+set "baseuri" "cic:/matita/TPTP/LCL227-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL227-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL227-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.81 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.81 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.86 v2.5.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 12 ( 1 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 1 singleton) *)
+
+(* Maximal term depth : 5 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include axioms of propositional logic *)
+
+(* Inclusion of: Axioms/LCL004-0.ax *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* File : LCL004-0 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Axioms : Propositional logic deduction axioms *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 8 ( 0 non-Horn; 6 unit; 2 RR) *)
+
+(* Number of literals : 11 ( 1 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 3 ( 0 constant; 1-2 arity) *)
+
+(* Number of variables : 16 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : This axiomatization follows [WR27], allowing full detachment *)
+
+(* but no chaining (which is a dependant theorem). Compare with *)
+
+(* LCL003-0.ax. *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* input_clause(rule_3,axiom, *)
+
+(* [++theorem(implies(X,Z)), *)
+
+(* --theorem(implies(X,Y)), *)
+
+(* --theorem(implies(Y,Z))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_this:
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q (implies r s)) (implies (or p q) (implies (or p r) (or p s))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)