2 include "logic/equality.ma".
3 (* Inclusion of: GRP509-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : GRP509-1 : TPTP v3.1.1. Released v2.6.0. *)
6 (* Domain : Group Theory (Abelian) *)
7 (* Problem : Axiom for Abelian group theory, in product and inverse, part 1 *)
8 (* Version : [McC93] (equality) axioms. *)
10 (* Refs : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
11 (* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
14 (* Status : Unsatisfiable *)
15 (* Rating : 0.00 v2.6.0 *)
16 (* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *)
17 (* Number of atoms : 2 ( 2 equality) *)
18 (* Maximal clause size : 1 ( 1 average) *)
19 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
20 (* Number of functors : 4 ( 2 constant; 0-2 arity) *)
21 (* Number of variables : 3 ( 0 singleton) *)
22 (* Maximal term depth : 4 ( 3 average) *)
23 (* Comments : A UEQ part of GRP085-1 *)
24 (* -------------------------------------------------------------------------- *)
25 theorem prove_these_axioms_1:
29 \forall inverse:\forall _:Univ.Univ.
30 \forall multiply:\forall _:Univ.\forall _:Univ.Univ.
31 \forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
34 autobatch paramodulation timeout=100;
38 (* -------------------------------------------------------------------------- *)