cases: fixes a1 :: "'a literal multiset set \<times> 'a literal multiset set \<times> 'a literal multiset set"   and a2 :: "'a literal multiset set \<times> 'a literal multiset set \<times> 'a literal multiset set" assumes "a1 \<leadsto> a2" obtains A :: "'a" and C :: "'a literal multiset" and N :: "'a literal multiset set" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" where "a1 = (N__ \<union> {C__}, P__, Q__)" and "a2 = (N__, P__, Q__)" and "Neg A \<in># C__" and "Pos A \<in># C__"   | D :: "'a literal multiset" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" and C :: "'a literal multiset" and N :: "'a literal multiset set" where "a1 = (Na__ \<union> {Ca__}, Pa__, Qa__)" and "a2 = (Na__, Pa__, Qa__)" and "D__ \<in> Pa__ \<union> Qa__" and "subsumes D__ Ca__"   | D :: "'a literal multiset" and N :: "'a literal multiset set" and C :: "'a literal multiset" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" where "a1 = (Nb__, Pb__ \<union> {Cb__}, Qb__)" and "a2 = (Nb__, Pb__, Qb__)" and "Da__ \<in> Nb__" and "strictly_subsumes Da__ Cb__"   | D :: "'a literal multiset" and N :: "'a literal multiset set" and C :: "'a literal multiset" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" where "a1 = (Nc__, Pc__, Qc__ \<union> {Cc__})" and "a2 = (Nc__, Pc__, Qc__)" and "Db__ \<in> Nc__" and "strictly_subsumes Db__ Cc__"   | D :: "'a literal multiset" and L' :: "'a literal" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" and L :: "'a literal" and \<sigma> :: "'s" and C :: "'a literal multiset" and N :: "'a literal multiset set" where "a1 = (Nd__ \<union> {Cd__ + {#L__#}}, Pd__, Qd__)" and "a2 = (Nd__ \<union> {Cd__}, Pd__, Qd__)" and "Dc__ + {#L'__#} \<in> Pd__ \<union> Qd__" and "- L__ = L'__ \<cdot>l \<sigma>__" and "Dc__ \<cdot> \<sigma>__ \<subseteq># Cd__"   | D :: "'a literal multiset" and L' :: "'a literal" and N :: "'a literal multiset set" and L :: "'a literal" and \<sigma> :: "'s" and C :: "'a literal multiset" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" where "a1 = (Ne__, Pe__ \<union> {Ce__ + {#La__#}}, Qe__)" and "a2 = (Ne__, Pe__ \<union> {Ce__}, Qe__)" and "Dd__ + {#L'a__#} \<in> Ne__" and "- La__ = L'a__ \<cdot>l \<sigma>'__" and "Dd__ \<cdot> \<sigma>'__ \<subseteq># Ce__"   | D :: "'a literal multiset" and L' :: "'a literal" and N :: "'a literal multiset set" and L :: "'a literal" and \<sigma> :: "'s" and C :: "'a literal multiset" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" where "a1 = (Nf__, Pf__, Qf__ \<union> {Cf__ + {#L#}})" and "a2 = (Nf__, Pf__ \<union> {Cf__}, Qf__)" and "D + {#L'#} \<in> Nf__" and "- L = L' \<cdot>l \<sigma>" and "D \<cdot> \<sigma> \<subseteq># Cf__"   | N :: "'a literal multiset set" and C :: "'a literal multiset" and P :: "'a literal multiset set" and Q :: "'a literal multiset set" where "a1 = (Ng__ \<union> {Cg__}, Pg__, Qg__)" and "a2 = (Ng__, Pg__ \<union> {Cg__}, Qg__)"   | N :: "'a literal multiset set" and Q :: "'a literal multiset set" and C :: "'a literal multiset" and P :: "'a literal multiset set" where "a1 = ({}, P \<union> {C}, Q)" and "a2 = (N, P, Q \<union> {C})" and "N = concls_of (ord_FO_resolution.inferences_between Q C)"