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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
784356 | modular_min_linear_v1_865884756_7331 | Let $n = 3$, $a = 627$, and $m = 1022$. Let $S$ be the set of all positive integers $x$ such that $xy = 242064$ and $x, y$ are positive integers. Define $T$ to be the set of all values $x + y$ where $(x, y)$ is in $S$. Let $b$ be the number of positive integers $j$ such that $j \leq \min(T)$ and $j^n \leq 952763904$. D... | 37,848 | graphs = [
Graph(
let={
"_n": Const(3),
"a": Const(627),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg... | NT | null | EXTREMUM | sympy | B3 | [
"B3/C3"
] | 3e4f89 | modular_min_linear_v1 | null | 6 | 0 | [
"B3",
"C3"
] | 2 | 0.042 | 2026-02-08T19:44:05.364054Z | {
"verified": true,
"answer": 37848,
"timestamp": "2026-02-08T19:44:05.405894Z"
} | b9ed29 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 3709
},
"timestamp": "2026-02-18T23:19:31.297Z",
"answer": 37848
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab7cbc | algebra_poly_eval_v1_1918700295_2141 | Let $n = 21$. Compute the value of
\[
3n^3 + 3n^2 + k n - 7,
\]
where $k$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. | 29,267 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(21),
"result": Sum(Mul(Const(3), Pow(Ref("n"), Ref("_n"))), Mul(Const(3), Pow(Ref("n"), Const(2))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T07:42:56.905157Z | {
"verified": true,
"answer": 29267,
"timestamp": "2026-02-08T07:42:56.907417Z"
} | ebd6f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 498
},
"timestamp": "2026-02-13T11:55:34.986Z",
"answer": 29267
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
dc03b7 | diophantine_fbi2_count_v1_1978505735_3735 | Let $s = \sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor$, where $\varphi$ denotes Euler's totient function. Let $d$ be a positive integer such that $s \leq d \leq 90$, $d$ divides $840$, and $2 \leq \frac{840}{d} \leq 89$. Compute $40804$ minus the number of such integers $d$. | 40,788 | graphs = [
Graph(
let={
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Summation(var="k1", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(2), Var("k1")))))), Leq(Var("d"), Const(90)), Divides(divisor=V... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.01 | 2026-02-08T17:49:36.730080Z | {
"verified": true,
"answer": 40788,
"timestamp": "2026-02-08T17:49:36.739681Z"
} | ba10cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1092
},
"timestamp": "2026-02-18T08:26:48.002Z",
"answer": 40788
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ebace | comb_factorial_compute_v1_1978505735_4805 | Let $n = 7$ and define $r = n!$. Let $s$ be the sum of the digits of $r$, where each digit in the $10^i$ place is multiplied by $(i+1)^2$. Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 12446784$. Compute $s + m$. | 7,152 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"result": Factorial(Ref("n")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result')), k=Var(name='... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 8e300c | comb_factorial_compute_v1 | digits_weighted_mod | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T18:34:13.877568Z | {
"verified": true,
"answer": 7152,
"timestamp": "2026-02-08T18:34:13.881026Z"
} | 29e16a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1439
},
"timestamp": "2026-02-18T17:44:52.852Z",
"answer": 7152
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
e96d13 | sequence_fibonacci_compute_v1_655260480_4799 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 129$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{5}$. Compute the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$.
| 75,025 | graphs = [
Graph(
let={
"_n": Const(129),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T18:07:11.675048Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T18:07:11.676687Z"
} | f75ff5 | 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": 1124
},
"timestamp": "2026-02-18T14:07:15.986Z",
"answer": 75025
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
30bfd5 | diophantine_product_count_v1_865884756_5142 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 14400$. Define $k$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $T$ be the set of all positive integers $x_1$ such that $1 \leq x_1 \leq 192$, $x_1$ divides $k$, and $\frac{k}{x_1} \leq 192$. Compute the number ... | 18 | graphs = [
Graph(
let={
"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(14400)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(19... | NT | null | COUNT | sympy | L3B | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"L3B"
] | 2 | 0.308 | 2026-02-08T18:23:40.335730Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T18:23:40.643826Z"
} | 56b685 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2162
},
"timestamp": "2026-02-18T16:40:41.694Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
abe4a1 | sequence_lucas_compute_v1_655260480_103 | Let $ n $ be the largest prime number less than or equal to 20. Compute the $ n $-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_n": Const(20),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_lucas_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T15:11:02.884804Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T15:11:02.886048Z"
} | 766960 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 625
},
"timestamp": "2026-02-16T00:31:29.911Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
058bf2 | nt_sum_divisors_compute_v1_1918700295_2644 | Let $n = 45360$. Compute the remainder when the difference between the maximum value of $xy$ and the sum of the positive divisors of $n$ is divided by $72617$, where the maximum is taken over all pairs of positive integers $(x, y)$ such that $x + y = 198$. | 47,604 | graphs = [
Graph(
let={
"_n": Const(72617),
"n": Const(45360),
"result": SumDivisors(n=Ref("n")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | nt_sum_divisors_compute_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T08:08:47.799014Z | {
"verified": true,
"answer": 47604,
"timestamp": "2026-02-08T08:08:47.800476Z"
} | 014cb6 | 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": 1251
},
"timestamp": "2026-02-13T14:56:34.690Z",
"answer": 47604
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b602a1 | modular_min_linear_v1_1918700295_3218 | Let $a$ be the largest positive integer $d$ such that $d \leq 670$ and $d$ divides $457610$. Let $b$ be the number of positive integers $n$ such that $1 \leq n \leq 15109$ and $\gcd(n, 15) = 1$. Let $m$ be the sum of all real solutions $x$ to the equation $x^2 - 9409x + 764814 = 0$. Let $r$ be the smallest positive int... | 16,450 | graphs = [
Graph(
let={
"_d": Const(2),
"_m": Const(15),
"_n": Const(15109),
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(670)), Divides(divisor=Var("d"), dividend=Const(457610))))),
"b":... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"VIETA_SUM",
"C4"
] | c36b57 | modular_min_linear_v1 | null | 6 | 0 | [
"C4",
"MAX_DIVISOR",
"VIETA_SUM"
] | 3 | 0.374 | 2026-02-08T08:27:29.581137Z | {
"verified": true,
"answer": 16450,
"timestamp": "2026-02-08T08:27:29.954647Z"
} | 92521c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 3647
},
"timestamp": "2026-02-13T19:07:46.228Z",
"answer": 16450
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
80612f | nt_min_coprime_above_v1_809748730_651 | Let $m$ be the number of positive integers $n \leq 5005$ such that $5$ divides $n$ and $\gcd(n, 6) = 1$. Find the smallest integer $n$ such that $85849 < n \leq 86193$ and $\gcd(n, m) = 1$. | 85,851 | graphs = [
Graph(
let={
"_n": Const(5005),
"start": Const(85849),
"upper": Const(86193),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(5), dividend=Var("n")), Eq(GC... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.041 | 2026-02-08T11:40:08.202190Z | {
"verified": true,
"answer": 85851,
"timestamp": "2026-02-08T11:40:08.243104Z"
} | 7e939d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1362
},
"timestamp": "2026-02-14T17:27:35.514Z",
"answer": 85851
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
56a9cc | nt_count_coprime_v1_1742523217_1896 | Let $m = 14$. Define $N$ to be the number of positive integers $n$ such that $1 \leq n \leq 2904$ and $m$ divides $F_n$, where $F_n$ is the $n$th Fibonacci number.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = N$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges... | 17,462 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2904)), Divides(divisor=Ref("_m"), dividend=Fibonacci(arg=Var(name='n')))))),
"upper": Const(38416),
"k": MinO... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/B3"
] | 3b8dd4 | nt_count_coprime_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 3.056 | 2026-02-08T04:19:21.128789Z | {
"verified": true,
"answer": 17462,
"timestamp": "2026-02-08T04:19:24.184889Z"
} | 7b22ac | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 3642
},
"timestamp": "2026-02-10T16:10:56.504Z",
"answer": 17462
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
99104f | algebra_vieta_sum_v1_784195855_2663 | Let $m = 25600$. Consider all ordered pairs of positive integers $(x, y)$ such that $xy = m$. Let $s$ be the smallest possible value of $x + y$ over all such pairs. Let $C$ be the number of positive integers $n \le s$ for which $7$ divides the $n$-th Fibonacci number. Determine the product of all positive integers $x$ ... | 40 | graphs = [
Graph(
let={
"_m": Const(25600),
"_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("_m")))), expr=Sum(Var("x"), Var("y")))),... | ALG | NT | COMPUTE | sympy | LTE_DIFF_P2 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | algebra_vieta_sum_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"LTE_DIFF_P2"
] | 3 | 0.083 | 2026-02-08T05:55:12.359183Z | {
"verified": true,
"answer": 40,
"timestamp": "2026-02-08T05:55:12.442425Z"
} | 1c14ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1499
},
"timestamp": "2026-02-12T16:58:03.820Z",
"answer": 40
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a8dc3e | geo_count_lattice_rect_v1_168721529_730 | Compute the number of lattice points in the rectangle $[0, 88] \times [0, 145]$. | 12,994 | graphs = [
Graph(
let={
"a": Const(88),
"b": Const(145),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T13:15:12.603825Z | {
"verified": true,
"answer": 12994,
"timestamp": "2026-02-08T13:15:12.604763Z"
} | 846c43 | 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": 322
},
"timestamp": "2026-02-09T08:27:09.286Z",
"answer": 12994
},
{
"i... | 1 | [] | {
"lo": -7.19,
"mid": -5.01,
"hi": -3.03
} | ||||
40d65e | comb_binomial_compute_v1_1742523217_562 | Let $n_1 = 0$ and $n_2 = 0$. Define
$$
h = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}
\quad\text{and}\quad
v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 16h$ and let $k = 8$. Define $\text{result} = \binom{n}{k}$. Compute the value of
$$
\text{result} + \phi(|\text{result}| + 1) + \tau(|\text{result}| + v),
$$
wh... | 25,474 | graphs = [
Graph(
let={
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"v": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_binomial_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T03:07:18.859341Z | {
"verified": true,
"answer": 25474,
"timestamp": "2026-02-08T03:07:18.860840Z"
} | e8a8f6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 1051
},
"timestamp": "2026-02-09T19:30:30.128Z",
"answer": 25474
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
0878a9 | nt_min_coprime_above_v1_677425708_4201 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 19518724$. Define $A$ to be the minimum value of $x + y$ over all such pairs.
Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 54756$. Define $B$ to be the minimum value of $x + y$ over all such pai... | 8,837 | graphs = [
Graph(
let={
"start": 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(19518724)))), expr=Sum(Var("x"), Var("y")))),
"upper": C... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.045 | 2026-02-08T06:29:24.925396Z | {
"verified": true,
"answer": 8837,
"timestamp": "2026-02-08T06:29:24.970576Z"
} | 663dd5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1303
},
"timestamp": "2026-02-13T00:32:10.417Z",
"answer": 8837
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
437d56_n | alg_telescope_v1_1218484723_4538 | An engineer is designing a system of coupled rotating shafts. First, she studies a small prototype with two adjustable gear parameters $a_1$ and $b_1$, each an integer from $1$ to $14$. For every such choice, the vibration cost is
$$600a_1 b_1^{2} + 128a_1^{3} + 480a_1^{2} b_1 + 250b_1^{3}.$$
She defines $C$ to be the ... | 347 | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN/QF_PSD_ORBIT/LIN_FORM",
"LIN_FORM/B3"
] | dbaa05 | alg_telescope_v1 | null | 7 | null | [
"B3",
"LIN_FORM",
"POLY3_MIN",
"QF_PSD_ORBIT"
] | 4 | 0.093 | 2026-02-25T06:12:30.751513Z | null | 02eb71 | 437d56 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 524,
"completion_tokens": 4943
},
"timestamp": "2026-03-30T21:48:59.782Z",
"answer": 3640
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
1823cf_n | sequence_count_fib_divisible_v1_601307018_3261 | A puzzle designer creates a sequence of challenges based on Fibonacci numbers. First, they define $M$ as the number of ways to factor 216 into two coprime positive integers $p < q$. Then, $R$ is the largest prime number no greater than the square root of 359999 and at least $M$. Finally, $S$ counts how many Fibonacci n... | 74,069 | ALG | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3_CLOSEST/MAX_PRIME_BELOW"
] | c05b12 | sequence_count_fib_divisible_v1 | null | 7 | null | [
"B3_CLOSEST",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-03-10T03:47:23.956490Z | null | 05c717 | 1823cf | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T17:21:30.047Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
315722 | nt_max_prime_below_v1_1915831931_2479 | Let $S$ be the set of all prime numbers $n$ such that $n \geq \sum_{d \mid 2} \varphi(d)$ and $n \leq 15376$, where $\varphi$ denotes Euler's totient function. Determine the value of the largest element in $S$. | 15,373 | graphs = [
Graph(
let={
"upper": Const(15376),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=Const(value=2), var='d', expr=EulerPhi(n=Var(name='d')))), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
},
goal=Ref("... | NT | null | EXTREMUM | sympy | K3 | [
"K3"
] | 54c41e | nt_max_prime_below_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.556 | 2026-02-08T16:51:40.962423Z | {
"verified": true,
"answer": 15373,
"timestamp": "2026-02-08T16:51:41.518615Z"
} | b2365c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1372
},
"timestamp": "2026-02-17T15:20:08.954Z",
"answer": 15373
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
274f59 | comb_count_derangements_v1_1978505735_3890 | Let $n$ be the smallest integer greater than or equal to 2 that divides 539539. Define $d_n$ to be the number of derangements of $n$ objects. Compute $21025 - d_n$. | 19,171 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(539539))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(21025),
"Q": Sub(Ref("_c"), Ref("result")... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T17:55:12.376199Z | {
"verified": true,
"answer": 19171,
"timestamp": "2026-02-08T17:55:12.377201Z"
} | bf135a | 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": 872
},
"timestamp": "2026-02-18T09:54:21.198Z",
"answer": 19171
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
85e82b | geo_count_lattice_rect_v1_1520064083_7066 | Let $a = 196$ and $b = 204$. Define a lattice point as a point in the plane with integer coordinates. Consider the rectangle consisting of all points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points contained in this rectangle. | 40,385 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(204),
"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 | 0.002 | 2026-02-08T08:45:23.535473Z | {
"verified": true,
"answer": 40385,
"timestamp": "2026-02-08T08:45:23.537240Z"
} | de280f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 392
},
"timestamp": "2026-02-24T09:58:40.173Z",
"answer": 40385
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
b2f5b0 | lin_form_endings_v1_124444284_7088 | Let $a = 63$ and $b = 45$. Let $m$ be the least common multiple of $a$ and $b$. Compute the remainder when $17374 \cdot m$ is divided by $60916$. | 51,286 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(45),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(17374),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(60916),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T08:50:25.304923Z | {
"verified": true,
"answer": 51286,
"timestamp": "2026-02-08T08:50:25.305347Z"
} | c1035d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 1500
},
"timestamp": "2026-02-13T22:08:32.467Z",
"answer": 51286
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b75c3a | comb_bell_compute_v1_1218484723_2207 | Let $n$ be the number of integers $t$ in the range $16 \le t \le 46$ that can be expressed as $t = 6a + 9b + 1$ for some integers $a, b$ with $1 \le a, b \le 3$. Let $Q = B_n$, where $B_n$ is the $n$-th Bell number. Compute $Q$. | 21,147 | 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=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-25T03:58:18.943000Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-25T03:58:18.943867Z"
} | f85cf0 | 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": 800
},
"timestamp": "2026-03-29T03:35:40.697Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.88
} | ||
ca2b24 | nt_min_coprime_above_v1_784195855_8196 | Let $S = \sum_{k=1}^{108} \phi(k) \left\lfloor \frac{108}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $N$ be the smallest integer greater than $S$ and at most $5912$ such that $\gcd(N, 16) = 1$. Determine the value of $N$. | 5,887 | graphs = [
Graph(
let={
"start": Summation(var="k", start=Const(1), end=Const(108), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(108), Var("k"))))),
"upper": Const(5912),
"modulus": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 6897ab | nt_min_coprime_above_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.008 | 2026-02-08T15:56:07.469323Z | {
"verified": true,
"answer": 5887,
"timestamp": "2026-02-08T15:56:07.476839Z"
} | 48669b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1047
},
"timestamp": "2026-02-16T17:41:03.202Z",
"answer": 5887
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
53182e | comb_count_partitions_v1_153355830_1034 | Let $n$ be the sum of $8$ and the number of integers $j$ with $0 \leq j \leq 466$ such that $\binom{466}{j}$ is odd. Define $r$ to be the number of integer partitions of $n$. Compute the remainder when $75351 \cdot r$ is divided by $53513$. | 9,663 | graphs = [
Graph(
let={
"_n": Const(8),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(466)), Eq(Mod(value=Binom(n=Const(466), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Ref("_n")),
... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_partitions_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T04:21:50.791210Z | {
"verified": true,
"answer": 9663,
"timestamp": "2026-02-08T04:21:50.792796Z"
} | 598315 | 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": 5818
},
"timestamp": "2026-02-24T00:15:29.989Z",
"answer": 9663
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
13c4e9 | modular_count_residue_v1_1978505735_4100 | Let $r$ be the sum of all positive integers $n$ such that $1 \leq n \leq 16$ and $n \equiv 0 \pmod{16}$. Let $m = 17$ and let $N$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 81225$ and $n_1 \equiv r \pmod{m}$. Compute $N$. | 4,778 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(81225),
"m": Const(17),
"r": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(16)), Const(0))))),
... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | modular_count_residue_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 2.636 | 2026-02-08T18:00:19.906859Z | {
"verified": true,
"answer": 4778,
"timestamp": "2026-02-08T18:00:22.543073Z"
} | 825ee9 | 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": 1162
},
"timestamp": "2026-02-18T12:31:29.246Z",
"answer": 4778
},
{... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
030d82 | modular_count_residue_v1_124444284_659 | Let $r$ be the number of integers $t$ such that $7 \leq t \leq 20$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Let $N = 54756$ and $m = 17$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$ and $n \equiv r \pmod{m}$. | 3,221 | graphs = [
Graph(
let={
"upper": Const(54756),
"m": Const(17),
