An arithmetic system comprising: a data acquisition unit that acquires operation data items from electrically driven vehicles of a certain electrically driven vehicle type via a network, the operation data items each indicating at least a voltage and a state of charge of a battery used in a corresponding one of the electrically driven vehicles, and a detector that performs statistical processing on the operation data items acquired by the data acquisition unit to detect, from among the electrically driven vehicles, an electrically driven vehicle using a battery of a battery type that is different from a battery type in conformity with specifications of the electrically driven vehicle type, wherein the data acquisition unit acquires, from the corresponding one of the electrically driven vehicles, operation data items at least including a voltage, a current, and a state of charge at a plurality of times measured on the corresponding one of the electrically driven vehicles, and the arithmetic system further includes an extractor that extracts, as sample data, a set of state of charge and voltage in a period in which the battery is regarded to be in a resting state, the set being specified based on the current, from a set of state of charge and voltage at a plurality of times included in each of the operation data items, and an estimator that estimates state of charge-open circuit voltage characteristics of a plurality of batteries each used in the electrically driven vehicles based on extracted sample data, and wherein the detector detects, from among the electrically driven vehicles, an electrically driven vehicle using a battery of a battery type that is different from a battery type in conformity with specifications of the electrically driven vehicle type based on a deviation degree from a representative value of state of charge-open circuit voltage characteristics of the plurality of batteries. a data acquisition unit that acquires operation data items from electrically driven vehicles of a certain electrically driven vehicle type via a network, the operation data items each indicating at least a voltage and a state of charge of a battery used in a corresponding one of the electrically driven vehicles, and a detector that performs statistical processing on the operation data items acquired by the data acquisition unit to detect, from among the electrically driven vehicles, an electrically driven vehicle using a battery of a battery type that is different from a battery type in conformity with specifications of the electrically driven vehicle type, wherein the data acquisition unit acquires, from the corresponding one of the electrically driven vehicles, operation data items at least including a voltage, a current, and a state of charge at a plurality of times measured on the corresponding one of the electrically driven vehicles, and the arithmetic system further includes an extractor that extracts, as sample data, a set of state of charge and voltage in a period in which the battery is regarded to be in a resting state, the set being specified based on the current, from a set of state of charge and voltage at a plurality of times included in each of the operation data items, and an estimator that estimates state of charge-open circuit voltage characteristics of a plurality of batteries each used in the electrically driven vehicles based on extracted sample data, and wherein the detector detects, from among the electrically driven vehicles, an electrically driven vehicle using a battery of a battery type that is different from a battery type in conformity with specifications of the electrically driven vehicle type based on a deviation degree from a representative value of state of charge-open circuit voltage characteristics of the plurality of batteries. an extractor that extracts, as sample data, a set of state of charge and voltage in a period in which the battery is regarded to be in a resting state, the set being specified based on the current, from a set of state of charge and voltage at a plurality of times included in each of the operation data items, and an estimator that estimates state of charge-open circuit voltage characteristics of a plurality of batteries each used in the electrically driven vehicles based on extracted sample data, and wherein the detector detects, from among the electrically driven vehicles, an electrically driven vehicle using a battery of a battery type that is different from a battery type in conformity with specifications of the electrically driven vehicle type based on a deviation degree from a representative value of state of charge-open circuit voltage characteristics of the plurality of batteries.