1 set "baseuri" "cic:/matita/TPTP/RNG011-5".
2 include "logic/equality.ma".
3 (* Inclusion of: RNG011-5.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : RNG011-5 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Ring Theory *)
7 (* Problem : In a right alternative ring (((X,X,Y)*X)*(X,X,Y)) = Add Id *)
8 (* Version : [Ove90] (equality) axioms : *)
9 (* Incomplete > Augmented > Incomplete. *)
11 (* Refs : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 *)
12 (* : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal *)
13 (* : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11 *)
14 (* : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in *)
15 (* Source : [Ove90] *)
16 (* Names : CADE-11 Competition Eq-10 [Ove90] *)
17 (* : THEOREM EQ-10 [LM93] *)
18 (* : PROBLEM 10 [Zha93] *)
19 (* Status : Unsatisfiable *)
20 (* Rating : 0.00 v2.0.0 *)
21 (* Syntax : Number of clauses : 22 ( 0 non-Horn; 22 unit; 2 RR) *)
22 (* Number of atoms : 22 ( 22 equality) *)
23 (* Maximal clause size : 1 ( 1 average) *)
24 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
25 (* Number of functors : 8 ( 3 constant; 0-3 arity) *)
26 (* Number of variables : 37 ( 2 singleton) *)
27 (* Maximal term depth : 5 ( 2 average) *)
29 (* -------------------------------------------------------------------------- *)
30 (* ----Commutativity of addition *)
31 (* ----Associativity of addition *)
32 (* ----Additive identity *)
33 (* ----Additive inverse *)
34 (* ----Inverse of identity is identity, stupid *)
35 (* ----Axiom of Overbeek *)
36 (* ----Inverse of (x + y) is additive_inverse(x) + additive_inverse(y), *)
37 (* ----Inverse of additive_inverse of X is X *)
38 (* ----Behavior of 0 and the multiplication operation *)
39 (* ----Axiom of Overbeek *)
40 (* ----x * additive_inverse(y) = additive_inverse (x * y), *)
41 (* ----Distributive property of product over sum *)
42 (* ----Right alternative law *)
45 (* ----Middle associator identity *)
46 theorem prove_equality:
49 \forall add:\forall _:Univ.\forall _:Univ.Univ.
50 \forall additive_identity:Univ.
51 \forall additive_inverse:\forall _:Univ.Univ.
52 \forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
54 \forall commutator:\forall _:Univ.\forall _:Univ.Univ.
55 \forall multiply:\forall _:Univ.\forall _:Univ.Univ.
56 \forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply (associator X X Y) X) (associator X X Y)) additive_identity.
57 \forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
58 \forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
59 \forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
60 \forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
61 \forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
62 \forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
63 \forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
64 \forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
65 \forall H9:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
66 \forall H10:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
67 \forall H11:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
68 \forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (additive_inverse (add X Y)) (add (additive_inverse X) (additive_inverse Y)).
69 \forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X (add (additive_inverse X) Y)) Y.
70 \forall H14:eq Univ (additive_inverse additive_identity) additive_identity.
71 \forall H15:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
72 \forall H16:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
73 \forall H17:\forall X:Univ.eq Univ (add additive_identity X) X.
74 \forall H18:\forall X:Univ.eq Univ (add X additive_identity) X.
75 \forall H19:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
76 \forall H20:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity
79 auto paramodulation timeout=600.
83 (* -------------------------------------------------------------------------- *)