Proof with simpl; auto.
intros H1 H2. unfold simplify. apply delete_resolved_sound.
apply clause_denote_foldl...
intros c0 d H3 H4; apply demodulate_sound...
Qed.

Lemma infer_list_sound c l s :
clause_denote c s -> listd clause_denote inter TT l s ->
listd clause_denote inter TT (infer_list c l) s.