What symbol would I use if I wanted to express that, in the context of some binary relation PP implied from context, that ∃(a,b)∈P:a≠b∃(a,b)∈P:a≠b, but not to the extent that ∀(a,b)∈P:a≠b∀(a,b)∈P:a≠b.
The use of this would be if one were discussing a more restricted system, but then move to discussing a less restricted one. Like, "if we know for sure that a⋅b=b⋅aa⋅b=b⋅a, then .... However, if a⋅b=?b⋅aa⋅b=?b⋅a, then the previous reasoning doesn't apply, so ...". ("=?=?" instead replaced with the real symbol)