1 include "logic/equality.ma".
3 (* Inclusion of: GRP203-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP203-1 : TPTP v3.7.0. Released v2.2.0. *)
9 (* Domain : Group Theory (Loops) *)
11 (* Problem : Left identity, left inverse, Moufang-3 => Moufang-2 *)
13 (* Version : [MP96] (equality) axioms : Especial. *)
17 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
19 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
21 (* Source : [McC98] *)
23 (* Names : MFL-7 [MP96] *)
25 (* Status : Unsatisfiable *)
27 (* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.2.0, 0.21 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0, 0.00 v2.2.1 *)
29 (* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *)
31 (* Number of atoms : 4 ( 4 equality) *)
33 (* Maximal clause size : 1 ( 1 average) *)
35 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
37 (* Number of functors : 6 ( 4 constant; 0-2 arity) *)
39 (* Number of variables : 5 ( 0 singleton) *)
41 (* Maximal term depth : 4 ( 3 average) *)
43 (* Comments : Given left identity and left inverse, Moufang-2 and Moufang-3 *)
45 (* are equivalent, but Moufang-1 is weaker (see MFL-8). *)
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 (multiply X Y) X) Z) (multiply X (multiply Y (multiply X Z))).
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 (* -------------------------------------------------------------------------- *)