--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ANA003-1".
+include "logic/equality.ma".
+
+(* Inclusion of: ANA003-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ANA003-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Analysis *)
+
+(* Problem : Lemma 1 for the sum of two continuous functions is continuous *)
+
+(* Version : [MOW76] axioms : Incomplete > Augmented > Complete. *)
+
+(* English : A lemma formed by adding in some resolvants and taking out *)
+
+(* the corresponding clauses. *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [ANL] *)
+
+(* Names : prob1.ver2.in [ANL] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.86 v3.1.0, 0.67 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.83 v2.3.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 21 ( 0 non-Horn; 7 unit; 16 RR) *)
+
+(* Number of atoms : 42 ( 5 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 15 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 35 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 2 average) *)
+
+(* Comments : No natural language descriptions are available. *)
+
+(* : Contributed to the ANL library by Woody Bledsoe. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include limits axioms *)
+
+(* Inclusion of: Axioms/ANA001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ANA001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Analysis (Limits) *)
+
+(* Axioms : Analysis (limits) axioms for continuous functions *)
+
+(* Version : [MOW76] axioms. *)
+
+(* English : *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 14 ( 0 non-Horn; 6 unit; 9 RR) *)
+
+(* Number of literals : 27 ( 5 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 6 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 27 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 1 average) *)
+
+(* Comments : No natural language descriptions are available. *)
+
+(* : "Contributed by W.W. Bledsoe in a private correspondence", *)
+
+(* [MOW76]. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Axiom 1 *)
+
+(* ----Less than transitivity *)
+
+(* ----Axiom 2 *)
+
+(* ----Axiom 3 *)
+
+(* ----Axiom 4 *)
+
+(* ----Axiom 5 *)
+
+(* ----Axiom 6 *)
+
+(* ----Axiom 7 *)
+
+(* ----Axiom 8 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Theorem clauses *)
+theorem c_16:
+ ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp32 X).less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp31 X).less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than X (half Xa).∀_:less_than Y (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than X Y.∀_:less_than Y Z.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than n0 X) (less_than (add (absolute (add (f (fp33 X)) (minus l1))) (absolute (add (g (fp33 X)) (minus l2)))) b)
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ANA004-1".
+include "logic/equality.ma".
+
+(* Inclusion of: ANA004-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ANA004-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Analysis *)
+
+(* Problem : Lemma 2 for the sum of two continuous functions is continuous *)
+
+(* Version : [MOW76] axioms : Incomplete > Augmented > Complete. *)
+
+(* English : A lemma formed by adding in some resolvants and taking out *)
+
+(* the corresponding clauses. *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.86 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 21 ( 0 non-Horn; 7 unit; 16 RR) *)
+
+(* Number of atoms : 42 ( 5 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 15 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 35 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 2 average) *)
+
+(* Comments : No natural language descriptions are available. *)
+
+(* : Contributed to the ANL library by Woody Bledsoe. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include limits axioms *)
+
+(* Inclusion of: Axioms/ANA001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ANA001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Analysis (Limits) *)
+
+(* Axioms : Analysis (limits) axioms for continuous functions *)
+
+(* Version : [MOW76] axioms. *)
+
+(* English : *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 14 ( 0 non-Horn; 6 unit; 9 RR) *)
+
+(* Number of literals : 27 ( 5 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 6 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 27 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 1 average) *)
+
+(* Comments : No natural language descriptions are available. *)
+
+(* : "Contributed by W.W. Bledsoe in a private correspondence", *)
+
+(* [MOW76]. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Axiom 1 *)
+
+(* ----Less than transitivity *)
+
+(* ----Axiom 2 *)
+
+(* ----Axiom 3 *)
+
+(* ----Axiom 4 *)
+
+(* ----Axiom 5 *)
+
+(* ----Axiom 6 *)
+
+(* ----Axiom 7 *)
+
+(* ----Axiom 8 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Clauses from the theorem *)
+theorem c_16:
+ ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp32 X).less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp31 X).less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than X (half Xa).∀_:less_than Y (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than X Y.∀_:less_than Y Z.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than n0 X) (less_than (absolute (add (add (f (fp33 X)) (minus l1)) (add (g (fp33 X)) (minus l2)))) b)
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ANA005-1".
+include "logic/equality.ma".
+
+(* Inclusion of: ANA005-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ANA005-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Analysis *)
+
+(* Problem : The sum of two continuous functions is continuous *)
+
+(* Version : [MOW76] axioms : Incomplete > Augmented > Complete. *)
+
+(* English : *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [ANL] *)
+
+(* Names : BL3 [MOW76] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.86 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 0.60 v2.4.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 21 ( 0 non-Horn; 7 unit; 16 RR) *)
+
+(* Number of atoms : 42 ( 5 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 15 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 35 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 2 average) *)
+
+(* Comments : No natural language descriptions are available. *)
+
+(* : Contributed to the ANL library by Woody Bledsoe. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include limits axioms *)
+
+(* Inclusion of: Axioms/ANA001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ANA001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Analysis (Limits) *)
+
+(* Axioms : Analysis (limits) axioms for continuous functions *)
+
+(* Version : [MOW76] axioms. *)
+
+(* English : *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 14 ( 0 non-Horn; 6 unit; 9 RR) *)
+
+(* Number of literals : 27 ( 5 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 6 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 27 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 1 average) *)
+
+(* Comments : No natural language descriptions are available. *)
+
+(* : "Contributed by W.W. Bledsoe in a private correspondence", *)
+
+(* [MOW76]. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Axiom 1 *)
+
+(* ----Less than transitivity *)
+
+(* ----Axiom 2 *)
+
+(* ----Axiom 3 *)
+
+(* ----Axiom 4 *)
+
+(* ----Axiom 5 *)
+
+(* ----Axiom 6 *)
+
+(* ----Axiom 7 *)
+
+(* ----Axiom 8 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Clauses from the theorem *)
+theorem c_16:
+ ∀Univ:Set.∀X:Univ.∀Xa:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀absolute:∀_:Univ.Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀f:∀_:Univ.Univ.∀fp31:∀_:Univ.Univ.∀fp32:∀_:Univ.Univ.∀fp33:∀_:Univ.Univ.∀g:∀_:Univ.Univ.∀half:∀_:Univ.Univ.∀l1:Univ.∀l2:Univ.∀less_than:∀_:Univ.∀_:Univ.Prop.∀minimum:∀_:Univ.∀_:Univ.Univ.∀minus:∀_:Univ.Univ.∀n0:Univ.∀H0:∀X:Univ.∀_:less_than n0 X.less_than (absolute (add (fp33 X) (minus a))) X.∀H1:less_than n0 b.∀H2:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp32 X).less_than (absolute (add (g Y) (minus l2))) X.∀H3:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp32 X).∀H4:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than (absolute (add Y (minus a))) (fp31 X).less_than (absolute (add (f Y) (minus l1))) X.∀H5:∀X:Univ.∀_:less_than n0 X.less_than n0 (fp31 X).∀H6:∀X:Univ.∀Y:Univ.eq Univ (minus (add X Y)) (add (minus X) (minus Y)).∀H7:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H8:∀Xa:Univ.∀_:less_than n0 Xa.less_than n0 (half Xa).∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than (add (absolute X) (absolute Y)) Xa.less_than (absolute (add X Y)) Xa.∀H12:∀X:Univ.∀Xa:Univ.∀Y:Univ.∀_:less_than X (half Xa).∀_:less_than Y (half Xa).less_than (add X Y) Xa.∀H13:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) Y.∀H14:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than (minimum X Y) X.∀H15:∀X:Univ.∀Y:Univ.∀_:less_than n0 X.∀_:less_than n0 Y.less_than n0 (minimum X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:less_than X Y.∀_:less_than Y Z.less_than X Z.∀H17:∀X:Univ.less_than X X.∀H18:∀X:Univ.eq Univ (add n0 X) X.∀H19:∀X:Univ.eq Univ (add X n0) X.∃X:Univ.And (less_than n0 X) (less_than (absolute (add (add (f (fp33 X)) (g (fp33 X))) (minus (add l1 l2)))) b)
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ANA031-2".
+include "logic/equality.ma".
+
+(* Inclusion of: ANA031-2.p *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* File : ANA031-2 : TPTP v3.2.0. Released v3.2.0. *)
+
+(* Domain : Analysis *)
+
+(* Problem : Problem about Big-O notation *)
+
+(* Version : [Pau06] axioms : Reduced > Especial. *)
+
+(* English : *)
+
+(* Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe *)
+
+(* Source : [Pau06] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0 *)
+
+(* Syntax : Number of clauses : 11 ( 0 non-Horn; 3 unit; 7 RR) *)
+
+(* Number of atoms : 21 ( 2 equality) *)
+
+(* Maximal clause size : 4 ( 2 average) *)
+
+(* Number of predicates : 7 ( 0 propositional; 1-3 arity) *)
+
+(* Number of functors : 9 ( 3 constant; 0-3 arity) *)
+
+(* Number of variables : 32 ( 20 singleton) *)
+
+(* Maximal term depth : 6 ( 2 average) *)
+
+(* Comments : The problems in the [Pau06] collection each have very many axioms, *)
+
+(* of which only a small selection are required for the refutation. *)
+
+(* The mission is to find those few axioms, after which a refutation *)
+
+(* can be quite easily found. This version has only the necessary *)
+
+(* axioms. *)
+
+(* ------------------------------------------------------------------------------ *)
+theorem cls_conjecture_1:
+ ∀Univ:Set.∀V_U:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀t_b:Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:∀_:Univ.Univ.∀H0:∀V_U:Univ.c_lessequals (c_HOL_Oabs (v_b V_U) t_b) (c_times v_c (c_HOL_Oabs (v_g V_U) t_b) t_b) t_b.∃V_U:Univ.c_lessequals (c_times (c_HOL_Oabs (v_b (v_x V_U)) t_b) (c_HOL_Oabs (v_f (v_x V_U)) t_b) t_b) (c_times V_U (c_times (c_HOL_Oabs (v_f (v_x V_U)) t_b) (c_HOL_Oabs (v_g (v_x V_U)) t_b) t_b) t_b) t_b
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* ------------------------------------------------------------------------------ *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ANA032-2".
