+
+include "logic/equality.ma".
+(* Inclusion of: ROB030-1.p *)
+(* ------------------------------------------------------------------------------ *)
+(* File : ROB030-1 : TPTP v3.1.1. Released v3.1.0. *)
+(* Domain : Robbins Algebra *)
+(* Problem : Exists absorbed element => Exists absorbed within negation element *)
+(* Version : [Win90] (equality) axioms. *)
+(* Theorem formulation : Denies Huntington's axiom. *)
+(* English : If there are elements c and d such that c+d=d, then the *)
+(* algebra is Boolean. *)
+(* Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(* : [Loe04] Loechner (2004), Email to Geoff Sutcliffe *)
+(* Source : [Loe04] *)
+(* Names : (1) [Loe04] *)
+(* Status : Unsatisfiable *)
+(* Rating : 0.00 v3.1.0 *)
+(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR) *)
+(* Number of atoms : 5 ( 5 equality) *)
+(* Maximal clause size : 1 ( 1 average) *)
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+(* Number of variables : 9 ( 1 singleton) *)
+(* Maximal term depth : 6 ( 2 average) *)
+(* Comments : *)
+(* ------------------------------------------------------------------------------ *)
+(* ----Include axioms for Robbins algebra *)
+(* Inclusion of: Axioms/ROB001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* File : ROB001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(* Domain : Robbins algebra *)
+(* Axioms : Robbins algebra axioms *)
+(* Version : [Win90] (equality) axioms. *)
+(* English : *)
+(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(* Source : [OTTER] *)
+(* Names : Lemma 2.2 [Win90] *)
+(* Status : *)
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
+(* Number of literals : 3 ( 3 equality) *)
+(* Maximal clause size : 1 ( 1 average) *)
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+(* Number of functors : 2 ( 0 constant; 1-2 arity) *)
+(* Number of variables : 7 ( 0 singleton) *)
+(* Maximal term depth : 6 ( 3 average) *)
+(* Comments : *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ------------------------------------------------------------------------------ *)
+theorem prove_absorption_within_negation:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall c:Univ.
+\forall d:Univ.
+\forall negate:\forall _:Univ.Univ.
+\forall H0:eq Univ (add c d) d.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).\exist A:Univ.\exist B:Univ.eq Univ (negate (add A B)) (negate B)
+.
+intros.
+exists[
+2:
+exists[
+2:
+autobatch paramodulation timeout=100;
+try assumption.
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+(* ------------------------------------------------------------------------------ *)