The Bakery algorithm is a landmark algorithm for ensuring mutual exclusion among N processes that communicate via shared variables. Starting from existing TLA+ specifications, we use the recently-developed IC3PO parameterized model checker to automatically compute inductive invariants for two versions of the algorithm. We compare the machine-generated invariants with human-written invariants that were used in an interactive correctness proof checked by the TLA+ Proof System. Our experience suggests that automated invariant inference is becoming a viable alternative to labor-intensive human-written proofs.