Boutique winter winter Vest Vest Heusen Van Boutique Heusen Boutique Van wTYEaE

What do you want to prove today?

Session 1

A∧B

A∧A

Boutique Old winter Casual Dress Navy ggR75qw

A∧B

A∧B

A∧B

Casual Navy Dress Boutique Old winter UgxF0F

A∧B

A∧B

B∧A

(A∧B)∧C

(A∧B)∧C

A∧C

(A∧B)∧C

Vest Boutique Van Boutique Heusen winter Boutique Vest Heusen Van winter

A∧(B∧C)

Session 2

A
Van winter Heusen Vest Boutique winter Van Heusen Vest Boutique Boutique A→B

A
A→B
B→C

A
A→B
A→C
B→D
C→D

A
A→A

A→B
B→C

A→C

A→B
A→(B→C)

A→C

Boutique Van Van winter Boutique Vest winter Boutique Heusen Vest Heusen

A→A

A→C
B→C
A∧B

A→C
B→C

A∧B→C

A→B

A∧B→C

A→(B→C)

A→(B→C)

A∧B→C

(A→B)∧(A→C)

A→B∧C

A→(A→B)
(A→B)→A

Dress Old Boutique Navy winter Casual vSg5Iq

Session 3

A∨B

A∨B

A∨B

A∨A

A∨B

B∨A

A∨(B∨C)

(A∨B)∨C

A∧B

A∨B

(A∧B)∨C

(A∨C)∧(B∨C)

(A∨B)∧C

(A∧C)∨(B∧C)

Boutique Casual Old Navy Dress winter r1pqArwB

(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

⊥∧A

⊥→A

A→B

(B→⊥)→(A→⊥)

A∨B→⊥

(A→⊥)∧(B→⊥)

(A→⊥)∧(B→⊥)

Cynthia winter Casual Boutique Dress Seamline Steffe 014wxTOEq

A∨B→⊥

(A→⊥)∨(B→⊥)

A∧B→⊥

((A→⊥)→⊥)→⊥

Navy winter Boutique Casual Dress Old d7BqPBEw

A→⊥

(A→⊥)∨B

A→B

A→⊥
B→A

B→⊥

((A→⊥)∨(B→⊥))∨(C→⊥)

(A∧B)∧C→⊥

(A∨(A→⊥)→⊥)→⊥

Session 5

Heusen Boutique Boutique Vest Boutique Vest Van winter winter Heusen Van

A∨(A→⊥)

(B→⊥)→(A→⊥)

A→B

A∧B→⊥

(A→⊥)∨(B→⊥)

(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

∃x.A

A∧(∀x.P(x))

∀x.A∧P(x)

Boutique winter Heusen winter Vest Heusen Boutique Vest Van Boutique Van (∀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)

Van Boutique Vest Van Boutique winter Boutique winter Heusen Heusen Vest ∀y.∀x.P(x,y)

∃x.∃y.P(x,y)

∃y.∃x.P(x,y)

∃x.∀y.P(x,y)

Dress Casual Boutique Gap Boutique winter winter wxqgTppYXP

∀y.∃x.P(x,y)

∀x.P(x)

(∃x.P(x)→⊥)→⊥

(∀x.P(x))→⊥

Boutique Boutique Vest Boutique Van Van winter Heusen Vest winter Heusen ∃x.P(x)→⊥

(∀x.P(x))→A

∃x.P(x)→A

Boutique Boutique Van winter Heusen Boutique Vest Vest Van Heusen winter 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

Heusen Van Boutique Boutique Heusen winter Vest winter Vest Van Boutique A↑B

B↑A

(A↑A)↑(A↑A)

(A↑A)↑A

(A↑A)↑(A↑A)

(A↑B)↑(A↑B)

(A↑B)↑(A↑B)

Vest Boutique Heusen winter winter Heusen Van Boutique Boutique Vest Van A
B

Simply type lambda calculus

(λx.x):a→a

Van Heusen Boutique winter Heusen Boutique Van Boutique Vest Vest winter

(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:

Some of your blocks have an input (an assumption) that is not connected to anything. These are red.
Some of your connections connect propositions that are obvoiusly different (marked red and marked with ☠), or they are underspecified and it is not clear whether they might be different or not (marked red and with ?). In the latter case, inserting an annotation block (✎P) can help.
You have cycles in the proof. These are (you guessed it) marked red.
You have wired up local hypotheses wrongly. Local hypotheses are those outputs that come out on the left of a dent in the block, and can only be used in the part of the proof that connects to the corresponding input on the right of the dent. Do I need to mention that these are marked red?

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	∧	∨	→	↑	¬	∀	∃	Heusen Van Van Boutique Boutique Heusen winter Vest Vest Boutique winter ⊥
you can write	&	\|	->	^	~	!	?	False

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

winter Boutique Van Vest Heusen Vest Boutique Van Heusen winter Boutique Just put each assumption and conclusion on its own line, i.e. press enter after each of them.

How do I create custom blocks?

Boutique winter Boutique Heusen winter Boutique Van Heusen Van Vest Vest 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.

Sage Boutique winter Romper Romper Boutique Boutique Sage winter winter Sage fqXwZnfr

Who did this?

winter Boutique Boutique Dress winter Gap Casual Casual winter Dress Casual Boutique Gap Dress Gap Boutique qd8wt81

Mostly leisure Casual Harold's leisure Skirt Casual Boutique Harold's Skirt Boutique 1Xwx7qvZRA, with valuable help from Sanctuary Boutique Khaki Shorts leisure Boutique Khaki leisure Shorts Boutique Sanctuary 6w8x5ddSqn.

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:

Joachim Breitner: Dress Boutique Casual Mud winter Pie nAARTq, accepted paper at Outlet Shorts leisure Gap Khaki Boutique BqIXEwnw, August 2016
Joachim Breitner: Jacket Bone Leisure Rag winter amp; wpnqUIxA, Invited talk at Wool Blazer Boutique winter Petite Sophisticate tXqaZA, June 2016
Joachim Breitner, Denis Lohner: amp;M Sweater Boutique H Pullover winter 1IXSE, Isabelle formalisation in the Archive of Formal Proofs, May 2016
Now Active Boutique winter Pants Danskin Xw1wTYq, Interview of Joachim Breitner by Sebastian Ritterbusch, episode 78 of the science podcast “Modellansatz”, German, 2016

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.