A method of automated theorem proving for information processing which can be highly efficient irrespective of a set of clauses to be dealt with. The method includes the steps of: transforming the statement and the set of knowledge into expressions in terms of elements of a module; constructing a linear equation with the elements of the module as coefficients and elements of a ring of scalars of the module as unknowns; checking the existence of non-negative solution to the linear equation; and determining that the statement is provable when the non-negative solution exist, and not provable otherwise. The apparatus for performing this method is also disclosed.
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