Original sentence: According to "mainstream" anarchists, the terms anarcho-capitalist and anarcho-capitalism are contradictions, because they claim capitalism is inherentially hierarchical and as such is opposed to anarchism.Anarcho-capitalism is a branch of libertarian political philosophy which calls for a society without a state and for a free market with private property.Anarcho-capitalists believe these should be privately operated and funded.Anarcho-capitalists differ from socialist anarchists in that anarcho-capitalists do not oppose private property (including private ownership of the means of production), they believe that contractual relationships between employers and employees (including profit arrangements) are voluntary , and they are not motivated by egalitarian concerns.Anarcho-capitalists favor a completely private system of law and order based on common law and explicit contract.Anarcho-capitalists the socialist anarchist movement.Minarchist libertarians wish to reduce the size and intrusiveness of the state, but unlike anarcho-capitalists, retain vital functions that they believe the private sector cannot adequately provide, like police, courts and the military.The difference between anarcho-capitalists and other libertarians is largely one of degree
Edited sentence: Anarcho-capitalism is a branch of libertarian capitalist political philosophy, not anarchism