1 include "logic/equality.ma".
3 (* Inclusion of: GRP394-3.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : GRP394-3 : TPTP v3.7.0. Released v2.5.0. *)
9 (* Domain : Group Theory *)
11 (* Problem : Group theory (equality) axioms *)
13 (* Version : [MOW76] (equality) axioms : *)
15 (* Reduced > Complete. *)
19 (* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
21 (* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
27 (* Status : Satisfiable *)
29 (* Rating : 0.00 v3.2.0, 0.33 v3.1.0, 0.00 v2.5.0 *)
31 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
33 (* Number of atoms : 3 ( 3 equality) *)
35 (* Maximal clause size : 1 ( 1 average) *)
37 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
39 (* Number of functors : 3 ( 1 constant; 0-2 arity) *)
41 (* Number of variables : 5 ( 0 singleton) *)
43 (* Maximal term depth : 3 ( 2 average) *)
47 (* -------------------------------------------------------------------------- *)
49 (* ----Include Group theory (equality) axioms *)
51 (* Inclusion of: Axioms/GRP004-0.ax *)
53 (* -------------------------------------------------------------------------- *)
55 (* File : GRP004-0 : TPTP v3.7.0. Released v1.0.0. *)
57 (* Domain : Group Theory *)
59 (* Axioms : Group theory (equality) axioms *)
61 (* Version : [MOW76] (equality) axioms : *)
63 (* Reduced > Complete. *)
67 (* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
69 (* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
77 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
79 (* Number of atoms : 3 ( 3 equality) *)
81 (* Maximal clause size : 1 ( 1 average) *)
83 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
85 (* Number of functors : 3 ( 1 constant; 0-2 arity) *)
87 (* Number of variables : 5 ( 0 singleton) *)
89 (* Maximal term depth : 3 ( 2 average) *)
91 (* Comments : [MOW76] also contains redundant right_identity and *)
93 (* right_inverse axioms. *)
95 (* : These axioms are also used in [Wos88] p.186, also with *)
97 (* right_identity and right_inverse. *)
99 (* -------------------------------------------------------------------------- *)
101 (* ----For any x and y in the group x*y is also in the group. No clause *)
103 (* ----is needed here since this is an instance of reflexivity *)
105 (* ----There exists an identity element *)
107 (* ----For any x in the group, there exists an element y such that x*y = y*x *)
109 (* ----= identity. *)
111 (* ----The operation '*' is associative *)
113 (* -------------------------------------------------------------------------- *)
115 (* -------------------------------------------------------------------------- *)