<p>Solving SAT does not solve all NP problems. It solves all NP problems that can be reduced to SAT by a P complexity algorithm. There exist problems that do not have a P complexity reduction to SAT. Some are reducible to SAT by NP reductions. Some of those by NP reductions for which the reduction algorithm has a P complexity reduction to SAT.</p>

<p>SAT has a P complexity solution. See arxiv.org/abs/cs/0205064.</p>
If a NP solved in polynomial time, can Satisfiability solved in polynomial time
<p>Based on the below link , I can know that solving of Satisfiability(NP Complete) in polynomial time means any other NP problem can be solved in polynomial time.
But is Vice - Versa true?</p>

<p>Also, If there is a polynimial for any other NP-Complete problemt does it mean , all the other NP-Complete can be solved in polynomial time?</p>

<p><a href="https://stackoverflow.com/questions/1857244/np-vs-np-complete-vs-np-hard-what-does-it-all-mean">What are the differences between NP, NP-Complete and NP-Hard?</a></p>