YES

proof:
The input problem is infeasible because

[1] the following set of Horn clauses is satisfiable:

	f(x, x) = f(a, b)
	F(a, b) = F(x, x) ==> true__ = false__
	true__ = false__ ==> \bottom

This holds because

[2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)):

E:
	t1(F(a, b)) = true__
	t1(F(x, x)) = false__
	t2(false__) = true__
	t2(true__) = false__
G:
	true__ = false__

This holds because

[3] the following ground-complete ordered TRS entails E but does not entail G:

	t1(F(a, b)) -> true__
	t1(F(x, x)) -> false__
	t2(false__) -> true__
	t2(true__) -> false__
with the LPO induced by
	t2 > b > a > F > t1 > false__ > true__