Solving a system of inequalities takes too long?

Questions
,
1

Hi all,
I am using Mathematica 12.1 student edition and I am trying to solve a system of inequalities with multiple radicals with three variables at some stage of my model. When I run the reduce function attached, Mathematica keeps running forever. Do you think something like Wolfram pro can help and is there any way that I call Wolfram Pro inside Mathematica? The Wolfram Alpha query in Mathematica does not help.

System of Inequalities.nb (7.91 KB)

2

the complexity of Reduce is double exponential

3

Thanks, do you have any idea how to take care of it?