@mmcdara 

If A inter B is an empty set then all the elements from A have to multiply with elements in B like

{x1,x2,x3} and {x4, x5} then the solution is x1x4, x2x4, x3x4, x2x4, x2x5, x3x4 and x3x5

@mmcdara 

Is it possible to create undirected graph? I suppose in this line something has to be changed and be {1,2}, {1,3} etc instead of [1,2],[1,3] 

@mmcdara 

Thank you very much! It works! :))))

@Carl Love 

I tried to do this in workshit "try2" which I posted above, but unsuccessfully :(

@Carl Love 

Here is the input form. Thank you in advance!

try2.mw

@Carl Love 

Thank you very much!!

@Carl Love 

Thank you very much!

Do you know what to do because when I enter your text, Maple says:

Error, invalid input: mul expects 2 arguments, but received 1
 

@Markiyan Hirnyk 

Thank you for your answer very much. I have troubles to solve this system in Maple because of slack variables. I know that one of the possible solution is x1=1, x7=1, x9=1, x10=1, x12=1, x18=1, x24=1, x25=1, x27=1 and x28=1, remaining x are all zeros. I don't know how to solve it now. In example 3 in paper you proposed, one equations has only one variable and in this system I don't have that. 
PS. I made a mistake in system, equation starting with x6: at the end it has to be 1 instead of 11, and equation starting with x12+x4+x13+... has to be x12+x15+x13+...

Thank you in advance!

@Kitonum 

Here is the system of inequalities I have to solve, but with Groebner Bases:

The first 30 are inequalities, and the last 30, form is x^2-x, are equalities, becasue all the solutions have to be binary.

I realy don't know how to solve this.

Download 30_buses.mw