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.
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.