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4
512
latex
stringlengths
1
188
sample_id
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S\vdash A\vee(C\wedge\neg C)
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train
human
lim_{x\rightarrow0^{-}}x^{-1}=-\infty
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train
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(\frac{3}{4})^{1}/(\frac{347}{455})^{8}
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train
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W_{i,j}\le-1/(k-1)
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train
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((\frac{7}{\sqrt{3}}+8)/197+87)
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train
human
\int sinx^{2}dx
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train
human
v\in(F_{2})^{d}
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train
human
\prod_{j<k=1}^{N}(z_{j}-z_{k})^{2p}
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train
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H(\varphi,\eta;x,t)
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train
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[\begin{matrix}.7&.2\\ .3&.8\end{matrix}]
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train
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R=\prod_{i=1}^{n}R_{i}
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train
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A=-\frac{1}{3}U
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train
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(\frac{7}{284}-5)^{56\cdot302^{282}}
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train
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0\notin\Phi
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train
human
\prod_{i\in I}X_{i}
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train
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[\begin{matrix}A&B\\ C&D\end{matrix}]
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train
human
\rho_{G_{1}...G_{m}}^{P_{G_{k_{1}}...G_{k_{q}}}}
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train
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\overline{y}_{x}=\frac{\sum_{i}y_{xi}}{n_{x}}
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train
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-\sqrt{3}
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train
human
\underline{P}(Cl_{t}^{\ge})
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train
human
2+\frac{24}{\sqrt{13}}
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train
human
\frac{(\frac{9}{6}+309)}{\frac{10}{10}}
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train
human
T_{c}=\frac{\sum_{x}xl_{x}m_{x}}{\sum_{x}l_{x}m_{x}}
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train
human
(\frac{6}{10})^{(\frac{58}{399}\cdot395)}
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train
human
b_{1}(\theta)sin(\theta)
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train
human
\sqrt{xi}
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train
human
(\begin{matrix}n\\ k\end{matrix})=(\begin{matrix}n-1\\ k\end{matrix})+(\begin{matrix}n-1\\ k-1\end{matrix})
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train
human
33.\overline{3}
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train
human
\frac{\beta_{n+1}}{\beta_{n}}=\frac{A(n)}{B(n)}
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train
human
\frac{df}{d\tau}=\sum_{\alpha=1}^{n}\frac{dx^{\alpha}}{d\tau}\frac{\partial f}{\partial x^{\alpha}}
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train
human
y=\sqrt{x}
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train
human
\frac{\partial L}{\partial y}
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train
human
\frac{(5-5)^{7}}{7\cdot7}
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train
human
\theta^{\prime}=0
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train
human
r_{ky}=\frac{\overline{ky}}{\sqrt{\overline{k^{3}}\overline{y^{3}}}}
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train
human
\hat{A}(t)
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train
human
s\{\begin{matrix}2\\ 4\end{matrix}\}
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train
human
t_{i}=\frac{\hat{\epsilon}_{i}}{\hat{\sigma}\sqrt{1-h_{ii}}}
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train
human
\int e^{-x}cos(x)dx
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train
human
(\begin{matrix}X\\ k\end{matrix})
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train
human
\frac{27}{25}
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train
human
\frac{\partial\omega}{\partial k}
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train
human
\frac{\partial(x,y)}{\partial(s,t)}
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train
human
\overline{l}
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train
human
r=k\frac{[O_{3}]^{2}}{[O_{2}]}
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train
human
\frac{171}{1}-8^{\sqrt{1}}
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train
human
\overline{\alpha}
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train
human
\frac{j}{i+j}<\rho
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train
human
\hat{p}_{x}=\frac{\hbar}{i}\frac{\partial}{\partial x}
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train
human
\eta(x)\frac{\partial w}{\partial t}
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train
human
\frac{10^{145}}{\frac{\frac{10}{376}}{234}}
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train
human
\frac{dy}{dt}
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train
human
(\begin{matrix}2\\ 6\end{matrix})
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train
human
WE[g(Y_{t},\theta)]=0
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train
human
(pq-1)\cdot t
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train
human
(J_{r})_{ij}=\frac{\partial r_{i}(\beta^{(s)})}{\partial\beta_{j}}
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train
human
\sqrt{10}
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train
human
\frac{\overline{Y}_{2}-\overline{Y}_{1}}{\sqrt{\sigma_{1}^{2}/n+\sigma_{2}^{2}/n}}
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train
human
\Delta\gamma=\gamma_{1}+\gamma_{2}-\gamma_{12}
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train
human
\tilde{d}=1
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train
human
\prod l_{i}=N>4\sqrt{q}
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train
human
\hat{\pi}
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train
human
\beta=\frac{4}{\sqrt{4-\frac{d^{9}}{c^{9}}}}
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train
human
Av_{t}=\mu_{t}dx
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train
human
\rho=\frac{1}{q(n\mu_{n}+p\mu_{p})}
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train
human
\hat{f}(x)
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train
human
\frac{\frac{\frac{5}{322}}{10}}{(\frac{\sqrt{10}}{70})^{8}}
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train
human
D(f)=
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train
human
\prod_{i=1}^{n}f(x_{i})
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train
human
\sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!}x^{2n}
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train
human
\overline{\nu}_{2}
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train
human
{1^{10}}^{\frac{500}{8}-234}
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train
human
\tilde{\Gamma}
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train
human
(P,J,E)
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train
human
\hat{y}=X\hat{\beta}
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train
human
\beta\le0.984\sqrt{2}
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train
human
\frac{\dot{\sigma}}{E}+\frac{\sigma}{\eta}=\dot{\epsilon}
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train
human
M_{A}=\frac{qL^{2}}{2}
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train
human
\overline{z_{l}}
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train
human
w(2)=\frac{2}{\sqrt{\pi}}
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train
human
f=\prod_{i=1}^{deg(f)}f_{i}^{i}
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train
human
J(y)=\int_{a}^{b}yy^{\prime}dx
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train
human
R=\frac{4\pi A}{P^{2}}
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train
human
\hat{W}_{T}
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train
human
(\begin{matrix}8\\ 4\end{matrix})
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train
human
\int d\mu O_{i}Ge^{iS}
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train
human
\langle\hat{T}\rangle
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train
human
\int|\kappa(s)|ds
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train
human
(\begin{matrix}X\\ k\end{matrix})
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train
human
\langle\sqrt{R}e^{i}\varphi,Z_{R}\rangle
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train
human
tc=\frac{1}{t_{n}-t_{1}}
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train
human
(\begin{matrix}6\\ 3\end{matrix})
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train
human
L=g_{\mu\nu}\frac{dx^{\mu}}{ds}\frac{dx^{\nu}}{ds}
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train
human
n^{2}=\sum_{i=1}^{n}2i-1
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train
human
V_{+}\oplus g_{0}\oplus V_{-}
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train
human
W=\int VdP
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train
human
\frac{x_{j}-x_{m}}{x_{j}-x_{m}}=1
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train
human
(1-p^{2})^{N-2}
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train
human
\hat{5}
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train
human
=(\frac{Q^{2}}{2gm^{2}y^{4}})+y
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train
human