Fallacious in a sentence

The Word fallacy is similar to the Word "fallible" which means that something or someone is wrong. Fallacy is just the state of being wrong so to speak. Googling fallacy shows that it is a false idea or argument that isn't valid.

The fallacy of the argument lay in its very idea that trains would one day fly.

Not the best sentence maybe, but the best that I can come up with off the top of my head.
The opposite of fallacy is actuality but sometimes it's hard to tell which is which.