+include "logic/equality.ma".
+
+(* Inclusion of: ANA032-2.p *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* File : ANA032-2 : TPTP v3.2.0. Released v3.2.0. *)
+
+(* Domain : Analysis *)
+
+(* Problem : Problem about Big-O notation *)
+
+(* Version : [Pau06] axioms : Reduced > Especial. *)
+
+(* English : *)
+
+(* Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe *)
+
+(* Source : [Pau06] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0 *)
+
+(* Syntax : Number of clauses : 11 ( 0 non-Horn; 3 unit; 8 RR) *)
+
+(* Number of atoms : 21 ( 2 equality) *)
+
+(* Maximal clause size : 4 ( 2 average) *)
+
+(* Number of predicates : 7 ( 0 propositional; 1-3 arity) *)
+
+(* Number of functors : 9 ( 4 constant; 0-3 arity) *)
+
+(* Number of variables : 30 ( 20 singleton) *)
+
+(* Maximal term depth : 5 ( 2 average) *)
+
+(* Comments : The problems in the [Pau06] collection each have very many axioms, *)
+
+(* of which only a small selection are required for the refutation. *)
+
+(* The mission is to find those few axioms, after which a refutation *)
+
+(* can be quite easily found. This version has only the necessary *)
+
+(* axioms. *)
+
+(* ------------------------------------------------------------------------------ *)
+theorem cls_conjecture_1:
+ ∀Univ:Set.∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀c_0:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀class_OrderedGroup_Oab__semigroup__mult:∀_:Univ.Prop.∀class_OrderedGroup_Olordered__ab__group__abs:∀_:Univ.Prop.∀class_OrderedGroup_Osemigroup__mult:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__semiring:∀_:Univ.Prop.∀t_b:Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:Univ.∀H0:c_lessequals (c_HOL_Oabs (v_b v_x) t_b) (c_times v_c (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b.∀H1:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀_:class_Ring__and__Field_Opordered__semiring T_a.∀_:c_lessequals V_a V_b T_a.∀_:c_lessequals c_0 V_c T_a.c_lessequals (c_times V_c V_a T_a) (c_times V_c V_b T_a) T_a.∀H2:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_OrderedGroup_Oab__semigroup__mult T_a.eq Univ (c_times V_a V_b T_a) (c_times V_b V_a T_a).∀H3:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀_:class_OrderedGroup_Osemigroup__mult T_a.eq Univ (c_times (c_times V_a V_b T_a) V_c T_a) (c_times V_a (c_times V_b V_c T_a) T_a).∀H4:∀T_a:Univ.∀V_a:Univ.∀_:class_OrderedGroup_Olordered__ab__group__abs T_a.c_lessequals c_0 (c_HOL_Oabs V_a T_a) T_a.c_lessequals (c_times (c_HOL_Oabs (v_b v_x) t_b) (c_HOL_Oabs (v_f v_x) t_b) t_b) (c_times v_c (c_times (c_HOL_Oabs (v_f v_x) t_b) (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b) t_b
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* ------------------------------------------------------------------------------ *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ANA034-2".
+include "logic/equality.ma".
+
+(* Inclusion of: ANA034-2.p *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* File : ANA034-2 : TPTP v3.2.0. Released v3.2.0. *)
+
+(* Domain : Analysis *)
+
+(* Problem : Problem about Big-O notation *)
+
+(* Version : [Pau06] axioms : Reduced > Especial. *)
+
+(* English : *)
+
+(* Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe *)
+
+(* Source : [Pau06] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0 *)
+
+(* Syntax : Number of clauses : 15 ( 0 non-Horn; 6 unit; 13 RR) *)
+
+(* Number of atoms : 31 ( 2 equality) *)
+
+(* Maximal clause size : 6 ( 2 average) *)
+
+(* Number of predicates : 8 ( 0 propositional; 1-3 arity) *)
+
+(* Number of functors : 11 ( 5 constant; 0-3 arity) *)
+
+(* Number of variables : 46 ( 40 singleton) *)
+
+(* Maximal term depth : 5 ( 2 average) *)
+
+(* Comments : The problems in the [Pau06] collection each have very many axioms, *)
+
+(* of which only a small selection are required for the refutation. *)
+
+(* The mission is to find those few axioms, after which a refutation *)
+
+(* can be quite easily found. This version has only the necessary *)
+
+(* axioms. *)
+
+(* ------------------------------------------------------------------------------ *)
+theorem cls_conjecture_5:
+ ∀Univ:Set.∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀V_x:Univ.∀V_y:Univ.∀c_0:Univ.∀c_HOL_Oabs:∀_:Univ.∀_:Univ.Univ.∀c_less:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_times:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀class_OrderedGroup_Olordered__ab__group__abs:∀_:Univ.Prop.∀class_Orderings_Oorder:∀_:Univ.Prop.∀class_Ring__and__Field_Oordered__idom:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__cancel__semiring:∀_:Univ.Prop.∀class_Ring__and__Field_Opordered__semiring:∀_:Univ.Prop.∀t_b:Univ.∀v_a:∀_:Univ.Univ.∀v_b:∀_:Univ.Univ.∀v_c:Univ.∀v_ca:Univ.∀v_f:∀_:Univ.Univ.∀v_g:∀_:Univ.Univ.∀v_x:Univ.∀H0:eq Univ (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) (c_times (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b).∀H1:c_lessequals (c_HOL_Oabs (v_b v_x) t_b) (c_times v_ca (c_HOL_Oabs (v_g v_x) t_b) t_b) t_b.∀H2:c_lessequals (c_HOL_Oabs (v_a v_x) t_b) (c_times v_c (c_HOL_Oabs (v_f v_x) t_b) t_b) t_b.∀H3:c_less c_0 v_c t_b.∀H4:∀T_a:Univ.∀V_a:Univ.∀_:class_OrderedGroup_Olordered__ab__group__abs T_a.c_lessequals c_0 (c_HOL_Oabs V_a T_a) T_a.∀H5:∀T_a:Univ.∀V_x:Univ.∀V_y:Univ.∀_:class_Orderings_Oorder T_a.∀_:c_less V_x V_y T_a.c_lessequals V_x V_y T_a.∀H6:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_Ring__and__Field_Opordered__cancel__semiring T_a.∀_:c_lessequals c_0 V_b T_a.∀_:c_lessequals c_0 V_a T_a.c_lessequals c_0 (c_times V_a V_b T_a) T_a.∀H7:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀V_c:Univ.∀V_d:Univ.∀_:class_Ring__and__Field_Opordered__semiring T_a.∀_:c_lessequals V_c V_d T_a.∀_:c_lessequals V_a V_b T_a.∀_:c_lessequals c_0 V_c T_a.∀_:c_lessequals c_0 V_b T_a.c_lessequals (c_times V_a V_c T_a) (c_times V_b V_d T_a) T_a.∀H8:∀T_a:Univ.∀V_a:Univ.∀V_b:Univ.∀_:class_Ring__and__Field_Oordered__idom T_a.eq Univ (c_HOL_Oabs (c_times V_a V_b T_a) T_a) (c_times (c_HOL_Oabs V_a T_a) (c_HOL_Oabs V_b T_a) T_a).c_lessequals (c_HOL_Oabs (c_times (v_a v_x) (v_b v_x) t_b) t_b) (c_times (c_times v_c v_ca t_b) (c_HOL_Oabs (c_times (v_f v_x) (v_g v_x) t_b) t_b) t_b) t_b
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* ------------------------------------------------------------------------------ *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/BOO012-3".
+include "logic/equality.ma".
