Datasets:
messages listlengths 3 3 | task_type stringclasses 4
values | source_ds stringclasses 5
values | lang stringclasses 1
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|---|---|---|---|---|
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Consider the terms of an arithmetic sequence: $-\\frac{1}{3}, y+2, 4y, \\ldo... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Suppose that $g(x) = 5x - 3$. What is $g^{-1}(g^{-1}(14))$?"
},
{
"r... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "A farmer has a rectangular field with dimensions $3m+8$ and $m-3$ where $m$ ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the functions $f(x) = \\log_a(1+x)$ and $g(x) = \\log_a(1-x)$, where $... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Find all solutions to the equation $\\displaystyle\\sqrt[3]{3 - \\frac{x}{3}... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "In $\\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, a... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Julian is writing a comic book. On average, his story has 280 frames per pag... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "If an arc of $60^{\\circ}$ on circle $C$ has the same length as an arc of $4... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given that $P$ is any point on the circle $C$: $(x-2)^{2}+(y-2)^{2}=1$, and ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Compute $\\cos 225^\\circ$."
},
{
"role": "assistant",
"content"... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given that $b$ is a multiple of $2373$, find the greatest common divisor of ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Let \\( a, b, c \\) be positive real numbers. Prove that\n\n$$\n\\frac{1}{a(... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "A set consists of five different odd positive integers, each greater than 2.... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Tom decides to open a theater. He knows it will cost $5 per square foot of s... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given real numbers \\( a, b, c \\) and a positive number \\( \\lambda \\) su... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Factorize: $x^{3}-6x^{2}+9x=\\_\\_\\_\\_\\_\\_.$"
},
{
"role": "assi... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "In triangle $ABC$, $CA = CB$, and $D$ is the midpoint of $AB$. Line $EF$ pas... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Consider the product of $x^5$, $x^2 + \\frac{1}{x^2}$, and $1 + \\frac{2}{x}... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The sum of three numbers $a$, $b$, and $c$ is 120. If we increase $a$ by 8, ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "A vessel of capacity 2 liters has a certain percentage of alcohol and anothe... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given that the sum of the first $n$ terms of a sequence $\\{a\\_n\\}$ is $S\... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Find the value of $k$ such that all roots of the polynomial $x^4 - 4x^3 + 4x... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "At its Grand Opening, the Guthrie Market distributed two different types of ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Let \\( p = 2^{3009}, q = 3^{2006}, \\) and \\( r = 5^{1003} \\). Which of t... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "For a car, what scams can be plotted with 0% financing vs rebate?"
},
{
... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "When \\( a < -1 \\), the nature of the roots for the equation\n$$\n\\left(a^... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Three vertices of a cube are $A = (5, 9, 6)$, $B = (5, 14, 6)$, and $C = (5,... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Suppose that $A, B, C, D$ are four points in the plane, and let $Q, R, S, T,... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the function $f(x)=x\\ln x$, if $0 \\lt x_{1} \\lt x_{2}$, then which ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given \\\\(f(x)=2a-\\sin x\\\\), then \\\\(f''(x)=\\\\) \nA: \\\\(\\cos x\\... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Jimmy decides to make sandwiches for a picnic. He makes 8 sandwiches in tot... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "How many two-digit positive integers are congruent to 1 (mod 5)?"
},
{
... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the following four propositions: \n① The negation of the proposition ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Why does it matter if a Central Bank has a negative rather than 0% interest ... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The molecular weight of a certain substance is 74. What is the molecular wei... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "We flip a fair coin 12 times. What is the probability that we get heads in e... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "How many distinct, positive factors does $1320$ have?"
},
{
"role": ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Observe the pattern of the following equations and answer the following ques... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Find the product of the solutions of the equation: $|z| = 3(|z| - 2)$."
},... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given that \\(1 \\leq x, y, z \\leq 6\\), how many cases are there in which ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "A square of side $4$ is dissected into four pieces such that $E$ and $F$ are... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Dilan, Martha, Phillip, and Veronica went to the park together to have some ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The following line is parameterized, so that its direction vector is of the ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Let \\( a_0, a_1, \\ldots \\) be a sequence of positive integers, and let \\... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Casey is going to stay at a motel while she works her summer job as a ski in... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The sum of the first 3000 terms of a geometric sequence is 500. The sum of t... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "David obtained 96 marks in English, 98 in Mathematics, 99 in Physics, some m... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "What is the least positive multiple of 25 that is greater than 500?"
},
... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given that an interior angle of a regular polygon is $144^{\\circ}$, then th... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "if p is the product of the integers from 1 to 35 , inclusive , what is the g... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the function $f(x)=(ax^2+x+a)e^{-x}$ $(a\\in \\mathbb{R})$.\n\n$(1)$ I... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Let $g_0(x) = x + |x-200|-|x+200|$, and for $n \\geq 1$, let $g_n(x) = |g_{n... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the plane vectors $\\overrightarrow{a}$, $\\overrightarrow{b}$, $\\ove... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Where should I be investing my money?"
},
{
"role": "assistant",
... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "In triangle \\( DEF \\), \\( DE = 6 \\), \\( EF = 8 \\), and \\( DF = 10 \\)... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Prove that for each \\( n \\geq 2 \\), there is a set \\( S \\) of \\( n \\)... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given $p$: $|4x-3|\\leqslant 1$ and $q$: $x^{2}-(2a+1)x+a^{2}+a\\leqslant 0$... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Compute\n\\[\n\\sum_{n=1}^\\infty \\frac{3n + 2}{n(n + 1)(n + 3)}.\n\\]"
}... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Solve the inequality\n\\[ -8x^2 + 6x - 1 < 0. \\]"
},
{
"role": "ass... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Each edge of a cube is colored either red or black. Every face of the cube h... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Specifically when do options expire?"
