id stringlengths 6 8 | alias stringlengths 24 50 | problem stringlengths 24 5.03k | answer int64 -16,384 80.2B | graph stringlengths 0 6.44k | domain stringclasses 4
values | secondary_domain stringclasses 4
values | goal stringclasses 4
values | evaluator_id stringclasses 1
value | root_lemma stringclasses 89
values | lemma_paths listlengths 0 5 | recipe_id stringlengths 0 6 | seed_template_id stringclasses 96
values | ending_id stringclasses 13
values | olympiad_level int64 2 9 | num_spawns int64 0 3 ⌀ | lemma_set listlengths 1 7 ⌀ | num_lemmas int64 1 7 ⌀ | generation_time float64 0 43.9 | created_at stringlengths 27 27 | verification dict | problem_hash stringlengths 6 6 | parent_id stringlengths 0 6 | variant stringclasses 3
values | license stringclasses 1
value | llm_solvers listlengths 1 13 ⌀ | solution_status int64 0 2 ⌀ | lemma_applicability listlengths 0 12 | irt_difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ec0a23 | nt_count_divisors_in_range_v1_168721529_386 | Let $n = 221760$ and $a = 41$. Let $b$ be the sum of all real solutions $x$ to the equation
$$
x^2 - 1683x + 120600 = 0.
$$
Let $r$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$.
Compute $1089 - r$. | 999 | graphs = [
Graph(
let={
"n": Const(221760),
"a": Const(41),
"b": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-1683), Var("x")), Const(120600)), Const(0)))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"),... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.079 | 2026-02-08T13:01:58.522467Z | {
"verified": true,
"answer": 999,
"timestamp": "2026-02-08T13:01:58.601767Z"
} | c49ca5 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 677
},
"timestamp": "2026-02-09T16:09:47.490Z",
"answer": 949
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -1.9,
"mid": 2.34,
"hi": 6.68
} | ||
bd3f20 | lin_form_endings_v1_784195855_5822 | Let $S$ be the set of all integers $t$ such that $37 \leq t \leq 969$ and there exist positive integers $a \leq 52$ and $b \leq 17$ for which $t = 12a + 20b + 5$. Let $r$ be the number of elements in $S$. Compute the remainder when $17724 \cdot r$ is divided by $77057$. | 75,717 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=52)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:07:31.587226Z | {
"verified": true,
"answer": 75717,
"timestamp": "2026-02-08T08:07:31.588303Z"
} | 9618b2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T09:00:04.779Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
a5c575 | antilemma_k3_v1_865884756_6989 | Let $n = 65457$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 65,457 | graphs = [
Graph(
let={
"_n": Const(65457),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T19:29:30.141271Z | {
"verified": true,
"answer": 65457,
"timestamp": "2026-02-08T19:29:30.141706Z"
} | 1aac67 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 342
},
"timestamp": "2026-02-16T18:41:42.671Z",
"answer": 65766
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
f10c24 | algebra_poly_eval_v1_1978505735_6327 | Let $z = 16$. Let $T$ be the set of all integers $t$ with $5 \leq t \leq 14$ for which there exist positive integers $a \leq 2$ and $b \leq 4$ such that $t = 3a + 2b$. Let $c$ be the number of elements in $T$. Compute $c \cdot z^2 + z + 3$. | 2,067 | graphs = [
Graph(
let={
"z": Const(16),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Ge... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T19:33:21.649691Z | {
"verified": true,
"answer": 2067,
"timestamp": "2026-02-08T19:33:21.651386Z"
} | 4fe264 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 683
},
"timestamp": "2026-02-16T18:41:17.975Z",
"answer": 1793
},
{
"id": 11,... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a3e652 | comb_binomial_compute_v1_151522320_301 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8100$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum element of $T$. Define $n$ to be the number of positive integers $k$ such that $1 \leq k \leq m$ and the $k$-th Fibonacci number is divisible... | 29,791 | graphs = [
Graph(
let={
"_m": Const(99237),
"_n": Const(80149),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | ALG | NT | COMPUTE | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | comb_binomial_compute_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.002 | 2026-02-08T03:08:53.006874Z | {
"verified": true,
"answer": 29791,
"timestamp": "2026-02-08T03:08:53.009272Z"
} | 87d464 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 3607
},
"timestamp": "2026-02-10T13:08:23.765Z",
"answer": 29791
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
df90f0 | nt_count_coprime_v1_1520064083_7615 | Let $k$ be the number of integers $t$ such that $28 \leq t \leq 120$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 7$, and $t = 14a + 6b + 8$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 13689$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 9,388 | graphs = [
Graph(
let={
"upper": Const(13689),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.177 | 2026-02-08T09:12:48.479314Z | {
"verified": true,
"answer": 9388,
"timestamp": "2026-02-08T09:12:49.655878Z"
} | 6c89d5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 2020
},
"timestamp": "2026-02-14T01:33:25.866Z",
"answer": 9388
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9b28ec | nt_num_divisors_compute_v1_1742523217_2466 | Let $n = \sum_{d \mid 4225} \varphi(d)$, where $\varphi$ denotes Euler's totient function. Compute the number of positive divisors of $n$. | 9 | graphs = [
Graph(
let={
"_n": Const(4225),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T04:47:22.633918Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T04:47:22.636104Z"
} | 864ab3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 467
},
"timestamp": "2026-02-11T22:04:06.856Z",
"answer": 9
},
{
"id":... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
59651a | comb_count_derangements_v1_655260480_1006 | Let $n$ be the number of integers $j$ with $0 \le j \le 41024$ such that $\binom{41024}{j}$ is odd. Define $Q = 31329 - !n$, where $!n$ denotes the subfactorial of $n$. Compute $Q$. | 16,496 | graphs = [
Graph(
let={
"_n": Const(41024),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(41024)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T15:51:49.556262Z | {
"verified": true,
"answer": 16496,
"timestamp": "2026-02-08T15:51:49.558305Z"
} | 1bb1b8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 675
},
"timestamp": "2026-02-24T18:52:24.938Z",
"answer": 16496
},
{
"... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
9aaf09 | comb_count_surjections_v1_1125832087_2348 | Let $T$ be the set of integers $t$ such that $10 \leq t \leq 28$ and there exist integers $a$, $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 6a + 4b$. Let $m = |T|$.
Let $S$ be the set of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 8$, $1 \leq j \leq 8$, and $i + j = m$. Let $n = |S|$.
Let $... | 30,920 | graphs = [
Graph(
let={
"_c": Const(14),
"_m": Const(70696),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), righ... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COMB1"
] | 81e769 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.012 | 2026-02-08T04:34:17.756992Z | {
"verified": true,
"answer": 30920,
"timestamp": "2026-02-08T04:34:17.769390Z"
} | 4f217a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 342,
"completion_tokens": 1054
},
"timestamp": "2026-02-24T01:01:10.342Z",
"answer": 30920
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
e1c2da | nt_min_coprime_above_v1_168721529_1140 | Let $p$ be the largest prime number satisfying $2 \leq p \leq 1577$. Let $n$ be the smallest integer greater than $p$ and at most $2048$ such that $\gcd(n, 467) = 1$. Let $m = 2n + 3$. Compute the multiplicative order of $2$ modulo $m$. | 262 | graphs = [
Graph(
let={
"start": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1577)), IsPrime(Var("n"))))),
"upper": Const(2048),
"modulus": Const(467),
"result": MinOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.085 | 2026-02-08T13:29:59.251265Z | {
"verified": true,
"answer": 262,
"timestamp": "2026-02-08T13:29:59.335915Z"
} | ebf43e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 5575
},
"timestamp": "2026-02-09T14:05:18.631Z",
"answer": 262
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
0f4c3e | modular_sum_quadratic_residues_v1_151522320_2437 | Let $ p $ be the largest prime number less than or equal to $ 258 $. Compute $ \frac{p(p-1)}{4} $. | 16,448 | graphs = [
Graph(
let={
"_n": Const(258),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:48:16.098460Z | {
"verified": true,
"answer": 16448,
"timestamp": "2026-02-08T04:48:16.099483Z"
} | 163a88 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 244
},
"timestamp": "2026-02-11T22:07:06.049Z",
"answer": 16448
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
6f8b3a | comb_bell_compute_v1_151522320_214 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 3150$, and $\gcd(p, q) = 1$. Let $r$ be the $n$-th Bell number, which counts the number of partitions of an $n$-element set. Compute the remainder when $23705 \cdot r$ is divided by $79066$. | 17,794 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=3150)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T03:03:54.987136Z | {
"verified": true,
"answer": 17794,
"timestamp": "2026-02-08T03:03:54.988097Z"
} | 4b92c2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1928
},
"timestamp": "2026-02-10T13:04:34.486Z",
"answer": 17794
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
fd2cf9 | diophantine_fbi2_count_v1_1915831931_1962 | Let $p_1, p_2, \ldots, p_m$ be the prime numbers satisfying $2 \leq p_i \leq 5$. Define $A$ to be the set of all positive integers $d$ such that:
- $d \geq \max\{p_1, p_2, \ldots, p_m\}$,
- $d \leq 92$,
- $d$ divides 180,
- $6 \leq \frac{180}{d} \leq 93$.
