inconsistency

Also, what you're guilty of if you think that the operating system and developers tools should be free software, but the stuff you write shouldn't.

Or maybe that's just hypocrisy.

Example: x, y, and z are real numbers. x > y, y > z, and z > x

To prove that the premises are inconsistent, assume one is true and use it to prove one of the others false.

In`con*sist"en*cy (?), n.; pl. Inconsistencies (#). [Cf. F. inconsistance.]

1.

The quality or state of being inconsistent; discordance in respect to sentiment or action; such contrariety between two things that both can not exist or be true together; disagreement; incompatibility.

There is a perfect inconsistency between that which is of debt and that which is of free gift. South.

2.

Absurdity in argument ore narration; incoherence or irreconcilability in the parts of a statement, argument, or narration; that which is inconsistent.

If a man would register all his opinions upon love, politics, religion, and learning, what a bundle of inconsistencies and contradictions would appear at last! Swift.

3.

Want of stability or uniformity; unsteadiness; changeableness; variableness.

Mutability of temper, and inconsistency with ourselves, is the greatest weakness of human nature. Addison.

© Webster 1913.