Christmas Streak 11/88: Mathematicians, Coffee, and Theorems

Hungarian mathematician Erdős Paul once asserted: "A mathematician is a device for turning coffee into theorems."

Why don't we prove it mathematically?

Solve the cryptogram below, and submit your answer as the 7-digit integer $\overline{\color{#3D99F6}T\color{#69047E}H\color{#20A900}E\color{#EC7300}O\color{#E81990}R\color{#20A900}E\color{#624F41}M}.$

$\begin{array}{ccccccccc} &&&\color{#D61F06}C&\color{#EC7300}O&\color{#CEBB00}F&\color{#CEBB00}F&\color{#20A900}E&\color{#20A900}E \\ &&&\color{#D61F06}C&\color{#EC7300}O&\color{#CEBB00}F&\color{#CEBB00}F&\color{#20A900}E&\color{#20A900}E \\ +&&&\color{#D61F06}C&\color{#EC7300}O&\color{#CEBB00}F&\color{#CEBB00}F&\color{#20A900}E&\color{#20A900}E \\ \hline &&\color{#3D99F6}T&\color{#69047E}H&\color{#20A900}E&\color{#EC7300}O&\color{#E81990}R&\color{#20A900}E&\color{#624F41}M \end{array}$

In a cryptogram, each symbol represents a distinct, non-negative, single digit, and all leading digits are non-zero.

This problem is a part of <Christmas Streak 2017> series.