2 include "logic/equality.ma".
3 (* Inclusion of: LAT034-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : LAT034-1 : TPTP v3.1.1. Bugfixed v2.5.0. *)
6 (* Domain : Lattice Theory *)
7 (* Problem : Idempotency of meet *)
8 (* Version : [McC88] (equality) axioms. *)
10 (* Refs : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
11 (* [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
12 (* Source : [DeN00] *)
13 (* Names : idemp_of_meet [DeN00] *)
14 (* Status : Unsatisfiable *)
15 (* Rating : 0.00 v2.5.0 *)
16 (* Syntax : Number of clauses : 7 ( 0 non-Horn; 7 unit; 1 RR) *)
17 (* Number of atoms : 7 ( 7 equality) *)
18 (* Maximal clause size : 1 ( 1 average) *)
19 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
20 (* Number of functors : 3 ( 1 constant; 0-2 arity) *)
21 (* Number of variables : 14 ( 2 singleton) *)
22 (* Maximal term depth : 3 ( 2 average) *)
24 (* Bugfixes : v2.5.0 - Used axioms without the conjecture *)
25 (* -------------------------------------------------------------------------- *)
26 (* ----Include lattice theory axioms *)
27 (* include('Axioms/LAT001-0.ax'). *)
28 (* -------------------------------------------------------------------------- *)
29 theorem idempotence_of_meet:
31 \forall join:\forall _:Univ.\forall _:Univ.Univ.
32 \forall meet:\forall _:Univ.\forall _:Univ.Univ.
34 \forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
35 \forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
36 \forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
37 \forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
38 \forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
39 \forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (meet xx xx) xx
42 autobatch paramodulation timeout=100;
46 (* -------------------------------------------------------------------------- *)