Generating a zero-knowledge proof requires a set of values known as a witness. If a witness exists for your statement, you would not need anything more than brute force and a lot of time to find it.
Also, zero-knowledge proofs can be forged with a nonzero probability, so the existence of a zero-knowledge proof of a statement does not necessarily imply the statement's truth. For example, interactive proving systems are constructed by exponentially reducing this probability.
Generating a zero-knowledge proof requires a set of values known as a witness. If a witness exists for your statement, you would not need anything more than brute force and a lot of time to find it.
Also, zero-knowledge proofs can be forged with a nonzero probability, so the existence of a zero-knowledge proof of a statement does not necessarily imply the statement's truth. For example, interactive proving systems are constructed by exponentially reducing this probability.