1 include "logic/equality.ma".
3 (* Inclusion of: GRP472-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP472-1 : TPTP v3.2.0. Released v2.6.0. *)
9 (* Domain : Group Theory *)
11 (* Problem : Axiom for group theory, in division and inverse, part 1 *)
13 (* Version : [McC93] (equality) axioms. *)
17 (* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
23 (* Status : Unsatisfiable *)
25 (* Rating : 0.07 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0 *)
27 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 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 : 5 ( 2 constant; 0-2 arity) *)
37 (* Number of variables : 6 ( 0 singleton) *)
39 (* Maximal term depth : 5 ( 3 average) *)
41 (* Comments : A UEQ part of GRP072-1 *)
43 (* -------------------------------------------------------------------------- *)
44 ntheorem prove_these_axioms_1:
45 ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.
48 ∀divide:∀_:Univ.∀_:Univ.Univ.
49 ∀inverse:∀_:Univ.Univ.
50 ∀multiply:∀_:Univ.∀_:Univ.Univ.
51 ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
52 ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
69 (* -------------------------------------------------------------------------- *)