Question: Phantom solution to linear inequalities using solve

I'm trying to use solve to find out if a system of equalities and inequalities has any solution or not, but maple 15 seems to be giving phantom solutions.  A simple example is the following:

  solve({ a + b = 1, a > 0, b > 1, c > 0 }, {a,b,c});

It gives the output

which is clearly wrong.

This seems like a bug.  Is there anyway to get maple to behave more sensibly?



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