Let $r$ be the number of elements in $A$. Compute the value of... | 521 | graphs = [
Graph(
let={
"_n": Const(63068),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n")))))), ... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.014 | 2026-02-08T16:33:10.048443Z | {
"verified": true,
"answer": 521,
"timestamp": "2026-02-08T16:33:10.062186Z"
} | ab4b89 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1155
},
"timestamp": "2026-02-17T06:50:37.480Z",
"answer": 521
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e4ae93 | sequence_count_fib_divisible_v1_1742523217_2001 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 228484$. Let $m$ be the minimum value of $x + y$ over all pairs in $S$. Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 12$ and $\gcd(p, q) = 1$. Let $c$ be the number ... | 191 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(228484)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3"
] | fdc414 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 4 | 0.055 | 2026-02-08T04:24:37.195104Z | {
"verified": true,
"answer": 191,
"timestamp": "2026-02-08T04:24:37.249983Z"
} | 41b2db | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 3264
},
"timestamp": "2026-02-10T16:25:50.577Z",
"answer": 191
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
867b91 | diophantine_product_count_v1_168721529_1709 | Let $k = 120$. Define $T$ as the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 2$, $1 \leq j \leq 66$, and $\gcd(i, j) = 1$. Let $u$ be the number of elements in $T$. Now, define $R$ as the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} ... | 14 | graphs = [
Graph(
let={
"k": Const(120),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), e... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.038 | 2026-02-08T13:53:11.009535Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T13:53:11.047940Z"
} | 557b51 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1541
},
"timestamp": "2026-02-09T20:34:10.811Z",
"answer": 14
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
58daed | antilemma_cartesian_v1_1520064083_7213 | Compute the number of ordered pairs $(a, b)$ such that $a$ and $b$ are integers with $1 \leq a \leq 8$ and $1 \leq b \leq 19$. | 152 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(19)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T08:50:37.143309Z | {
"verified": true,
"answer": 152,
"timestamp": "2026-02-08T08:50:37.143545Z"
} | 4c7ea1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 196
},
"timestamp": "2026-02-24T10:04:02.111Z",
"answer": 152
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
828baa | modular_sum_quadratic_residues_v1_1918700295_1361 | Let $n = 2$. Define $p$ to be the smallest divisor of $12432181$ that is at least $n$. Compute the value of $\frac{p(p-1)}{4}$. | 13,053 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(12432181))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T05:48:06.733233Z | {
"verified": true,
"answer": 13053,
"timestamp": "2026-02-08T05:48:06.734215Z"
} | 5739a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 2104
},
"timestamp": "2026-02-12T14:17:31.992Z",
"answer": 13053
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
bae116 | nt_count_coprime_and_v1_677425708_506 | Let $k_1$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 16$. Let $k_2 = 9$.
Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 5055$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$.
Compute the number of elements in $S$. | 1,685 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(5055),
"k1": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.895 | 2026-02-08T03:34:49.093959Z | {
"verified": true,
"answer": 1685,
"timestamp": "2026-02-08T03:34:49.988521Z"
} | baba1a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 765
},
"timestamp": "2026-02-10T04:54:33.574Z",
"answer": 1685
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d4c245 | comb_count_surjections_v1_1520064083_9044 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k = 3$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $44121 \cdot \text{result}$ is divided by $82157$. Compute $Q$. | 72,393 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T10:30:41.876362Z | {
"verified": true,
"answer": 72393,
"timestamp": "2026-02-08T10:30:41.878919Z"
} | 654c02 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2190
},
"timestamp": "2026-02-24T12:05:16.582Z",
"answer": 72393
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
65bc68 | comb_count_partitions_v1_971394319_153 | Let $n$ be the number of positive integers $k$ such that $1 \le k \le 8036$ and $196$ divides $k$. Determine the value of the number of integer partitions of $n$. | 44,583 | graphs = [
Graph(
let={
"_n": Const(196),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(8036)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": Partition(arg=Ref(name='n'... | NT | COMB | COUNT | sympy | C2 | [
"C2"
] | 9685eb | comb_count_partitions_v1 | null | 5 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T12:51:32.326257Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T12:51:32.327260Z"
} | 886f43 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 657
},
"timestamp": "2026-02-15T06:53:08.809Z",
"answer": 44583
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e17982 | nt_sum_totient_over_divisors_v1_677425708_333 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 20985561$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute $\sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. | 9,162 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(20985561)))), expr=Sum(Var("x"), Var("y")))),
"result": SumO... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T03:13:22.972958Z | {
"verified": true,
"answer": 9162,
"timestamp": "2026-02-08T03:13:22.976744Z"
} | c25984 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 4454
},
"timestamp": "2026-02-08T20:27:51.408Z",
"answer": 9162
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
7f27f1 | algebra_quadratic_discriminant_v1_1874849503_752 | Let $a=2$, $b=-2$, and $c=-24$. Define
$$D=b^2-4ac.$$
Compute $D$. | 196 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(-2),
"c": Const(-24),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"LTE_SUM/MOBIUS_COPRIME/MAX_DIVISOR/B1",
"LIN_FORM/MAX_DIVISOR/B1"
] | 2463ce | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B1",
"BINOMIAL_ALTERNATING",
"LIN_FORM",
"LTE_SUM",
"MAX_DIVISOR",
"MOBIUS_COPRIME"
] | 6 | 0.053 | 2026-02-08T13:16:49.692636Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-08T13:16:49.745952Z"
} | 3f28b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 100
},
"timestamp": "2026-02-09T20:32:12.833Z",
"answer": 196
},
{
"id"... | 2 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
c0c945 | modular_product_range_v1_124444284_86 | Let $a = 561073402121731173607666208963712157775646236340963964052513752233891761335201$ and $b = 1806603476925444932335424721892206685421837981932696835378964188981494974061222060845344519871619704007$. Let $k$ be the largest integer such that $7^k$ divides $a \cdot b$. Define $P = \prod_{i=16}^{k} i$. Compute the rem... | 4,299 | graphs = [
Graph(
let={
"_n": Const(10259),
"prod": MathProduct(expr=Var("i"), var="i", start=Const(16), end=MaxKDivides(target=Mul(Const(561073402121731173607666208963712157775646236340963964052513752233891761335201), Const(18066034769254449323354247218922066854218379819326968353789... | NT | null | COMPUTE | sympy | K13 | [
"K13"
] | 8d970a | modular_product_range_v1 | null | 5 | 0 | [
"K13"
] | 1 | 0.004 | 2026-02-08T02:57:42.836133Z | {
"verified": true,
"answer": 4299,
"timestamp": "2026-02-08T02:57:42.840178Z"
} | b1a6db | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 341,
"completion_tokens": 532
},
"timestamp": "2026-02-17T16:34:54.898Z",
"answer": 10952
}
] | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
6b0341 | nt_sum_totient_over_divisors_v1_865884756_502 | Let $n = 44021$ and $N = 55207$. Let $R = \sum_{d \mid n} \varphi(d)$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 53361000$, $\gcd(p, q) = 1$, and $p < q$. Let $C$ be the number of elements in $S$. Let $M$ be the maximum value of $xy$ over all pairs of ... | 16,780 | graphs = [
Graph(
let={
"_n": Const(55207),
"n": Const(44021),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B1"
] | 838c69 | nt_sum_totient_over_divisors_v1 | quadratic_mod | 5 | 0 | [
"B1",
"COPRIME_PAIRS"
] | 2 | 0.006 | 2026-02-08T15:27:28.195307Z | {
"verified": true,
"answer": 16780,
"timestamp": "2026-02-08T15:27:28.200930Z"
} | 3922fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2994
},
"timestamp": "2026-02-16T06:24:25.817Z",
"answer": 16780
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8a4b82 | nt_count_divisors_in_range_v1_1520064083_3342 | Let $N=50400$, $a=16$, $b=1686$, and $c=6889$.
Let $D$ be the set of all positive integers $d$ such that $d$ divides $N$ and $a\le d\le b$. Let $R$ be the number of elements in $D$.
