Sorry to be blunt, but this is not the case

Theorem provers, Prolog, and the backtracking strategy they share absolutely use if/then logic.

In Prolog, for example, your "program" is broken up into "facts" and "rules", which correspond to if/then statements.

Theorem proving is exactly the same - repeated use of modus ponens and modus tollens, both "if/then".

Backtracking is simply a strategy to find a set of values that satisfies every statement in some collection of if/then statements.

There is no fuzzy logic or probability used. Once you have computed the truth value of a statement, it will be either true or false.

The different between this and modern AI is that we now use fuzzier logic, where, conceptually, "true" is 1, "false" is zero, but values between 0 and 1 are also possible.