+
+(* Inclusion of: BOO012-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : BOO012-3 : TPTP v3.2.0. Bugfixed v1.2.1. *)
+
+(* Domain : Boolean Algebra *)
+
+(* Problem : Inverse is an involution *)
+
+(* Version : [MOW76] axioms : Augmented. *)
+
+(* English : *)
+
+(* Refs : [Whi61] Whitesitt (1961), Boolean Algebra and Its Applications *)
+
+(* : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [MOW76] *)
+
+(* Names : B8 [MOW76] *)
+
+(* : prob8.ver1 [ANL] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.22 v2.7.0, 0.00 v2.4.0, 0.17 v2.3.0, 0.33 v2.2.1, 0.62 v2.2.0, 0.50 v2.1.0, 0.33 v2.0.0 *)
+
+(* Syntax : Number of clauses : 35 ( 0 non-Horn; 17 unit; 19 RR) *)
+
+(* Number of atoms : 87 ( 3 equality) *)
+
+(* Maximal clause size : 5 ( 2 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 2-3 arity) *)
+
+(* Number of functors : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 120 ( 6 singleton) *)
+
+(* Maximal term depth : 3 ( 1 average) *)
+
+(* Comments : *)
+
+(* Bugfixes : v1.2.1 - Clause x_plus_multiplicative_identity fixed. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include boolean algebra axioms *)
+
+(* Inclusion of: Axioms/BOO002-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : BOO002-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Boolean Algebra *)
+
+(* Axioms : Boolean algebra axioms *)
+
+(* Version : [MOW76] axioms. *)
+
+(* English : *)
+
+(* Refs : [Whi61] Whitesitt (1961), Boolean Algebra and Its Applications *)
+
+(* : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [MOW76] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 22 ( 0 non-Horn; 10 unit; 12 RR) *)
+
+(* Number of literals : 60 ( 2 equality) *)
+
+(* Maximal clause size : 5 ( 3 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 2-3 arity) *)
+
+(* Number of functors : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 82 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -----Well definedness of the operations *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse_is_an_involution:
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀additive_identity:Univ.∀inverse:∀_:Univ.Univ.∀multiplicative_identity:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀product:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀sum:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀x:Univ.∀H0:∀X:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀_:product X Y X_times_Y.∀_:product Y Z Y_times_Z.∀_:product X_times_Y Z X_times_Y_times_Z.product X Y_times_Z X_times_Y_times_Z.∀H1:∀X:Univ.∀X_times_Y:Univ.∀X_times_Y_times_Z:Univ.∀Y:Univ.∀Y_times_Z:Univ.∀Z:Univ.∀_:product X Y X_times_Y.∀_:product Y Z Y_times_Z.∀_:product X Y_times_Z X_times_Y_times_Z.product X_times_Y Z X_times_Y_times_Z.∀H2:∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Z:Univ.∀_:sum X Y X_plus_Y.∀_:sum Y Z Y_plus_Z.∀_:sum X_plus_Y Z X_plus_Y_plus_Z.sum X Y_plus_Z X_plus_Y_plus_Z.∀H3:∀X:Univ.∀X_plus_Y:Univ.∀X_plus_Y_plus_Z:Univ.∀Y:Univ.∀Y_plus_Z:Univ.∀Z:Univ.∀_:sum X Y X_plus_Y.∀_:sum Y Z Y_plus_Z.∀_:sum X Y_plus_Z X_plus_Y_plus_Z.sum X_plus_Y Z X_plus_Y_plus_Z.∀H4:∀X:Univ.∀Y:Univ.product X (add X Y) X.∀H5:∀X:Univ.∀Y:Univ.sum X (multiply X Y) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y Z.product X Z X.∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y Z.sum X Z X.∀H8:∀X:Univ.product X additive_identity additive_identity.∀H9:∀X:Univ.sum X multiplicative_identity multiplicative_identity.∀H10:∀X:Univ.product X X X.∀H11:∀X:Univ.sum X X X.∀H12:∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀_:product X Y U.∀_:product X Y V.eq Univ U V.∀H13:∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀_:sum X Y U.∀_:sum X Y V.eq Univ U V.∀H14:∀X:Univ.product X (inverse X) additive_identity.∀H15:∀X:Univ.product (inverse X) X additive_identity.∀H16:∀X:Univ.sum X (inverse X) multiplicative_identity.∀H17:∀X:Univ.sum (inverse X) X multiplicative_identity.∀H18:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum Y X V1.∀_:sum Z X V2.∀_:product Y Z V3.∀_:product V1 V2 V4.sum V3 X V4.∀H19:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum Y X V1.∀_:sum Z X V2.∀_:product Y Z V3.∀_:sum V3 X V4.product V1 V2 V4.∀H20:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y V1.∀_:sum X Z V2.∀_:product Y Z V3.∀_:product V1 V2 V4.sum X V3 V4.∀H21:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y V1.∀_:sum X Z V2.∀_:product Y Z V3.∀_:sum X V3 V4.product V1 V2 V4.∀H22:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product Y X V1.∀_:product Z X V2.∀_:sum Y Z V3.∀_:sum V1 V2 V4.product V3 X V4.∀H23:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product Y X V1.∀_:product Z X V2.∀_:sum Y Z V3.∀_:product V3 X V4.sum V1 V2 V4.∀H24:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y V1.∀_:product X Z V2.∀_:sum Y Z V3.∀_:sum V1 V2 V4.product X V3 V4.∀H25:∀V1:Univ.∀V2:Univ.∀V3:Univ.∀V4:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y V1.∀_:product X Z V2.∀_:sum Y Z V3.∀_:product X V3 V4.sum V1 V2 V4.∀H26:∀X:Univ.product X multiplicative_identity X.∀H27:∀X:Univ.product multiplicative_identity X X.∀H28:∀X:Univ.sum X additive_identity X.∀H29:∀X:Univ.sum additive_identity X X.∀H30:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:product X Y Z.product Y X Z.∀H31:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:sum X Y Z.sum Y X Z.∀H32:∀X:Univ.∀Y:Univ.product X Y (multiply X Y).∀H33:∀X:Univ.∀Y:Univ.sum X Y (add X Y).eq Univ (inverse (inverse x)) x
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/CAT018-4".
+include "logic/equality.ma".
+
+(* Inclusion of: CAT018-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : CAT018-4 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Category Theory *)
+
+(* Problem : If xy and yz exist, then so does x(yz) *)
+
+(* Version : [Sco79] axioms : Reduced > Complete. *)
+
+(* English : *)
+
+(* Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.17 v2.2.1, 0.44 v2.2.0, 0.57 v2.1.0, 0.80 v2.0.0 *)
+
+(* Syntax : Number of clauses : 14 ( 0 non-Horn; 6 unit; 11 RR) *)
+
+(* Number of atoms : 24 ( 7 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 19 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : The dependent axioms have been removed. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Scott's axioms for category theory *)
+
+(* Inclusion of: Axioms/CAT004-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : CAT004-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Category Theory *)
+
+(* Axioms : Category theory axioms *)
+
+(* Version : [Sco79] axioms : Reduced > Complete. *)
+
+(* English : *)
+
+(* Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 11 ( 0 non-Horn; 3 unit; 8 RR) *)
+
+(* Number of literals : 21 ( 7 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 3 ( 0 constant; 1-2 arity) *)
+
+(* Number of variables : 19 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : The dependent axioms have been removed. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Non-standard in that E(x) stands for "x exists", i.e. a system -for *)
+
+(* ----intuitionistic logic. Viewed classically, this can be -taken *)
+
+(* ----as a partitioning of models M into elements of E and -other elements *)
+
+(* ----of M; then Scott's quantifiers are relativized -to range only over *)
+
+(* ----E, whereas free variables range over all of -M. *)
+
+(* ----Quaife has this written: (this looks really weird, but results -from *)
+
+(* ----having = here stand for equivalence, and it is a strange -fact from *)
+
+(* ----Scott's conception that all non-existent things are -equivalent. all *)
+
+(* ----x all y ((x = y) | E(x) | E(y))). *)
+
+(* -----Restricted equality axioms *)
+
+(* -----Category theory axioms *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_bc_exists:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀codomain:∀_:Univ.Univ.∀compose:∀_:Univ.∀_:Univ.Univ.∀domain:∀_:Univ.Univ.∀equivalent:∀_:Univ.∀_:Univ.Prop.∀there_exists:∀_:Univ.Prop.∀H0:there_exists (compose b c).∀H1:there_exists (compose a b).∀H2:∀X:Univ.eq Univ (compose (codomain X) X) X.∀H3:∀X:Univ.eq Univ (compose X (domain X)) X.∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (compose X (compose Y Z)) (compose (compose X Y) Z).∀H5:∀X:Univ.∀Y:Univ.∀_:there_exists (domain X).∀_:eq Univ (domain X) (codomain Y).there_exists (compose X Y).∀H6:∀X:Univ.∀Y:Univ.∀_:there_exists (compose X Y).eq Univ (domain X) (codomain Y).∀H7:∀X:Univ.∀Y:Univ.∀_:there_exists (compose X Y).there_exists (domain X).∀H8:∀X:Univ.∀_:there_exists (codomain X).there_exists X.∀H9:∀X:Univ.∀_:there_exists (domain X).there_exists X.∀H10:∀X:Univ.∀Y:Univ.∀_:there_exists X.∀_:eq Univ X Y.equivalent X Y.∀H11:∀X:Univ.∀Y:Univ.∀_:equivalent X Y.eq Univ X Y.∀H12:∀X:Univ.∀Y:Univ.∀_:equivalent X Y.there_exists X.there_exists (compose a (compose b c))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-10".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-10.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-10 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.50 v2.2.1, 0.88 v2.2.0, 0.83 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 5 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b (apply b w)) (apply (apply b b) b)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-2".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 5 ( 3 average) *)
+
+(* Comments : This the J sage of [McCune & Wos, 1987], found by Statman. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-3".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-3 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 0.80 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 3 average) *)
+
+(* Comments : This the K sage of [McCune & Wos, 1987]. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b (apply (apply b w) b)) b))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-4".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-4 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 0.80 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 3 average) *)
+
+(* Comments : This the L sage of [McCune & Wos, 1987]. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply (apply b w) b))) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-5".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-5.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-5 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 0.80 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 3 average) *)
+
+(* Comments : This the M sage of [McCune & Wos, 1987]. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) w)) (apply (apply b b) b))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-6".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-6.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-6 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 0.80 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : This the N sage of [McCune & Wos, 1987]. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w w)) w)) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-7".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-7.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-7 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [Wos93] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.44 v2.7.0, 0.33 v2.6.0, 0.14 v2.5.0, 0.40 v2.4.0, 0.50 v2.2.1, 0.75 v2.2.0, 0.67 v2.1.0, 0.67 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-8".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-8.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-8 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [Wos93] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.29 v2.5.0, 0.40 v2.4.0, 0.50 v2.2.1, 0.88 v2.2.0, 0.83 v2.1.0, 0.67 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply b w))) (apply (apply b b) b))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL003-9".
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-9.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-9 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [Wos93] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.44 v2.7.0, 0.33 v2.6.0, 0.14 v2.5.0, 0.40 v2.4.0, 0.50 v2.2.1, 0.75 v2.2.0, 0.67 v2.1.0, 0.67 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 7 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL006-2".
+include "logic/equality.ma".
+
+(* Inclusion of: COL006-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL006-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for S and K *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators S and K alone, where *)
+
+(* ((Sx)y)z = (xz)(yz), (Kx)y = x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.1.0, 0.67 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.67 v2.2.1, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 1 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply k (apply (apply s s) (apply s k)))) (apply (apply s (apply k s)) k)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL006-3".
+include "logic/equality.ma".
+
+(* Inclusion of: COL006-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL006-3 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for S and K *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators S and K alone, where *)
+
+(* ((Sx)y)z = (xz)(yz), (Kx)y = x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.89 v2.7.0, 0.67 v2.6.0, 0.71 v2.5.0, 0.80 v2.4.0, 0.83 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 1 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply (apply s (apply k s)) k)) (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL006-4".
+include "logic/equality.ma".
