Why does an automated theorem prover use Proof by Contradiction to validate a mathematical statement?

💡 Explanation

The theorem prover uses Proof by Contradiction because it assumes the negation of the statement, and attempts to derive a contradiction. If a contradiction is found, the negation is false; therefore, the original statement is true, rather than trying to directly prove the statement.

• If a cryptographic key's generation relies on two extremely large prime numbers, which outcome occurs with the 'strength' of encryption as computational power increases exponentially?
• If a finite state machine is proven to require more states than physically available in a microcontroller, which consequence follows?
• A network of interconnected sensors monitors a chemical reaction; if a communications outage affects critical nodes, which outcome occurs?
• If a finite state machine transitions according to Kleene's theorem, which outcome concerning the set of recognizable languages results?
• If a signal passes through an ideal corner reflector, which consequence follows?
• A recursive function calculates the factorial of a number; if a user accidentally provides a negative input, which outcome is most likely?