--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ANA034-2".
+include "logic/equality.ma".
+
+(* Inclusion of: ANA034-2.p *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* File : ANA034-2 : TPTP v3.2.0. Released v3.2.0. *)
+
+(* Domain : Analysis *)
+
+(* Problem : Problem about Big-O notation *)
+
+(* Version : [Pau06] axioms : Reduced > Especial. *)
+
+(* English : *)
+
+(* Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe *)
+
+(* Source : [Pau06] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0 *)
+
+(* Syntax : Number of clauses : 15 ( 0 non-Horn; 6 unit; 13 RR) *)
+
+(* Number of atoms : 31 ( 2 equality) *)
+
+(* Maximal clause size : 6 ( 2 average) *)
+
+(* Number of predicates : 8 ( 0 propositional; 1-3 arity) *)
+
+(* Number of functors : 11 ( 5 constant; 0-3 arity) *)
+
+(* Number of variables : 46 ( 40 singleton) *)
+
+(* Maximal term depth : 5 ( 2 average) *)
+
+(* Comments : The problems in the [Pau06] collection each have very many axioms, *)
+
+(* of which only a small selection are required for the refutation. *)
+
+(* The mission is to find those few axioms, after which a refutation *)
+
+(* can be quite easily found. This version has only the necessary *)
+
+(* axioms. *)
+
+(* ------------------------------------------------------------------------------ *)
+theorem cls_conjecture_5:
+ ∀Univ:Set.∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀V_x:Univ.∀V_y:Univ.∀c_0:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_less:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀class_OrderedGroup_Olordered__ab__group__abs:∀_:Univ.Prop.∀class_Orderings_Oorder:∀_:Univ.Prop.∀class_Ring__and__Field_Oordered__idom:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__cancel__semiring:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__semiring:∀_:Univ.Prop.∀t_b:Univ.∀v_a:∀_:Univ.Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_ca:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:Univ.∀H0:eq Univ (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) (c_times (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b).∀H1:c_lessequals (c_HOL_Oabs (v_b v_x) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b.∀H2:c_lessequals (c_HOL_Oabs (v_a v_x) t_b) (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) t_b.∀H3:c_less c_0 v_c t_b.∀H4:∀T_a:Univ.∀V_a:Univ.∀_:class_OrderedGroup_Olordered__ab__group__abs T_a.c_lessequals c_0 (c_HOL_Oabs V_a T_a) T_a.∀H5:∀T_a:Univ.∀V_x:Univ.∀V_y:Univ.∀_:c_less V_x V_y T_a.∀_:class_Orderings_Oorder T_a.c_lessequals V_x V_y T_a.∀H6:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:c_lessequals c_0 V_a T_a.∀_:c_lessequals c_0 V_b T_a.∀_:class_Ring__and__Field_Opordered__cancel__semiring T_a.c_lessequals c_0 (c_times V_a V_b T_a) T_a.∀H7:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀_:c_lessequals c_0 V_b T_a.∀_:c_lessequals c_0 V_c T_a.∀_:c_lessequals V_a V_b T_a.∀_:c_lessequals V_c V_d T_a.∀_:class_Ring__and__Field_Opordered__semiring T_a.c_lessequals (c_times V_a V_c T_a) (c_times V_b V_d T_a) T_a.∀H8:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_Ring__and__Field_Oordered__idom T_a.eq Univ (c_HOL_Oabs (c_times V_a V_b T_a) T_a) (c_times (c_HOL_Oabs V_a T_a) (c_HOL_Oabs V_b T_a) T_a).c_lessequals (c_HOL_Oabs (c_times (v_a v_x) (v_b v_x) t_b) t_b) (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) t_b
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* ------------------------------------------------------------------------------ *)