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2. Geometry Dash - Wikipedia

   en.wikipedia.org/wiki/Geometry_Dash

   Geometry Dash Lite is a free version of the game with advertisements and gameplay restrictions. Geometry Dash Lite includes only main levels 1-19, all tower levels, and a few selected levels that are either Featured, Daily, weekly or Event levels but does not offer the option to create levels or play most player-made levels. It also has a ...

3. Proof assistant - Wikipedia

   en.wikipedia.org/wiki/Proof_assistant

   In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface , with which a human can guide the search for proofs, the details of which are ...

4. Proof-number search - Wikipedia

   en.wikipedia.org/wiki/Proof-number_search

   Proof-number search (short: PN search) is a game tree search algorithm invented by Victor Allis, [1] with applications mostly in endgame solvers, but also for sub-goals during games. Using a binary goal (e.g. first player wins the game), game trees of two-person perfect-information games can be mapped to an and–or tree .

5. Lean (proof assistant) - Wikipedia

   en.wikipedia.org/wiki/Lean_(proof_assistant)

   theorem and_swap (p q : Prop) : p ∧ q → q ∧ p := by intro h -- assume p ∧ q with proof h, the goal is q ∧ p apply And.intro -- the goal is split into two subgoals, one is q and the other is p · exact h.right -- the first subgoal is exactly the right part of h : p ∧ q · exact h.left -- the second subgoal is exactly the left part of ...

6. Proof game - Wikipedia

   en.wikipedia.org/wiki/Proof_game

   A proof game is called a shortest proof game if no shorter solution exists. In this case the task is simply to construct a shortest possible game ending with the given position. When published, shortest proof games will normally present the solver with a diagram - which is the final position to be reached - and a caption such as "SPG in 9.0".

7. Automated theorem proving - Wikipedia

   en.wikipedia.org/wiki/Automated_theorem_proving

   A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof that was essentially impossible to verify by humans due to the enormous size of the program's calculation (such proofs are called non-surveyable proofs).