Four men met in a bar, and they soon found that all four of them had been to the Amazon Jungle. After a few more beers, they also realized that they had all been captured at least once, by fierce natives who ruled amazing fortresses. They soon got around to talking about their experiences, and their escapes. The first man said, "Well, I was once caught by natives who ruled a diamond palace. They caught me and took me to their king. He decreed that I was to die in one month. They threw me into a cell. Thank God that they didn't take my equipment. I had stolen a quartz file from one of the natives. I filed away the bars (it had curtains so they couldn't see) and escaped mere hours before I was to die."
The second man said, "I was also captured, but they took me to a simple copper structure. I did not have any such luxury of a month to escape, instead, a single day. Luckily they did not count on my desperation, and I was able to claw my way out of there using only my fingernails and pure adrenaline."
The third man said, "I was taken to the most amazing fortress of all. It was made out of black topaz. I was also the smartest of all of you," he bragged, "for I had brought with me a steel file. I was out in a jiff, and I was able to steal some of the topaz as well," he said as he showed everyone a piece of topaz hanging from a string around his neck.
The fourth man had been looking amused at the first and second men's stories, but as the third man finished he threw up his head and laughed. The other three men were looking slightly peeved, and asked him what he found so funny. He declared that they were all liars, and he could prove it.
How could he prove it, and when did each of the three men lie?