#1357E 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, x5: x2*x3, x6:x2*x4, x7:x2*x5+x4*x6})
M.inject_variables()
M.cohomology(4)

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

# Corollary 5.3. Use X=x5, Y=x7, U=<x2*x4,x2*x6>