"r": 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'), rig... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.833 | 2026-02-08T03:26:17.627007Z | {
"verified": true,
"answer": 3221,
"timestamp": "2026-02-08T03:26:19.460308Z"
} | 7043df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1485
},
"timestamp": "2026-02-09T20:21:58.165Z",
"answer": 3221
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
a742d4 | lin_form_endings_v1_124444284_6160 | Let $a = 45$ and $b = 75$. Define $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $T$ be the set of all integers of the form $a x + b y$ where $1 \leq x \leq 36$ and $1 \leq y \leq 11$. The number of distinct elements in $T$ is given by $a' \cdot 3... | 2,178 | graphs = [
Graph(
let={
"a_coeff": Const(45),
"b_coeff": Const(75),
"A_val": Const(36),
"B_val": Const(11),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:10:43.878420Z | {
"verified": true,
"answer": 2178,
"timestamp": "2026-02-08T08:10:43.879500Z"
} | 53769f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 646
},
"timestamp": "2026-02-15T19:43:31.238Z",
"answer": 2178
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"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": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
3efa36 | alg_poly3_sum_v1_601307018_4864 | Find the remainder when $$\sum_{\substack{a=1}}^{22} \sum_{b=1}^{22} \sum_{c=1}^{22} \left( 20c^3 + 108a^2c + 138bc^2 + 249b^3 + 270a^2b + 180abc + 72ac^2 + \left| \left\{ (a_1, b_1) \in [1,20]^2 : -12a_1b_1 + 41a_1^2 + 20b_1^2 \leq 10468 \right\} \right| \cdot b^2c \right)$$ is divided by $56013$. | 18,548 | graphs = [
Graph(
let={
"_n": Const(2),
"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(22)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(22)), Geq(Var("c"),... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.054 | 2026-03-10T05:34:12.340941Z | {
"verified": true,
"answer": 18548,
"timestamp": "2026-03-10T05:34:12.395136Z"
} | 827caa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 12119
},
"timestamp": "2026-03-29T13:42:10.008Z",
"answer": 26717
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
a5f321 | nt_sum_divisors_range_v1_1520064083_2199 | Let $n = 39204$. Define $u$ to be the number of integers $k$ with $1 \leq k \leq 19998$ such that the sum of the decimal digits of $k$ is even. Let $S$ be the set of all positive integers from $1$ to $u$. Compute the sum of $\tau(k)$ for all $k$ in $S$, where $\tau(k)$ is the number of positive divisors of $k$. Let $r$... | 16,164 | graphs = [
Graph(
let={
"_n": Const(39204),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19998)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"result": SumOverSet(set=MapOverSet(set=S... | NT | null | SUM | sympy | L3B | [
"L3B"
] | cc148f | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.674 | 2026-02-08T04:33:16.628908Z | {
"verified": true,
"answer": 16164,
"timestamp": "2026-02-08T04:33:17.302792Z"
} | 0ed7b1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 5679
},
"timestamp": "2026-02-10T17:08:32.620Z",
"answer": 16164
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
9360c9 | antilemma_k2_v1_458359167_3996 | Compute the value of $$
\sum_{k=1}^{395} \phi(k) \left\lfloor \frac{395}{k} \right\rfloor,
$$ where $\phi(k)$ denotes Euler's totient function. | 78,210 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(395), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(395), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T11:28:15.032978Z | {
"verified": true,
"answer": 78210,
"timestamp": "2026-02-08T11:28:15.033497Z"
} | 0741cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 582
},
"timestamp": "2026-02-14T14:26:11.070Z",
"answer": 78210
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
2a6bee | modular_modexp_compute_v1_655260480_5178 | Let $a = 19$ and $m = 53361$. Define $e$ as the sum
$$
\sum_{k=1}^{t} \phi(k) \left\lfloor \frac{135}{k} \right\rfloor,
$$
where $t$ is the number of prime numbers $n$ satisfying $2 \leq n \leq 761$. Let $r$ be the remainder when $a^e$ is divided by $m$. Compute the remainder when $23421 \cdot r$ is divided by $70328$. | 61,294 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(70328),
"a": Const(19),
"e": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(761)), IsPrime(Var("n"))))), expr=Mu... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/K2"
] | bfba02 | modular_modexp_compute_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"K2"
] | 2 | 0.002 | 2026-02-08T18:20:14.448736Z | {
"verified": true,
"answer": 61294,
"timestamp": "2026-02-08T18:20:14.450806Z"
} | 48ce01 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 4807
},
"timestamp": "2026-02-18T16:29:06.972Z",
"answer": 61294
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
70b6f4 | alg_sum_ap_v1_1419126231_1854 | Let $S$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $18a^2 + 32b^2 \le 47906$. Let $T$ be the number of integers $t$ in the range $5 \le t \le 4156$ that can be written as $t = 3a + 2b$ for some integers $a, b$ with $1 \le a \le 932$, $1 \le b \le 680$. Define $R = \l... | 17,623 | graphs = [
Graph(
let={
"_m": Const(80312),
"_n": Const(15005),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b")... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"LIN_FORM"
] | 74f7c5 | alg_sum_ap_v1 | null | 5 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.018 | 2026-02-25T11:24:22.979948Z | {
"verified": true,
"answer": 17623,
"timestamp": "2026-02-25T11:24:22.997449Z"
} | 269671 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T14:22:18.142Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
62480f | geo_count_lattice_rect_v1_655260480_1108 | Let $a = 113$ and $b = 180$. Define $L$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $B_n$ denote the $n$-th Bell number. Compute $B_{|L| \bmod 11}$. | 21,147 | graphs = [
Graph(
let={
"a": Const(113),
"b": Const(180),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T15:54:23.439062Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T15:54:23.441403Z"
} | 845a6c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 565
},
"timestamp": "2026-02-24T19:07:04.632Z",
"answer": 21147
},
{
"... | 1 | [] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||||
a7901b | alg_qf_psd_orbit_v1_1218484723_6583 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 63$ such that $272b^2 - 544ab + 272a^2 = 13328$. | 56 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(63)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(63)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(272), Pow(Var("b"), Const(2))), ... | ALG | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_DIVISIBLE",
"LIN_FORM/SUM_DIVISIBLE"
] | 9f5269 | alg_qf_psd_orbit_v1 | null | 3 | null | [
"LIN_FORM",
"SUM_ARITHMETIC",
"SUM_DIVISIBLE"
] | 3 | 0.078 | 2026-02-25T08:07:39.208512Z | {
"verified": true,
"answer": 56,
"timestamp": "2026-02-25T08:07:39.286689Z"
} | 9b2aa3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 573
},
"timestamp": "2026-03-30T02:17:51.881Z",
"answer": 56
},
{
"id":... | 2 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
}
] | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
bf0b11 | diophantine_fbi2_count_v1_1978505735_5676 | Let $k$ be the largest positive divisor of $34740$ that is at most $180$. Compute the number of positive integers $d_1$ such that $4 \leq d_1 \leq 80$, $d_1$ divides $k$, and the quotient $k/d_1$ is at least $2$ and at most $78$. | 13 | graphs = [
Graph(
let={
"_n": Const(78),
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(180)), Divides(divisor=Var("d"), dividend=Const(34740))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d1"), condition=... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_DIVISOR"
] | 2 | 0.144 | 2026-02-08T19:09:38.859336Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T19:09:39.003525Z"
} | bdb96c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 2672
},
"timestamp": "2026-02-18T21:31:43.508Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
512f18 | alg_qf_psd_min_v1_1218484723_2581 | Let $S = \{ v : 25 \le v \le 7225,\ \text{there exist integers } a, b \in [1,17] \text{ such that } 25a^2 + 2b^2 - 2ab = v \}$. Find the minimum value of $18032a^2 - 27048ab + 65366b^2$ over all positive integers $a \le 223$, $b \le |S|$. | 56,350 | graphs = [
Graph(
let={
"_n": Const(18032),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(223)), 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 | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.087 | 2026-02-25T04:19:59.865288Z | {
"verified": true,
"answer": 56350,
"timestamp": "2026-02-25T04:19:59.952279Z"
} | a695e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:33:45.754Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
56f353 | nt_min_with_divisor_count_v1_865884756_6332 | Let $n$ be a positive integer such that $1 \leq n \leq 42849$ and the number of positive divisors of $n$ is exactly 6. Let $A$ be the smallest such $n$.
Let $B$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 2025$.
