2 include "logic/equality.ma".
3 (* Inclusion of: LAT039-2.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : LAT039-2 : TPTP v3.1.1. Released v2.4.0. *)
6 (* Domain : Lattice Theory *)
7 (* Problem : Every distributive lattice is modular *)
8 (* Version : [McC88] (equality) axioms. *)
9 (* English : Theorem formulation : Modularity is expressed by: *)
10 (* x <= y -> x v (y & z) = (x v y) & (x v z) *)
11 (* Refs : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
12 (* [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
13 (* Source : [DeN00] *)
14 (* Names : lattice-mod-3 [DeN00] *)
15 (* Status : Unsatisfiable *)
16 (* Rating : 0.00 v2.4.0 *)
17 (* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 2 RR) *)
18 (* Number of atoms : 12 ( 12 equality) *)
19 (* Maximal clause size : 1 ( 1 average) *)
20 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
21 (* Number of functors : 5 ( 3 constant; 0-2 arity) *)
22 (* Number of variables : 22 ( 2 singleton) *)
23 (* Maximal term depth : 3 ( 2 average) *)
25 (* -------------------------------------------------------------------------- *)
26 (* ----Include lattice theory axioms *)
27 (* Inclusion of: Axioms/LAT001-0.ax *)
28 (* -------------------------------------------------------------------------- *)
29 (* File : LAT001-0 : TPTP v3.1.1. Released v1.0.0. *)
30 (* Domain : Lattice Theory *)
31 (* Axioms : Lattice theory (equality) axioms *)
32 (* Version : [McC88] (equality) axioms. *)
34 (* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
35 (* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
36 (* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
37 (* Source : [McC88] *)
40 (* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
41 (* Number of literals : 8 ( 8 equality) *)
42 (* Maximal clause size : 1 ( 1 average) *)
43 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
44 (* Number of functors : 2 ( 0 constant; 2-2 arity) *)
45 (* Number of variables : 16 ( 2 singleton) *)
46 (* Maximal term depth : 3 ( 2 average) *)
48 (* -------------------------------------------------------------------------- *)
49 (* ----The following 8 clauses characterise lattices *)
50 (* -------------------------------------------------------------------------- *)
51 (* -------------------------------------------------------------------------- *)
54 \forall join:\forall _:Univ.\forall _:Univ.Univ.
55 \forall meet:\forall _:Univ.\forall _:Univ.Univ.
59 \forall H0:eq Univ (join xx yy) yy.
60 \forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet X (join Y Z)) (join (meet X Y) (meet X Z)).
61 \forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join X (meet Y Z)) (meet (join X Y) (join X Z)).
62 \forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
63 \forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
64 \forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
65 \forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
66 \forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
67 \forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.
68 \forall H9:\forall X:Univ.eq Univ (join X X) X.
69 \forall H10:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet (join xx yy) (join xx zz))
72 autobatch paramodulation timeout=100;
76 (* -------------------------------------------------------------------------- *)