Watermarking based ownership dispute resolution schemes are vulnerable to a simple but effective class of attacks, called ambiguity attacks, which cast doubt on the reliability of resulting decision by exploiting the high false-positive rate of the watermarking scheme. To mitigate such attacks, we propose a new scheme that embeds multiple watermarks, as opposed to embedding a single watermark, while constraining the embedding distortion, and detects a randomly selected subset of them during an ownership proof. The crux of the scheme lies in both watermark generation, which deploys a family of one-way functions, and selective detection, which injects uncertainty to detection process. The reduction in false-positive probability is analyzed and compared to single watermark embedding for the additive watermarking technique through numerical solutions. Moreover, we examine the exact security level that can be achieved by our scheme with different combinations of parameters. We adopt a previous security proof of non-invertible watermarking schemes with modified notion of security that is more realistic in practice, which allows us to derive the achievable security with typical parameters.