+
+(* Inclusion of: COL006-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL006-4 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for S and K *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators S and K alone, where *)
+
+(* ((Sx)y)z = (xz)(yz), (Kx)y = x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.89 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.83 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 1 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀k:Univ.∀s:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).fixed_point (apply (apply s (apply k (apply (apply (apply s s) (apply (apply s k) k)) (apply (apply s s) (apply s k))))) (apply (apply s (apply k s)) k))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL042-2".
+include "logic/equality.ma".
+
+(* Inclusion of: COL042-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL042-2 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W1 *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W1, where ((Bx)y)z *)
+
+(* = x(yz), (W1x)y = (yx)x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.33 v2.3.0, 0.50 v2.2.1, 0.62 v2.2.0, 0.67 v2.1.0, 0.67 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL042-3".
+include "logic/equality.ma".
+
+(* Inclusion of: COL042-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL042-3 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W1 *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W1, where ((Bx)y)z *)
+
+(* = x(yz), (W1x)y = (yx)x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.33 v2.3.0, 0.50 v2.2.1, 0.75 v2.2.0, 0.83 v2.1.0, 0.67 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) (apply (apply b b) b))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL042-4".
+include "logic/equality.ma".
+
+(* Inclusion of: COL042-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL042-4 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W1 *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W1, where ((Bx)y)z *)
+
+(* = x(yz), (W1x)y = (yx)x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.33 v2.3.0, 0.50 v2.2.1, 0.75 v2.2.0, 0.83 v2.1.0, 0.67 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 7 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) b))) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL042-5".
+include "logic/equality.ma".
+
+(* Inclusion of: COL042-5.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL042-5 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W1 *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W1, where ((Bx)y)z *)
+
+(* = x(yz), (W1x)y = (yx)x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.33 v2.3.0, 0.50 v2.2.1, 0.75 v2.2.0, 0.83 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 5 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀w1:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) (apply (apply b b) b)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL043-2".
+include "logic/equality.ma".
+
+(* Inclusion of: COL043-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL043-2 : TPTP v3.2.0. Bugfixed v2.3.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and H *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and H, where ((Bx)y)z *)
+
+(* = x(yz), ((Hx)y)z = ((xy)z)y. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : - [Wos93] *)
+
+(* 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, 0.40 v2.4.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 0 singleton) *)
+
+(* Maximal term depth : 11 ( 4 average) *)
+
+(* Comments : *)
+
+(* Bugfixes : v2.3.0 - Clause prove_strong_fixed_point fixed. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀h:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL044-2".
+include "logic/equality.ma".
+
+(* Inclusion of: COL044-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL044-2 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and N *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and N, where ((Bx)y)z *)
+
+(* = x(yz), ((Nx)y)z = ((xz)y)z. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* 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, 0.40 v2.4.0, 0.67 v2.3.0, 0.83 v2.2.1, 0.75 v2.2.0, 0.83 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 0 singleton) *)
+
+(* Maximal term depth : 12 ( 4 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply (apply b b) n)) n))) n)) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL044-3".
+include "logic/equality.ma".
+
+(* Inclusion of: COL044-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL044-3 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and N *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and N, where ((Bx)y)z *)
+
+(* = x(yz), ((Nx)y)z = ((xz)y)z. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* 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, 0.40 v2.4.0, 0.67 v2.3.0, 0.83 v2.2.1, 0.75 v2.2.0, 0.83 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 0 singleton) *)
+
+(* Maximal term depth : 12 ( 4 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply n (apply b b))) n))) n)) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL044-4".
+include "logic/equality.ma".
+
+(* Inclusion of: COL044-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL044-4 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and N *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and N, where ((Bx)y)z *)
+
+(* = x(yz), ((Nx)y)z = ((xz)y)z. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.83 v2.2.1, 0.88 v2.2.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 0 singleton) *)
+
+(* Maximal term depth : 12 ( 4 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply (apply b b) n))))) n)) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/COL044-5".
+include "logic/equality.ma".
+
+(* Inclusion of: COL044-5.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL044-5 : TPTP v3.2.0. Released v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and N *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and N, where ((Bx)y)z *)
+
+(* = x(yz), ((Nx)y)z = ((xz)y)z. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.67 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.83 v2.2.1, 0.88 v2.2.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 0 singleton) *)
+
+(* Maximal term depth : 12 ( 4 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_strong_fixed_point:
+ ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply n (apply b b)))))) n)) b)) b)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/HEN011-3".
+include "logic/equality.ma".
+
+(* Inclusion of: HEN011-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HEN011-3 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Henkin Models *)
+
+(* Problem : This operation is commutative *)
+
+(* Version : [MOW76] axioms. *)
+
+(* English : Define & on the set of Z', where Z' = identity/Z, *)
+
+(* by X' & Y'=X'/(identity/Y'). The operation is commutative. *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [ANL] *)
+
+(* Names : HP11 [ANL] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.50 v2.3.0, 0.33 v2.2.1, 0.67 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 13 ( 0 non-Horn; 10 unit; 9 RR) *)
+
+(* Number of atoms : 17 ( 9 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 9 ( 8 constant; 0-2 arity) *)
+
+(* Number of variables : 13 ( 3 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Henkin model axioms for equality formulation *)
+
+(* Inclusion of: Axioms/HEN002-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HEN002-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Henkin Models *)
+
+(* Axioms : Henkin model axioms *)
+
+(* Version : [MOW76] axioms. *)
+
+(* English : *)
+
+(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 7 ( 0 non-Horn; 4 unit; 3 RR) *)
+
+(* Number of literals : 11 ( 3 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 13 ( 3 singleton) *)
+
+(* Maximal term depth : 3 ( 1 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----A0: Definition of less_equal *)
+
+(* ----A1: x/y <= x *)
+
+(* ----A2: (x/z) / (y/z) <= (x/y) / z *)
+
+(* ----A3: 0<=x *)
+
+(* ----A4: x <= y and y <= x implies that x = y *)
+
+(* ----A5: x <= identity (Thus an implicative model with unit ) *)
+
+(* ----Implicit in equality formulation: '/' is well defined *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_commutativity:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀divide:∀_:Univ.∀_:Univ.Univ.∀e:Univ.∀g:Univ.∀identity:Univ.∀less_equal:∀_:Univ.∀_:Univ.Prop.∀zero:Univ.∀H0:eq Univ (divide identity d) g.∀H1:eq Univ (divide identity c) e.∀H2:eq Univ (divide identity b) d.∀H3:eq Univ (divide identity a) c.∀H4:eq Univ (divide (divide identity a) (divide identity (divide identity b))) (divide (divide identity b) (divide identity (divide identity a))).∀H5:∀X:Univ.less_equal X identity.∀H6:∀X:Univ.∀Y:Univ.∀_:less_equal X Y.∀_:less_equal Y X.eq Univ X Y.∀H7:∀X:Univ.less_equal zero X.∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.less_equal (divide (divide X Z) (divide Y Z)) (divide (divide X Y) Z).∀H9:∀X:Univ.∀Y:Univ.less_equal (divide X Y) X.∀H10:∀X:Univ.∀Y:Univ.∀_:eq Univ (divide X Y) zero.less_equal X Y.∀H11:∀X:Univ.∀Y:Univ.∀_:less_equal X Y.eq Univ (divide X Y) zero.eq Univ (divide c g) (divide d e)
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/HWC002-1".
+include "logic/equality.ma".
