Intuit (verb)

1. To know or understand something without being told or without proof.
2. To have a feeling or understanding of something without conscious reasoning.
3. To come to an understanding or knowledge of something through intuition.

Origin:

Early 19th century (as a noun denoting an intuition): from latin intuitus "a looking at", from the verb intueri.

Examples:

1. He intuited that there was something wrong with the engine.
2. She intuited that he was lying.
3. I intuited that it was the right thing to do.
4. He intuited the solution to the problem.
5. I intuited that it was a trap.