{
"NTCIR12-MathIR-1": [["math:U!plus", "math:V!x", "math:?"], ["text:mean"], ["text:arithmetic"]],
"NTCIR12-MathIR-2": [["math:U!times", "math:N!1", "math:?"], ["text:factorial"], ["text:product"]],
"NTCIR12-MathIR-3": [["math:U!plus", "math:N!1", "math:?"], ["text:progression"], ["text:arithmetic"]],
"NTCIR12-MathIR-4": [["math:U!plus", "math:N!1", "math:?"], ["text:progression"], ["text:geometric"]],
"NTCIR12-MathIR-5": [["math:O!divide", "math:V!x", "math:?"], ["text:ratio"], ["text:division"]],
"NTCIR12-MathIR-6": [["text:prospect"], ["text:interference"]],
"NTCIR12-MathIR-7": [["math:U!eq", "math:?", "math:U!times", "math:V!f", "math:M!V-3", "math:?", "math:?", "math:?"], ["text:boltzmann"], ["text:machine"]],
"NTCIR12-MathIR-8": [["text:neural"], ["text:network"]],
"NTCIR12-MathIR-9": [["text:thermodynamic"], ["text:hamiltonian"]],
"NTCIR12-MathIR-10": [["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:?", "math:?", "math:U!times", "math:?", "math:?", "math:U!times", "math:?", "math:U!plus", "math:?", "math:?"]],
"NTCIR12-MathIR-13": [["math:U!eq", "math:U!plus", "math:?", "math:?", "math:U!times", "math:?", "math:U!plus", "math:?", "math:?"]],
"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:?", "math:N!1"], ["text:collatz"], ["text:conjecture"]],
"NTCIR12-MathIR-16": [],
"NTCIR12-MathIR-17": [["math:N!2015"], ["text:sequence"], ["text:generating"], ["text:function"]],
"NTCIR12-MathIR-18": [["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:?", "math:M!V-3", "math:V!x", "math:V!y", "math:V!\u03bb", "math:?"], ["math:U!eq", "math:U!times", "math:V!L", "math:M!V-3", "math:V!x", "math:V!y", "math:V!\u03bb", "math:?"], ["text:lagrange"], ["text:multiplier"]],
"NTCIR12-MathIR-21": [["math:U!eq", "math:U!times", "math:V!L", "math:O!interval(O-O)", "math:?", "math:?", "math:?"], ["text:loss", "text:function"]],
"NTCIR12-MathIR-22": [["math:O!geq", "math:?", "math:O!divide", "math:?", "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": [["text:invariance"], ["text:point"], ["text:interaction"]],
"NTCIR12-MathIR-25": [["text:entropy"], ["text:bound"], ["text:bekenstein", "text:hawking"]],
"NTCIR12-MathIR-26": [["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:?"]],
"NTCIR12-MathIR-28": [["text:categorical", "text:simple", "text:theory"]],
"NTCIR12-MathIR-29": [],
}