+
+(* Inclusion of: HWC002-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC002-1 : TPTP v3.2.0. Released v1.1.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Problem : Interchange inputs to outputs *)
+
+(* Version : [ANL] axioms. *)
+
+(* English : Design a circuit with inputs x and y whose outputs are y and *)
+
+(* x, and contains no crossings of wires *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : interchange.ver1.clauses [ANL] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.56 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.00 v2.4.0, 0.17 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 38 ( 0 non-Horn; 23 unit; 30 RR) *)
+
+(* Number of atoms : 53 ( 20 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-3 arity) *)
+
+(* Number of functors : 11 ( 3 constant; 0-4 arity) *)
+
+(* Number of variables : 99 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : We represent the circuit built up so far by circuit(top(X), *)
+
+(* middle(Y),bottom(Z)), where top and bottom are lists of *)
+
+(* outputs, counting outward from the middle. *)
+
+(* : The original uses the equality clauses as demodulators. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definitions of AND, OR and NOT *)
+
+(* Inclusion of: Axioms/HWC001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Axioms : Definitions of AND, OR and NOT *)
+
+(* Version : [WO+92] axioms. *)
+
+(* Axiom formulation : Ground axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 10 RR) *)
+
+(* Number of literals : 10 ( 10 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 : 0 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Problem axioms Split the middle, keeping the middle *)
+
+(* ----Split the middle, omitting the middle *)
+
+(* ----Join across the middle if it is empty, not keeping the sides *)
+
+(* ----Join across the middle, keeping the sides *)
+
+(* ----Join to middle, keeping the sides *)
+
+(* ----Join the two wires nearest the middle *)
+
+(* ----Put inverter on the middle wire *)
+
+(* ----Put inverter on the adjacent wires *)
+
+(* ----Subsumer to get rid of circuits which are the same on top and bottom *)
+
+(* ----Cannot construct the answer *)
+theorem prove_output_configuration:
+ ∀Univ:Set.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀Y:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Z:Univ.∀Z1:Univ.∀Z2:Univ.∀Z3:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀bottom:∀_:Univ.Univ.∀circuit:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀connect:∀_:Univ.∀_:Univ.Univ.∀middle:∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀nil:Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀table:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀top:∀_:Univ.Univ.∀H0:circuit (top (connect (table n0 n0 n1 n1) nil)) nil (bottom (connect (table n0 n1 n0 n1) nil)).∀H1:∀X:Univ.∀Y:Univ.eq Univ (connect X (connect X Y)) (connect X Y).∀H2:∀X:Univ.eq Univ (connect nil X) X.∀H3:eq Univ (table n1 n1 n1 n1) nil.∀H4:eq Univ (table n0 n0 n0 n0) nil.∀H5:eq Univ (not nil) nil.∀H6:∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.eq Univ (not (table X1 X2 X3 X4)) (table (not X1) (not X2) (not X3) (not X4)).∀H7:∀X:Univ.eq Univ (or nil X) X.∀H8:∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.eq Univ (or (table X1 X2 X3 X4) (table Y1 Y2 Y3 Y4)) (table (or X1 Y1) (or X2 Y2) (or X3 Y3) (or X4 Y4)).∀H9:∀X:Univ.eq Univ (myand nil X) X.∀H10:∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.eq Univ (myand (table X1 X2 X3 X4) (table Y1 Y2 Y3 Y4)) (table (myand X1 Y1) (myand X2 Y2) (myand X3 Y3) (myand X4 Y4)).∀H11:∀X:Univ.∀Y:Univ.circuit (top X) Y (bottom X).∀H12:∀X1:Univ.∀X2:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) nil (bottom (connect Z1 Z2)).circuit (top (connect (not X1) X2)) nil (bottom (connect (not Z1) Z2)).∀H13:∀X1:Univ.∀X2:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) (middle Y) (bottom (connect Z1 Z2)).circuit (top (connect (not X1) X2)) (middle Y) (bottom (connect (not Z1) Z2)).∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:circuit (top X) (middle Y) (bottom Z).circuit (top X) (middle (not Y)) (bottom Z).∀H15:∀X1:Univ.∀X2:Univ.∀X3:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀Z3:Univ.∀_:circuit (top (connect X1 (connect X2 X3))) (middle Y) (bottom (connect Z1 (connect Z2 Z3))).circuit (top (connect (or X1 X2) X3)) (middle Y) (bottom (connect (or Z1 Z2) Z3)).∀H16:∀X1:Univ.∀X2:Univ.∀X3:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀Z3:Univ.∀_:circuit (top (connect X1 (connect X2 X3))) (middle Y) (bottom (connect Z1 (connect Z2 Z3))).circuit (top (connect (myand X1 X2) X3)) (middle Y) (bottom (connect (myand Z1 Z2) Z3)).∀H17:∀X1:Univ.∀X2:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) (middle Y) (bottom (connect Z1 Z2)).circuit (top (connect (or Y X1) (connect X1 X2))) nil (bottom (connect (or Y Z1) (connect Z1 Z2))).∀H18:∀X1:Univ.∀X2:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) (middle Y) (bottom (connect Z1 Z2)).circuit (top (connect (myand Y X1) (connect X1 X2))) nil (bottom (connect (myand Y Z1) (connect Z1 Z2))).∀H19:∀X1:Univ.∀X2:Univ.∀Y1:Univ.∀Y2:Univ.∀_:circuit (top (connect X1 X2)) nil (bottom (connect Y1 Y2)).circuit (top (connect X1 X2)) (middle (or X1 Y1)) (bottom (connect Y1 Y2)).∀H20:∀X1:Univ.∀X2:Univ.∀Y1:Univ.∀Y2:Univ.∀_:circuit (top (connect X1 X2)) nil (bottom (connect Y1 Y2)).circuit (top (connect X1 X2)) (middle (myand X1 Y1)) (bottom (connect Y1 Y2)).∀H21:∀X1:Univ.∀X2:Univ.∀Y1:Univ.∀Y2:Univ.∀_:circuit (top (connect X1 X2)) nil (bottom (connect Y1 Y2)).circuit (top X2) (middle (or X1 Y1)) (bottom Y2).∀H22:∀X1:Univ.∀X2:Univ.∀Y1:Univ.∀Y2:Univ.∀_:circuit (top (connect X1 X2)) nil (bottom (connect Y1 Y2)).circuit (top X2) (middle (myand X1 Y1)) (bottom Y2).∀H23:∀X1:Univ.∀X2:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) (middle Y) (bottom (connect Z1 Z2)).circuit (top (connect (or Y X1) X2)) nil (bottom (connect (or Y Z1) Z2)).∀H24:∀X1:Univ.∀X2:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) (middle Y) (bottom (connect Z1 Z2)).circuit (top (connect (myand Y X1) X2)) nil (bottom (connect (myand Y Z1) Z2)).∀H25:∀X1:Univ.∀X2:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) (middle Y) (bottom (connect Z1 Z2)).circuit (top (connect (or Y X1) X2)) (middle Y) (bottom (connect (or Y Z1) Z2)).∀H26:∀X1:Univ.∀X2:Univ.∀Y:Univ.∀Z1:Univ.∀Z2:Univ.∀_:circuit (top (connect X1 X2)) (middle Y) (bottom (connect Z1 Z2)).circuit (top (connect (myand Y X1) X2)) (middle Y) (bottom (connect (myand Y Z1) Z2)).∀H27:eq Univ (not n1) n0.∀H28:eq Univ (not n0) n1.∀H29:eq Univ (or n1 n1) n1.∀H30:eq Univ (or n1 n0) n1.∀H31:eq Univ (or n0 n1) n1.∀H32:eq Univ (or n0 n0) n0.∀H33:eq Univ (myand n1 n1) n1.∀H34:eq Univ (myand n1 n0) n0.∀H35:eq Univ (myand n0 n1) n0.∀H36:eq Univ (myand n0 n0) n0.circuit (top (connect (table n0 n1 n0 n1) nil)) nil (bottom (connect (table n0 n0 n1 n1) nil))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/HWC003-1".
+include "logic/equality.ma".
+
+(* Inclusion of: HWC003-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC003-1 : TPTP v3.2.0. Released v1.1.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Problem : Invert 3 inputs with 2 not gates *)
+
+(* Version : [WO+92] axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : two.inverter.ver1.in [ANL] *)
+
+(* : - [WO+92] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.78 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.33 v2.3.0, 0.50 v2.2.1, 0.78 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 24 ( 0 non-Horn; 19 unit; 7 RR) *)
+
+(* Number of atoms : 32 ( 16 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 2-10 arity) *)
+
+(* Number of functors : 25 ( 16 constant; 0-8 arity) *)
+
+(* Number of variables : 86 ( 9 singleton) *)
+
+(* Maximal term depth : 14 ( 1 average) *)
+
+(* Comments : The original uses the equality axioms as demodulators. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definitions of AND, OR and NOT *)
+
+(* Inclusion of: Axioms/HWC002-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC002-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Axioms : Definitions of AND, OR and NOT *)
+
+(* Version : [WO+92] axioms. *)
+
+(* Axiom formulation : Non-ground axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 6 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 : 4 ( 2 singleton) *)
+
+(* Maximal term depth : 2 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Problem axioms *)
+theorem prove_cannot_construct_this:
+ ∀Univ:Set.∀V:Univ.∀X:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X1:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xname:Univ.∀Xrevlist:Univ.∀Y:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀Z:Univ.∀add_inverter:∀_:Univ.∀_:Univ.Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀end:Univ.∀inverter_table:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀list:∀_:Univ.∀_:Univ.Univ.∀list_reversion:∀_:Univ.∀_:Univ.Univ.∀make_reverse_list:∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀not_reversion:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀possible_reversion:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀r00m:Univ.∀r01m:Univ.∀r0m0:Univ.∀r0m1:Univ.∀r10m:Univ.∀r11m:Univ.∀r1m0:Univ.∀r1m1:Univ.∀rm00:Univ.∀rm01:Univ.∀rm10:Univ.∀rm11:Univ.∀test:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀H0:∀X:Univ.output n0 n1 n0 n1 n0 n1 n0 n1 X.∀H1:∀X:Univ.output n0 n0 n1 n1 n0 n0 n1 n1 X.∀H2:∀X:Univ.output n0 n0 n0 n0 n1 n1 n1 n1 X.∀H3:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xrevlist:Univ.∀_:test X1 X2 X3 X4 X5 X6 X7 X8 V Xrevlist.output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H4:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.test (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8) (add_inverter V (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8))) (make_reverse_list (list (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8)) V)).∀H5:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.output (or X1 Y1) (or X2 Y2) (or X3 Y3) (or X4 Y4) (or X5 Y5) (or X6 Y6) (or X7 Y7) (or X8 Y8) V.∀H6:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.output (myand X1 Y1) (myand X2 Y2) (myand X3 Y3) (myand X4 Y4) (myand X5 Y5) (myand X6 Y6) (myand X7 Y7) (myand X8 Y8) V.∀H7:∀X:Univ.∀Y:Univ.eq Univ (list_reversion X (list_reversion X Y)) (list_reversion X Y).∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (list_reversion X (list_reversion Y Z)) (list_reversion Y (list_reversion X Z)).∀H9:∀X:Univ.eq Univ (list_reversion not_reversion X) X.∀H10:∀X:Univ.∀Xname:Univ.eq Univ (possible_reversion Xname X X) not_reversion.∀H11:∀Xname:Univ.eq Univ (possible_reversion Xname n0 n1) not_reversion.∀H12:∀Xname:Univ.eq Univ (possible_reversion Xname n1 n0) Xname.∀H13:∀V:Univ.eq Univ (make_reverse_list V) end.∀H14:∀V:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.eq Univ (make_reverse_list (list (inverter_table X000 X001 X010 X011 X100 X101 X110 X111) V)) (list_reversion (possible_reversion r00m X000 X001) (list_reversion (possible_reversion r01m X010 X011) (list_reversion (possible_reversion r10m X100 X101) (list_reversion (possible_reversion r11m X110 X111) (list_reversion (possible_reversion r0m0 X000 X010) (list_reversion (possible_reversion r0m1 X001 X011) (list_reversion (possible_reversion r1m0 X100 X110) (list_reversion (possible_reversion r1m1 X101 X111) (list_reversion (possible_reversion rm00 X000 X100) (list_reversion (possible_reversion rm01 X001 X101) (list_reversion (possible_reversion rm10 X010 X110) (list_reversion (possible_reversion rm11 X011 X111) (make_reverse_list V))))))))))))).∀H15:∀X:Univ.∀Y:Univ.eq Univ (add_inverter X Y) (list Y X).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add_inverter (list X Y) Z) (list X (add_inverter Y Z)).∀H17:eq Univ (not n1) n0.∀H18:eq Univ (not n0) n1.∀H19:∀X:Univ.eq Univ (or X n1) n1.∀H20:∀X:Univ.eq Univ (or X n0) X.∀H21:∀X:Univ.eq Univ (myand X n1) X.∀H22:∀X:Univ.eq Univ (myand X n0) n0.∃V:Univ.And (output n1 n1 n1 n1 n0 n0 n0 n0 V) (And (output n1 n1 n0 n0 n1 n1 n0 n0 V) (output n1 n0 n1 n0 n1 n0 n1 n0 V))
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/HWC003-2".
