Set Theory and Logic


Refutation of the Schaefer Theorem for the P, NP Problem (Undecided)

Authors: Colin James III

We evaluate the Schaefer theorem for the P, NP problem by two examples for Graph-SAT(Ψ ). Neither example is tautologous; while claimed to be different, they result in the same truth table values. (The injection of NP-intermediate does not describe our result.) This refutes NP-complete (and P, NP, NP-hard). We also evaluate the P, NP problem as based on P≤NP with the same result. Therefore P, NP, NP-complete, NP-hard, NP-intermediate form a non tautologous fragment of the universal logic VŁ4.

Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at

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[v1] 2019-05-30 11:26:45

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