--- /dev/null
+
+include "logic/equality.ma".
+(* Inclusion of: BOO005-2.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : BOO005-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(* Domain : Boolean Algebra *)
+(* Problem : Addition is bounded (X + 1 = 1) *)
+(* Version : [ANL] (equality) axioms. *)
+(* English : *)
+(* Refs : *)
+(* Source : [ANL] *)
+(* Names : prob3_part1.ver2.in [ANL] *)
+(* Status : Unsatisfiable *)
+(* Rating : 0.00 v2.1.0, 0.14 v2.0.0 *)
+(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 1 RR) *)
+(* Number of atoms : 15 ( 15 equality) *)
+(* Maximal clause size : 1 ( 1 average) *)
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+(* Number of functors : 6 ( 3 constant; 0-2 arity) *)
+(* Number of variables : 24 ( 0 singleton) *)
+(* Maximal term depth : 3 ( 2 average) *)
+(* Comments : *)
+(* Bugfixes : v1.2.1 - Clause prove_a_plus_1_is_a fixed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation *)
+(* Inclusion of: Axioms/BOO003-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* File : BOO003-0 : TPTP v3.1.1. Released v1.0.0. *)
+(* Domain : Boolean Algebra *)
+(* Axioms : Boolean algebra (equality) axioms *)
+(* Version : [ANL] (equality) axioms. *)
+(* English : *)
+(* Refs : *)
+(* Source : [ANL] *)
+(* Names : *)
+(* Status : *)
+(* Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 0 RR) *)
+(* Number of literals : 14 ( 14 equality) *)
+(* Maximal clause size : 1 ( 1 average) *)
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+(* Number of functors : 5 ( 2 constant; 0-2 arity) *)
+(* Number of variables : 24 ( 0 singleton) *)
+(* Maximal term depth : 3 ( 2 average) *)
+(* Comments : *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_plus_1_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)