Why INTLINPROG returns non-integer?

Why the solution of intlinprog is not integer? Few of many components returned are 0.5 despite being instructed as integer.

load intlinprogfail.mat % file attached
[x, ~, flag] = intlinprog(fdummy, intcon, [], [], Aeq, beq, lb, ub);

Returns x and tells solution is found

LP:                Optimal objective value is -14.414878.                                           


Optimal solution found.

Intlinprog stopped at the root node because the objective value is within a gap tolerance of the optimal value,
options.AbsoluteGapTolerance = 0 (the default value). The intcon variables are integer within tolerance,
options.IntegerTolerance = 1e-05 (the default value).

But when take a close look, some components returned are 0.5 despite being instructed as integer.

>> x(intcon==1)

ans =

    1.0000
    1.0000
         0
    1.0000
         0
    0.5000
    1.0000
    1.0000
         0
    1.0000
    1.0000
    1.0000
    0.5000
    0.5000
    1.0000
         0
         0
         0
         0
         0
    1.0000
         0
         0
         0
    1.0000
    0.5000
         0
         0
    1.0000
         0
    1.0000
    1.0000
    0.5000
         0
    1.0000
    0.5000
         0
         0
         0
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000

Answer 1

[Stephan]

load intlinprogfail.mat % file attached
intcon = 1:45;
[x, ~, flag] = intlinprog(fdummy, intcon, [], [], Aeq, beq, lb, ub);

result:

P:                Optimal objective value is -14.414878.                                           

Cut Generation:    Applied 5 strong CG cuts.                                                        
                   Lower bound is -14.265036.                                                       
                   Relative gap is 0.00%.                                                          


Optimal solution found.

Intlinprog stopped at the root node because the objective value is within a gap tolerance of the optimal value, options.AbsoluteGapTolerance = 0 (the default value). The intcon
variables are integer within tolerance, options.IntegerTolerance = 1e-05 (the default value).

x

x =

     1
     1
     0
     1
     1
     0
     1
     0
     0
     1
     1
     1
     1
     0
     1
     0
     0
     0
     0
     0
     1
     0
     0
     0
     1
     1
     0
     0
     1
     0
     1
     1
     1
     0
     1
     0
     0
     0
     0
     1
     1
     1
     1
     1
     1