--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ROB006-3".
+include "logic/equality.ma".
+
+(* Inclusion of: ROB006-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ROB006-3 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Robbins Algebra *)
+
+(* Problem : c + d=d => Boolean *)
+
+(* Version : [Win90] (equality) axioms : Augmented. *)
+
+(* 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 : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+
+(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(* : [Wos92] Wos (1992), An Opportunity to Test Your Skills, and th *)
+
+(* Source : [Wos92] *)
+
+(* Names : Theorem 1.1 [Win90] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 13 ( 0 non-Horn; 8 unit; 8 RR) *)
+
+(* Number of atoms : 19 ( 14 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 9 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 19 ( 0 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : Commutativity, associativity, and Huntington's axiom *)
+
+(* axiomatize Boolean algebra. *)
+
+(* : The extra lemmas are suggested by Winker (1990). *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include axioms for Robbins algebra *)
+
+(* Inclusion of: Axioms/ROB001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ROB001-0 : TPTP v3.2.0. 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 : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include axioms for Robbins algebra numbers *)
+
+(* Inclusion of: Axioms/ROB001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ROB001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Robbins Algebra *)
+
+(* Axioms : Robbins algebra numbers axioms *)
+
+(* Version : [Win90] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+
+(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(* Source : [Win90] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 2 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 4 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : Requires ROB001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----The following are extra lemmas *)
+
+(* ----Hypothesis of the theorem *)
+theorem prove_huntingtons_axiom:
+ ∀Univ:Set.∀V:Univ.∀V2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (add c d) d.∀H1:∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add (negate Y) (negate (add X (negate Y))))) X.eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add X (negate Y))) (negate Y).eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).∀H3:∀V2:Univ.∀X:Univ.∀Y:Univ.∀_:positive_integer V2.∀_:eq Univ (negate (add X Y)) (negate Y).eq Univ (negate (add Y (multiply V2 (add X (negate (add X (negate Y))))))) (negate Y).∀H4:∀X:Univ.eq Univ (add X X) X.∀H5:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H6:positive_integer one.∀H7:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H8:∀X:Univ.eq Univ (multiply one X) X.∀H9:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
projects / helm.git / blobdiff