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formulas(sos).
(x*(y*z)=(x*y)*z).
(x*I=x).
(x*inv(x)=I).
end_of_list.
formulas(goals).
all x (I*x=x).
all x (inv(inv(x))=x).
all x (inv(x)*x=I).
all x all y (x*y=y*x).
end_of_list.
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