Block[{Print},<<xAct`xTras`];
$Pre=ScreenDollarIndices;
$DefInfoQ=False;
$UndefInfoQ=False;
$CommuteCovDsOnScalars=True;

DefManifold[M4, 4, {α,β,γ,δ,ζ,η,θ,ι,κ,λ,μ,ο,ς,σ,τ,υ,χ,ω,ν}]
DefMetric[-1,gb[-α,-β],CD,SymbolOfCovD->{"D","▽"}]
DefTensor[A[μ],M4]
DefTensor[F[μ,ν],M4,Antisymmetric[{μ,ν}]]
DefTensor[HDF[μ,ν],M4,Antisymmetric[{μ,ν}],PrintAs->"(Overscript[F, *])"]
DefTensor[ϕ[],M4]

L1=MakeContractionAnsatz[(CD@ϕ )^2 F^3//IndexFree//FromIndexFree,ConstantPrefix->"C"]

L2=MakeContractionAnsatz[(CD@ϕ )^2 F HDF //IndexFree//FromIndexFree,ConstantPrefix->"S"]

L3=MakeContractionAnsatz[(CD@CD@ϕ )^2 F HDF^2 //IndexFree//FromIndexFree,ConstantPrefix->"g"]