Write $|R|$ in base $10$, and let it have $k$ digits. For each integer $i$ with $0\le i\le k-1$, let $d_i$ be the $i$-th decimal digit o... | 6,922 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(50400),
"a": Const(16),
"b": Const(1686),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Re... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/SUM_PRIMES/L3C"
] | c1e306 | nt_count_divisors_in_range_v1 | digits_weighted_mod | 7 | 0 | [
"L3C",
"MAX_DIVISOR",
"SUM_PRIMES"
] | 3 | 0.027 | 2026-02-08T05:35:56.418511Z | {
"verified": true,
"answer": 6922,
"timestamp": "2026-02-08T05:35:56.445945Z"
} | 67e508 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 385,
"completion_tokens": 3606
},
"timestamp": "2026-02-12T10:53:44.787Z",
"answer": 6922
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a8e0ef | comb_bell_compute_v1_1520064083_3550 | Let $n$ be the number of integers $j$ with $0\le j\le 1408$ such that the binomial coefficient $\binom{1408}{j}$ is odd. Let $B_n$ denote the $n$th Bell number, the number of ways to partition a set of $n$ elements into nonempty subsets. Compute $B_n$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(1408),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(1408), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 8 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T05:44:11.148128Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T05:44:11.148976Z"
} | c609bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 705
},
"timestamp": "2026-02-24T04:27:15.097Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
bd4d84 | geo_visible_lattice_v1_458359167_3855 | Let $n = 50$. Define $\text{result}$ as the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$, where a point $(x, y)$ is visible if $\gcd(x, y) = 1$. Let $Q$ be the remainder when $44121 \cdot \text{result}$ is divided by $83417$. Compute $Q$. | 20,081 | graphs = [
Graph(
let={
"n": Const(50),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(83417)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.119 | 2026-02-08T11:23:52.999395Z | {
"verified": true,
"answer": 20081,
"timestamp": "2026-02-08T11:23:53.118450Z"
} | 2f2f29 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 9896
},
"timestamp": "2026-02-24T13:46:16.526Z",
"answer": 20081
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
171241 | diophantine_product_count_v1_151522320_1099 | Let $N = 32400$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = N$. Let $T$ be the set of all integers $t$ with $18 \leq t \leq 458$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 17$ and $1 \leq b \leq 36$, such that $t = 10a + 8b$.... | 22 | graphs = [
Graph(
let={
"_n": Const(32400),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 3 | 21.387 | 2026-02-08T03:48:07.160600Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T03:48:28.547398Z"
} | 8cda5d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 6183
},
"timestamp": "2026-02-10T14:28:16.544Z",
"answer": 22
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
248139 | nt_count_divisible_v1_548369836_346 | Let $A$ be the set of all integers $n$ such that $0 \leq n \leq 39601$, $n$ is divisible by $24$, and $n \geq \sum_{d \mid \gcd(3,5)} \mu(d)$. Determine the number of elements in $A$. | 1,650 | graphs = [
Graph(
let={
"upper": Const(39601),
"divisor": Const(24),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=3), b=Const(value=5)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Ref(... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 1.258 | 2026-02-08T02:52:52.643394Z | {
"verified": true,
"answer": 1650,
"timestamp": "2026-02-08T02:52:53.901498Z"
} | 294663 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 777
},
"timestamp": "2026-02-08T20:21:44.547Z",
"answer": 1650
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"st... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.74
} | ||
6e7606 | geo_count_lattice_rect_v1_458359167_3029 | Compute the number of lattice points in the rectangle $[0, 111] \times [0, 127]$, including the boundary. | 14,336 | graphs = [
Graph(
let={
"a": Const(111),
"b": Const(127),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T06:53:59.487125Z | {
"verified": true,
"answer": 14336,
"timestamp": "2026-02-08T06:53:59.488091Z"
} | b19e85 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 211
},
"timestamp": "2026-02-24T07:16:03.187Z",
"answer": 14336
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
66defe | modular_count_residue_v1_168721529_167 | Let $a$ be the greatest common divisor of 11 and 13. Define $S$ as the set of all integers $n$ such that $n \geq \sum_{d \mid a} \mu(d)$, $n \leq 53361$, and $n \equiv 1 \pmod{6}$. Let $r$ be the number of elements in $S$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $... | 1,104 | graphs = [
Graph(
let={
"upper": Const(53361),
"m": Const(6),
"r": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=11), b=Const(value=13)), var='d', expr=MoebiusMu(n=Var(name='d'))... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_count_residue_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 2.435 | 2026-02-08T12:52:12.098287Z | {
"verified": true,
"answer": 1104,
"timestamp": "2026-02-08T12:52:14.533594Z"
} | 445b31 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1999
},
"timestamp": "2026-02-10T00:44:14.608Z",
"answer": 1104
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -6.5,
"mid": 0,
"hi": 6.5
} | ||
572d84 | antilemma_sum_equals_v1_1978505735_6036 | Let $m$ be the number of ordered pairs $(i, j)$ where $i$ is an integer from 1 to 6 and $j$ is an integer from 1 to 11. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 65$, $1 \leq j \leq 66$, such that $i + j = m$. Compute the number of ordered pairs $(i_1, j_1)$ of positive in... | 64 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(11)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Re... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | fb4a94 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.04 | 2026-02-08T19:23:35.583827Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T19:23:35.623497Z"
} | 946ae8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1193
},
"timestamp": "2026-02-18T22:09:16.662Z",
"answer": 64
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
898e0d | modular_modexp_compute_v1_601307018_8458 | Let $e$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 2426600$. Let $M = 13^e \bmod 11399$. Find the remainder when $43487M$ is divided by $98142$. | 54,775 | graphs = [
Graph(
let={
"_n": Const(43487),
"a": Const(13),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2426600)))),... | NT | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | modular_modexp_compute_v1 | null | 4 | 0 | [
"B3_DIFF"
] | 1 | 0.005 | 2026-03-10T08:57:00.931659Z | {
"verified": true,
"answer": 54775,
"timestamp": "2026-03-10T08:57:00.937049Z"
} | 955a2c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 6362
},
"timestamp": "2026-04-19T09:06:15.007Z",
"answer": 54775
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e8547b | nt_sum_over_divisible_v1_1116507919_384 | Let $ p $ be the largest prime number less than or equal to 5944. Compute the sum of all positive integers $ n $ such that $ 1 \leq n \leq p $ and $ n $ is divisible by 195. | 90,675 | graphs = [
Graph(
let={
"_n": Const(5944),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"divisor": Const(195),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | SUM | sympy | K2 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 6.988 | 2026-02-08T02:33:08.024086Z | {
"verified": true,
"answer": 90675,
"timestamp": "2026-02-08T02:33:15.011689Z"
} | af6044 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1507
},
"timestamp": "2026-02-08T19:27:57.223Z",
"answer": 90675
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.84,
"mid": -0.85,
"hi": 1.08
} | ||
627be1 | alg_poly3_sum_v1_1218484723_1642 | Let $T = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ 10a_1^2 - 18a_1b_1 + 25b_1^2 \le 3877 \}\right|$. Find the remainder when $$\sum_{a=1}^{23} \sum_{b=1}^{23} \sum_{c=1}^{23} \left( 19c^3 - 42b c^2 + 30b^2 c + 277a^3 + 171a c^2 + 177a^2 b + T a b^2 + 171a^2 c + 57b^3 - 216a b c \right)$$ is divided by $81394$. | 61,646 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(23)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(23)), Geq(Var("c"),... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.064 | 2026-02-25T03:20:40.776405Z | {
"verified": true,
"answer": 61646,
"timestamp": "2026-02-25T03:20:40.840570Z"
} | 68b29c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 7532
},
"timestamp": "2026-03-29T00:40:07.902Z",
"answer": 61646
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
81a87d | diophantine_fbi2_min_v1_1439011603_1664 | Let $T$ be the set of integers $t$ such that $19 \leq t \leq 173$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 22$, and $t = 10a + 4b + 5$. Let $u$ be the number of elements in $T$. Let $d$ be a positive integer such that $3 \leq d \leq u$, $d$ divides 64, and $\frac{64}{d} \geq ... | 4 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(64),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.012 | 2026-02-08T16:12:49.368869Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T16:12:49.380970Z"
} | 57d7e8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2906
},
"timestamp": "2026-02-16T22:56:27.210Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHME... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
43c04c | diophantine_product_count_v1_717093673_3649 | Let $t$ be an integer such that $10 \leq t \leq 318$ and there exist integers $a$ and $b$ with $1 \leq a \leq 15$, $1 \leq b \leq 39$, and $t = 3a + 7b$. Let $\text{upper}$ be the number of such integers $t$. Let $k = 420$. Define $x$ to be a positive integer such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and... | 1,324 | graphs = [
Graph(
let={
"_n": Const(36),
"k": Const(420),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), righ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.025 | 2026-02-08T17:45:00.742427Z | {
"verified": true,
"answer": 1324,
"timestamp": "2026-02-08T17:45:00.767782Z"
} | 8de4e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 5232
},
"timestamp": "2026-02-18T07:14:15.448Z",
"answer": 1324
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a51ffc | comb_count_surjections_v1_238844314_833 | Let $r$ be the value of $2!\cdot S(6,2)$, where $S(6,2)$ is the number of ways to partition a $6$-element set into $2$ nonempty unlabeled subsets.
