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### Test if an inequality is feasible under assumptions

I want to test if an inequality system is feasible under non-negativity assumptions. I run into the problem that the assumptions seem not be used by the inequality solver. Here is a minimal example

sage: (l1,l2) = var("l1 l2")
sage: assume (l1>=0)
sage: assume (l2>=0)
sage: solve (l1*l2<0, [l1,l2])
[[l1 < 0, 0 < l2], [0 < l1, l2 < 0]]


Is it possible to have the solver use the assumptions and determine infeasibility of the system?