Compute $B - A$. | 78 | graphs = [
Graph(
let={
"upper": Const(42849),
"div_count": Const(6),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"_c": MinOverSet(set... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"B3"
] | fc629c | nt_min_with_divisor_count_v1 | negation_mod | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 4.898 | 2026-02-08T19:09:28.619591Z | {
"verified": true,
"answer": 78,
"timestamp": "2026-02-08T19:09:33.517680Z"
} | 1e9d67 | 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": 1199
},
"timestamp": "2026-02-18T21:25:06.620Z",
"answer": 78
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a4424a | antilemma_k3_v1_458359167_1727 | Let $n = 86008$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 86,008 | graphs = [
Graph(
let={
"_n": Const(86008),
"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 | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:49:25.858681Z | {
"verified": true,
"answer": 86008,
"timestamp": "2026-02-08T04:49:25.859325Z"
} | af3f9a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 515
},
"timestamp": "2026-02-11T21:56:28.192Z",
"answer": 12960
},
{
"id": 11,... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
f93a3d | antilemma_k2_v1_865884756_2384 | Compute the value of
$$
\sum_{k=1}^{383} \phi(k) \left\lfloor \frac{383}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function.
Find the value of this sum. | 73,536 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(383), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(383), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T16:43:41.192316Z | {
"verified": true,
"answer": 73536,
"timestamp": "2026-02-08T16:43:41.194592Z"
} | e19cf5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 975
},
"timestamp": "2026-02-17T11:00:42.779Z",
"answer": 73536
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
935e84 | antilemma_sum_equals_v1_349078426_1314 | Let $c = 29555$. Let $m$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, \dots, 11\}$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 21$, $1 \leq j \leq 22$, such that $i + j = m$. Let $x$ be the number of ordered pairs $(i, j)$ of positi... | 37,894 | graphs = [
Graph(
let={
"_c": Const(29555),
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(11)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), conditio... | 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 | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.02 | 2026-02-08T13:33:10.955914Z | {
"verified": true,
"answer": 37894,
"timestamp": "2026-02-08T13:33:10.976115Z"
} | bab0ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 1773
},
"timestamp": "2026-02-24T18:39:17.226Z",
"answer": 37894
},
{
"... | 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": "V8",
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
b33fe1_n | comb_factorial_compute_v1_601307018_427 | A puzzle game has levels numbered from $2$ to $8$. A level is unlocked only if its number is prime. The final challenge uses the factorial of the highest unlocked level number, $n!$, where $n$ is the largest prime between $2$ and $8$. Let $M = n!$. What is the remainder when $55849M$ is divided by $54195$? | 44,325 | COMB | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 3 | null | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-03-10T00:57:03.703876Z | null | f34778 | b33fe1 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 997
},
"timestamp": "2026-03-29T14:06:06.116Z",
"answer": 44325
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
5a00ae | nt_sum_gcd_range_mod_v1_458359167_1901 | Let $N = \sum_{k=1}^{55} \phi(k) \left\lfloor \frac{55}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $k = 168$ and $M = 10343$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Let $\text{result}$ be the remainder when $\text{sum}$ is divided by $M$, and let $Q = 40000 - \text{result}$. Comp... | 38,473 | graphs = [
Graph(
let={
"N": Summation(var="k", start=Const(1), end=Const(55), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(55), Var("k"))))),
"k": Const(168),
"M": Const(10343),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.121 | 2026-02-08T04:55:41.938282Z | {
"verified": true,
"answer": 38473,
"timestamp": "2026-02-08T04:55:42.059047Z"
} | acba92 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 4098
},
"timestamp": "2026-02-11T22:27:23.655Z",
"answer": 38473
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
81820d | algebra_quadratic_discriminant_v1_784195855_8010 | Let $d = 70$ and $m = 3$. Define $T$ to be the set of all integers $t$ such that there exist positive integers $a$ and $b$ satisfying $1 \le a \le 22$, $1 \le b \le 32$, $28 \le t \le 632$, and $t = 14a + 10b + 4$. Let $n = |T|$. Define $C$ to be the set of all positive integers $n'$ such that $1 \le n' \le n$, $m$ div... | 0 | graphs = [
Graph(
let={
"_d": Const(70),
"_c": Const(4),
"_m": Const(3),
"_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(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C5",
"COPRIME_PAIRS",
"COMB1/C5"
] | fbded7 | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"C5",
"COMB1",
"COPRIME_PAIRS",
"LIN_FORM"
] | 4 | 0.006 | 2026-02-08T09:39:38.024392Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T09:39:38.030755Z"
} | a43d04 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 292,
"completion_tokens": 4208
},
"timestamp": "2026-02-14T08:32:10.669Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6b52c5 | nt_count_coprime_and_v1_1125832087_1904 | Let $k_1 = 8$. Let $k_2$ be the number of positive integers $n$ such that $1 \leq n \leq 43$ and $\gcd(n, 6) = 1$. Compute the number of positive integers $n$ such that $1 \leq n \leq 71775$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 19,140 | graphs = [
Graph(
let={
"upper": Const(71775),
"k1": Const(8),
"k2": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(43)), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"C4"
] | 1 | 7.415 | 2026-02-08T04:12:52.099560Z | {
"verified": true,
"answer": 19140,
"timestamp": "2026-02-08T04:12:59.514152Z"
} | ed6246 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1834
},
"timestamp": "2026-02-10T15:55:31.068Z",
"answer": 19140
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
71468d | comb_count_permutations_fixed_v1_1915831931_1257 | Let $n' = 16392$ and $n = 8$. Define $k$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq 16392$ and $\binom{16392}{j}$ is odd. Compute $\binom{8}{k} \cdot !(8 - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 630 | graphs = [
Graph(
let={
"_n": Const(16392),
"n": Const(8),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16392)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_... | COMB | null | COUNT | sympy | MAX_PRIME_BELOW | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"V8"
] | 2 | 0.041 | 2026-02-08T15:58:04.926664Z | {
"verified": true,
"answer": 630,
"timestamp": "2026-02-08T15:58:04.967728Z"
} | 0c8dc2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 697
},
"timestamp": "2026-02-24T19:09:02.665Z",
"answer": 630
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
254d7b | nt_count_intersection_v1_124444284_5389 | Let $N = 20000$. Let $a$ be the smallest divisor of 105 that is at least 2, and let $b = 20$. Determine the number of positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. | 2,666 | graphs = [
Graph(
let={
"_n": Const(105),
"N": Const(20000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"b": Const(20),
"result": CountOverSet(set=Solution... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.149 | 2026-02-08T06:34:13.056472Z | {
"verified": true,
"answer": 2666,
"timestamp": "2026-02-08T06:34:14.205924Z"
} | fcfbbf | 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": 1736
},
"timestamp": "2026-02-13T02:09:19.048Z",
"answer": 2666
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
7b4c96 | sequence_lucas_compute_v1_1874849503_766 | Let $ n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor $, where $ \phi $ denotes Euler's totient function. Let $ L_n $ denote the $ n $th Lucas number. Compute the remainder when $ 12720 \cdot L_n $ is divided by $ 96293 $. | 19,451 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(12720), Ref("result")), modulus=Const(9... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_lucas_compute_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:18:15.397440Z | {
"verified": true,
"answer": 19451,
"timestamp": "2026-02-08T13:18:15.398435Z"
} | 464456 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1859
},
"timestamp": "2026-02-09T20:41:59.428Z",
"answer": 19451
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
76dbf0 | nt_count_gcd_equals_v1_1470522791_1576 | Let $k$ be the smallest divisor of $61309901$ that is at least $2$. Let $d$ be the largest prime number less than or equal to $391$. Find the number of positive integers $n \leq 31684$ such that $\gcd(n, k) = d$. | 81 | graphs = [
Graph(
let={
"upper": Const(31684),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(61309901))))),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | 9f9e96 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 6.44 | 2026-02-08T13:45:00.978470Z | {
"verified": true,
"answer": 81,
"timestamp": "2026-02-08T13:45:07.418799Z"
} | 15acbc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 831
},
"timestamp": "2026-02-16T04:56:28.410Z",
"answer": 70
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"statu... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
25c4a5 | sequence_lucas_compute_v1_153355830_1322 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 12$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $N$ be the number of elements in $T$. Define $n = \sum_{k=1}^{N} k$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $... | 24,476 | 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=2)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/SUM_ARITHMETIC"
] | 5a2696 | sequence_lucas_compute_v1 | null | 2 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.001 | 2026-02-08T06:19:05.743595Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T06:19:05.744829Z"
} | 66513d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1135
},
"timestamp": "2026-02-12T23:01:23.792Z",
"answer": 24476
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_la... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
5b67b3 | antilemma_k3_v1_1353956133_712 | Let $ n = 60409 $. Compute the sum of $ \phi(d) $ over all positive divisors $ d $ of $ n $. | 60,409 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=60409), 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 | 2026-02-08T11:48:37.092853Z | {
"verified": true,
"answer": 60409,
"timestamp": "2026-02-08T11:48:37.093257Z"
} | 3b334c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 665
},
"timestamp": "2026-02-16T03:23:20.384Z",
"answer": 105265
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
c1f3df | nt_max_prime_below_v1_168721529_1917 | Let $p$ and $q$ be positive integers such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all such $p$. Compute the number of elements in $S$. Let $n$ be a prime number satisfying $n \geq |S|$ and $n \leq 21609$. Determine the value of the largest such $n$. | 21,601 | graphs = [
Graph(
let={
"upper": Const(21609),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("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'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.497 | 2026-02-08T13:59:07.230396Z | {
"verified": true,
"answer": 21601,
"timestamp": "2026-02-08T13:59:07.726994Z"
} | 971d27 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 3047
},
"timestamp": "2026-02-09T23:30:29.043Z",
"answer": 21601
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
1a5f5a | modular_count_residue_v1_1915831931_194 | Let $m$ be the sum of the solutions to the equation $x^2 - 24x - 7252 = 0$. Let $r$ be the minimum value of $x_1 + y$ over all ordered pairs $(x_1, y)$ of positive integers such that $x_1 y = 25$.
Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 80200$ and $n \equiv r \pmod{m}$. Determine the num... | 3,342 | graphs = [
Graph(
let={
"upper": Const(80200),
"m": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-24), Var("x")), Const(-7252)), Const(0)))),
"r": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Va... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"VIETA_SUM",
"B3"
] | 018050 | modular_count_residue_v1 | null | 4 | 0 | [
"B3",
"SUM_ARITHMETIC",
"VIETA_SUM"
] | 3 | 7.623 | 2026-02-08T15:13:34.585067Z | {
"verified": true,
"answer": 3342,
"timestamp": "2026-02-08T15:13:42.208108Z"
} | e9e21e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 642
},
"timestamp": "2026-02-16T01:59:17.117Z",
"answer": 3342
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
effcd0 | antilemma_k3_v1_1125832087_95 | Let $x = \sum_{d \mid 51941} \phi(d)$. Let $y = |x| + 1$.
Compute $x + \phi(y) + \tau(y)$, where $\tau(y)$ denotes the number of positive divisors of $y$. | 67,677 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=51941), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"K3"
] | feee28 | antilemma_k3_v1 | null | 4 | 0 | [
"IDENTITY_POW_ZERO",
"K3"
] | 2 | 0.001 | 2026-02-08T02:52:10.248026Z | {
"verified": true,
"answer": 67677,
"timestamp": "2026-02-08T02:52:10.249007Z"
} | 83a501 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 4595
},
"timestamp": "2026-02-10T11:42:45.784Z",
"answer": 67677
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"... | {
"lo": 1.08,
"mid": 2.76,
"hi": 4.31
} | ||
903219 | comb_sum_binomial_row_v1_124444284_7269 | Let $n$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 8$. Compute the remainder when $56861 \cdot 2^n$ is divided by $55046$. | 48,480 | graphs = [
Graph(
let={
"_n": Const(55046),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(8)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B1 | [
"B1"
] | 5b950e | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T08:58:50.842942Z | {
"verified": true,
"answer": 48480,
"timestamp": "2026-02-08T08:58:50.843915Z"
} | c5b45a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1103
},
"timestamp": "2026-02-13T23:41:11.886Z",
"answer": 48480
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bd1178 | sequence_fibonacci_compute_v1_1520064083_2106 | Let $n = 22$ and define $\text{result} = F_n$, the $n$-th Fibonacci number. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 32400$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $c$ be the minimum value in $T$. Let $P$ be the set of all positive integers $p$ fo... | 12,457 | graphs = [
Graph(
let={
"_n": Const(16),
"n": Const(22),
"result": Fibonacci(arg=Ref(name='n')),
"_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'... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1e3e48 | sequence_fibonacci_compute_v1 | quadratic_mod | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T04:30:51.674415Z | {
"verified": true,
"answer": 12457,
"timestamp": "2026-02-08T04:30:51.676658Z"
} | a953fe | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 291,
"completion_tokens": 3092
},
"timestamp": "2026-02-10T16:56:47.644Z",
"answer": 12457
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_D... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8fc44b | alg_poly_orbit_legendre_v1_601307018_7076 | Let $a$ be a non-negative integer with $0 \le a \le 13956$. Define $N = a^8 \bmod 17$, $M = (a^4 - a^3 - 5a^2 - 3a + 1) \bmod 17$, $R = M^8 \bmod 17$, $S = N + R$, and $T = (M^4 - M^3 - 5M^2 - 3M + 1) \bmod 17$. Find the number of such $a$ for which $T = a$, $S \equiv 0 \pmod{3}$, and $M \ne a$. | 1,642 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(-1), Pow(Var("a"), Const(3))), Mul(Const(-5), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(1)), modulus=Const(17)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(-1), Pow(Ref("p1"), ... | NT | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 7 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.068 | 2026-03-10T07:44:07.281638Z | {
"verified": true,
"answer": 1642,
"timestamp": "2026-03-10T07:44:07.349788Z"
} | 9d6f37 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 8903
},
"timestamp": "2026-04-19T05:57:21.136Z",
"answer": 1642
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
8c2017 | nt_min_coprime_above_v1_1978505735_3237 | Let $ \text{start} = 1949 $. Define $ \text{upper} $ to be the number of integers $ n $ such that $ 1 \leq n \leq 4384 $ and the sum of the decimal digits of $ n $ is odd. Let $ \text{modulus} = 234 $. Let $ S $ be the set of all integers $ n_1 $ such that $ n_1 > \text{start} $, $ n_1 \leq \text{upper} $, and $ \gcd(n... | 1,951 | graphs = [
Graph(
let={
"start": Const(1949),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4384)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"modulus": Const(234),
"resu... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | nt_min_coprime_above_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.022 | 2026-02-08T17:31:16.761758Z | {
"verified": true,
"answer": 1951,
"timestamp": "2026-02-08T17:31:16.784017Z"
} | fbcc93 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2711
},
"timestamp": "2026-02-18T03:42:31.229Z",
"answer": 1951
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0f9a23 | antilemma_k2_v1_655260480_1233 | Let $m$ be the sum of all real solutions $x_1$ to the equation $x_1^2 - 424x_1 - 4340 = 0$. Let $S$ be the set of all positive integers $x_2$ such that $x_2^2 - 424x_2 + 26175 = 0$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of the sum of the elements in $S$, where $\phi$ denotes Euler's totient fun... | 90,100 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-424), Var("x1")), Const(-4340)), Const(0)))),
"_n": SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='x2'), condition=E... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K3/K2",
"K2"
] | 9e3bdc | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3",
"VIETA_SUM"
] | 4 | 0.004 | 2026-02-08T16:00:10.397193Z | {
"verified": true,
"answer": 90100,
"timestamp": "2026-02-08T16:00:10.401180Z"
} | cfea36 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1246
},
"timestamp": "2026-02-16T19:14:53.438Z",
"answer": 90100
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
49d28e | nt_sum_totient_over_divisors_v1_717093673_517 | Let $n$ be the number of ordered pairs $(a, b)$ where $a$ is an integer from 1 to 21 and $b$ is an integer from 1 to 331. Compute $\sum_{d \mid n} \phi(d)$. | 6,951 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(331)))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("res... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.006 | 2026-02-08T15:29:56.812917Z | {
"verified": true,
"answer": 6951,
"timestamp": "2026-02-08T15:29:56.819043Z"
} | 666b30 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 517
},
"timestamp": "2026-02-16T06:57:47.250Z",
"answer": 6951
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
795c2d | diophantine_fbi2_count_v1_1915831931_3069 | Let $k = 420$. Consider the set of all integers $d$ such that $2 \leq d \leq 56$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Additionally, require that $\frac{k}{d}$ is less than or equal to the sum of all positive integers $n$ not exceeding 57 for which $n$ is divisible by 57.