Let $T$ be the set of all integers $t$ such that $5\le t\le 22$ and there exist integers $a$ and $b$ with $1\le a\le 5$, $1\le b\le 4$, and
$$t=2a+3b.$$
Let $N$ be the numb... | 104 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(6),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Binom(n=CountOverSet(set=Solu... | COMB | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM/ONE_BINOM_N",
"ONE_BINOM_0"
] | 4eeaec | comb_count_surjections_v1 | arith_invariants | 5 | 0 | [
"LIN_FORM",
"ONE_BINOM_0",
"ONE_BINOM_N"
] | 3 | 0.006 | 2026-02-08T13:38:40.159507Z | {
"verified": true,
"answer": 104,
"timestamp": "2026-02-08T13:38:40.165478Z"
} | 343407 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 349,
"completion_tokens": 1260
},
"timestamp": "2026-02-24T18:44:55.563Z",
"answer": 104
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
b192bc | nt_count_divisors_in_range_v1_124444284_3281 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = 14288400$. Let $n$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive divisors $d$ of $n$ such that $6 \leq d \leq 639$. Compute the remainder when $22367$ times this number is divided by $902... | 13,151 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(6),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T05:20:15.480919Z | {
"verified": true,
"answer": 13151,
"timestamp": "2026-02-08T05:20:15.490998Z"
} | 9ecaab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 3710
},
"timestamp": "2026-02-12T06:44:46.479Z",
"answer": 13151
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1924dc | comb_count_surjections_v1_1918700295_3695 | Let $n = 4$ and $k = 2$. Let $s = k! \cdot S(n,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Compute $\sum_{i=0}^{|s|} \phi(i)$, where $\phi$ denotes Euler's totient function and the summation runs over all integers $i$ from $0!$ to $|s|$ inclusive. | 64 | graphs = [
Graph(
let={
"n": Const(4),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Summation(var="n", start=Factorial(Const(0)), end=Abs(arg=Ref(name='result')), expr=EulerPhi(n=Var("n"))),
},
... | COMB | NT | COUNT | sympy | ONE_FACTORIAL_0 | [
"ONE_FACTORIAL_0"
] | 7064c7 | comb_count_surjections_v1 | null | 4 | 0 | [
"ONE_FACTORIAL_0"
] | 1 | 0.002 | 2026-02-08T08:50:00.714398Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T08:50:00.716612Z"
} | 5776a7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 941
},
"timestamp": "2026-02-24T10:00:33.690Z",
"answer": 64
},
{
"id":... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
bcabff | nt_count_coprime_and_v1_1978505735_2120 | Let $U=40172$. Let $k_1$ be the smallest integer $d\ge 2$ such that $d$ divides $35$, and let $k_2=7$.
Let $R$ be the number of integers $n$ such that
\[1\le n\le U,\quad \gcd(n,k_1)=1,\quad \gcd(n,k_2)=1.
\]
Let $M$ be the number of ordered pairs $(x_1,x_2)$ of positive integers such that $x_1$ and $x_2$ are odd and... | 16,593 | graphs = [
Graph(
let={
"upper": Const(40172),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(35))))),
"k2": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | null | COUNT | sympy | COMB1 | [
"COMB1/SUM_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | ca5cf9 | nt_count_coprime_and_v1 | affine_mod | 6 | 0 | [
"COMB1",
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 3 | 5.125 | 2026-02-08T16:40:18.622919Z | {
"verified": true,
"answer": 16593,
"timestamp": "2026-02-08T16:40:23.747956Z"
} | bad77f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 2295
},
"timestamp": "2026-02-17T08:57:06.562Z",
"answer": 16593
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
047cca | sequence_fibonacci_compute_v1_1915831931_2600 | Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 308$ and there exist positive integers $a \leq 18$ and $b \leq 32$ satisfying $t = 10a + 4b$. Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = |T|$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 ... | 46,368 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=18)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T16:58:07.373098Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T16:58:07.376780Z"
} | 579503 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 3927
},
"timestamp": "2026-02-17T17:16:22.794Z",
"answer": 46368
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c782a | sequence_fibonacci_compute_v1_655260480_919 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 100$. Let $F_n$ denote the $n$th Fibonacci number. Compute the remainder when $44121 \cdot F_n$ is divided by 93565. | 6,215 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T15:44:55.175395Z | {
"verified": true,
"answer": 6215,
"timestamp": "2026-02-08T15:44:55.177385Z"
} | b3a641 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1730
},
"timestamp": "2026-02-16T12:54:37.338Z",
"answer": 6215
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9b7215 | antilemma_k3_v1_1978505735_3099 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $94764$, where $\phi$ denotes Euler's totient function. | 94,764 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=94764), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T17:20:50.419448Z | {
"verified": true,
"answer": 94764,
"timestamp": "2026-02-08T17:20:50.419893Z"
} | d6731e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 432
},
"timestamp": "2026-02-16T09:39:10.098Z",
"answer": 1080
},
{
"id": 11,
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
6d93e2 | comb_binomial_compute_v1_601307018_5176 | For each integer $a$ with $0 \le a \le 66$, define the sequence $M = a^2 + a - 19 \bmod 67$, $R = M^2 + M - 19 \bmod 67$, $S = R^2 + R - 19 \bmod 67$, $T = S^2 + S - 19 \bmod 67$, $K = T^2 + T - 19 \bmod 67$. Let $n$ be the number of values of $a$ for which $K = a$ but $M, R, S, T \ne a$. Compute $\binom{n}{6}$. | 5,005 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(66)), Eq(Ref("_po_p5"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a")), Neq(Ref("_p... | COMB | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | comb_binomial_compute_v1 | null | 7 | 0 | [
"POLY_ORBIT_COUNT"
] | 1 | 0.004 | 2026-03-10T05:50:41.163697Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-03-10T05:50:41.167562Z"
} | caaa0d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 4476
},
"timestamp": "2026-04-19T01:26:39.773Z",
"answer": 5005
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
1c3aaa | alg_qf_psd_min_v1_1218484723_5343 | Let $T = \min\{ 16a_1^3 + 84a_1b_1^2 + 174a_1b_1^2 + 133b_1^3 : a_1, b_1 \in \mathbb{Z}^+,\, 1 \le a_1, b_1 \le 17 \}$. Find the minimum value of $76032a^2 + 19008b^2$ over all positive integers $a, b$ with $1 \le a \le 407$ and $1 \le b \le T$. | 95,040 | graphs = [
Graph(
let={
"_n": Const(133),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(407)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=SolutionsSet... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"POLY3_MIN"
] | 1 | 0.234 | 2026-02-25T06:57:01.045873Z | {
"verified": true,
"answer": 95040,
"timestamp": "2026-02-25T06:57:01.279469Z"
} | 6964d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 3730
},
"timestamp": "2026-03-29T20:38:06.572Z",
"answer": 95040
},
{
"... | 2 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
0edec2 | comb_sum_binomial_row_v1_1520064083_9223 | Let $n = 11$, and let $r = 2^n$. Let $s$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 625$. Let $m$ be the minimum value of $x + y$ over all pairs in $s$. Compute the remainder when $m - r$ is divided by 84874. | 82,876 | graphs = [
Graph(
let={
"_n": Const(625),
"n": Const(11),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var... | NT | null | SUM | sympy | B3 | [
"B3"
] | fc629c | comb_sum_binomial_row_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T10:36:59.656789Z | {
"verified": true,
"answer": 82876,
"timestamp": "2026-02-08T10:36:59.657891Z"
} | 0436b9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 414
},
"timestamp": "2026-02-15T21:01:31.724Z",
"answer": 82876
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
143d27 | algebra_quadratic_discriminant_v1_168721529_474 | Let $a = -1$, $b = 6$, and $n_0 = 4$. Define $S$ as the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 20963250$, and $\gcd(p, q) = 1$. Let $c$ be the number of elements in $S$. Compute $b^2 - n_0 a c$. | 100 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": Const(6),
"c": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MOBIUS_SUM"
] | 2 | 0.009 | 2026-02-08T13:04:01.383538Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T13:04:01.392214Z"
} | e1dff0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2559
},
"timestamp": "2026-02-09T05:27:02.312Z",
"answer": 100
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.84
} | ||
7acd02 | comb_binomial_compute_v1_898971024_248 | Let $m = 2$ and let $s = \sum_{k=1}^5 k$. Let $n$ be the largest prime number between $m$ and $s$, inclusive. Compute $\binom{n}{5}$. | 1,287 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Summation(var="k1", start=Const(1), end=Const(5), expr=Var("k1")),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_m")), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"k": Con... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | bde608 | comb_binomial_compute_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T15:18:38.128527Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T15:18:38.131552Z"
} | 619874 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 248
},
"timestamp": "2026-02-16T05:23:02.561Z",
"answer": 143
},
{
"id": 11,
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "o... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
2a2971 | sequence_fibonacci_compute_v1_2051736721_2118 | Let $n$ be the number of integers $t$ such that $24 \leq t \leq 108$ and there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 3$, and $t = 9a + 15b$. Let $f$ be the $n$-th Fibonacci number. Compute $12996 - f$. | 2,050 | graphs = [
