#257D It does not have (purely) coclosed G2-structure. First obstruction

A.<x1,x2,x3,x4,x5,x6,x7> = GradedCommutativeAlgebra(QQ)
M=A.cdg_algebra({x3:x1*x2,x6:x1*x3+x2*x4,x7:x1*x4+x2*x5})
M.inject_variables()
M.cohomology(4)

Defining x1, x2, x3, x4, x5, x6, x7
Free module generated by {[x1*x2*x3*x6], [x1*x3*x4*x6], [x2*x3*x4*x6], [x1*x3*x5*x6 + x2*x3*x5*x7], [x2*x3*x5*x6], [x1*x4*x5*x6], [x2*x4*x5*x6 + x2*x3*x5*x7], [x3*x4*x5*x6 - x1*x4*x6*x7], [x2*x3*x4*x7], [x1*x3*x5*x7], [x1*x4*x5*x7], [x3*x4*x5*x7 - x1*x5*x6*x7]} over Rational Field

# Corollary 5.3. Use X=x6, Y=x7, U=<x1*x4,x1*x5>