  Monotone Boolean functions (MBFs) are Boolean functions $f: {0,1}^n
\rightarrow {0,1}$ satisfying the monotonicity condition $x \leq y \Rightarrow
f(x) \leq f(y)$ for any $x,y \in {0,1}^n$. The number of MBFs in n variables is
known as the $n$th Dedekind number. It is a longstanding computational
challenge to determine these numbers exactly - these values are only known for
$n$ at most 8. Two monotone Boolean functions are inequivalent if one can be
obtained from the other by renaming the variables. The number of inequivalent
MBFs in $n$ variables was known only for up to $n = 6$. In this paper we
propose a strategy to count inequivalent MBF's by breaking the calculation into
parts based on the profiles of these functions. As a result we are able to
compute the number of inequivalent MBFs in 7 variables. The number obtained is
490013148.