Graph(
let={
"_n": Const(12996),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T16:29:34.179196Z | {
"verified": true,
"answer": 2050,
"timestamp": "2026-02-08T16:29:34.185805Z"
} | e55dac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1819
},
"timestamp": "2026-02-17T05:19:58.690Z",
"answer": 2050
},
{... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
90b818 | diophantine_product_count_v1_458359167_4453 | Let $k = \sum_{j=1}^{15} \phi(j) \left\lfloor \frac{15}{j} \right\rfloor$. Let $T$ be the set of all integers $t$ such that $18 \leq t \leq 116$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 7$, and $t = 10a + 8b$. Let $u$ be the number of elements in $T$. Consider the set of all pos... | 10 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": Const(15),
"k": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(nam... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"K2"
] | b46b5e | diophantine_product_count_v1 | null | 7 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.078 | 2026-02-08T11:47:53.808053Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T11:47:53.885838Z"
} | c473c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 2326
},
"timestamp": "2026-02-14T18:40:47.667Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
11ae4b | comb_count_permutations_fixed_v1_48377204_189 | Let $n$ be the smallest prime divisor of $41327$. Compute $\binom{n}{6} \cdot !(n - 6)$, where $!k$ denotes the number of derangements of $k$ elements. | 20,328 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(41327))))),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Re... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.022 | 2026-02-08T15:17:31.662101Z | {
"verified": true,
"answer": 20328,
"timestamp": "2026-02-08T15:17:31.684579Z"
} | 11bda1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 1049
},
"timestamp": "2026-02-16T02:24:29.076Z",
"answer": 20328
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e902c4 | modular_modexp_compute_v1_717093673_3365 | Let $a = 29$. Let $e$ be the smallest integer $d \geq 2$ that divides $250997$. Define $m = 13456$ and let $r$ be the remainder when $a^e$ is divided by $m$. Let $k$ be the remainder when $|r|$ is divided by $11$. Compute the Bell number $B_k$, and let $Q$ be the remainder when $B_k$ is divided by $71064$. Find the val... | 44,911 | graphs = [
Graph(
let={
"a": Const(29),
"e": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(250997))))),
"m": Const(13456),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_modexp_compute_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.121 | 2026-02-08T17:30:43.551312Z | {
"verified": true,
"answer": 44911,
"timestamp": "2026-02-08T17:30:43.671905Z"
} | c9b9a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 3873
},
"timestamp": "2026-02-18T03:56:41.671Z",
"answer": 44911
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c36df0 | comb_sum_binomial_row_v1_1978505735_3052 | Let $n$ be the largest prime number less than or equal to 12. Compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(12)), IsPrime(Var("n1"))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T17:18:59.318242Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T17:18:59.319406Z"
} | 9212eb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 239
},
"timestamp": "2026-02-16T09:38:49.097Z",
"answer": 2048
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"s... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
83ced4 | modular_modexp_compute_v1_1978505735_3672 | Let $a = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$. Let $e$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 74$. Let $r$ be the remainder when $a^e$ is divided by $67081$. Compute the remainder when $44768 \cdot r$ is divided by $56007$. | 39,433 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(56007),
"a": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"B1",
"K2"
] | 7fde97 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B1",
"K2",
"LIN_FORM"
] | 3 | 0.036 | 2026-02-08T17:47:40.181544Z | {
"verified": true,
"answer": 39433,
"timestamp": "2026-02-08T17:47:40.217211Z"
} | 8217e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 3217
},
"timestamp": "2026-02-18T08:23:10.306Z",
"answer": 39433
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4784a1 | modular_count_residue_v1_1742523217_1847 | Let $m = 802$. Define $k$ to be the number of nonnegative integers $j \leq m$ for which $\binom{802}{j}$ is odd. Let $r$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = k$. Determine the number of positive integers $n \leq 65536$ such that $n \equiv r \pmod{15}$. Let ... | 43,196 | graphs = [
Graph(
let={
"_m": Const(802),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(802), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"uppe... | ALG | COMB | COUNT | sympy | V8 | [
"V8/B3"
] | b4fc86 | modular_count_residue_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 7.156 | 2026-02-08T04:18:33.366731Z | {
"verified": true,
"answer": 43196,
"timestamp": "2026-02-08T04:18:40.522490Z"
} | f58596 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 4732
},
"timestamp": "2026-02-24T00:13:40.609Z",
"answer": 43196
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
83e399 | antilemma_k2_v1_458359167_5005 | Let $n = 68$. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{68}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function.
Compute the value of $x$. | 2,346 | graphs = [
Graph(
let={
"_n": Const(68),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(68), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T12:11:22.603483Z | {
"verified": true,
"answer": 2346,
"timestamp": "2026-02-08T12:11:22.603932Z"
} | 821a5b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 482
},
"timestamp": "2026-02-14T23:11:56.046Z",
"answer": 2346
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8d2132 | sequence_count_fib_divisible_v1_1353956133_404 | Let $n = 13$. Define $d = \sum_{k \mid n} \phi(k)$, where $\phi$ is Euler's totient function. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 156816$. Let $M$ be the minimum value of $x + y$ over all such pairs.
Compute the number of positive integers $k \leq M$ such that $d$ div... | 113 | graphs = [
Graph(
let={
"_n": Const(13),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(156816)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3",
"K3"
] | b88822 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"K3"
] | 2 | 0.143 | 2026-02-08T11:26:14.769600Z | {
"verified": true,
"answer": 113,
"timestamp": "2026-02-08T11:26:14.912701Z"
} | 8911f0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1545
},
"timestamp": "2026-02-14T13:43:46.238Z",
"answer": 113
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bbdce8 | antilemma_k3_v1_2051736721_1165 | Compute $\sum_{d \mid 41257} \phi(d)$, where the sum is taken over all positive divisors $d$ of $41257$ and $\phi$ denotes Euler's totient function. | 41,257 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=41257), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:52:30.686410Z | {
"verified": true,
"answer": 41257,
"timestamp": "2026-02-08T15:52:30.687150Z"
} | d134f5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 493
},
"timestamp": "2026-02-16T06:36:11.981Z",
"answer": 41256
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
51a141_n | geo_visible_lattice_v1_1419126231_439 | A city planner designs a square grid neighborhood with streets numbered from $1$ to $n$, where $n = \sum_{k=1}^{11} \varphi(k) \cdot \left\lfloor \frac{11}{k} \right\rfloor$. A cross-street at intersection $(x,y)$ is considered *visible* from the origin if $\gcd(x,y) = 1$. How many visible intersections are there in th... | 2,655 | GEOM | GEOM | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_visible_lattice_v1 | null | 4 | null | [
"K2"
] | 1 | 0.088 | 2026-02-25T09:58:23.079381Z | null | a3654f | 51a141 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 22117
},
"timestamp": "2026-03-31T03:41:29.604Z",
"answer": 2655
},
{
"... | 1 | [
{
"lemma": "K2",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
73cd6c | antilemma_k2_v1_1520064083_8867 | Compute the remainder when $27309 \cdot \sum_{k=1}^{63} \phi(k) \left\lfloor \frac{63}{k} \right\rfloor$ is divided by $82406$, where $\phi(k)$ denotes Euler's totient function. | 7,736 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(63), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(63), Var("k"))))),
"Q": Mod(value=Mul(Const(27309), Ref("x")), modulus=Const(82406)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2"
] | 2 | 0.001 | 2026-02-08T10:25:35.098931Z | {
"verified": true,
"answer": 7736,
"timestamp": "2026-02-08T10:25:35.100267Z"
} | 61b2ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 813
},
"timestamp": "2026-02-14T07:22:04.965Z",
"answer": 7736
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2ed1bf | comb_catalan_compute_v1_601307018_6768 | Let $B_n$ denote the $n$-th Bell number and $C_n$ the $n$-th Catalan number. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 13$. Define $M = C_n$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Compute $B_{M \bmod k}$. | 2 | graphs = [
Graph(
let={
"_n": Const(13),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 8e32ac | comb_catalan_compute_v1 | bell_mod | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.041 | 2026-03-10T07:25:45.560078Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-03-10T07:25:45.601350Z"
} | 364204 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1018
},
"timestamp": "2026-04-19T05:13:45.183Z",
"answer": 2
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
16c956 | comb_sum_binomial_mod_v1_458359167_172 | Let $M$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy=3025$.
