I suspect it's effectively impossible to produce the kind of answer you are looking for. In order to make a determination that a species went extinct solely due to predation, we would need to have observed it very closely, which effectively excludes your qualifier "free of human interference." Also, you can't really attribute extinction solely to any one factor, unless you mean, "was the last individual killed by as predator, in its natural environment without human interaction of any kind?", or some other really specifically qualified question.

I guarantee that many species have gone extinct in large part due to pressure from predation. The Lotka–Volterra equations describe an idealized predator-prey dynamic where the populations have a stable oscillation without a possibility of extinction. In reality, many predation dynamics come so close to prey extinction that small fluctuations at the right time can reduce the prey population below a viable size.

Keep in mind, that natural selection can only act on existing variation in a population, so a prey species likely won't even have the ability to respond in a meaningful way to a significant predatory adaptations. This will normally just alter the dynamic and result in more extreme oscillations, but not necessarily result in extinction.