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Quod Erat Demonstrandum

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Quod Erat Demonstrandum screenshot 1
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Quod Erat Demonstrandum

Ad Dominum Games · Published by Ad Dominum Games

Last updated 28 Sept 2026

Discover the challenging fun of validating logical proofs, beginning with simple propositional calculus and ending with complex, multi-domain predicate calculus. Prove yourself to be a master of logical thinking!

Free to PlayComing SoonDJCTQ l

Free

View on Steam

Prices can lag the live Steam store — always confirm before buying.

Indie, Strategy, Casual · 2026 · More free games

About this game

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 — step by step — until you reach the conclusion. Each level is a proof waiting to be completed.

As a newly aware intelligence, each proof explores themes of being and essence, virtue, the soul, causality, and the pursuit of truth. Simply put, you are a mind reasoning its way from first principles toward understanding.

Features

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

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

  • Gentle learning curve — 18 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 10+ derivation steps

  • Intuitive drag-and-drop interface — slot propositions into rules, see the result, and build your proof step by step

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

  • No time pressure — think as long as you need; every proof waits for you

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

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

System Requirements

Will my PC run this? →

Minimum

Minimum:
  • Requires a 64-bit processor and operating system
  • OS: Windows 10
  • Processor: 1.6 GHz dual-core
  • Memory: 4 GB RAM
  • Graphics: Integrated graphics
  • DirectX: Version 11
  • Storage: 500 MB available space
  • Sound Card: Any

Recommended

Recommended:
  • Requires a 64-bit processor and operating system
  • OS: Windows 10
  • Processor: 2.0 GHz dual-core
  • Memory: 4 GB RAM
  • Graphics: Integrated graphics
  • DirectX: Version 11
  • Storage: 500 MB available space
  • Sound Card: Any

Supported Languages

English

Latest news

  • Patch NotesOfficial

    Version v0.1.1 now available

    Hello again, here's hoping everyone enjoyed Steam Next Fest and found plenty of games to look forward to! While there's still plenty of work to be done on some of the non-demo content, I am trying to also sprinkle in some user requests as I'm able so that you can get a more accurate image of the final game. To that end, here's a look at what's in the latest update and what's to come, and special shoutout to Chris Martin, differentdiff, and 15-151 for their suggestions which made it into this update:What's changedImproved timing for the mouseover tooltip for rulesWide view option for propositions and rules. Should keep most propositions on screen, and will always keep all Rules on screenDetailed view option for Rules. See all information about a rule in the rule list area, at the cost of precious spaceClick to toggle option (via right click) for mouse usersMeta: versioned updates. You can see what version you're on in the options screen.What's coming nextBetter in-game explanations, reference sheets, less jargon, etcDark mode? I'll at least look into it, it got some mentions in the feedback formBetter narrative features, e.g., levels constructed from the conclusions of prior levels and gated on their completionEverything needed for the full game launch
    Read full article on Community Announcements (AdDominumDev)
  • Patch NotesOfficial

    Minor Update 1 Now Live (demo)

    First of all, I hope everyone is enjoying Steam Next Fest. I appreciate all the feedback so far, both in the Steam discussions tab and the google form linked on the main menu. This update contains a few things I've been working on while working on the main game build, to include a few player requests (shoutout to Diogo and (ᵔᴗᵔ) for some of the features in this update). Some of the google form requests will be in the next update, I promise!What's changedInsight levels (formerly tutorials) are now more visually obvious on the level selection screenUnless a level actively restricts a Rule (I dont think any of those are in the demo), the Rule list will show all unlocked RulesYou can now left-click to proceed / speed up text scrolling in addition to spaceRules/propositions can be dragged out of the central fixture and otherwise swapped aroundRules/propositions in use are now still visible in their respective listsImproved visibility for the desired conclusion at the bottom of the screenConfirmation dialogue added to the clear level data buttonWhat's coming nextMore control optimizations (e.g., better drag mechanics, single click operations)Better in game references (e.g., easier reference for rule forms, better introduction to core concepts)General quality control, continued full game release development
    Read full article on Community Announcements (AdDominumDev)
  • AnnouncementsOfficial

    Game Demo Now Available

    In anticipation of Steam Next Fest in June, I'm doing an early release of the demo! Or, rather, I did an early release of the demo last week and forgot to hit "Publish" on this announcement... Anyway, while I'll still be publishing updates between now and then, the core substance of the demo is in place and ready to be played. A few things to note:The demo showcases a pretty big subset of rules, but it does not include any predicate logic (i.e., the quantifier rules)The demo should run on all platforms, but Windows is the most heavily testedYou can send your thoughts on the game either through the in-game link (which goes to Google Forms) or through the Steam Discussion boardThe full game is still well on track to be released in August, and potentially sooner if I can dedicate enough time to it. To the tens of people who even know this game exists, I appreciate your patience!
    Read full article on Community Announcements (AdDominumDev)

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