{
"NTCIR12-MathIR-1": [["math:U!plus", "math:V!x", "math:?y"], ["text:mean"], ["text:arithmetic"]],
"NTCIR12-MathIR-2": [["math:U!times", "math:N!1", "math:?x"], ["text:factorial"], ["text:product"]],
"NTCIR12-MathIR-3": [["math:U!plus", "math:N!1", "math:?y"], ["text:progression"], ["text:arithmetic"]],
"NTCIR12-MathIR-4": [["math:U!plus", "math:N!1", "math:?y"], ["text:progression"], ["text:geometric"]],
"NTCIR12-MathIR-5": [["math:O!divide", "math:V!x", "math:?y"], ["text:ratio"], ["text:division"]],
"NTCIR12-MathIR-6": [["math:U!eq", "math:O!SUB", "math:V!\u03c0", "math:?a", "math:U!times", "math:V!A", "math:U!plus", "math:?b", "math:?c"], ["text:prospect"], ["text:interference"]],
"NTCIR12-MathIR-7": [["math:U!eq", "math:?a", "math:U!times", "math:V!f", "math:M!V-3", "math:?b", "math:?c", "math:?d"], ["text:boltzmann"], ["text:machine"]],
"NTCIR12-MathIR-8": [["math:U!eq", "math:?a", "math:O!plus-or-minus", "math:N!1"], ["text:neural"], ["text:network"]],
"NTCIR12-MathIR-9": [["math:U!eq", "math:?a", "math:U!times", "math:O!divide", "math:N!1", "math:?b", "math:+!O!SUB", "math:O!SUP", "math:O!SUB", "math:O!sum", "math:U!eq", "math:?c", "math:N!1", "math:?b", "math:M!D-lsqb;]", "math:O!minus", "math:?d", "math:?e"], ["text:thermodynamic"], ["text:hamiltonian"]],
"NTCIR12-MathIR-10": [["math:U!eq", "math:O!SUB", "math:?a", "math:U!times", "math:?i", "math:?j", "math:N!1"], ["text:drums"], ["text:rhythms"]],
"NTCIR12-MathIR-11": [["math:U!times", "math:V!l", "math:V!i", "math:V!s", "math:V!t"], ["text:polymorphic"]],
"NTCIR12-MathIR-12": [["math:U!eq", "math:U!plus", "math:U!times", "math:?f", "math:?a", "math:U!times", "math:?f", "math:?b", "math:U!times", "math:?f", "math:U!plus", "math:?b", "math:?a"]],
"NTCIR12-MathIR-13": [["math:U!eq", "math:U!plus", "math:?a", "math:?b", "math:U!times", "math:?f", "math:U!plus", "math:?b", "math:?a"]],
"NTCIR12-MathIR-14": [["math:U!eq", "math:V!P", "math:U!times", "math:V!N", "math:V!P"], ["text:complexity"]],
"NTCIR12-MathIR-15": [["math:U!plus", "math:U!times", "math:N!3", "math:?n", "math:N!1"], ["text:collatz"], ["text:conjecture"]],
"NTCIR12-MathIR-16": [["math:U!eq", "math:O!SUB", "math:V!F", "math:V!n", "math:+!O!SUB", "math:O!SUP", "math:O!SUB", "math:O!sum", "math:?e", "math:V!n", "math:O!binomial", "math:?x", "math:?y"]],
"NTCIR12-MathIR-17": [["math:N!2015"], ["text:sequence"], ["text:generating"], ["text:function"]],
"NTCIR12-MathIR-18": [["math:U!eq", "math:U!times", "math:U!plus", "math:U!times", "math:C!hbar", "math:?x", "math:U!times", "math:V!i", "math:V!m", "math:V!c", "math:V!normal-\u03a6", "math:O!interval(O-O)", "math:V!t", "math:V!x", "math:N!0"], ["text:maxwell"]],
"NTCIR12-MathIR-19": [["math:U!times", "math:N!2", "math:V!normal-\u03a0"], ["math:V!normal-\u03a0"], ["text:pi"], ["text:tau"]],
"NTCIR12-MathIR-20": [["math:U!eq", "math:U!times", "math:?L", "math:M!V-3", "math:V!x", "math:V!y", "math:V!\u03bb", "math:?z"], ["math:U!eq", "math:U!times", "math:V!L", "math:M!V-3", "math:V!x", "math:V!y", "math:V!\u03bb", "math:?z"], ["text:lagrange"], ["text:multiplier"]],
"NTCIR12-MathIR-21": [["math:U!eq", "math:U!times", "math:V!L", "math:O!interval(O-O)", "math:?x", "math:?y", "math:?z"], ["text:loss", "text:function"]],
"NTCIR12-MathIR-22": [["math:O!geq", "math:?f", "math:O!divide", "math:?h", "math:U!times", "math:N!2", "math:V!\u03c0"], ["text:uncertainty"]],
"NTCIR12-MathIR-23": [["math:V!c"], ["text:warp", "text:drive"], ["text:alcubierre", "text:drive"], ["text:faster", "text:than", "text:light", "text:travel"]],
"NTCIR12-MathIR-24": [["math:U!eq", "math:U!times", "math:?B", "math:O!SUB", "math:V!\u03c3", "math:N!3", "math:?B", "math:O!SUB", "math:V!\u03c3", "math:N!3"], ["text:invariance"], ["text:point"], ["text:interaction"]],
"NTCIR12-MathIR-25": [["math:U!eq", "math:O!SUB", "math:V!S", "math:U!times", "math:V!E", "math:V!H", "math:U!times", "math:O!divide", "math:N!1", "math:O!SUB", "math:V!G", "math:N!3", "math:?o", "math:O!SUP", "math:V!d", "math:N!3", "math:V!x", "math:O!root", "math:O!SUP", "math:V!g", "math:N!3", "math:N!2"], ["text:entropy"], ["text:bound"], ["text:bekenstein", "text:hawking"]],
"NTCIR12-MathIR-26": [["math:U!eq", "math:?S", "math:U!times", "math:O!SUB", "math:?T", "math:?p", "math:O!int", "math:U!times", "math:O!SUP", "math:?d", "math:U!plus", "math:?p", "math:N!1", "math:?x", "math:O!root", "math:?g", "math:N!2", "math:W!", "math:W!"], ["text:brane"], ["text:action"], ["text:cosmological"]],
"NTCIR12-MathIR-27": [["math:U!times", "math:V!C", "math:V!o", "math:V!n", "math:U!plus", "math:U!times", "math:V!Z", "math:V!F", "math:V!C", "math:?x"]],
"NTCIR12-MathIR-28": [["math:O!SUB", "math:V!normal-\u05d0", "math:N!0"], ["text:categorical", "text:simple", "text:theory"]],
"NTCIR12-MathIR-29": [["math:O!assign", "math:U!times", "math:V!d", "math:V!c", "math:V!l", "math:?a", "math:?f"]],
}