Let
$$S=\sum_{k=11}^{84} \binom{M}{k}.$$
Let $R$ be the remainder when $S$ is divided by $10289$.
Let $L$ be the set of all integers $d$ with $2\le d\le D$ such that $d$ is prime, where $D$ is the minimum e... | 65,245 | graphs = [
Graph(
let={
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3025)))), expr=Sum(Var("x"), Var("y")))),
"_n": Const(73581... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_PRIMES",
"B3/MIN_PRIME_FACTOR"
] | 955cc8 | comb_sum_binomial_mod_v1 | negation_mod | 8 | 0 | [
"B3",
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 3 | 0.018 | 2026-02-08T03:03:07.468597Z | {
"verified": true,
"answer": 65245,
"timestamp": "2026-02-08T03:03:07.486572Z"
} | 215bf7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 304,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:43:32.563Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},... | {
"lo": 4.31,
"mid": 6.37,
"hi": 9.39
} | ||
1c2b26 | antilemma_k2_v1_717093673_1463 | Let $n = 158$. Compute the value of $$\sum_{k=1}^{158} \phi(k) \left\lfloor \frac{158}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. Multiply the result by 5885, and find the remainder when this product is divided by 92568. | 52,221 | graphs = [
Graph(
let={
"_n": Const(158),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(158), Var("k"))))),
"Q": Mod(value=Mul(Const(5885), Ref("x")), modulus=Const(92568)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.004 | 2026-02-08T16:06:03.169414Z | {
"verified": true,
"answer": 52221,
"timestamp": "2026-02-08T16:06:03.173259Z"
} | b7e517 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 2488
},
"timestamp": "2026-02-16T20:41:06.991Z",
"answer": 52221
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
909c97 | nt_count_divisible_and_v1_238844314_764 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 24$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 4a + 3b$. Let $d_2 = |T|$. Compute the number of positive integers $n$ such that $1 \leq n \leq 280020$, $n$ is divisible by $10$, and $n$ is divisible by... | 4,667 | graphs = [
Graph(
let={
"upper": Const(280020),
"d1": Const(10),
"d2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"LIN_FORM",
"MOBIUS_SUM"
] | 2 | 14.664 | 2026-02-08T13:35:44.201760Z | {
"verified": true,
"answer": 4667,
"timestamp": "2026-02-08T13:35:58.866116Z"
} | 320476 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1529
},
"timestamp": "2026-02-15T18:35:08.254Z",
"answer": 4667
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3891a5 | comb_catalan_compute_v1_1248542787_871 | Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 10$ and $1 \leq j \leq 10$ such that $i + j = 11$. Define $\text{result}$ to be the $n$-th Catalan number. Compute the remainder when $31151 \cdot \text{result}$ is divided by $51080$. | 50,836 | graphs = [
Graph(
let={
"_n": Const(31151),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(11)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T03:28:10.402802Z | {
"verified": true,
"answer": 50836,
"timestamp": "2026-02-08T03:28:10.414186Z"
} | 636b4f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1733
},
"timestamp": "2026-02-09T09:19:38.801Z",
"answer": 50836
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
b9fd59 | antilemma_cartesian_v1_458359167_924 | Let $A$ be the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 42$ and $1 \leq j \leq 48$. Let $x$ be the number of elements in $A$. Let $c = 44756$. Compute the remainder when $c \cdot x$ is divided by $73219$. | 22,288 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(42)), right=IntegerRange(start=Const(1), end=Const(48)))),
"_c": Const(44756),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(73219)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:11:07.492704Z | {
"verified": true,
"answer": 22288,
"timestamp": "2026-02-08T04:11:07.493232Z"
} | 6795d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2195
},
"timestamp": "2026-02-23T23:38:08.405Z",
"answer": 22288
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
cfe236 | antilemma_k3_v1_677425708_2479 | Let $x = \sum_{d \mid 72177} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $16 - x$ is divided by $61766$. | 51,371 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=72177), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(16), Ref("x")), modulus=Const(61766)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T05:04:25.159630Z | {
"verified": true,
"answer": 51371,
"timestamp": "2026-02-08T05:04:25.161323Z"
} | 5aa6d7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 916
},
"timestamp": "2026-02-11T22:13:46.418Z",
"answer": 10405
},
{
"id": 11... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
cdb910 | geo_count_lattice_triangle_v1_601307018_7541 | Let $M = |180 \cdot 111 + 256 \cdot (-64)|$, and let $R = \gcd(180, 64) + \gcd(|256 - 180|, |111 - 64|) + \gcd\left(\left|40^2 - \left|\{ (a, b) : 1 \leq a, b \leq 40,\ 10a^2 - 18ab + 25b^2 \leq 3277 \}\right|\right|, 111\right)$. Let $S = \frac{M + 2 - R}{2}$. Compute $58081 - S$. | 56,285 | graphs = [
Graph(
let={
"_n": Const(64),
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=111)), Mul(Const(value=256), Sub(left=Const(value=0), right=Ref(name='_n'))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=180)), b=Abs(arg=Const(value=64))), GCD(a=Abs(arg=Su... | GEOM | NT | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.017 | 2026-03-10T08:05:00.252716Z | {
"verified": true,
"answer": 56285,
"timestamp": "2026-03-10T08:05:00.269385Z"
} | 8c9772 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 3735
},
"timestamp": "2026-04-19T06:56:58.162Z",
"answer": 56286
},
{
... | 1 | [
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
ace5fa | comb_factorial_compute_v1_1218484723_3251 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 20$ such that $32a^2 - 64ab + 32b^2 = 5408$. Let $Q$ be the factorial of this number. Compute $Q$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(32), Pow(... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_factorial_compute_v1 | null | 3 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.002 | 2026-02-25T04:57:23.001415Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T04:57:23.003404Z"
} | b944a4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 473
},
"timestamp": "2026-03-29T09:14:40.678Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
da6702 | nt_count_with_divisor_count_v1_238844314_41 | Let $N = 96529$. Define $A$ to be the number of positive integers $n \leq 69756$ such that the $n$-th Fibonacci number is divisible by 12. Let $B$ be the number of positive integers $n \leq A$ such that $n$ has exactly 5 positive divisors. Compute the remainder when $44121 \cdot B$ is divided by $N$. | 79,955 | graphs = [
Graph(
let={
"_n": Const(96529),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(69756)), Divides(divisor=Const(12), dividend=Fibonacci(arg=Var(name='n')))))),
"div_count": Const(5),
"r... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_with_divisor_count_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.675 | 2026-02-08T13:05:56.723246Z | {
"verified": true,
"answer": 79955,
"timestamp": "2026-02-08T13:05:57.398499Z"
} | 069336 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1278
},
"timestamp": "2026-02-15T09:30:55.864Z",
"answer": 79955
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0a05dc | modular_sum_quadratic_residues_v1_1125832087_2452 | Let $p$ be the number of integers $t$ such that $18 \leq t \leq 726$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 171$, $1 \leq b \leq 3$, and $t = 4a + 14b$. Compute $\frac{p(p-1)}{4}$. | 30,363 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=171)), Geq(left=Var(... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:37:24.431405Z | {
"verified": true,
"answer": 30363,
"timestamp": "2026-02-08T04:37:24.432637Z"
} | 8ab103 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 2277
},
"timestamp": "2026-02-10T17:22:43.582Z",
"answer": 30363
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
79a1b5 | comb_binomial_compute_v1_2051736721_5907 | Let $n$ be the smallest divisor of $221$ that is at least $2$. Compute the remainder when $44121 \cdot \binom{n}{5}$ is divided by $91424$. | 9,423 | graphs = [
Graph(
let={
"_n": Const(91424),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(221))))),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(va... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T18:51:41.802128Z | {
"verified": true,
"answer": 9423,
"timestamp": "2026-02-08T18:51:41.804964Z"
} | 54b69b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 1340
},
"timestamp": "2026-02-18T19:56:45.173Z",
"answer": 9423
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f85b41 | nt_sum_gcd_range_mod_v1_717093673_4196 | Let $N = \sum_{k_1=1}^{136} \phi(k_1) \left\lfloor \frac{1}{k_1} \sum_{k_2=1}^{16} \phi(k_2) \left\lfloor \frac{16}{k_2} \right\rfloor \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k = 336$ and $M = 10771$. Define $S = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remainder when $S$ is divided by $M$. | 164 | graphs = [
Graph(
let={
"_m": Const(16),
"_n": Const(136),
"N": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Summation(var="k2", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k2")), Floor(Div(Const(16), Var("k2")))... | NT | null | COMPUTE | sympy | K2 | [
"K2/K2"
] | ddede2 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.487 | 2026-02-08T18:05:47.919152Z | {
"verified": true,
"answer": 164,
"timestamp": "2026-02-08T18:05:48.405779Z"
} | 922e6c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 3887
},
"timestamp": "2026-02-18T13:32:10.341Z",
"answer": 164
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
12b1df | nt_sum_divisors_range_v1_1874849503_118 | Let $C$ be the number of integers $t$ with $5 \leq t \leq 17$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $D$ be the largest integer $k$ such that $C^k$ divides $100012!$. Compute the sum of the number of positive divisors of $n$ for all positive int... | 93,643 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/V1"
