Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / TPTP / HEQ / COL003-5.ma

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+set "baseuri" "cic:/matita/TPTP/COL003-5".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-5.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL003-5 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Strong fixed point for B and W *)
+
+(*  Version  : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(*             Theorem formulation : The fixed point is provided and checked. *)
+
+(*  English  : The strong fixed point property holds for the set  *)
+
+(*             P consisting of the combinators B and W alone, where ((Bx)y)z  *)
+
+(*             = x(yz) and (Wx)y = (xy)y. *)
+
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(*           : [MW87]  McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(*           : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(*           : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.43 v3.2.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 0.80 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    4 (   0 non-Horn;   3 unit;   2 RR) *)
+
+(*             Number of atoms       :    5 (   3 equality) *)
+
+(*             Maximal clause size   :    2 (   1 average) *)
+
+(*             Number of predicates  :    2 (   0 propositional; 1-2 arity) *)
+
+(*             Number of functors    :    4 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :    6 (   0 singleton) *)
+
+(*             Maximal term depth    :    6 (   3 average) *)
+
+(*  Comments : This the M sage of [McCune & Wos, 1987]. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) w)) (apply (apply b b) b))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)