Let $r$ be the number of such integers $... | 29,975 | graphs = [
Graph(
let={
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(56)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(Ref("k"), Var("d")), SumOverSe... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.011 | 2026-02-08T17:20:25.207734Z | {
"verified": true,
"answer": 29975,
"timestamp": "2026-02-08T17:20:25.219003Z"
} | 343a51 | 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": 1654
},
"timestamp": "2026-02-18T01:06:40.347Z",
"answer": 29975
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7e2e56 | sequence_lucas_compute_v1_458359167_4744 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 20$. Let $P$ be the maximum value of $xy$ over all pairs in $T$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $n$ be the minimum value of $x + y$ over all pairs in $S$. Define $L_n$ ... | 25,866 | graphs = [
Graph(
let={
"_m": Const(75052),
"_n": Const(96917),
"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")), MaxOverSet(set... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | sequence_lucas_compute_v1 | null | 3 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T12:01:35.051248Z | {
"verified": true,
"answer": 25866,
"timestamp": "2026-02-08T12:01:35.053274Z"
} | 314bb7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1726
},
"timestamp": "2026-02-14T21:48:24.044Z",
"answer": 25866
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lem... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cdf237 | alg_linear_system_2x2_v1_1218484723_5986 | Let $\det = -3 \cdot 11 - 3 \cdot (-7)$. Let $R = -243966 \cdot \left|\{ (a, b) : 1 \leq a, b \leq 30,\, 16a^2 + b^2 - 8ab = 144 \}\right| - 244254 \cdot (-7)$, and $S = -3 \cdot 244254 - 3 \cdot (-243966)$. Define $T = \frac{R}{\det} + \frac{S}{\det}$. Find the remainder when $20808T$ is divided by $56357$. | 4,178 | graphs = [
Graph(
let={
"_n": Const(30),
"num_x": Sub(Mul(Const(-243966), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Eq(Sum(Mul(Const(16), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | alg_linear_system_2x2_v1 | null | 4 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-02-25T07:34:18.605471Z | {
"verified": true,
"answer": 4178,
"timestamp": "2026-02-25T07:34:18.607464Z"
} | 37d46a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 6971
},
"timestamp": "2026-03-29T23:44:17.680Z",
"answer": 4178
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
831b43 | comb_count_partitions_v1_601307018_4915 | Find the number of positive integers $t$ such that $23 \leq t \leq 65$ and $t = 2a + 3b + 18$ for some integers $a, b$ with $1 \leq a \leq 10$ and $1 \leq b \leq 9$. Let $n$ denote this count. Compute $p(n)$, where $p(n)$ denotes the number of partitions of $n$ into positive integers. | 44,583 | 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=10)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-03-10T05:37:42.010847Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-03-10T05:37:42.013203Z"
} | e125c0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 10033
},
"timestamp": "2026-04-19T00:31:28.205Z",
"answer": 44583
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
c707a8 | comb_count_surjections_v1_1742523217_2505 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 14$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = |T|$. Compute the value of $55555 - k! \cdot... | 55,531 | graphs = [
Graph(
let={
"n": Const(4),
"k": 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")), Coun... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T04:48:07.264042Z | {
"verified": true,
"answer": 55531,
"timestamp": "2026-02-08T04:48:07.268236Z"
} | ae964a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 1372
},
"timestamp": "2026-02-24T01:54:57.565Z",
"answer": 55531
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
b171e8 | nt_count_digit_sum_v1_124444284_9918 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 29995$ and $\gcd(n, 6) = 1$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq N$ and the sum of the decimal digits of $n$ is $22$. | 540 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(29995)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"target_sum": Const(22),
"result": CountOverSet(set=... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.369 | 2026-02-08T12:43:38.147220Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T12:43:38.516128Z"
} | a03e1f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1716
},
"timestamp": "2026-02-15T04:33:00.479Z",
"answer": 540
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dcc1ca | diophantine_product_count_v1_898971024_466 | Let $n = 360$. Let $k$ be the largest positive divisor of $132120$ that is at most $n$. Let $\text{upper} = 26$. Compute the number of positive integers $x \leq \text{upper}$ such that $x$ divides $k$ and $\frac{k}{x} \leq \text{upper}$. | 4 | graphs = [
Graph(
let={
"_n": Const(360),
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(132120))))),
"upper": Const(26),
"result": CountOverSet(set=Solut... | NT | null | COUNT | sympy | LIN_FORM | [
"MAX_DIVISOR"
] | 51757e | diophantine_product_count_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 0.125 | 2026-02-08T15:27:55.915280Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T15:27:56.040213Z"
} | 7ff9b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1352
},
"timestamp": "2026-02-16T07:23:42.148Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cda1dc | antilemma_k3_v1_2051736721_5501 | Let $c = 2$. Let $m$ be the sum of all positive real solutions $x_1$ to the equation $x_1^2 - 1658x_1 + 139641 = 0$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $m$. Compute the sum of $\phi(d_1)$ over all positive divisors $d_1$ of the sum of $\phi(d_2)$ over all positive divisors $d_2$ of $n$. | 1,658 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Ref("_c")), Mul(Const(-1658), Var("x1")), Const(139641)), Const(0)))),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d')))... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K3",
"K3/K3",
"K3"
] | f2b5b1 | antilemma_k3_v1 | null | 5 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T18:37:47.217842Z | {
"verified": true,
"answer": 1658,
"timestamp": "2026-02-08T18:37:47.219216Z"
} | 8dd8d1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2288
},
"timestamp": "2026-02-18T18:25:31.417Z",
"answer": 1658
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0dab05 | nt_min_coprime_above_v1_397696148_2653 | Let $S$ be the set of all integers $n$ such that $1024 < n \leq 1257$ and $\gcd(n, 223) = 1$. Let $r$ be the smallest element of $S$. Let $d$ be the number of positive integers $k \leq 7325$ that are divisible by 25. Compute $$ (r \bmod d) + 1009 \cdot (r \bmod 337). $$ | 14,272 | graphs = [
Graph(
let={
"start": Const(1024),
"upper": Const(1257),
"modulus": Const(223),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(1)... | NT | null | EXTREMUM | sympy | C2 | [
"C2"
] | 580f49 | nt_min_coprime_above_v1 | two_moduli | 4 | 0 | [
"C2"
] | 1 | 0.023 | 2026-02-08T13:28:46.311955Z | {
"verified": true,
"answer": 14272,
"timestamp": "2026-02-08T13:28:46.334664Z"
} | 4d65d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 912
},
"timestamp": "2026-02-15T16:39:41.187Z",
"answer": 14272
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f9b32b | diophantine_fbi2_count_v1_2051736721_1258 | Let $k = 480$. Let $S$ be the set of integers $t$ such that $7 \leq t \leq 156$ and there exist integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 63$, and $t = 5a + 2b$. Let $D$ be the number of integers $d$ satisfying $3 \leq d \leq |S|$, $d$ divides $k$, and $2 \leq k/d \leq 145$. Compute the remainder when $6... | 19,254 | graphs = [
Graph(
let={
"k": Const(480),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(le... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.013 | 2026-02-08T15:55:22.131135Z | {
"verified": true,
"answer": 19254,
"timestamp": "2026-02-08T15:55:22.144477Z"
} | f5d861 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 3359
},
"timestamp": "2026-02-16T16:05:07.120Z",
"answer": 19254
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e807dd | antilemma_sum_factor_cartesian_v1_1874849503_756 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 25$ and $1 \le j \le 20$. Let $T$ be the set of all values $\mu(d)$, where $d$ divides $\gcd(4, 9)$, and $\mu$ denotes the Möbius function. For each pair $(i,j) \in S$, compute the product $ij$. Let $U$ be the set of all such pr... | 68,250 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=4), b=Const(value=9)), var='d', expr=MoebiusMu(n=Var(name='d'))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME"
] | 1428b5 | antilemma_sum_factor_cartesian_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T13:18:14.032383Z | {
"verified": true,
"answer": 68250,
"timestamp": "2026-02-08T13:18:14.033177Z"
} | 82b467 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 702
},
"timestamp": "2026-02-23T00:00:25.650Z",
"answer": 68250
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "o... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
e7c89d | algebra_poly_eval_v1_1978505735_7283 | Let $z$ be the number of integers $t$ such that $18 \le t \le 86$ and there exist positive integers $a \le 11$ and $b \le 3$ with $t = 4a + 14b$. Compute $9z^2 - 9z - 9$. | 7,299 | graphs = [
Graph(
let={
"_n": Const(2),
"z": 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=11)), Geq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T20:09:18.710699Z | {
"verified": true,
"answer": 7299,
"timestamp": "2026-02-08T20:09:18.713281Z"
} | 60a177 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 2682
},
"timestamp": "2026-02-19T00:02:19.327Z",
"answer": 7299
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2d9c2d | sequence_count_fib_divisible_v1_2051736721_2103 | Let $n = 795$. Let $u$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Let $d = 13$. Determine the value of the number of positive integers $k$ such that $1 \le k \le u$ and the $k$-th Fibonacci number is divisible by $d$. | 113 | graphs = [
Graph(
let={
"_n": Const(795),
"upper": SumOverDivisors(n=Ref(name='_n'), var='d1', expr=EulerPhi(n=Var(name='d1'))),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upp... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K3"
] | 2 | 0.093 | 2026-02-08T16:28:58.116468Z | {
"verified": true,
"answer": 113,
"timestamp": "2026-02-08T16:28:58.208972Z"
} | 033d53 | 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": 1452
},
"timestamp": "2026-02-17T05:17:23.352Z",
"answer": 113
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c0caa4 | modular_sum_quadratic_residues_v1_784195855_6941 | Let $n = 2$. Let $p$ be the smallest divisor of $34571$ that is greater than or equal to $n$. Compute $\frac{p(p-1)}{4}$. | 8,145 | 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(34571))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T09:00:57.116159Z | {
"verified": true,
"answer": 8145,
"timestamp": "2026-02-08T09:00:57.119048Z"
} | 5ed53e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 762
},
"timestamp": "2026-02-13T23:06:36.862Z",
"answer": 8145
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
36e112 | nt_min_with_divisor_count_v1_124444284_2043 | Let $U$ be the total number of ordered pairs $(i,j)$ such that $1 \le i \le 25$ and $1 \le j \le 125$. Consider the set of all positive integers $n$ such that $1 \le n \le U$ and the number of positive divisors of $n$ is exactly 9. Let $r$ be the smallest such $n$.
