2 include "logic/equality.ma".
3 (* Inclusion of: COL010-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : COL010-1 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Combinatory Logic *)
7 (* Problem : Weak fixed point for B and S2 *)
8 (* Version : [WM88] (equality) axioms. *)
9 (* English : The weak fixed point property holds for the set P consisting *)
10 (* of the combinators B and S2, where ((Bx)y)z = x(yz), *)
11 (* ((S2x)y)z = (xz)(yy). *)
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 : 0.07 v3.1.0, 0.11 v2.7.0, 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 : 7 ( 0 singleton) *)
26 (* Maximal term depth : 4 ( 3 average) *)
28 (* -------------------------------------------------------------------------- *)
29 theorem prove_fixed_point:
31 \forall apply:\forall _:Univ.\forall _:Univ.Univ.
33 \forall combinator:Univ.
35 \forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply s2 X) Y) Z) (apply (apply X Z) (apply Y Y)).
36 \forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
41 autobatch paramodulation timeout=100;
47 (* -------------------------------------------------------------------------- *)