1 include "logic/equality.ma".
3 (* Inclusion of: GRP207-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP207-1 : TPTP v3.7.0. Released v2.4.0. *)
9 (* Domain : Group Theory *)
11 (* Problem : Single non-axiom for group theory, in product & inverse *)
13 (* Version : [McC93] (equality) axioms. *)
15 (* English : This is a single axiom for group theory, in terms of product *)
19 (* Refs : [Pel98] Peltier (1998), A New Method for Automated Finite Mode *)
21 (* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
23 (* Source : [Pel98] *)
25 (* Names : 4.2.2 [Pel98] *)
27 (* Status : Satisfiable *)
29 (* Rating : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.4.0 *)
31 (* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *)
33 (* Number of atoms : 2 ( 2 equality) *)
35 (* Maximal clause size : 1 ( 1 average) *)
37 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
39 (* Number of functors : 6 ( 4 constant; 0-2 arity) *)
41 (* Number of variables : 3 ( 0 singleton) *)
43 (* Maximal term depth : 8 ( 4 average) *)
47 (* -------------------------------------------------------------------------- *)
48 ntheorem try_prove_this_axiom:
49 (∀Univ:Type.∀U:Univ.∀Y:Univ.∀Z:Univ.
50 ∀inverse:∀_:Univ.Univ.
51 ∀multiply:∀_:Univ.∀_:Univ.Univ.
56 ∀H0:∀U:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply U (inverse (multiply Y (multiply (multiply (multiply Z (inverse Z)) (inverse (multiply U Y))) U)))) U.eq Univ (multiply x (inverse (multiply y (multiply (multiply (multiply z (inverse z)) (inverse (multiply u y))) x)))) u)
70 ntry (nassumption) ##;
73 (* -------------------------------------------------------------------------- *)