Hi Constantine,
haven't seen you here for quite some time. To use an operational amplifier as a comparator you should include positive feedback for stability,
see e.g. here. It is, by the way, possible but not good practice to use an opamp as a comparator. These chips are designed for linear operation. When used as a comparator they can saturate (and yes, they do) and will come out of saturation rather slowly. Very much contrary to a true comparator which you want to switch very fast.
As a test circuit your design is imho not suitable. It will check only wheter the opamp can switch between "+" and "-" output in a rather coarse fashion. To test the function of an opamp one would put it into an anlog amplifier circuit and measure gain, distortion, bandwidth etc.
Cheers,
Harald