A demonstration on how to use MaTest to prove/test some logical system properties. In this example we define a 3-valued logic according to Łukasiewicz's model (default), then we redefine the conditional so 1→1 = 1, i.e. a "vague" proposition implying another vague proposition is vague (tenable). But a logic system with such a truth-value assignment hasn't got any theorems. We show this property by falsifying the identity theorem (Cpp in polish notation).