2 include "logic/equality.ma".
3 (* Inclusion of: GRP010-4.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : GRP010-4 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Group Theory *)
7 (* Problem : Inverse is a symmetric relationship *)
8 (* Version : [Wos65] (equality) axioms : Incomplete. *)
9 (* English : If a is an inverse of b then b is an inverse of a. *)
10 (* Refs : [Wos65] Wos (1965), Unpublished Note *)
11 (* : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
12 (* Source : [Pel86] *)
13 (* Names : Pelletier 64 [Pel86] *)
14 (* Status : Unsatisfiable *)
15 (* Rating : 0.00 v2.1.0, 0.13 v2.0.0 *)
16 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR) *)
17 (* Number of atoms : 5 ( 5 equality) *)
18 (* Maximal clause size : 1 ( 1 average) *)
19 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
20 (* Number of functors : 5 ( 3 constant; 0-2 arity) *)
21 (* Number of variables : 5 ( 0 singleton) *)
22 (* Maximal term depth : 3 ( 2 average) *)
23 (* Comments : [Pel86] says "... problems, published I think, by Larry Wos *)
24 (* (but I cannot locate where)." *)
25 (* -------------------------------------------------------------------------- *)
26 (* ----The operation '*' is associative *)
27 (* ----There exists an identity element 'e' defined below. *)
28 theorem prove_b_times_c_is_e:
32 \forall identity:Univ.
33 \forall inverse:\forall _:Univ.Univ.
34 \forall multiply:\forall _:Univ.\forall _:Univ.Univ.
35 \forall H0:eq Univ (multiply c b) identity.
36 \forall H1:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
37 \forall H2:\forall X:Univ.eq Univ (multiply identity X) X.
38 \forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b c) identity
41 autobatch paramodulation timeout=100;
45 (* -------------------------------------------------------------------------- *)