--- /dev/null
+
+include "logic/equality.ma".
+(* Inclusion of: RNG024-7.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : RNG024-7 : TPTP v3.1.1. Released v1.0.0. *)
+(* Domain : Ring Theory (Alternative) *)
+(* Problem : Right alternative *)
+(* Version : [Ste87] (equality) axioms : Augmented. *)
+(* Theorem formulation : In terms of associators *)
+(* English : *)
+(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+(* : [Ste92] Stevens (1992), Unpublished Note *)
+(* Source : [TPTP] *)
+(* Names : *)
+(* Status : Unsatisfiable *)
+(* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0 *)
+(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *)
+(* Number of atoms : 23 ( 23 equality) *)
+(* Maximal clause size : 1 ( 1 average) *)
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+(* Number of functors : 8 ( 3 constant; 0-3 arity) *)
+(* Number of variables : 45 ( 2 singleton) *)
+(* Maximal term depth : 5 ( 3 average) *)
+(* Comments : *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include nonassociative ring axioms *)
+(* Inclusion of: Axioms/RNG003-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* File : RNG003-0 : TPTP v3.1.1. Released v1.0.0. *)
+(* Domain : Ring Theory (Alternative) *)
+(* Axioms : Alternative ring theory (equality) axioms *)
+(* Version : [Ste87] (equality) axioms. *)
+(* English : *)
+(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+(* Source : [Ste87] *)
+(* Names : *)
+(* Status : *)
+(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *)
+(* Number of literals : 15 ( 15 equality) *)
+(* Maximal clause size : 1 ( 1 average) *)
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+(* Number of functors : 6 ( 1 constant; 0-3 arity) *)
+(* Number of variables : 27 ( 2 singleton) *)
+(* Maximal term depth : 5 ( 2 average) *)
+(* Comments : *)
+(* -------------------------------------------------------------------------- *)
+(* ----There exists an additive identity element *)
+(* ----Multiplicative zero *)
+(* ----Existence of left additive additive_inverse *)
+(* ----Inverse of additive_inverse of X is X *)
+(* ----Distributive property of product over sum *)
+(* ----Commutativity for addition *)
+(* ----Associativity for addition *)
+(* ----Right alternative law *)
+(* ----Left alternative law *)
+(* ----Associator *)
+(* ----Commutator *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----The next 7 clause are extra lemmas which Stevens found useful *)
+theorem prove_right_alternative:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall commutator:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+\forall H8:\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)))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H15:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H16:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+\forall H17:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H18:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H19:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H20:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H21:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)
projects / helm.git / blobdiff