  In this paper we study the solvability of the equality negation task in a
simple wait-free model where processes communicate by reading and writing
shared variables or exchanging messages. In this task, two processes start with
a private input value in the set {0,1,2}, and after communicating, each one
must decide a binary output value, so that the outputs of the processes are the
same if and only if the input values of the processes are different. This task
is already known to be unsolvable; our goal here is to prove this result using
the dynamic epistemic logic (DEL) approach introduced by Goubault, Ledent and
Rajsbaum in GandALF 2018. We show that in fact, there is no epistemic logic
formula that explains why the task is unsolvable. We fix this issue by
extending the language of our DEL framework, which allows us to construct such
a formula, and discuss its utility.
