Counterexamples to conjectures about Subset Takeaway and counting linear extensions of a Boolean lattice

We develop an algorithm for efficiently computing recursively defined functions on posets. We illustrate this algorithm by disproving conjectures about the game Subset Takeaway (Chomp on a hypercube) and computing the number of linear extensions of the lattice of a 7-cube and related lattices.
Comment: 5 pages. v2 has improvements throughout and is to appear in Order