+include "logic/equality.ma".
+
+(* Inclusion of: HWC003-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC003-2 : TPTP v3.2.0. Released v1.1.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Problem : Invert 3 inputs with 2 not gates *)
+
+(* Version : [WO+92] axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : two.inverter.ver2.in [ANL] *)
+
+(* : - [WO+92] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.80 v2.0.0 *)
+
+(* Syntax : Number of clauses : 25 ( 0 non-Horn; 19 unit; 8 RR) *)
+
+(* Number of atoms : 34 ( 16 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 4 ( 0 propositional; 2-10 arity) *)
+
+(* Number of functors : 25 ( 16 constant; 0-8 arity) *)
+
+(* Number of variables : 95 ( 9 singleton) *)
+
+(* Maximal term depth : 14 ( 1 average) *)
+
+(* Comments : The original uses the equality axioms as demodulators. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definitions of AND, OR and NOT *)
+
+(* Inclusion of: Axioms/HWC002-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC002-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Axioms : Definitions of AND, OR and NOT *)
+
+(* Version : [WO+92] axioms. *)
+
+(* Axiom formulation : Non-ground axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 6 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 : 4 ( 2 singleton) *)
+
+(* Maximal term depth : 2 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Problem axioms *)
+theorem prove_cannot_construct_this:
+ ∀Univ:Set.∀V:Univ.∀X:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X1:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xname:Univ.∀Xrevlist:Univ.∀Y:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀Z:Univ.∀add_inverter:∀_:Univ.∀_:Univ.Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀basic_output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀end:Univ.∀inverter_table:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀list:∀_:Univ.∀_:Univ.Univ.∀list_reversion:∀_:Univ.∀_:Univ.Univ.∀make_reverse_list:∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀not_reversion:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀output:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀possible_reversion:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀r00m:Univ.∀r01m:Univ.∀r0m0:Univ.∀r0m1:Univ.∀r10m:Univ.∀r11m:Univ.∀r1m0:Univ.∀r1m1:Univ.∀rm00:Univ.∀rm01:Univ.∀rm10:Univ.∀rm11:Univ.∀test:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀H0:∀X:Univ.output n0 n1 n0 n1 n0 n1 n0 n1 X.∀H1:∀X:Univ.output n0 n0 n1 n1 n0 n0 n1 n1 X.∀H2:∀X:Univ.output n0 n0 n0 n0 n1 n1 n1 n1 X.∀H3:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Xrevlist:Univ.∀_:test X1 X2 X3 X4 X5 X6 X7 X8 V Xrevlist.basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H4:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.output X1 X2 X3 X4 X5 X6 X7 X8 V.∀H5:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀_:output X1 X2 X3 X4 X5 X6 X7 X8 V.test (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8) (add_inverter V (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8))) (make_reverse_list (list (inverter_table (not X1) (not X2) (not X3) (not X4) (not X5) (not X6) (not X7) (not X8)) V)).∀H6:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.output (or X1 Y1) (or X2 Y2) (or X3 Y3) (or X4 Y4) (or X5 Y5) (or X6 Y6) (or X7 Y7) (or X8 Y8) V.∀H7:∀V:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y1:Univ.∀Y2:Univ.∀Y3:Univ.∀Y4:Univ.∀Y5:Univ.∀Y6:Univ.∀Y7:Univ.∀Y8:Univ.∀_:basic_output X1 X2 X3 X4 X5 X6 X7 X8 V.∀_:basic_output Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 V.basic_output (myand X1 Y1) (myand X2 Y2) (myand X3 Y3) (myand X4 Y4) (myand X5 Y5) (myand X6 Y6) (myand X7 Y7) (myand X8 Y8) V.∀H8:∀X:Univ.∀Y:Univ.eq Univ (list_reversion X (list_reversion X Y)) (list_reversion X Y).∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (list_reversion X (list_reversion Y Z)) (list_reversion Y (list_reversion X Z)).∀H10:∀X:Univ.eq Univ (list_reversion not_reversion X) X.∀H11:∀X:Univ.∀Xname:Univ.eq Univ (possible_reversion Xname X X) not_reversion.∀H12:∀Xname:Univ.eq Univ (possible_reversion Xname n0 n1) not_reversion.∀H13:∀Xname:Univ.eq Univ (possible_reversion Xname n1 n0) Xname.∀H14:∀V:Univ.eq Univ (make_reverse_list V) end.∀H15:∀V:Univ.∀X000:Univ.∀X001:Univ.∀X010:Univ.∀X011:Univ.∀X100:Univ.∀X101:Univ.∀X110:Univ.∀X111:Univ.eq Univ (make_reverse_list (list (inverter_table X000 X001 X010 X011 X100 X101 X110 X111) V)) (list_reversion (possible_reversion r00m X000 X001) (list_reversion (possible_reversion r01m X010 X011) (list_reversion (possible_reversion r10m X100 X101) (list_reversion (possible_reversion r11m X110 X111) (list_reversion (possible_reversion r0m0 X000 X010) (list_reversion (possible_reversion r0m1 X001 X011) (list_reversion (possible_reversion r1m0 X100 X110) (list_reversion (possible_reversion r1m1 X101 X111) (list_reversion (possible_reversion rm00 X000 X100) (list_reversion (possible_reversion rm01 X001 X101) (list_reversion (possible_reversion rm10 X010 X110) (list_reversion (possible_reversion rm11 X011 X111) (make_reverse_list V))))))))))))).∀H16:∀X:Univ.∀Y:Univ.eq Univ (add_inverter X Y) (list Y X).∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add_inverter (list X Y) Z) (list X (add_inverter Y Z)).∀H18:eq Univ (not n1) n0.∀H19:eq Univ (not n0) n1.∀H20:∀X:Univ.eq Univ (or X n1) n1.∀H21:∀X:Univ.eq Univ (or X n0) X.∀H22:∀X:Univ.eq Univ (myand X n1) X.∀H23:∀X:Univ.eq Univ (myand X n0) n0.∃V:Univ.And (output n1 n1 n1 n1 n0 n0 n0 n0 V) (And (output n1 n1 n0 n0 n1 n1 n0 n0 V) (output n1 n0 n1 n0 n1 n0 n1 n0 V))
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/HWV002-1".
+include "logic/equality.ma".
+
+(* Inclusion of: HWV002-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWV002-1 : TPTP v3.2.0. Released v1.1.0. *)
+
+(* Domain : Hardware Verification *)
+
+(* Problem : Invert 3 inputs with 2 not gates *)
+
+(* Version : [ANL] axioms : Reduced > Complete. *)
+
+(* English : This is made to validate the circuit that inverts 3 inputs *)
+
+(* using as many AND and OR gates as you like, but using only *)
+
+(* two NOT gates. *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : two.inverter.val.ver1.in [ANL] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.1.0, 0.56 v2.7.0, 0.67 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 v2.2.1, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 51 ( 0 non-Horn; 50 unit; 34 RR) *)
+
+(* Number of atoms : 53 ( 47 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 39 ( 35 constant; 0-2 arity) *)
+
+(* Number of variables : 28 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : Some duplicate clauses have been removed from the [ANL] version. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Canonicalizing an exclusive-or/and expression *)
+
+(* ----Associativity and symmetry *)
+
+(* ----Problem clauses *)
+theorem prove_inversion:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a1:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀circuit:∀_:Univ.Prop.∀i1:Univ.∀i2:Univ.∀i3:Univ.∀inv1:Univ.∀inv2:Univ.∀n0:Univ.∀n1:Univ.∀n10:Univ.∀n11:Univ.∀n12:Univ.∀n13:Univ.∀n14:Univ.∀n15:Univ.∀n16:Univ.∀n17:Univ.∀n18:Univ.∀n19:Univ.∀n2:Univ.∀n20:Univ.∀n21:Univ.∀n22:Univ.∀n23:Univ.∀n24:Univ.∀n25:Univ.∀n3:Univ.∀n4:Univ.∀n5:Univ.∀n6:Univ.∀n7:Univ.∀n8:Univ.∀n9:Univ.∀not:∀_:Univ.Univ.∀o1:Univ.∀o2:Univ.∀o3:Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀xor:∀_:Univ.∀_:Univ.Univ.∀H0:circuit o3.∀H1:circuit o2.∀H2:circuit o1.∀H3:eq Univ inv2 (not n9).∀H4:eq Univ inv1 (not n20).∀H5:eq Univ n25 (or n2 n24).∀H6:eq Univ n24 (myand i1 inv1).∀H7:eq Univ n23 (myand i1 i3).∀H8:eq Univ n22 (or n23 n6).∀H9:eq Univ n21 (myand inv1 inv2).∀H10:eq Univ n20 (or n22 n14).∀H11:eq Univ n19 (myand n23 inv2).∀H12:eq Univ n18 (or n19 n25).∀H13:eq Univ n17 (or n18 n21).∀H14:eq Univ n16 (myand n14 inv2).∀H15:eq Univ n15 (myand inv2 n6).∀H16:eq Univ n14 (myand i2 i3).∀H17:eq Univ n13 (or n12 n21).∀H18:eq Univ n12 (or n11 n16).∀H19:eq Univ n11 (or a1 n2).∀H20:eq Univ n10 (or n24 n7).∀H21:eq Univ n9 (or n8 n2).∀H22:eq Univ n8 (or a1 n10).∀H23:eq Univ n7 (myand n6 i3).∀H24:eq Univ n6 (myand i1 i2).∀H25:eq Univ n5 (or n4 n21).∀H26:eq Univ n4 (or n15 n3).∀H27:eq Univ n3 (or a1 n24).∀H28:eq Univ n2 (myand inv1 i3).∀H29:eq Univ a1 (myand inv1 i2).∀H30:eq Univ o3 n5.∀H31:eq Univ o2 n17.∀H32:eq Univ o1 n13.∀H33:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand Y (myand X Z)) (myand X (myand Y Z)).∀H34:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (myand Y X).∀H35:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (xor Y (xor X Z)) (xor X (xor Y Z)).∀H36:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (xor Y X).∀H37:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (xor (myand X Y) (xor X Y)).∀H38:∀X:Univ.eq Univ (not X) (xor n1 X).∀H39:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand X (xor Y Z)) (xor (myand X Y) (myand X Z)).∀H40:∀X:Univ.∀Y:Univ.eq Univ (myand X (myand X Y)) (myand X Y).∀H41:∀X:Univ.eq Univ (myand X X) X.∀H42:∀X:Univ.eq Univ (myand X n1) X.∀H43:∀X:Univ.eq Univ (myand n1 X) X.∀H44:∀X:Univ.eq Univ (myand X n0) n0.∀H45:∀X:Univ.eq Univ (myand n0 X) n0.∀H46:∀X:Univ.∀Y:Univ.eq Univ (xor X (xor X Y)) Y.∀H47:∀X:Univ.eq Univ (xor X X) n0.∀H48:∀X:Univ.eq Univ (xor X n0) X.∀H49:∀X:Univ.eq Univ (xor n0 X) X.∀_:circuit (not i1).∀_:circuit (not i2).circuit (not i3)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/HWV003-1".