] | 6f88e7 | nt_sum_divisors_range_v1 | null | 7 | 0 | [
"LIN_FORM",
"V1"
] | 2 | 0.352 | 2026-02-08T12:48:48.558862Z | {
"verified": true,
"answer": 93643,
"timestamp": "2026-02-08T12:48:48.911239Z"
} | 7f8fbd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 6466
},
"timestamp": "2026-02-09T13:55:43.178Z",
"answer": 93643
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": ... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
c950ca | antilemma_cartesian_v1_1520064083_5812 | Let $x$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 10$ and $1 \leq j \leq 16$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $x + 2$. Determine the value of $k$. | 108 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(16)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T07:40:11.251575Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T07:40:11.252376Z"
} | a1e648 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 4460
},
"timestamp": "2026-02-24T08:19:25.457Z",
"answer": 108
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
810602 | comb_count_partitions_v1_784195855_7817 | Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 102$ and $t = 8a + 6b$ for some integers $a$ and $b$ with $1 \leq a \leq 9$ and $1 \leq b \leq 5$. Let $n$ be the number of elements in $T$. Compute the number of integer partitions of $n$. | 31,185 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:32:55.628924Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T09:32:55.630401Z"
} | dae4ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 8906
},
"timestamp": "2026-02-24T11:31:16.670Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
827c24 | nt_sum_divisors_mod_v1_1742523217_5178 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 840x + 45356 = 0$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11093$. | 2,880 | graphs = [
Graph(
let={
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-840), Var("x")), Const(45356)), Const(0)))),
"M": Const(11093),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modu... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T10:50:55.999262Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T10:50:56.000311Z"
} | 5f3fcc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1173
},
"timestamp": "2026-02-14T09:01:45.802Z",
"answer": 2880
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7bb9dc | nt_count_divisors_in_range_v1_238844314_1085 | Let $a = 2$ and $b$ be the number of positive integers $j$ such that $1 \leq j \leq 87$ and $j^4 \leq 57289761$. Let $n = 1260$. Define $r$ as the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the remainder when $34385 \cdot r$ is divided by $56936$. | 28,136 | graphs = [
Graph(
let={
"_n": Const(56936),
"n": Const(1260),
"a": Const(2),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(87)), Leq(Pow(Var("j"), Const(4)), Const(57289761))), domain='positive_inte... | NT | null | COUNT | sympy | C3 | [
"C3"
] | 8a214c | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.004 | 2026-02-08T13:54:33.244139Z | {
"verified": true,
"answer": 28136,
"timestamp": "2026-02-08T13:54:33.248471Z"
} | 0d9e1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1879
},
"timestamp": "2026-02-15T22:49:03.398Z",
"answer": 28136
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
41ae71 | alg_qf_psd_min_v1_1218484723_3026 | Let $B = \left|\{ v : v \geq 2, v \leq 18277, \text{ there exist integers } a, b \text{ with } 1 \leq a \leq 26, 1 \leq b \leq 26 \text{ such that } -52ab + 29b^2 + 25a^2 = v \}\right|$. Find the minimum value of $118970a^2 - 47588ab + 23794b^2$ over all positive integers $a, b$ with $1 \leq a \leq 500$ and $1 \leq b \... | 95,176 | graphs = [
Graph(
let={
"_n": Const(500),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Var("v"),... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_min_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.834 | 2026-02-25T04:47:06.966723Z | {
"verified": true,
"answer": 95176,
"timestamp": "2026-02-25T04:47:07.800274Z"
} | 48cc44 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 6974
},
"timestamp": "2026-03-29T07:56:40.206Z",
"answer": 95176
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
e300f8 | modular_modexp_compute_v1_655260480_977 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 3844$. Let $\sigma$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Compute
\[
\sum_{k=1}^{\sigma} \varphi(k) \left\lfloor \frac{124}{k} \right\rfloor,
\]
where $\varphi(k)$ denotes Euler's totient function. Raise $43$ ... | 3,349 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3844)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(43),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/K2"
] | 9f3175 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.002 | 2026-02-08T15:49:58.748382Z | {
"verified": true,
"answer": 3349,
"timestamp": "2026-02-08T15:49:58.750554Z"
} | ab865d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 3957
},
"timestamp": "2026-02-16T15:09:10.688Z",
"answer": 3349
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"l... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
927331_n | alg_sum_ap_v1_1419126231_255 | A music festival schedules performances over two stages, X1 and X2. Each day, both stages host exactly one show, and each show lasts an odd number of minutes. The total daily runtime across both stages is 16868 minutes. How many distinct daily schedules are possible if each stage's show length is a positive odd integer... | 6,548 | ALG | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | alg_sum_ap_v1 | null | 4 | null | [
"COMB1"
] | 1 | 0.005 | 2026-02-25T09:48:19.472900Z | null | 63b7de | 927331 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 723
},
"timestamp": "2026-03-31T03:21:24.046Z",
"answer": 6548
},
{
"id... | 2 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
b7c424 | algebra_quadratic_discriminant_v1_1978505735_1957 | Let $b = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Define
$$
\text{result} = b^2 - 4(-1)(-54).
$$
Compute the remainder when $19329 \cdot \text{result}$ is divided by $78325$. | 17,311 | graphs = [
Graph(
let={
"_n": Const(5),
"a": Const(-1),
"b": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"c": Const(-54),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Re... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T16:34:29.326416Z | {
"verified": true,
"answer": 17311,
"timestamp": "2026-02-08T16:34:29.328832Z"
} | 104433 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 728
},
"timestamp": "2026-02-17T07:13:29.412Z",
"answer": 17311
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ff5f9 | nt_min_phi_inverse_v1_1915831931_291 | Let $n = 3$. Define $\mathcal{S}$ as the set of all positive integers $j$ such that $1 \le j \le 10$ and $j^n \le 1000$. Let $U$ be the number of elements in $\mathcal{S}$. Determine the value of $Q$, where $Q$ is the smallest positive integer $n$ such that $1 \le n \le U$ and $\phi(n) = 1$, and then take $Q$ to be the... | 4 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(10)), Leq(Pow(Var("j"), Ref("_n")), Const(1000))), domain='positive_integers')),
"k": Const(1),
"result": Mi... | NT | null | EXTREMUM | sympy | K2 | [
"C3"
] | 8a214c | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"C3",
"K2"
] | 2 | 0.058 | 2026-02-08T15:19:39.046435Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T15:19:39.104281Z"
} | 2dc0d5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1203
},
"timestamp": "2026-02-16T04:08:27.396Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c1390 | comb_factorial_compute_v1_124444284_609 | Let $T$ be the set of all integers $t$ with $29 \le t \le 43$ that can be expressed as $4a + 6b + 19$ for some integers $a, b$ satisfying $1 \le a \le 3$ and $1 \le b \le 2$. Let $m = |T|$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Define $n$ to be the largest prime nu... | 12,916 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1/MAX_PRIME_BELOW"
] | c219ab | comb_factorial_compute_v1 | null | 5 | 0 | [
"B1",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T03:24:03.178715Z | {
"verified": true,
"answer": 12916,
"timestamp": "2026-02-08T03:24:03.181597Z"
} | ef0bcf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 994
},
"timestamp": "2026-02-09T19:44:59.711Z",
"answer": 12916
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"st... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
899842 | antilemma_k3_v1_124444284_6959 | Let $n = 81097$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 81,097 | graphs = [
Graph(
let={
"_n": Const(81097),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T08:44:00.555612Z | {
"verified": true,
"answer": 81097,
"timestamp": "2026-02-08T08:44:00.556068Z"
} | f93f54 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 351
},
"timestamp": "2026-02-15T20:21:18.015Z",
"answer": 81097
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
b0cd4d | nt_count_divisible_v1_1918700295_2577 | Let $d_0$ be the greatest common divisor of $7$ and the minimum divisor $d$ of $6125$ such that $d \geq 2$. Let $s$ be the sum of $\mu(d)$ over all positive divisors $d$ of $d_0$, where $\mu$ is the M\"obius function. Determine the number of positive integers $n$ such that $n \leq 46665$, $n \geq s$, and $n$ is divisib... | 5,833 | graphs = [
Graph(
let={
"upper": Const(46665),
"divisor": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=MinOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(left=Var(name='d'), right=Const(v... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME"
] | 60ba20 | nt_count_divisible_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 8.073 | 2026-02-08T07:59:58.135444Z | {
"verified": true,
"answer": 5833,
"timestamp": "2026-02-08T08:00:06.208484Z"
} | ba1804 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 469
},
"timestamp": "2026-02-20T09:24:20.354Z",
"answer": 5833
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
