invalid

这一推论是无效的，不符合逻辑规则。

The inference is ___invalid because it does not follow the rules of logic.

这张优惠券因为过期而无效了。

This coupon is ___invalid due to its expiration.

这张优惠券已经过期，所以无效了。

This coupon is ___invalid because it has expired.