Quod Erat Demonstrandum

Every argument begins with set of premises that, if true, necessitate some conclusion. Your task is to prove that the conclusion does indeed follow.

Given a set of premises, apply rules of inference and replacement to derive new propositions until you reach the conclusion. Each level is a proof waiting to be completed.

Explore philosophical themes grounded in the works of Plato, Aristotle, St. Thomas Aquinas, and more! Though be prepared: while the levels start off easy and resemble the sort of proofs you might encounter in the wild, they soon evolve to challenge your logical thinking and pattern recognition abilities.

Features

• 180+ handcrafted levels spanning propositional logic and predicate calculus, levels varying both thematically and mechanically

• 23 rules of logic — 7 rules of inference (e.g., Modus Ponens, Modus Tollens, Hypothetical Syllogism), 11 rules of replacement (e.g., Double Negation, De Morgan's Laws, Transposition), and 5 quantifier rules (Universal/Existential Instantiation and Generalization, Quantifier Negation)

• Gentle learning curve — 23 tutorial levels introduce one rule at a time, building from simple one-step proofs to multi-step chains

• Deep complexity — later levels feature nested quantifiers, multi-variable domains, and proofs requiring many steps involving complex statements

• Par system — every level has an optimal solution length; can you find the shortest proof?

• No time pressure — think as long as you need, a par score isn't needed to beat the game

• 60+ Steam achievements — milestones, rule mastery challenges, and other fun achievements for completionists

• Cloud saves — pick up where you left off on any machine