1 include "logic/equality.ma".
3 (* Inclusion of: GRP119-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP119-1 : TPTP v3.7.0. Bugfixed v1.2.1. *)
9 (* Domain : Group Theory *)
11 (* Problem : Derive order 4 from a single axiom for groups order 4 *)
13 (* Version : [Wos96] (equality) axioms. *)
17 (* Refs : [Wos96] Wos (1996), The Automation of Reasoning: An Experiment *)
19 (* Source : [OTTER] *)
21 (* Names : groups.exp4.in part 1 [OTTER] *)
23 (* Status : Unsatisfiable *)
25 (* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.57 v2.1.0, 0.29 v2.0.0 *)
27 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 2 RR) *)
29 (* Number of atoms : 3 ( 3 equality) *)
31 (* Maximal clause size : 1 ( 1 average) *)
33 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
35 (* Number of functors : 3 ( 2 constant; 0-2 arity) *)
37 (* Number of variables : 3 ( 0 singleton) *)
39 (* Maximal term depth : 6 ( 2 average) *)
43 (* Bugfixes : v1.2.1 - Clause prove_order4 fixed. *)
45 (* -------------------------------------------------------------------------- *)
46 ntheorem prove_order4:
47 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
50 ∀multiply:∀_:Univ.∀_:Univ.Univ.
51 ∀H0:eq Univ (multiply identity identity) identity.
52 ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a (multiply a (multiply a a))) identity)
64 ntry (nassumption) ##;
67 (* -------------------------------------------------------------------------- *)