Here are several disproof’s of P=NP P DOES not equal NP as verified solutions can always be different than solved solutions. One can use any solution or find any solution for a problem or of a problem, but then verify a different solution. Bird or Case Disproof We have solved that there are birds, but my verification method will always be different for each person. Each person’s verification method will always be different than what someone sees as a solution. The problem of bird’s existence is solved. BIRDS EXIST. How do we verify that? Verification is always a different solution or process for every individual than the solution. The way we as machines verify something is different. Computers also are capable of verifying things differently. See how a computer would verify a bird’s existence differently than it would solve the question. Computer Example P is a solution verified by computer.100 people differ on the solution of problem 100 P100 people feel there is a certain solution to a problem. 100P# 100 people do not believe there is a solution to a problem. 100 P Null A computer is capable of verifying the solutions or non solutions of problems, and it is possible for the computer to find the solutions or non solutions to the problem. The computers solutions found or verified, however, would not be the solutions for those who do not feel there is a solution. The different solutions found by 100 people would not be the same as the 100 people who feel there is a certain solution P # or no solution P Null. Belief is solution does not equal belief no solution 100 P and 100P # and 100 P Null can be verified and found, but P cannot =NP as 100 P Null do not agree with solutions of 100 P#, 100 of a certain solution, or 100 P 100 different solutions The computer could verify some solution, but if that solution is not 100 P # certain or 100 P Null, then the P=NP hypothesis is disproved as P NULL and P # certain do not agree with solutions of 100P different solutions. Verified solutions cannot be found as different solutions are perceived by problem solvers for which the verified solutions will not equal the found solutions. Solutions have a subjective nature to them such that a problem solver can always see a solution verified or found but not be the verified or found solutions of other problem solvers hence P is not equal to NP.A related question would then come to mind. When P is found, is that equal to what is verified or P=NP for the same found solution? Stated in that manner the question is different as further limits are placed on the Clay Medal question. As the problem is currently stated, one solution found will not always equal what is verified as solutions differ between observations and observers. The way a solution can be verified and found is not always the same. One can find some solution but not have the same way of verifying the solution between different observers. Therefore since finding and verification methods can differ, P =NP can be denied. Even for the same found solution, the method of finding something does not have to equal the method of verifying such solution. Therefore, we have here a disproof of P =NP as solutions differ and verification and finding methods differ too. A computer finds that blue birds are a solution to a problem. The computer uses a different method to verify that blue birds solve the problem. A different computer uses a different finding method to show that cardinals are the solution. A different verification method shows hawks to be the problem solution verified. P Does not = NP as verification method, finding method and solutions differ with each computer and with different computers. We can make solution different than verification by design or verification can be different than solution by processes too.

- P=NP Disproved,
- Solve different than verified

*Travaux, Belgian Math, Illinois Math Journal, Chicago Tribune, Sun Times, American Journal of math, Mathematics magazine*(2014)

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