--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL274-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL274-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL274-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.31 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.31 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.33 v2.3.0 *)
+
+(* Syntax : Number of clauses : 11 ( 0 non-Horn; 9 unit; 3 RR) *)
+
+(* Number of atoms : 14 ( 3 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 2 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* Inclusion of: Axioms/LCL004-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL004-1 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Axioms : Propositional logic deduction axioms for AND *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 1 ( 0 non-Horn; 1 unit; 0 RR) *)
+
+(* Number of literals : 1 ( 1 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 0 constant; 1-2 arity) *)
+
+(* Number of variables : 2 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 3 average) *)
+
+(* Comments : Requires LCL004-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* Inclusion of: Axioms/LCL004-2.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL004-2 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Axioms : Propositional logic deduction axioms for EQUIVALENT *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 1 ( 0 non-Horn; 1 unit; 0 RR) *)
+
+(* Number of literals : 1 ( 1 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 0 constant; 2-2 arity) *)
+
+(* Number of variables : 2 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : Requires LCL004-0.ax LCL004-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_this:
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀P:Univ.∀Q:Univ.∀X:Univ.∀Y:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀axiomP:∀_:Univ.Prop.∀equivalent:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (equivalent P Q) (myand (implies P Q) (implies Q P)).∀H1:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H2:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent (or p q) (or q p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)