In mathematics, how to express "两者不能同时成立"?
are you looking for "contradictory", in mathematic, it would be:

"contradictory opposite"　"矛盾否定"

"contradictory propositions"　"矛盾命題"

教育研究院, of taiwan has documentations of bilingual academic terms, the mathematical one is here, you may download it:

http://terms.naer.edu.tw/download/301/