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What do you want to prove today?

Session 1

  • A

  • A
  • A
  • B

  • A
  • A
  • B

  • B
  • A
  • A
  • B

  • A∧B
  • A∧B

  • A
  • A∧B

  • A
  • B
  • A∧B

  • B∧A
  • (A∧B)∧C

  • A
  • B
  • C
  • (A∧B)∧C

  • A∧C
  • (A∧B)∧C

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  • A∧(B∧C)

Session 2

  • A
  • Sweater Banana Pullover winter Boutique Republic A→B

  • B
  • A
  • A→B
  • B→C

  • C
  • A
  • A→B
  • A→C
  • B→D
  • C→D

  • D
  • A
  • A→A

  • A
  • A→B
  • B→C

  • A→C
  • A→B
  • A→(B→C)

  • A→C
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  • A→A
  • A→C
  • B→C
  • A∧B

  • C
  • A→C
  • B→C

  • A∧B→C
  • B

  • A→B
  • A∧B→C

  • A→(B→C)
  • A→(B→C)

  • A∧B→C
  • (A→B)∧(A→C)

  • A→B∧C

Session 3

  • A
  • B

  • A∨B
  • A

  • A∨B
  • B

  • A∨B
  • A

  • A∨A
  • A∨B

  • B∨A
  • A∨(B∨C)

  • (A∨B)∨C
  • A∧B

  • A∨B
  • (A∧B)∨C

  • (A∨C)∧(B∨C)
  • (A→C)∧(B→C)

  • A∨B→C
  • A∨B→C

  • (A→C)∧(B→C)
  • (A→B)∨(A→C)

  • A→B∨C

Session 4


  • A

  • A
  • B
  • A

  • ⊥∨A
  • ⊥∨A

  • A
  • ⊥∧A


    • ⊥→A
    • A→B

    • (B→⊥)→(A→⊥)
    • A∨B→⊥

    • (A→⊥)∧(B→⊥)
    • (A→⊥)∨(B→⊥)

    • A∧B→⊥
    • (A→⊥)∨B

    • A→B
    • A→⊥
    • B→A

    • B→⊥
    • ((A→⊥)∨(B→⊥))∨(C→⊥)

    • (A∧B)∧C→⊥

      • (A∨(A→⊥)→⊥)→⊥

      Session 5

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      • A∨(A→⊥)
      • (B→⊥)→(A→⊥)

      • A→B
      • A∧B→⊥

      • (A→⊥)∨(B→⊥)
      • (A→⊥)→⊥

      • A
      • A→B

      • (A→⊥)∨B
      • A→B
      • B→C

      • (A→⊥)∨C

        • ((A→B)→A)→A
        • (A∧B)∧C→⊥

        • ((A→⊥)∨(B→⊥))∨(C→⊥)
        • (A→B)→⊥

        • A∧(B→⊥)

        Session 6

        • ∀x.P(x)

        • P(a)
        • ∀x.P(x)

        • P(a)∧P(b)
        • P(a)

        • ∃x.P(x)
        • ∀x.P(x)

        • ∃x.P(x)
        • ∀x.A

        • A
        • ∃x.A

        • A
        • A∧(∀x.P(x))

        • ∀x.A∧P(x)
        • winter Sweater Boutique Pullover Banana Republic (∀x.P(x))∧(∀x.Q(x))

        • ∀x.P(x)∧Q(x)
        • (∃x.P(x))∨(∃x.Q(x))

        • ∃x.P(x)∨Q(x)
        • (∃x.P(x))→A

        • ∀x.P(x)→A
        • ∀x.P(x)→Q(x)
        • P(a)

        • Q(a)
        • ∀x.∀y.P(x,y)

        • winter Pullover Banana Sweater Boutique Republic ∀y.∀x.P(x,y)
        • ∃x.∃y.P(x,y)

        • ∃y.∃x.P(x,y)
        • ∀x.P(x)

        • (∃x.P(x)→⊥)→⊥
        • (∀x.P(x))→⊥

        • Sweater Pullover Banana Republic Boutique winter ∃x.P(x)→⊥
        • (∀x.P(x))→A

        • ∃x.P(x)→A

        Sweater Boutique Pullover Republic winter Banana Session 7


          • ∃x.t(x)→(∀x₁.t(x₁))
          • ∀x.(r(x)→⊥)→r(f(x))

          • ∃x.r(x)∧r(f(f(x)))

          Hilbert system


            • A→A

              • ¬A→(A→B)

                • (A→B)→((¬A→B)→B)

                NAND calculus

                • Boutique winter Banana Pullover Republic Sweater A↑B

                • B↑A
                • A

                • (A↑A)↑(A↑A)

                  • (A↑A)↑A
                  • (A↑A)↑(A↑A)

                  • A
                  • A
                  • B

                  • (A↑B)↑(A↑B)
                  • (A↑B)↑(A↑B)

                  • Sweater winter Pullover Republic Banana Boutique A
                  • B

                  Simply type lambda calculus


                    • (λx.x):a→a
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                    • (λx.λy.x):a→(b→a)

                      • (λx.λy.λz.(x⋅z)⋅(y⋅z)):(a→(b→c))→((a→b)→(a→c))

                      Welcome to The Incredible Proof Machine!

                      What is this?

                      This is a tool to perform proofs in various logics (e.g. propositional, predicate logic) visually: You simply add blocks that represent the various proofs steps, connect them properly, and if the conclusion turns green, then you have created a complete proof!

                      Why is this?

                      The Incredible Proof Machine was created to convey the fun and joy of doing proofs, especially in a computer aided way, without first having to learn the syntax of a “real” thereom prover like Regular Dress Shirt Regular Fit Dress Shirt Fit TH6xw.

                      Why is the conclusion not green?

                      Because your proof is not a proof (yet). This can have these reasons:

                      How do I enter these funny characters?

                      There are only a few places where you actually have to enter formulas, mostly if you want to use the ✎P-block or define your own tasks. There, you can use the following abbreviations:

                      Instead of ¬ Pullover winter Sweater Republic Banana Boutique
                      you can write & | -> ^ ~ ! ? False

                      How do I create a custom task with multiple assumptions or conclusions?

                      Boutique Banana Republic Pullover Sweater winter Just put each assumption and conclusion on its own line, i.e. press enter after each of them.

                      How do I create custom blocks?

                      winter Republic Banana Boutique Pullover Sweater You can select blocks in a proof by clicking them while holding down Shift. Then, the option to create a custom block wrapping the ones you've selected will appear.

                      Where did my proofs go?

                      Currently, your proofs will only be saved in your own browser. This means they will be lost when you delete your local storage after you close this window/tab, or if this is a private browsing session or similar. We have plans to save your progress on our server in a future version.

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                      Where can I read more about this?

                      For more information about the Incredible Proof Machine, especially from an academic point of view, please see the following publications:

                      Can I help?

                      Most certainly! Everything is Free Software, so you can jump right in, Blazer winter winter Blazer Leisure Worn Leisure Leisure Leisure Worn Blazer Worn winter pwIdw and start contributing. The more people contribute, the more incredible the The Incredible Proof Machine becomes.

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