent execution, 2 hours for verification, and 4 hours for environment builds. Use Harbor's timeout multiplier to scale them:

harbor run \
  --dataset formal-conjectures-gold@1.1.0 \
  --registry-url https://raw.githubusercontent.com/AllenGrahamHart/FormalConjectures-Bench/v1.1.0/registry.json \
  --timeout-multiplier 0.25

Files

tasks.jsonl contains one metadata row per task.
The executable task directories live in the GitHub repository.
registry.json in the GitHub repository is the Harbor dataset registry.

Versions

Dataset: formal-conjectures-gold@1.1.0
Task source commit: a3674901510f2f8d8a8c1de0c28c568fcd48828e
Lean toolchain: leanprover/lean4:v4.27.0
Mathlib commit: a3a10db0e9d66acbebf76c5e6a135066525ac900
Formal Conjectures commit: 233a10e857ef78e79fd9fe661d37db724089170a

Licensing

The task statements derive from Google DeepMind's Formal Conjectures project. Bundled oracle metadata is recorded per task in tasks.jsonl; the source repository also includes manifest/licence_review.csv.

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