},
{
"role": "assistant",
... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "If $3x - y = 9$ and $x + 4y = 11$, what is the value of $x$?"
},
{
"... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Consider a quadratic polynomial \\[x^2 - tx + q,\\] where the roots \\(r_1\\... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Jane has sixteen slips of paper with numbers $2, 2, 2.5, 2.5, 3, 3, 3.5, 3.5... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Jason drives past 3 convenience stores on his way to work. The distance betw... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the function $f(x)=-x^{5}-3x^{3}-5x+3$, if $f(a)+f(a-2) > 6$, then the... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Find all prime numbers \\( p \\) such that for any prime number \\( q < p \\... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Sally had 27 Pokemon cards. Dan has some new Pokemon cards. Sally bought 20 ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The correct statement is \\_\\_\\_\\_\\_\\_ (only fill in the number of the ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given that ( ( ( 13 ! ) ^ some_power ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "For the nonzero numbers $a$, $b$, and $c$, define $$\n\\text{{J}}(a,b,c) = \... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Negative Balance from Automatic Options Exercise. What to do?"
},
{
... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the sequence ${a_n}$, the sum of the first n terms, S<sub>n</sub>, is ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "In acute triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, a... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given a complex number $z$ satisfying $\\frac {2i}{z}=- \\sqrt {3}-i$ (where... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Alice's white water rafting class is composed of some students and 10 instru... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Approximation of equity value for company in default"
},
{
"role": "... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$,... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Define a regular \\(n\\)-pointed star as described in the original problem, ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The greatest prime number that is a divisor of $16,385$ is $3$ because $16,3... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "If the circle $(x-a)^2+(x+4)^2=9$ is tangent to the y-axis, then $a=$ ___."
... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "If the tangent line to the curve $y=e^{x}$ at $x=1$ is perpendicular to the ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The value range of the function $f(x)=\\sin x-\\cos \\left(x+ \\frac {\\pi }... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that sati... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given ellipse $C_{1}: \\dfrac {x^{2}}{a^{2}}+ \\dfrac {y^{2}}{b^{2}}=1(a > b... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "To earn money for her new computer, Tina sells handmade postcards. In a day,... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Is it true that 90% of investors lose their money?"
},
{
"role": "as... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Eric has a chicken farm with some chickens. His chickens lay 3 eggs each day... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Given the sequence $a_n$: $\\frac{1}{1}$, $\\frac{2}{1}$, $\\frac{1}{2}$, $\... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Nine families have an average of 3 children per family. If exactly three of ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Let $n$ and $k$ be integers, $1\\le k\\le n$ . Find an integer $b$ an... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "A rectangle is divided into three equal parts along its length and two equal... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Kaleb revises his definition of a $\\emph{clever integer}$ as an even intege... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Suppose $\\sin y = 0$ and $\\cos(y+w) = -\\frac{1}{2}$. What is the smallest... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "The reciprocal of the real number $-2$ is ( )\n\nA: $2$\n\nB: $-2$\n\nC: $\\... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "How many four-digit numbers satisfy the property that the second digit is th... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Can a company charge you for services never requested or received?"
},
{... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Find all real numbers $x$ so that the product $(x + i)((x + 1) + i)((x + 2) ... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "Working out if I should be registered as self-employed in the UK"
},
{
... | finance_instruction | gbharti/finance-alpaca | en | genesis_default |
[
{
"role": "system",
"content": "Tu es GENESIS, prover symbolique de AetherEngine V4. Tu construis preuves formelles, selectionnes premises, chaines inferences (Lean/Coq/Isabelle style)."
},
{
"role": "user",
"content": "A triangle with vertices \\(A = (2, 6)\\), \\(B = (5, -2)\\), and \\(C = (7,... | math_symbolic | AI-MO/NuminaMath-CoT | en | genesis_default |
End of preview. Expand in Data Studio
YAML Metadata Warning:The task_categories "conversational" is not in the official list: text-classification, token-classification, table-question-answering, question-answering, zero-shot-classification, translation, summarization, feature-extraction, text-generation, fill-mask, sentence-similarity, text-to-speech, text-to-audio, automatic-speech-recognition, audio-to-audio, audio-classification, audio-text-to-text, voice-activity-detection, depth-estimation, image-classification, object-detection, image-segmentation, text-to-image, image-to-text, image-to-image, image-to-video, unconditional-image-generation, video-classification, reinforcement-learning, robotics, tabular-classification, tabular-regression, tabular-to-text, table-to-text, multiple-choice, text-ranking, text-retrieval, time-series-forecasting, text-to-video, image-text-to-text, image-text-to-image, image-text-to-video, visual-question-answering, document-question-answering, zero-shot-image-classification, graph-ml, mask-generation, zero-shot-object-detection, text-to-3d, image-to-3d, image-feature-extraction, video-text-to-text, keypoint-detection, visual-document-retrieval, any-to-any, video-to-video, other
genesis-sft-v1-mix
AETHER family SFT dataset — group mix.
Format: JSONL ChatML messages, task_type tagged, MinHash dedup applied (threshold 0.85).
Schema:
{
"messages": [{"role": "system|user|assistant", "content": "..."}],
"task_type": "function_calling|code|reasoning_cot|...",
"source_ds": "<HF dataset_id>",
"lang": "en|fr|...",
"system_source": "archon_default|overridden_from_source"
}
Generated by prepare_sft.py pipeline (2026-05-25).
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