1 include "logic/equality.ma".
3 (* Inclusion of: GRP456-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP456-1 : TPTP v3.7.0. Released v2.6.0. *)
9 (* Domain : Group Theory *)
11 (* Problem : Axiom for group theory, in division and identity, part 3 *)
13 (* Version : [McC93] (equality) axioms. *)
17 (* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
23 (* Status : Unsatisfiable *)
25 (* Rating : 0.00 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0 *)
27 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *)
29 (* Number of atoms : 5 ( 5 equality) *)
31 (* Maximal clause size : 1 ( 1 average) *)
33 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
35 (* Number of functors : 7 ( 4 constant; 0-2 arity) *)
37 (* Number of variables : 7 ( 0 singleton) *)
39 (* Maximal term depth : 8 ( 3 average) *)
41 (* Comments : A UEQ part of GRP066-1 *)
43 (* -------------------------------------------------------------------------- *)
44 ntheorem prove_these_axioms_3:
45 (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.
49 ∀divide:∀_:Univ.∀_:Univ.Univ.
51 ∀inverse:∀_:Univ.Univ.
52 ∀multiply:∀_:Univ.∀_:Univ.Univ.
53 ∀H0:∀A:Univ.eq Univ identity (divide A A).
54 ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
55 ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
56 ∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
73 nauto by H0,H1,H2,H3 ##;
74 ntry (nassumption) ##;
77 (* -------------------------------------------------------------------------- *)