8b9353 | comb_count_permutations_fixed_v1_1978505735_6249 | Let $k$ be the number of nonnegative integers $j$ such that $0 \le j \le 4608$ and $\binom{4608}{j}$ is odd. Compute the value of $\binom{9}{k} \cdot !(9 - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 5,544 | graphs = [
Graph(
let={
"_n": Const(4608),
"n": Const(9),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4608)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_in... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T19:32:01.958846Z | {
"verified": true,
"answer": 5544,
"timestamp": "2026-02-08T19:32:01.960852Z"
} | aab3f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1997
},
"timestamp": "2026-02-18T22:32:38.740Z",
"answer": 5544
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
589f99 | diophantine_product_count_v1_1439011603_876 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Define $k$ to be the minimum value of $x + y$ over all such pairs. Let $p_{\text{max}}$ be the largest prime number less than or equal to $122$. Compute the number of positive integers $x_1$ such that $1 \leq x_1 \leq p_{\tex... | 18 | graphs = [
Graph(
let={
"_n": Const(122),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.013 | 2026-02-08T15:47:15.820537Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T15:47:15.833079Z"
} | 2ac094 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 2605
},
"timestamp": "2026-02-16T14:06:03.362Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a16d0 | antilemma_cartesian_v1_124444284_9335 | Compute the number of ordered pairs $(a, b)$ such that $a$ is an integer satisfying $1 \leq a \leq 19$ and $b$ is an integer satisfying $1 \leq b \leq 32$. | 608 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(19)), right=IntegerRange(start=Const(1), end=Const(32)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T12:25:00.279846Z | {
"verified": true,
"answer": 608,
"timestamp": "2026-02-08T12:25:00.280277Z"
} | 00e40f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 138
},
"timestamp": "2026-02-24T15:38:16.424Z",
"answer": 608
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
e276cc | comb_sum_binomial_row_v1_124444284_4205 | Let $ p $ and $ q $ be positive integers. Define $ a $ to be the number of ordered pairs $ (p, q) $ such that $ p \cdot q = 6 $, $ \gcd(p, q) = 1 $, and $ p < q $. Define $ b $ to be the number of ordered pairs $ (p, q) $ such that $ p \cdot q = 2037420 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ r = |a^b| $. Compute t... | 660 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), L... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T05:51:11.395436Z | {
"verified": true,
"answer": 660,
"timestamp": "2026-02-08T05:51:11.397424Z"
} | 8cefd2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2677
},
"timestamp": "2026-02-12T15:29:33.961Z",
"answer": 660
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
fc2c34 | nt_sum_divisors_mod_v1_1915831931_1699 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $11597$, and then compute the remainde... | 7,747 | graphs = [
Graph(
let={
"_n": Const(72382),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T16:23:33.522802Z | {
"verified": true,
"answer": 7747,
"timestamp": "2026-02-08T16:23:33.530473Z"
} | fb146e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1830
},
"timestamp": "2026-02-17T02:09:20.936Z",
"answer": 7747
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c6cd9d | nt_sum_over_divisible_v1_168721529_442 | Let $t$ be an integer. Determine the number of integers $t$ such that $22 \leq t \leq 70$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 6a + 8b + 8$. Call this number $d$.
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 50000$ and $n$ is divi... | 11,098 | graphs = [
Graph(
let={
"upper": Const(50000),
"divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Ge... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 4.447 | 2026-02-08T13:03:22.481468Z | {
"verified": true,
"answer": 11098,
"timestamp": "2026-02-08T13:03:26.928280Z"
} | 10bdec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 6297
},
"timestamp": "2026-02-09T05:02:00.321Z",
"answer": 11098
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -2.02,
"mid": 1.85,
"hi": 5.2
} | ||
24c316 | nt_sum_over_divisible_v1_717093673_1436 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16000000$. Let $u$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $R$ be the sum of all positive integers $n \leq u$ that are divisible by $82$. Let $P$ be the number of ordered pairs $(p, q)$ of positive integers su... | 52,988 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16000000)))), expr=Sum(Var("x"), Var("y... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | e09b60 | nt_sum_over_divisible_v1 | mod_exp | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.285 | 2026-02-08T16:04:59.149010Z | {
"verified": true,
"answer": 52988,
"timestamp": "2026-02-08T16:04:59.434044Z"
} | e68104 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2635
},
"timestamp": "2026-02-16T20:42:00.916Z",
"answer": 52988
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fe3ca3 | antilemma_v8_lucas_677425708_1577 | Let $n = 23807$. Determine the value of the number of nonnegative integers $j$ such that $0 \leq j \leq n$ and $\binom{n}{j} \equiv 1 \pmod{2}$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(23807),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(23807), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
},
... | NT | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | antilemma_v8_lucas | null | 4 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T04:17:21.680377Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T04:17:21.681692Z"
} | 6330ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1658
},
"timestamp": "2026-02-09T21:42:24.059Z",
"answer": 4096
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
647781 | algebra_quadratic_discriminant_v1_397696148_681 | Let $a = 2$ and $b = -20$. Let $c$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 441$. Define $D = b^2 - 4ac$. Let $\alpha = 1$ if $D > 0$, and $0$ otherwise. Let $\beta = 1$ if $D = 0$, and $0$ otherwise. Define $\text{result} = 2\alpha + \beta$. Let $Q = 34225 - \text{result}... | 34,223 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(-20),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(441)))), expr=Su... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T11:41:07.642448Z | {
"verified": true,
"answer": 34223,
"timestamp": "2026-02-08T11:41:07.645237Z"
} | 073178 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 309
},
"timestamp": "2026-02-16T03:09:52.552Z",
"answer": 34223
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
4d931d | antilemma_cartesian_v1_1820931509_120 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 17, inclusive, and $b$ is an integer from 1 to 25, inclusive. Define
$$
S = \sum_{i=0}^{d-1} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^2,
$$
where $d$ is the number of digits in $|x|$, and digit positions are indexed... | 5,089 | graphs = [
Graph(
let={
"_n": Const(2),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(25)))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), ba... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | b51a54 | antilemma_cartesian_v1 | digits_weighted_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM",
"ONE_FACTORIAL_0"
] | 3 | 0.004 | 2026-02-08T11:22:05.244473Z | {
"verified": true,
"answer": 5089,
"timestamp": "2026-02-08T11:22:05.248026Z"
} | e9665b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 4722
},
"timestamp": "2026-02-24T13:39:13.141Z",
"answer": 5089
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
8042ca | geo_visible_lattice_v1_124444284_3518 | Let $n = 77$. Define $L$ to be the number of visible lattice points $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $68940 \cdot L$ is divided by $64603$. | 58,696 | graphs = [
Graph(
let={
"n": Const(77),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(68940), Ref("result")), modulus=Const(64603)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.426 | 2026-02-08T05:26:09.210959Z | {
"verified": true,
"answer": 58696,
"timestamp": "2026-02-08T05:26:09.637308Z"
} | 53cce3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 6067
},
"timestamp": "2026-02-24T03:35:24.884Z",
"answer": 58696
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
e0416b | diophantine_fbi2_min_v1_1978505735_2760 | Let $k = 77$ and let $u$ be the number of positive integers $n$ such that $1 \le n \le 217$ and $\gcd(n, 20) = 1$. Let $r$ be the smallest integer $d$ such that $4 \le d \le u$, $d$ divides $k$, and $k/d \ge 4$. Define
$$
Q = (61107 \cdot r) \mod 98182.
$$
Compute $Q$. | 35,021 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(77),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(217)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"result": MinOverSet(set=SolutionsSet(... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | 08d162 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.009 | 2026-02-08T17:09:31.300789Z | {
"verified": true,
"answer": 35021,
"timestamp": "2026-02-08T17:09:31.309913Z"
} | 68d906 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 818
},
"timestamp": "2026-02-17T20:14:35.345Z",
"answer": 35021
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
32fa7c | antilemma_k3_v1_1520064083_1250 | Let $n = 33647$. Compute the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Let this sum be $x$. Find the remainder when $17956 - x$ is divided by $91619$. | 75,928 | graphs = [
Graph(
let={
"_n": Const(33647),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(17956), Ref("x")), modulus=Const(91619)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:53:23.209718Z | {
"verified": true,
"answer": 75928,
"timestamp": "2026-02-08T03:53:23.210255Z"
} | c0bde2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 341
},
"timestamp": "2026-02-10T16:05:05.151Z",
"answer": 75928
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} |
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