In order for there to be a solution, both sides need to come to the negotiating table secure in the knowledge that the other party will abide by any agreement signed. Neither side trusts the other to stick to an agreement. Therefore, there cannot be lasting peace.
The threat of violence through groups like Hamas makes a lasting peace impossible. Israelis are not willing to make concessions to a population that could compromise the safety of Israeli citizens at any moment. Without concessions, there will be no agreement. Without an agreement, there will be no peace.  On the other side, Palestinians do not trust Israelis not to deprive Palestinians of rights (under a one-state solution) or territory (under a two-state). Until both sides can trust the other to negotiate in good faith, a solution will remain elusive. 
Other international governments can broker peace. Even if neither side trusts the other to implement a solution, they might trust an international government to use its diplomatic or financial leverage to pressure the other side into upholding an agreement. Therefore, the inclusion of governments like the US, Egypt, Jordan or Saudi Arabia in the peace negotiations could bring about a solution to the conflict. 
[P1] To negotiate a solution, both sides need to trust the other to implement a deal. [P2] Currently, neither Palestinians nor Israelis trust the other party. [P3] Therefore, under the current circumstances, there can be no solution.
Rejecting the premises
[Rejecting P1] A solution could be brokered by an international government that both sides trust.