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¿Do you know if there is any mathematical theory (or axiomatic theory) whose axioms, or at least one of them, contradict with other axioms of another theory?

Thanks for reading.

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    Do you mean like whether you assume the axiom of choice or not?2017-02-01
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    No, because, if I am not mistaken, the axiom of choice is not contradicted by any other axiom of any other theory.2017-02-02
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    https://en.m.wikipedia.org/wiki/Non-Euclidean_geometry2017-06-14

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