+include "logic/equality.ma".
+
+(* Inclusion of: HWV003-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWV003-1 : TPTP v3.2.0. Released v1.1.0. *)
+
+(* Domain : Hardware Verification *)
+
+(* Problem : One bit Full Adder *)
+
+(* Version : [WO+92] axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [WO+92] *)
+
+(* Names : - [WO+92] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.86 v2.5.0, 0.80 v2.4.0, 0.83 v2.3.0, 1.00 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 47 ( 0 non-Horn; 47 unit; 13 RR) *)
+
+(* Number of atoms : 47 ( 45 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 20 ( 14 constant; 0-3 arity) *)
+
+(* Number of variables : 69 ( 14 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definitions of AND, OR and NOT *)
+
+(* Inclusion of: Axioms/HWC002-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC002-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Axioms : Definitions of AND, OR and NOT *)
+
+(* Version : [WO+92] axioms. *)
+
+(* Axiom formulation : Non-ground axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 6 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 : 4 ( 2 singleton) *)
+
+(* Maximal term depth : 2 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Simplifiers *)
+
+(* ----Evaluators *)
+
+(* ----Evaluators of lists of 3 terms *)
+
+(* ----Simplifiers for products of 4 terms *)
+
+(* ----Subsumption type demodulators *)
+
+(* ----Karnaugh map technique *)
+
+(* ----Karnaugh simplifier of inside product *)
+
+(* ----Circuit description *)
+theorem prove_circuit:
+ ∀Univ:Set.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀a11:Univ.∀a12:Univ.∀a13:Univ.∀a14:Univ.∀a15:Univ.∀a16:Univ.∀a17:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀c1:Univ.∀carryin:Univ.∀carryout:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀circuit:∀_:Univ.∀_:Univ.Prop.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀s1:Univ.∀sum:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀xor:∀_:Univ.∀_:Univ.Univ.∀H0:circuit s1 c1.∀H1:eq Univ c1 (not (myand a11 a15)).∀H2:eq Univ s1 (not (myand a16 a17)).∀H3:eq Univ a17 (not (myand a15 carryin)).∀H4:eq Univ a16 (not (myand a14 a15)).∀H5:eq Univ a15 (not (myand a14 carryin)).∀H6:eq Univ a14 (not (myand a12 a13)).∀H7:eq Univ a13 (not (myand a11 b)).∀H8:eq Univ a12 (not (myand a11 a)).∀H9:eq Univ a11 (not (myand a b)).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (sum X Y Z) (xor (xor X Y) Z).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (carryout X Y Z) (or (myand X (or Y Z)) (myand (not X) (myand Y Z))).∀H12:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand Y (not X))).∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (myand (myand X Y) (not Z)) (myand X Z)) (or (myand X Y) (myand X Z)).∀H14:∀X:Univ.∀Y:Univ.eq Univ (or (myand (not X) (not Y)) Y) (or Y (not X)).∀H15:∀X:Univ.∀Y:Univ.eq Univ (or (myand X (not Y)) Y) (or X Y).∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or X (myand Y Z)) Z) (or X Z).∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or (myand X Y) Z) Y) (or Z Y).∀H18:∀X:Univ.∀Y:Univ.eq Univ (or (myand X Y) X) X.∀H19:∀X:Univ.∀Y:Univ.eq Univ (or (myand X Y) Y) Y.∀H20:∀X1:Univ.∀X2:Univ.∀X3:Univ.eq Univ (myand (myand (myand X1 X2) X3) (not X2)) n0.∀H21:∀X1:Univ.∀X2:Univ.∀X3:Univ.eq Univ (myand (myand (myand X1 X2) X3) (not X1)) n0.∀H22:∀X:Univ.∀Y:Univ.eq Univ (or (or X Y) Y) (or X Y).∀H23:∀X:Univ.∀Y:Univ.eq Univ (myand (myand X Y) Y) (myand X Y).∀H24:∀X:Univ.∀Y:Univ.eq Univ (or (or X Y) (not X)) n1.∀H25:∀X:Univ.∀Y:Univ.eq Univ (or (or X Y) (not Y)) n1.∀H26:∀X:Univ.∀Y:Univ.eq Univ (myand (myand X Y) (not X)) n0.∀H27:∀X:Univ.∀Y:Univ.eq Univ (myand (myand X Y) (not Y)) n0.∀H28:∀X:Univ.eq Univ (or X X) X.∀H29:∀X:Univ.eq Univ (myand X X) X.∀H30:∀X:Univ.eq Univ (or X (not X)) n1.∀H31:∀X:Univ.eq Univ (myand X (not X)) n0.∀H32:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or X Y) Z) (or (or X Z) Y).∀H33:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand (myand X Y) Z) (myand (myand X Z) Y).∀H34:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand (or X Y) Z) (or (myand X Z) (myand Y Z)).∀H35:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (or Y X).∀H36:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (myand Y X).∀H37:∀X:Univ.eq Univ (not (not X)) X.∀H38:∀X:Univ.∀Y:Univ.eq Univ (not (or X Y)) (myand (not X) (not Y)).∀H39:∀X:Univ.∀Y:Univ.eq Univ (not (myand X Y)) (or (not X) (not Y)).∀H40:eq Univ (not n1) n0.∀H41:eq Univ (not n0) n1.∀H42:∀X:Univ.eq Univ (or X n1) n1.∀H43:∀X:Univ.eq Univ (or X n0) X.∀H44:∀X:Univ.eq Univ (myand X n1) X.∀H45:∀X:Univ.eq Univ (myand X n0) n0.circuit (sum a b carryin) (carryout a b carryin)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/HWV004-1".
+include "logic/equality.ma".
