2 include "logic/equality.ma".
3 (* Inclusion of: COL014-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : COL014-1 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Combinatory Logic *)
7 (* Problem : Weak fixed point for L and O *)
8 (* Version : [WM88] (equality) axioms. *)
9 (* English : The weak fixed point property holds for the set P consisting *)
10 (* of the combinators L and O, where (Lx)y = x(yy), (Ox)y *)
12 (* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
13 (* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
14 (* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
15 (* : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb *)
17 (* Names : - [MW88] *)
18 (* Status : Unsatisfiable *)
19 (* Rating : 0.00 v2.0.0 *)
20 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
21 (* Number of atoms : 3 ( 3 equality) *)
22 (* Maximal clause size : 1 ( 1 average) *)
23 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
24 (* Number of functors : 4 ( 3 constant; 0-2 arity) *)
25 (* Number of variables : 5 ( 0 singleton) *)
26 (* Maximal term depth : 3 ( 2 average) *)
28 (* -------------------------------------------------------------------------- *)
29 theorem prove_fixed_point:
31 \forall apply:\forall _:Univ.\forall _:Univ.Univ.
32 \forall combinator:Univ.
35 \forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)).
36 \forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).\exist Y:Univ.eq Univ Y (apply combinator Y)
41 autobatch paramodulation timeout=100;
47 (* -------------------------------------------------------------------------- *)