(A) Hall-Heroult process: Used for the extraction of Aluminium. It involves the electrolysis of fused mixture of alumina ($Al_2O_3$) and cryolite ($Na_3AlF_6$). This fits the description.
(B) Van Arkel method: Used for refining Zirconium (Zr) or Titanium (Ti). It is a vapour phase refining process (formation and decomposition of iodide). No electrolysis.
(C) Mond process: Used for refining Nickel (Ni). It involves the formation of volatile nickel tetracarbonyl and its subsequent thermal decomposition. No electrolysis.
(D) Solvay process: Used for the manufacture of Sodium Carbonate ($Na_2CO_3$). It involves chemical precipitation reactions (using brine, ammonia, $CO_2$). No electrolysis.
Step 2: Conclusion:
Only the Hall-Heroult process uses electrolysis.