You not correctly repeat what is written on the slide. The slide says that we pick a variable with a non-integer solution v, and add the constraint x<=floor(v) to restart the simplex procedure. It repeats that with other variables, but if not integer solution is found, we remove the constraint x<=floor(v) and add instead x>=ceil(v) to restart the simplex procedure. Again, it continues with strengthening constraints for other non-integer solutions until a solution is found or no solutions exists. If the latter is the case, we tried both x<=floor(v) and x>=ceil(v) and if that does not lead to a integer solution, then there is none.
That far that good, but it may happen that the constraint for the same variable x is strengthened further in the recursive calls, and the example shown in the lecture shows that the procedure may not terminate.
For this reason, one can compute a bound to enforce termination, but how these bounds are computed was not shown in the lecture. The teaching tool simply stops after some thousand steps, and guesses that there is probably no solution.