Compute the value of
$$
\sum_{n=1}^{|r|} \tau(n),
$$... | 140 | graphs = [
Graph(
let={
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(125)))),
"div_count": Const(9),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n")... | NT | null | EXTREMUM | sympy | B3 | [
"COUNT_CARTESIAN"
] | 409d7d | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 0.59 | 2026-02-08T04:16:52.816106Z | {
"verified": true,
"answer": 140,
"timestamp": "2026-02-08T04:16:53.406413Z"
} | f25cd9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1366
},
"timestamp": "2026-02-10T15:59:22.226Z",
"answer": 140
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
04e563 | nt_max_prime_below_v1_1874849503_136 | Let $n$ be an integer. Consider the set of all prime numbers $n$ such that $2 \le n \le 80000$. Let $p$ be the largest element in this set. Let $d$ be a positive divisor of $41327$ such that $d \ge 2$, and let $m$ be the smallest such $d$. Compute the value of the Bell number $B_k$, where $k$ is the remainder when $|p|... | 877 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(80000),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulu... | NT | COMB | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_max_prime_below_v1 | bell_mod | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.681 | 2026-02-08T12:49:42.837857Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T12:49:45.518804Z"
} | f36d56 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 3031
},
"timestamp": "2026-02-10T03:31:34.707Z",
"answer": 877
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
90f52c | antilemma_cartesian_v1_1520064083_5010 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 27$ and $1 \leq b \leq 28$. Let $A$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 614$. Let $B$ be the number of positive integers $t$ with $15 \leq t \leq 969$ such that there exist positive integers ... | 15,998 | graphs = [
Graph(
let={
"_m": Const(614),
"_n": Const(64482),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(27)), right=IntegerRange(start=Const(1), end=Const(28)))),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=CountOver... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COMB1",
"COUNT_CARTESIAN"
] | 45c37c | antilemma_cartesian_v1 | two_moduli | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T06:33:05.120209Z | {
"verified": true,
"answer": 15998,
"timestamp": "2026-02-08T06:33:05.124168Z"
} | 1ed902 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 311,
"completion_tokens": 28062
},
"timestamp": "2026-02-24T06:35:48.052Z",
"answer": 15998
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
440f4e | modular_sum_quadratic_residues_v1_1520064083_2436 | Let $p$ be the largest prime number less than or equal to 198. Compute $\frac{p(p-1)}{4}$. | 9,653 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(198)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goal=Ref("re... | NT | null | SUM | sympy | B3 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T04:44:12.622529Z | {
"verified": true,
"answer": 9653,
"timestamp": "2026-02-08T04:44:12.626513Z"
} | 9b989c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 344
},
"timestamp": "2026-02-11T21:50:31.562Z",
"answer": 9653
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
7d144a | algebra_quadratic_discriminant_v1_124444284_440 | Let $d$ be a positive integer such that $1 \leq d \leq 362$ and $d$ divides $135026$. Let $\_n$ be the largest such $d$.
Let $a = -5$, $b = -9$, and $c = 6$. Define
$$
\text{result} = b^2 - \left(\text{the largest integer } k \text{ such that } 5^k \text{ divides } \binom{905}{\_n}\right) \cdot a \cdot c.
$$
Find the... | 36,364 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(362)), Divides(divisor=Var("d"), dividend=Const(135026))))),
"a": Const(-5),
"b": Const(-9),
"c": Con... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/V7"
] | aa4c63 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"MAX_DIVISOR",
"V7"
] | 2 | 0.004 | 2026-02-08T03:17:43.547148Z | {
"verified": true,
"answer": 36364,
"timestamp": "2026-02-08T03:17:43.551610Z"
} | b54e0d | 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": 1936
},
"timestamp": "2026-02-09T17:42:59.461Z",
"answer": 36364
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
cba58a | nt_max_prime_below_v1_1978505735_1931 | Let $s$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 24$ and $\gcd(p, q) = 1$. Let $n$ be a prime number satisfying $s \leq n \leq 52900$. Determine the largest such prime number $n$. Compute the value of $n$. | 52,889 | graphs = [
Graph(
let={
"upper": Const(52900),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("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'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.043 | 2026-02-08T16:31:51.728426Z | {
"verified": true,
"answer": 52889,
"timestamp": "2026-02-08T16:31:54.770951Z"
} | 83b923 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 3389
},
"timestamp": "2026-02-17T07:13:13.335Z",
"answer": 52889
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ebae57 | diophantine_fbi2_count_v1_168721529_1233 | Let $ n = 12 $. Define $ A $ to be the set of all positive integers $ n' $ such that $ 1 \leq n' \leq 36 $ and $ n $ divides $ F_{n'} $, where $ F_k $ denotes the $ k $-th Fibonacci number. Let $ m = |A| $. Now consider the set of all positive integers $ d $ such that:
- $ d \geq m $,
- $ d \leq 52 $,
- $ d $ divides ... | 55,430 | graphs = [
Graph(
let={
"_n": Const(12),
"k": Const(720),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(36)), Divides(divisor=Ref("_n... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.007 | 2026-02-08T13:32:49.304113Z | {
"verified": true,
"answer": 55430,
"timestamp": "2026-02-08T13:32:49.311261Z"
} | 4cb8b3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 3325
},
"timestamp": "2026-02-09T14:52:24.669Z",
"answer": 55430
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
63a44f | comb_count_surjections_v1_48377204_2398 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 24$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 6a + 4b$. Let $k = 3$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty u... | 540 | 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=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:45:34.939546Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T16:45:34.942043Z"
} | 016ae0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1016
},
"timestamp": "2026-02-17T10:41:18.353Z",
"answer": 540
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
3e0964 | geo_count_lattice_rect_v1_1978505735_736 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 169$ and $0 \leq y \leq 95$. | 16,320 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(95),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T15:34:40.553102Z | {
"verified": true,
"answer": 16320,
"timestamp": "2026-02-08T15:34:40.553772Z"
} | db4c26 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 192
},
"timestamp": "2026-02-24T17:57:45.713Z",
"answer": 16320
},
{
"... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
a56751 | nt_min_with_divisor_count_v1_1918700295_3544 | Let $n = 46011$. Let $U$ be the number of nonnegative integers $j$ with $0 \le j \le 46011$ such that $\binom{n}{j}$ is odd. Let $m$ be the smallest positive integer such that $m \le U$ and $m$ has exactly two positive divisors. Determine the value of $m$. | 2 | graphs = [
Graph(
let={
"_n": Const(46011),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(46011)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | EXTREMUM | sympy | V8 | [
"V8"
] | 86348e | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.08 | 2026-02-08T08:41:59.675961Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T08:41:59.756415Z"
} | 043eac | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 739
},
"timestamp": "2026-02-15T20:20:19.884Z",
"answer": 1031
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
ad4be1 | sequence_lucas_compute_v1_601307018_8946 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 25$ and $1 \le b \le N$, where $$N = \left|\{ (a_1, b_1) \in \mathbb{Z}^+ \times \mathbb{Z}^+ : 1 \le a_1, b_1 \le 25,\ 2a_1^4 + 8a_1^3b_1 + 12a_1^2b_1^2 + 8a_1b_1^3 + 2b_1^4 = 913952 \}\right|,$$ such that $$17a^4 + 68a^3b + 102a^2b... | 3,508 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(77005),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(v... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/POLY4_COUNT"
] | fd26b0 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"POLY4_COUNT"
] | 1 | 0.007 | 2026-03-10T09:22:42.727023Z | {
"verified": true,
"answer": 3508,
"timestamp": "2026-03-10T09:22:42.733825Z"
} | 929088 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 336,
"completion_tokens": 2826
},
"timestamp": "2026-04-19T10:13:36.118Z",
"answer": 3508
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
3aec69 | sequence_fibonacci_compute_v1_48377204_2887 | Let $T$ be the set of all integers $t$ such that $20 \leq t \leq 52$ and there exist positive integers $a \leq 5$ and $b \leq 5$ satisfying $t = 3a + 5b + 12$. Let $n$ be the number of elements in $T$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-... | 75,025 | 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=5)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:03:29.804874Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T17:03:29.807032Z"
} | f891d7 | 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": 2292
},
"timestamp": "2026-02-17T18:00:03.144Z",
"answer": 75025
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
90fd99 | nt_sum_gcd_range_mod_v1_397696148_2799 | Let $N$ be the number of positive integers $n \leq 15488$ such that $7$ divides the $n$th Fibonacci number. Let $k = 96$ and $M = 10597$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $c = 32768$ and $Q = c - (\text{sum} \bmod M)$. Find the value of $Q$. | 32,099 | graphs = [
Graph(
let={
"_n": Const(7),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(15488)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"k": Const(96),
"M": Const(10597)... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.857 | 2026-02-08T13:33:47.099111Z | {
"verified": true,
"answer": 32099,
"timestamp": "2026-02-08T13:33:47.956327Z"
} | 84655b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2342
},
"timestamp": "2026-02-16T00:05:59.088Z",
"answer": 32099
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d103e9 | diophantine_product_count_v1_677425708_492 | Let $k = 120$ and $u = 97$. Determine the number of positive integers $x$ such that $1 \le x \le u$, $x$ divides $k$, and $\frac{k}{x} \le u$. | 14 | graphs = [
