Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / COL066-3.ma

diff --git a/matita/matita/contribs/ng_TPTP/COL066-3.ma b/matita/matita/contribs/ng_TPTP/COL066-3.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: COL066-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL066-3 : TPTP v3.7.0. Bugfixed v1.2.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Find combinator equivalent to P from B, Q and W *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*             Theorem formulation : The combinator is provided and checked. *)
+
+(*  English  : Construct from B, Q and W alone a combinator that behaves as *)
+
+(*             the combinator P does, where ((Bx)y)z = x(yz), ((Qx)y)z = *)
+
+(*             y(xz), (Wx)y = (xy)y, (((Px)y)y)z = (xy)((xy)z) *)
+
+(*  Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(*           : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to  *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.1.0, 0.29 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    4 (   0 non-Horn;   4 unit;   1 RR) *)
+
+(*             Number of atoms       :    4 (   4 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    7 (   6 constant; 0-2 arity) *)
+
+(*             Number of variables   :    8 (   0 singleton) *)
+
+(*             Maximal term depth    :   10 (   4 average) *)
+
+(*  Comments :  *)
+
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----This is the P equivalent *)
+ntheorem prove_p_combinator:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀q:Univ.
+∀w:Univ.
+∀x:Univ.
+∀y:Univ.
+∀z:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply (apply b (apply w (apply q (apply q q)))) q) x) y) y) z) (apply (apply x y) (apply (apply x y) z)))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#q ##.
+#w ##.
+#x ##.
+#y ##.
+#z ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+nauto by H0,H1,H2 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)