1 include "logic/equality.ma".
3 (* Inclusion of: COL042-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : COL042-1 : TPTP v3.7.0. Released v1.0.0. *)
9 (* Domain : Combinatory Logic *)
11 (* Problem : Strong fixed point for B and W1 *)
13 (* Version : [WM88] (equality) axioms. *)
15 (* English : The strong fixed point property holds for the set *)
17 (* P consisting of the combinators B and W1, where ((Bx)y)z *)
19 (* = x(yz), (W1x)y = (yx)x. *)
21 (* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
23 (* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
25 (* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
27 (* : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb *)
29 (* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
33 (* Names : - [MW88] *)
35 (* : Question 5 [Wos93] *)
37 (* Status : Unsatisfiable *)
39 (* Rating : 0.67 v3.4.0, 0.75 v3.3.0, 0.86 v3.1.0, 0.89 v2.7.0, 0.91 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.33 v2.2.1, 0.89 v2.2.0, 1.00 v2.0.0 *)
41 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
43 (* Number of atoms : 3 ( 3 equality) *)
45 (* Maximal clause size : 1 ( 1 average) *)
47 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
49 (* Number of functors : 4 ( 2 constant; 0-2 arity) *)
51 (* Number of variables : 6 ( 0 singleton) *)
53 (* Maximal term depth : 4 ( 3 average) *)
57 (* -------------------------------------------------------------------------- *)
58 ntheorem prove_fixed_point:
59 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
60 ∀apply:∀_:Univ.∀_:Univ.Univ.
64 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).
65 ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))))
77 napply (ex_intro ? ? ? ?) ##[
81 ntry (nassumption) ##;
84 (* -------------------------------------------------------------------------- *)