2 include "logic/equality.ma".
3 (* Inclusion of: GRP206-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : GRP206-1 : TPTP v3.1.1. Released v2.3.0. *)
6 (* Domain : Group Theory (Loops) *)
7 (* Problem : In Loops, Moufang-4 => Moufang-1. *)
8 (* Version : [MP96] (equality) axioms. *)
10 (* Refs : [Wos96] Wos (1996), OTTER and the Moufang Identity Problem *)
11 (* Source : [Wos96] *)
12 (* Names : - [Wos96] *)
13 (* Status : Unsatisfiable *)
14 (* Rating : 0.00 v2.3.0 *)
15 (* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *)
16 (* Number of atoms : 10 ( 10 equality) *)
17 (* Maximal clause size : 1 ( 1 average) *)
18 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
19 (* Number of functors : 9 ( 4 constant; 0-2 arity) *)
20 (* Number of variables : 15 ( 0 singleton) *)
21 (* Maximal term depth : 4 ( 2 average) *)
23 (* -------------------------------------------------------------------------- *)
24 (* ----Loop axioms: *)
26 (* ----Denial of Moufang-1 *)
27 theorem prove_moufang1:
32 \forall identity:Univ.
33 \forall left_division:\forall _:Univ.\forall _:Univ.Univ.
34 \forall left_inverse:\forall _:Univ.Univ.
35 \forall multiply:\forall _:Univ.\forall _:Univ.Univ.
36 \forall right_division:\forall _:Univ.\forall _:Univ.Univ.
37 \forall right_inverse:\forall _:Univ.Univ.
38 \forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply Y Z) X)) (multiply (multiply X Y) (multiply Z X)).
39 \forall H1:\forall X:Univ.eq Univ (multiply (left_inverse X) X) identity.
40 \forall H2:\forall X:Univ.eq Univ (multiply X (right_inverse X)) identity.
41 \forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (right_division (multiply X Y) Y) X.
42 \forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (right_division X Y) Y) X.
43 \forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (left_division X (multiply X Y)) Y.
44 \forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (left_division X Y)) Y.
45 \forall H7:\forall X:Univ.eq Univ (multiply X identity) X.
46 \forall H8:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a))
49 autobatch paramodulation timeout=100;
53 (* -------------------------------------------------------------------------- *)