NOVELTY - A method (M1) of remediating landfill waste involves mining the waste from a landfill; screening it; shredding it; magnetically separating ferrous metals from the waste; performing a solid distillation de-polymerization process on the waste to produce hydrocarbon gas, water vapor, and dry solid waste; distilling the hydrocarbon gas to produce hydrocarbon liquid; recycling hydrocarbon gas to produce heat to operate the solid distillation process; and cracking and hydrotreating the hydrocarbon liquid to produce synthetic fuel.    USE - For remediating wastes particularly landfill waste (Claimed) e.g., municipal solid waste, waste water sludge, coal mine tailing, industrial wastes, etc and converting into recaptured metals, minerals, carbon compounds and synthetic fuels.    ADVANTAGE - The present method provides a landfill waste remediation process that effectively extracts and recycles substantially all valuable constituents from landfills, while simultaneously reclaiming the landfill space, removing a dangerous source of groundwater contamination and greenhouse gases (methane leakage from aging landfills), and produces energy to run the process. The method converts waste into recaptured metals, minerals and carbon compounds without the need to inefficiently burn the waste and thus without producing substantial amounts of smoke or other environmental contaminants. The existing landfill sites can be economically mined and remediated for much higher and better use. The solid waste which is subjected to an ultra-high temperature gasification process, produces inorganic material and a hydrocarbon gas and/or mixed with coal for power generation, thereby reducing demand for freshly mined coal. All material put into the process is processed and reused for some purpose, resulting in a zero or near zero (e.g., less than 10%, 5%, 1%, etc. of input mass) waste process. The process effectively extracts and recycles valuable constituents from the waste, and also produces its own energy from the waste, facilitating the recapture and beneficial and environmentally-sound reuse of metals, minerals and carbon compounds present in the waste. This process produces very few if any harmful admissions by applying indirect thermal energy in the absence of oxygen to reduce materials to a combustible gas and a non- hazardous, non-leachable inorganic material.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following    (1) a method (M2) of remediating waste involving providing the waste; magnetically separating ferrous metals from the waste; performing a solid distillation de-polymerization process on the waste to produce hydrocarbon gas, water vapor, and dry solid waste; distilling the water vapor; recycling hydrocarbon gas from the solid distillation de-polymerization process to produce heat to operate the solid distillation process; and cracking and hydrotreating hydrocarbon liquid to produce synthetic fuel; and    (2) a method (M3) of remediating waste involving providing the waste; performing a solid distillation de-polymerization process on the waste to produce hydrocarbon gas, water vapor, and dry solid waste; performing an ultra-high temperature gasification process to the dry solid waste to produce inorganic material and a hydrocarbon gas.