Internal Palestinian divisions block a solution to Israel Palestine conflict
Internal divisions among Palestinians make negotiations impossible.
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Palestinians are largely divided into two political groups, Hamas and Fatah. Although both groups support a Palestinian state, they have many differing beliefs. Fatah formed out of the original Palestinian Liberation Organization (PLO) in the late 1950s, now supports peaceful negotiations with Israel with the goal of a two-party state. Hamas is a more militant group that provides social welfare for Palestinians suffering under Israeli occupation but primarily focuses on violent terrorist acts against the state of Israel with the goal of a single Palestinian state. The primary differences between the two are that Hamas uses violent action while Fatah solely uses peaceful negotiations and that Hamas is religiously Islamist-based while Fatah is secular. 
The two Palestinian camps will never be able to achieve a suitable compromise. The violent Hamas group makes peaceful negotiations impossible and prevents progress from being made. Israel occupies and subjugates Palestinians out of fear about the safety of Israeli citizens, and that fear will not cease if Hamas continues its violence. Peaceful negotiations between the Israeli government and Fatah will never fully solve the conflict because the Hamas group will not be happy with a two-state, secular solution when they desire a single Islamic Palestinian state. The internal conflict among the Palestinians prevents true progress from being made toward peace. The already difficult task of a solution to the Israeli and Palestinian conflict is made impossible because the Palestinians do not have a united front.
Though the two groups are strongly opposed, with creative negotiations and a compromise from both Palestinian parties a suitable solution could be reached. Especially if a solution was backed by other Arabic nations or the United Nations, an agreement could be enforced even if all parties were not entirely content with it.
[P1] For a solution to be reached, all parties must uphold it. [P2] The Hamas and Fatah Palestinian parties fundamentally disagree, and neither will compromise. [P3] Both parties could not be happy with a solution simultaneously. [P4] Since both parties cannot be pleased at the same time, no suitable solution exists.
Rejecting the premises
[Rejecting P2] Parties could be forced to compromise.