2 include "logic/equality.ma".
3 (* Inclusion of: COL015-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : COL015-1 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Combinatory Logic *)
7 (* Problem : Weak fixed point for Q and M *)
8 (* Version : [WM88] (equality) axioms. *)
9 (* English : The weak fixed point property holds for the set P consisting *)
10 (* of the combinators Q and M, where Mx = xx, ((Qx)y)z = y(xz). *)
11 (* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
12 (* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
13 (* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
14 (* : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb *)
16 (* Names : - [MW88] *)
17 (* Status : Unsatisfiable *)
18 (* Rating : 0.00 v2.0.0 *)
19 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
20 (* Number of atoms : 3 ( 3 equality) *)
21 (* Maximal clause size : 1 ( 1 average) *)
22 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
23 (* Number of functors : 4 ( 3 constant; 0-2 arity) *)
24 (* Number of variables : 5 ( 0 singleton) *)
25 (* Maximal term depth : 4 ( 2 average) *)
27 (* -------------------------------------------------------------------------- *)
28 theorem prove_fixed_point:
30 \forall apply:\forall _:Univ.\forall _:Univ.Univ.
31 \forall combinator:Univ.
34 \forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
35 \forall H1:\forall X:Univ.eq Univ (apply m X) (apply X X).\exist Y:Univ.eq Univ Y (apply combinator Y)
40 autobatch paramodulation timeout=100;
46 (* -------------------------------------------------------------------------- *)