1 include "logic/equality.ma".
3 (* Inclusion of: GRP204-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP204-1 : TPTP v3.7.0. Released v2.2.0. *)
9 (* Domain : Group Theory (Loops) *)
11 (* Problem : A non-basis for Moufang loops. *)
13 (* Version : [MP96] (equality) axioms : Especial. *)
15 (* English : Left identity, left inverse, Moufang-1 do not imply Moufang-2; *)
17 (* that is, is not a basis for Moufang loops. *)
19 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
21 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
23 (* Source : [McC98] *)
25 (* Names : MFL-8 [MP96] *)
27 (* Status : Satisfiable *)
29 (* Rating : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.4.0, 0.67 v2.3.0, 1.00 v2.2.1 *)
31 (* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *)
33 (* Number of atoms : 4 ( 4 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 : 5 ( 0 singleton) *)
43 (* Maximal term depth : 4 ( 3 average) *)
45 (* Comments : The smallest model has 3 elements. *)
47 (* -------------------------------------------------------------------------- *)
49 (* ----Left identity and left inverse: *)
53 (* ----Denial of Moufang-2: *)
54 ntheorem prove_moufang2:
55 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
60 ∀left_inverse:∀_:Univ.Univ.
61 ∀multiply:∀_:Univ.∀_:Univ.Univ.
62 ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X (multiply Y Z)) X) (multiply (multiply X Y) (multiply Z X)).
63 ∀H1:∀X:Univ.eq Univ (multiply (left_inverse X) X) identity.
64 ∀H2:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b))))
80 ntry (nassumption) ##;
83 (* -------------------------------------------------------------------------- *)