Cf: Animated Logical Graphs • 32
At: 
http://inquiryintoinquiry.com/2020/06/14/animated-logical-graphs-%e2%80%a2-32/

Re: R.J. Lipton and K.W. Regan
https://rjlipton.wordpress.com/about-me/
::: Proof Checking
https://rjlipton.wordpress.com/2020/06/13/proof-checking-not-line-by-line/

Here's a place where I explore several different shapes of proofs within propositional calculus deriving from the graphical systems of Charles S. Peirce and G. Spencer Brown.

• Propositional Equation Reasoning Systems • Analysis of Contingent Propositions
https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems#Analysis_of_contingent_propositions

I don't know whether that helps any with P ≟ NP but it does supply a lot of 
nice pictures to contemplate.

Resources
=========

• Logical Graphs
https://oeis.org/wiki/Logical_Graphs

• Propositional Equation Reasoning Systems
https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems

Regards,

Jon

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