Editing Automated Theorem Proving (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Proof Search' (Visualizing how an AI explores logic):'''
<syntaxhighlight lang="python">
def prove_theorem(starting_facts, goal, max_steps):
    """
    Simulates a 'Breadth-First Search' for a proof.
    """
    queue = [starting_facts]
    for step in range(max_steps):
        current_logic = queue.pop(0)
        
        # 'Inference': If we know A and B, we can 'Prove' C
        if "P" in current_logic and "P->Q" in current_logic:
            new_fact = "Q"
            if new_fact == goal:
                return f"SUCCESS: Goal '{goal}' proved in {step+1} steps!"
            queue.append(current_logic + [new_fact])
            
    return "FAILURE: No proof found within the search limit."

# Facts: P is true, and P implies Q. Goal: Prove Q.
print(prove_theorem(["P", "P->Q"], "Q", 10))
</syntaxhighlight>

; ATP Landmarks
: '''The Logic Theorist (1955)''' → The first-ever AI program (by Newell and Simon) that proved 38 theorems from 'Principia Mathematica,' even finding a "Better proof" for one of them than the authors.
: '''Coq (1984)''' → The "Grandfather" of modern proof assistants, used to prove everything from the "Feit-Thompson Theorem" to the correctness of the "CompCert" C compiler.
: '''The 'Lean' Theorem Prover (2013)''' → A modern prover developed by Microsoft Research that has become the "Hottest" tool in the math community, currently being used to formalize all of modern undergraduate math.
: '''AlphaProof (2024)''' → Google DeepMind's AI that reached "Silver Medal" level at the International Math Olympiad, proving that "Learning" (Neural Networks) can be merged with "Proving" (Logic).
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