Proof with simpl; auto.
intros A B; destruct c as [gamma delta| |]; destruct d as [gamma' delta'| |]...
2: simpl; destruct gamma, delta... 2: destruct p...
2: simpl; destruct gamma, delta... 2: destruct p...
destruct gamma, delta... destruct p... destruct gamma'... destruct p...
remember (expr_eq e e1) as b; destruct b. 2: simpl; auto.
if_tac; [simpl|simpl; auto]; rewrite interS; simpl. intro H3. split...
rewrite (@listd_insert_uniq_inter _ state)... 2: apply pure_atom_cmp_eq.
intros [H1 H2].
assert ((e2 === e0) s). if_tac in H1; simpl in H1... apply var_eq_sym...
simpl in A; spec A... inversion A.
simpl in B; spec B. split... apply expr_eq_eq' in Heqb; subst e1.
eapply var_eq_trans; eapply var_eq_sym in H; eauto.
apply listd_merge_un2... solve[apply pure_atom_cmp_eq].
apply listd_merge_un1... solve[apply pure_atom_cmp_eq].
Qed.

Lemma reflexivity_resolution_sound c l0 s :
clause_denote c s -> listd clause_denote inter TT l0 s ->
listd clause_denote inter TT (reflexivity_resolution c l0) s.