1 include "logic/equality.ma".
3 (* Inclusion of: RNG043-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : RNG043-1 : TPTP v3.7.0. Released v2.5.0. *)
9 (* Domain : Ring Theory (Alternative) *)
11 (* Problem : Alternative ring theory (equality) axioms *)
13 (* Version : [Ste87] (equality) axioms. *)
17 (* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
19 (* Source : [Ste87] *)
23 (* Status : Satisfiable *)
25 (* Rating : 0.00 v3.2.0, 0.33 v3.1.0, 0.00 v2.5.0 *)
27 (* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *)
29 (* Number of atoms : 15 ( 15 equality) *)
31 (* Maximal clause size : 1 ( 1 average) *)
33 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
35 (* Number of functors : 6 ( 1 constant; 0-3 arity) *)
37 (* Number of variables : 27 ( 2 singleton) *)
39 (* Maximal term depth : 5 ( 2 average) *)
43 (* -------------------------------------------------------------------------- *)
45 (* ----Include Alternative ring theory (equality) axioms *)
47 (* Inclusion of: Axioms/RNG003-0.ax *)
49 (* -------------------------------------------------------------------------- *)
51 (* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *)
53 (* Domain : Ring Theory (Alternative) *)
55 (* Axioms : Alternative ring theory (equality) axioms *)
57 (* Version : [Ste87] (equality) axioms. *)
61 (* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
63 (* Source : [Ste87] *)
69 (* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *)
71 (* Number of atoms : 15 ( 15 equality) *)
73 (* Maximal clause size : 1 ( 1 average) *)
75 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
77 (* Number of functors : 6 ( 1 constant; 0-3 arity) *)
79 (* Number of variables : 27 ( 2 singleton) *)
81 (* Maximal term depth : 5 ( 2 average) *)
85 (* -------------------------------------------------------------------------- *)
87 (* ----There exists an additive identity element *)
89 (* ----Multiplicative zero *)
91 (* ----Existence of left additive additive_inverse *)
93 (* ----Inverse of additive_inverse of X is X *)
95 (* ----Distributive property of product over sum *)
97 (* ----Commutativity for addition *)
99 (* ----Associativity for addition *)
101 (* ----Right alternative law *)
103 (* ----Left alternative law *)
109 (* -------------------------------------------------------------------------- *)
111 (* -------------------------------------------------------------------------- *)