An example of the contradictory premises fallacy is a pastor telling his congregation God is so powerful he possesses the power to do anything, including make a mountain so heavy that even God himself can't lift it. Another example is, "This is a false statement."
A contradictory premises fallacy occurs when someone presents a conclusion that cannot be accurate based on the premises set forth. Another name for this type of fallacy is a logical paradox. A pastor's argument that God possesses the power to do anything, including create a landform too heavy for Him to lift, is considered a contradictory premise because the pastor is claiming that God can do anything but also that it's possible for God to be unable to perform a particular action. If God can do anything, it's illogical to conclude that it's possible for God to be unable to lift a mountain.
"This is a false statement," is also a contradictory premise because the sentence simultaneously implies that the speaker's words are true and false. If it's true that the statement is false, then it's not a false statement. If it is, in fact, not a false statement, the claim that the statement is false is actually untrue.