Graph(
let={
"k": Const(120),
"upper": Const(97),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper")))... | NT | null | COUNT | sympy | LIN_FORM | [
"COPRIME_PAIRS/MOBIUS_SQUAREFREE",
"WILSON"
] | c7b528 | diophantine_product_count_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MOBIUS_SQUAREFREE",
"WILSON"
] | 4 | 0.051 | 2026-02-08T03:34:23.133888Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T03:34:23.184747Z"
} | 3d9a3f | 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": 1116
},
"timestamp": "2026-02-08T20:39:23.268Z",
"answer": 14
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0396c1 | antilemma_sum_equals_v1_717093673_202 | Let $n = 36$. Determine the value of $x$, where $x$ is the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 36$, $1 \leq j \leq 36$, and $i + j = 36$. | 35 | graphs = [
Graph(
let={
"_n": Const(36),
"x": 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(36)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.094 | 2026-02-08T15:14:16.323180Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T15:14:16.416723Z"
} | 8411cf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 360
},
"timestamp": "2026-02-24T20:09:21.826Z",
"answer": 35
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -8,
"mid": -4.75,
"hi": -2.29
} | ||
a0e7e5 | geo_count_lattice_rect_v1_1439011603_2053 | Compute the number of lattice points in the rectangle $[0, 289] \times [0, 191]$. | 55,680 | graphs = [
Graph(
let={
"a": Const(289),
"b": Const(191),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T16:29:02.315847Z | {
"verified": true,
"answer": 55680,
"timestamp": "2026-02-08T16:29:02.316784Z"
} | 645610 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 284
},
"timestamp": "2026-05-03T10:19:17.076Z",
"answer": 55680
},
{
"... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
7818af | nt_max_prime_below_v1_458359167_641 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $n \geq |S|$ and $n \leq 76176$. Determine the value of the largest element in $T$. | 76,163 | graphs = [
Graph(
let={
"upper": Const(76176),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("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'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.594 | 2026-02-08T03:27:25.242735Z | {
"verified": true,
"answer": 76163,
"timestamp": "2026-02-08T03:27:28.837178Z"
} | f9697a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 6475
},
"timestamp": "2026-02-10T13:38:41.805Z",
"answer": 76163
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"st... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7a09b7 | algebra_quadratic_discriminant_v1_1431428450_225 | Let $n = 41503$. Let $a = 2$ and $b = 5$. Let $c$ be the smallest divisor of $n$ that is at least 2. Define $S$ as the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 27000$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be the number of elements in $S$. Compute the value ... | 39,133 | graphs = [
Graph(
let={
"_n": Const(41503),
"a": Const(2),
"b": Const(5),
"c": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Sub(Pow(Ref("b"), Const(2)),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | a3b634 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T13:18:41.637014Z | {
"verified": true,
"answer": 39133,
"timestamp": "2026-02-08T13:18:41.641012Z"
} | 908225 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1572
},
"timestamp": "2026-02-15T13:54:11.188Z",
"answer": 39133
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b124d3 | modular_sum_quadratic_residues_v1_971394319_246 | Let $p = 197$. Compute the value of $\frac{p(p-1)}{k}$, where $k$ is the number of positive integers $j$ such that $1 \leq j \leq 4$ and $j^2 \leq 16$. | 9,653 | graphs = [
Graph(
let={
"_n": Const(4),
"p": Const(197),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(2)), Const(16))), domain='po... | NT | null | SUM | sympy | C3 | [
"C3"
] | 8a214c | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"C3"
] | 1 | 0.002 | 2026-02-08T12:55:00.182800Z | {
"verified": true,
"answer": 9653,
"timestamp": "2026-02-08T12:55:00.184725Z"
} | b5a800 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 504
},
"timestamp": "2026-02-15T08:02:11.905Z",
"answer": 9653
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0a523f | nt_count_divisible_v1_2051736721_7 | Let $n$ be a positive integer such that $1 \leq n \leq 84681$. Define $s$ to be the sum
$$
\sum_{k=0}^{3} (-1)^k \binom{a}{k},
$$
where $a$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers satisfying $x_1 + x_2 = 6$. Suppose that $n$ satisfies
$$
n \equiv s \pmod{20}.
$$
Let $N$ be the number of suc... | 54,640 | graphs = [
Graph(
let={
"upper": Const(84681),
"divisor": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | nt_count_divisible_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 2.567 | 2026-02-08T15:07:22.754316Z | {
"verified": true,
"answer": 54640,
"timestamp": "2026-02-08T15:07:25.321540Z"
} | 780f05 | 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": 5748
},
"timestamp": "2026-02-24T20:01:49.803Z",
"answer": 54640
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SU... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
2263c9 | nt_count_coprime_v1_1248542787_337 | Let $S$ be the set of all positive integers $n \leq 22801$ such that $\gcd(n, 22) = 1$. Let $r = |S|$. Let $p$ be the largest prime number at most $1012$. Compute the remainder when $r \bmod 307 + p \cdot (r \bmod 317)$ is divided by $80552$. | 62,119 | graphs = [
Graph(
let={
"upper": Const(22801),
"k": Const(22),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
"Q": Mod(value=Sum(Mod(value=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_coprime_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.726 | 2026-02-08T03:03:56.806852Z | {
"verified": true,
"answer": 62119,
"timestamp": "2026-02-08T03:03:58.532455Z"
} | 79d050 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1857
},
"timestamp": "2026-02-09T03:01:54.692Z",
"answer": 62119
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
e775d4 | diophantine_fbi2_min_v1_1918700295_636 | Let $d$ be a positive integer such that $6 \leq d \leq 34$, $d$ divides $24$, and $\frac{24}{d} \geq 3$. Let $r$ be the smallest such $d$. Compute the remainder when $43922r$ is divided by $57879$. | 32,016 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(24),
"upper": Const(34),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"),... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.007 | 2026-02-08T03:21:22.092182Z | {
"verified": true,
"answer": 32016,
"timestamp": "2026-02-08T03:21:22.099642Z"
} | 4a7726 | 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": 722
},
"timestamp": "2026-02-10T13:57:05.088Z",
"answer": 32016
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
55bf85 | nt_sum_totient_over_divisors_v1_153355830_1115 | Let $n = 91546$. Define $r$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8970025$. Define $\sigma$ to be the minimum value of $x + y$ over all such pairs. Let $c$ be ... | 27,402 | graphs = [
Graph(
let={
"_n": Const(98122),
"n": Const(91546),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var... | NT | null | COMPUTE | sympy | B3 | [
"B3/COMB1"
] | a99932 | nt_sum_totient_over_divisors_v1 | affine_mod | 5 | 0 | [
"B3",
"COMB1"
] | 2 | 0.003 | 2026-02-08T04:24:33.618179Z | {
"verified": true,
"answer": 27402,
"timestamp": "2026-02-08T04:24:33.621672Z"
} | e1e0fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 2039
},
"timestamp": "2026-02-12T20:23:56.626Z",
"answer": 27402
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e778e9 | nt_count_coprime_v1_784195855_10051 | Let $k = \sum_{i=1}^{5} i$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 67600$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 36,053 | graphs = [
Graph(
let={
"upper": Const(67600),
"k": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), C... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_coprime_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 5.324 | 2026-02-08T17:23:48.850501Z | {
"verified": true,
"answer": 36053,
"timestamp": "2026-02-08T17:23:54.174365Z"
} | 14e7bf | 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": 594
},
"timestamp": "2026-02-18T01:44:47.481Z",
"answer": 36053
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
00e68b | lte_diff_endings_v1_1742523217_1238 | Let $a = 19$, $b = 9$, $p = 2$, and $n = 1280$. Define $v_p$ to be the largest integer $k$ such that $2^k$ divides $19^{1280} - 9^{1280}$. Let $k = 12491$. Compute $(k \cdot v_p) \bmod 100000$. | 24,910 | graphs = [
Graph(
let={
"a_val": Const(19),
"b_val": Const(9),
"p_val": Const(2),
"n_val": Const(1280),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("b... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:34:41.331900Z | {
"verified": true,
"answer": 24910,
"timestamp": "2026-02-08T03:34:41.332623Z"
} | 52a2f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 537
},
"timestamp": "2026-02-10T05:27:17.313Z",
"answer": 24910
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
534b60 | nt_num_divisors_compute_v1_1116507919_267 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 2912816907000$, $\gcd(p, q) = 1$, and $p < q$. Compute the number of positive divisors of $n$. | 8 | 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=2912816907000)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(v... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T02:30:12.816701Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T02:30:12.817760Z"
} | 48a15c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T13:59:29.259Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 2.22,
"mid": 3.62,
"hi": 5.01
} | ||
06fa02 | antilemma_sum_equals_v1_458359167_25 | Let $T$ be the set of integers $t$ with $7 \le t \le 64$ for which there exist integers $a$ and $b$ such that $1 \le a \le 4$, $1 \le b \le 13$, and $t = 3a + 4b$. Let $m = |T|$. Let $P$ be the set of ordered pairs $(i,j)$ of integers with $1 \le i \le 50$ and $1 \le j \le 51$ such that $i + j = m$. Let $n = |P|$. Let ... | 47 | 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=4)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b43a9c | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.04 | 2026-02-08T02:57:17.414167Z | {
"verified": true,
"answer": 47,
"timestamp": "2026-02-08T02:57:17.454346Z"
} | c78c7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 3077
},
"timestamp": "2026-02-10T11:59:50.250Z",
"answer": 47
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} |
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