Question: Solve with assuming fails to incorporates the assumptions: how to force maple to completely impose the assumptions?

Dear Fellows, greetings

I am solving a system of equations under some assumptions and those assupmtions are a must to impose. However maple fails to apply those while solving the equations. For example solution 4 gives b=c as a solution but in assumtion it is clrealy mentioned that b<>c. Kindly guide me what mistake am I making in the code.

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