at least one of your premises is logically inconsistent with he others -- that they cannot all be true.

Suppose I have three axioms: A, B, and C.

A: x=5

B: x+y=4

C: 2x+y=6

Which axiom is logically inconsistent with the others? (A, B), (B, C), and (A, C) are all consistent systems, so I can't declare any of the axioms to be false, just that for any particular model of anything remotely interesting, at least one of them must not apply.