Question: Solve inequality system whose variable is indexed by two params using LinearMultivariateSystem

My problem

I have the following inequality system : 

              [ U_1,2 + U_1,3 -1 = 0,

U_2,3 - U_1,2 = 0, 

-U_1,3 -U_2,3+1 = 0,

0 <=U_1,2,

0 <= U_1,3,

0 <= U_2,3]

I want to solve it using LinearMultivariateSystem, namely I excuted a command : 

LinearMultivariateSystem(

[ U_1,2 + U_1,3 -1 = 0, U_2,3 - U_1,2 = 0, -U_1,3 -U_2,3+1 = 0, 0 <=U_1,2, 0 <= U_1,3, 0 <= U_2,3],

[U_1,2,  U_1,3, U_2,3] )

Then the following is return : 

Error, (in Utilities:-SimpleAnd) invalid input: a string/name list is expected for sort method `lexorder`

 I tried that sort([U_1,2,  U_1,3, U_2,3] , lexorder) but it dosen't work well.

Also I tried replacing variables so that [U_1,2,  U_1,3, U_2,3] -> [x, y, z], then it is succesfull.

Question

My question is that how do you use LinearMultivariateSystem for varibles indexed by two params.

Thank you.