+
+(* Inclusion of: HWV004-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWV004-1 : TPTP v3.2.0. Released v1.1.0. *)
+
+(* Domain : Hardware Verification *)
+
+(* Problem : Two bit Full Adder *)
+
+(* Version : [WO+92] axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [WO+92] *)
+
+(* Names : - [WO+92] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 1.00 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 0.40 v2.4.0, 0.83 v2.3.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 41 ( 0 non-Horn; 41 unit; 7 RR) *)
+
+(* Number of atoms : 41 ( 39 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-3 arity) *)
+
+(* Number of functors : 15 ( 9 constant; 0-3 arity) *)
+
+(* Number of variables : 69 ( 14 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definitions of AND, OR and NOT *)
+
+(* Inclusion of: Axioms/HWC002-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : HWC002-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Hardware Creation *)
+
+(* Axioms : Definitions of AND, OR and NOT *)
+
+(* Version : [WO+92] axioms. *)
+
+(* Axiom formulation : Non-ground axioms. *)
+
+(* English : *)
+
+(* Refs : [WO+92] Wos et al. (1992), Automated Reasoning: Introduction a *)
+
+(* Source : [ANL] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 6 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 : 4 ( 2 singleton) *)
+
+(* Maximal term depth : 2 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Simplifiers *)
+
+(* ----Evaluators *)
+
+(* ----Evaluators of lists of 3 terms *)
+
+(* ----Simplifiers for products of 4 terms *)
+
+(* ----Subsumption type demodulators *)
+
+(* ----Karnaugh map technique *)
+
+(* ----Karnaugh simplifier of inside product *)
+
+(* ----Circuit description *)
+theorem prove_circuit:
+ ∀Univ:Set.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀Y:Univ.∀Z:Univ.∀a0:Univ.∀a1:Univ.∀myand:∀_:Univ.∀_:Univ.Univ.∀b0:Univ.∀b1:Univ.∀carryout:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀circuit:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀n0:Univ.∀n1:Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀overflow:Univ.∀s0:Univ.∀s1:Univ.∀sum:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀xor:∀_:Univ.∀_:Univ.Univ.∀H0:circuit s0 s1 overflow.∀H1:eq Univ overflow (carryout a1 b1 (carryout a0 b0 n0)).∀H2:eq Univ s1 (sum a1 b1 (carryout a0 b0 n0)).∀H3:eq Univ s0 (sum a0 b0 n0).∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (sum X Y Z) (xor (xor X Y) Z).∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (carryout X Y Z) (or (myand X (or Y Z)) (myand (not X) (myand Y Z))).∀H6:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand Y (not X))).∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (myand (myand X Y) (not Z)) (myand X Z)) (or (myand X Y) (myand X Z)).∀H8:∀X:Univ.∀Y:Univ.eq Univ (or (myand (not X) (not Y)) Y) (or Y (not X)).∀H9:∀X:Univ.∀Y:Univ.eq Univ (or (myand X (not Y)) Y) (or X Y).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or X (myand Y Z)) Z) (or X Z).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or (myand X Y) Z) Y) (or Z Y).∀H12:∀X:Univ.∀Y:Univ.eq Univ (or (myand X Y) X) X.∀H13:∀X:Univ.∀Y:Univ.eq Univ (or (myand X Y) Y) Y.∀H14:∀X1:Univ.∀X2:Univ.∀X3:Univ.eq Univ (myand (myand (myand X1 X2) X3) (not X2)) n0.∀H15:∀X1:Univ.∀X2:Univ.∀X3:Univ.eq Univ (myand (myand (myand X1 X2) X3) (not X1)) n0.∀H16:∀X:Univ.∀Y:Univ.eq Univ (or (or X Y) Y) (or X Y).∀H17:∀X:Univ.∀Y:Univ.eq Univ (myand (myand X Y) Y) (myand X Y).∀H18:∀X:Univ.∀Y:Univ.eq Univ (or (or X Y) (not X)) n1.∀H19:∀X:Univ.∀Y:Univ.eq Univ (or (or X Y) (not Y)) n1.∀H20:∀X:Univ.∀Y:Univ.eq Univ (myand (myand X Y) (not X)) n0.∀H21:∀X:Univ.∀Y:Univ.eq Univ (myand (myand X Y) (not Y)) n0.∀H22:∀X:Univ.eq Univ (or X X) X.∀H23:∀X:Univ.eq Univ (myand X X) X.∀H24:∀X:Univ.eq Univ (or X (not X)) n1.∀H25:∀X:Univ.eq Univ (myand X (not X)) n0.∀H26:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or X Y) Z) (or (or X Z) Y).∀H27:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand (myand X Y) Z) (myand (myand X Z) Y).∀H28:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand (or X Y) Z) (or (myand X Z) (myand Y Z)).∀H29:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (or Y X).∀H30:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (myand Y X).∀H31:∀X:Univ.eq Univ (not (not X)) X.∀H32:∀X:Univ.∀Y:Univ.eq Univ (not (or X Y)) (myand (not X) (not Y)).∀H33:∀X:Univ.∀Y:Univ.eq Univ (not (myand X Y)) (or (not X) (not Y)).∀H34:eq Univ (not n1) n0.∀H35:eq Univ (not n0) n1.∀H36:∀X:Univ.eq Univ (or X n1) n1.∀H37:∀X:Univ.eq Univ (or X n0) X.∀H38:∀X:Univ.eq Univ (myand X n1) X.∀H39:∀X:Univ.eq Univ (myand X n0) n0.circuit (xor a0 b0) (xor (xor a1 b1) (carryout a0 b0 n0)) (or (myand a1 b1) (myand (myand a0 b0) (or a1 b1)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LAT001-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LAT001-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Problem : If X' = U v V and Y' = U ^ V, then U' = X v (Y ^ V) *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : The theorem states that there is a complement of "a" in a *)
+
+(* modular lattice with 0 and 1. *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [GO+69] Guard et al. (1969), Semi-Automated Mathematics *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : L1a [McC88] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 19 ( 0 non-Horn; 15 unit; 6 RR) *)
+
+(* Number of atoms : 24 ( 18 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 6 constant; 0-2 arity) *)
+
+(* Number of variables : 29 ( 4 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : No further information is available from [McC88] or [GO+69] *)
+
+(* about [Bum65]. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include lattice axioms *)
+
+(* Inclusion of: Axioms/LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
+
+(* Number of literals : 8 ( 8 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 2 ( 0 constant; 2-2 arity) *)
+
+(* Number of variables : 16 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----The following 8 clauses characterise lattices *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include modular lattice axioms *)
+
+(* Inclusion of: Axioms/LAT001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory modularity (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 5 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 6 ( 6 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* : These axioms, with 4 extra redundant axioms about 0 & 1, are *)
+
+(* used in [Wos88] p.217. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include 1 and 0 in the lattice *)
+
+(* ----Require the lattice to be modular *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definition of complement *)
+
+(* Inclusion of: Axioms/LAT001-2.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory complement (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 0 unit; 3 RR) *)
+
+(* Number of literals : 7 ( 4 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definition of complement *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_complememt:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (meet X Y) n0.∀_:eq Univ (join X Y) n1.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.complement a (join r1 (meet r2 b))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LAT002-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LAT002-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT002-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Problem : If X' = U v V and Y' = U ^ V, then U' exists *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : The theorem states that there is a complement of "a" in a *)
+
+(* modular lattice with 0 and 1. *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [GO+69] Guard et al. (1969), Semi-Automated Mathematics *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : L1b [McC88] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 1.00 v2.4.0, 0.83 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 19 ( 0 non-Horn; 15 unit; 6 RR) *)
+
+(* Number of atoms : 24 ( 18 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 6 constant; 0-2 arity) *)
+
+(* Number of variables : 30 ( 5 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include lattice axioms *)
+
+(* Inclusion of: Axioms/LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
+
+(* Number of literals : 8 ( 8 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 2 ( 0 constant; 2-2 arity) *)
+
+(* Number of variables : 16 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----The following 8 clauses characterise lattices *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include modular lattice axioms *)
+
+(* Inclusion of: Axioms/LAT001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory modularity (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 5 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 6 ( 6 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* : These axioms, with 4 extra redundant axioms about 0 & 1, are *)
+
+(* used in [Wos88] p.217. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include 1 and 0 in the lattice *)
+
+(* ----Require the lattice to be modular *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definition of complement *)
+
+(* Inclusion of: Axioms/LAT001-2.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory complement (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 0 unit; 3 RR) *)
+
+(* Number of literals : 7 ( 4 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definition of complement *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_complememt_exists:
+ ∀Univ:Set.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (meet X Y) n0.∀_:eq Univ (join X Y) n1.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.∃W:Univ.complement a W
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LAT005-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LAT005-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT005-3 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Problem : SAM's lemma *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : Let L be a modular lattice with 0 and 1. Suppose that A and *)
+
+(* B are elements of L such that (A v B) and (A ^ B) both have *)
+
+(* not necessarily unique complements. Then, (A v B)' = *)
+
+(* ((A v B)' v ((A ^ B)' ^ B)) ^ ((A v B)' v ((A ^ B)' ^ A)). *)
+
+(* Refs : [GO+69] Guard et al. (1969), Semi-Automated Mathematics *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : SAM's lemma [McC88] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.44 v2.7.0, 0.50 v2.6.0, 0.43 v2.5.0, 0.80 v2.4.0, 1.00 v2.3.0, 0.83 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 19 ( 0 non-Horn; 15 unit; 6 RR) *)
+
+(* Number of atoms : 24 ( 19 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 6 constant; 0-2 arity) *)
+
+(* Number of variables : 29 ( 4 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : [McC88] specifies that the axioms for complement should not be *)
+
+(* included ("clauses 1-13 from axioms"). However, if this makes *)
+
+(* clauses 87 and 88 pure. I have assumed a typo in the paper and *)
+
+(* included axioms 14-16. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include lattice axioms *)
+
+(* Inclusion of: Axioms/LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
+
+(* Number of literals : 8 ( 8 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 2 ( 0 constant; 2-2 arity) *)
+
+(* Number of variables : 16 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----The following 8 clauses characterise lattices *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include modular lattice axioms *)
+
+(* Inclusion of: Axioms/LAT001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory modularity (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 5 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 6 ( 6 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* : These axioms, with 4 extra redundant axioms about 0 & 1, are *)
+
+(* used in [Wos88] p.217. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include 1 and 0 in the lattice *)
+
+(* ----Require the lattice to be modular *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definition of complement *)
+
+(* Inclusion of: Axioms/LAT001-2.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory complement (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 0 unit; 3 RR) *)
+
+(* Number of literals : 7 ( 4 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definition of complement *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_lemma:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (meet X Y) n0.∀_:eq Univ (join X Y) n1.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.eq Univ r1 (meet (join r1 (meet r2 b)) (join r1 (meet r2 a)))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LAT041-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LAT041-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT041-1 : TPTP v3.2.0. Released v2.4.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Problem : A hyperbase for type <2,2> lattice hyperidentities *)
+
+(* Version : [PP00] axioms. *)
+
+(* English : *)
+
+(* Refs : [PP00] Padmanabhan & Penner (2000), A Hyperbase for Binary La *)
+
+(* Source : [PP00] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.78 v2.7.0, 1.00 v2.4.0 *)
+
+(* Syntax : Number of clauses : 17 ( 0 non-Horn; 14 unit; 7 RR) *)
+
+(* Number of atoms : 21 ( 11 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 15 ( 11 constant; 0-3 arity) *)
+
+(* Number of variables : 29 ( 2 singleton) *)
+
+(* Maximal term depth : 6 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_q4:
+ ∀Univ:Set.∀V:Univ.∀W:Univ.∀W1:Univ.∀W2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀big_p:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀big_t:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c:Univ.∀d:Univ.∀e:Univ.∀plus:∀_:Univ.∀_:Univ.Univ.∀term:∀_:Univ.Prop.∀term1:Univ.∀term2:Univ.∀term3:Univ.∀term4:Univ.∀term5:Univ.∀term6:Univ.∀times:∀_:Univ.∀_:Univ.Univ.∀H0:∀W1:Univ.∀W2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W1.∀_:term W2.eq Univ (big_t W1 (big_p W2 (big_t W1 X Y) Z) (big_p W2 Y Z)) (big_p W2 (big_t W1 X Y) Z).∀H1:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W.eq Univ (big_p W (big_p W X Y) (big_p W Z V)) (big_p W (big_p W X Z) (big_p W Y V)).∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:term W.eq Univ (big_p W (big_p W X Y) Z) (big_p W X (big_p W Y Z)).∀H3:term term6.∀H4:term term5.∀H5:term term4.∀H6:term term3.∀H7:term term2.∀H8:term term1.∀H9:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (big_t W X Y) (big_p W X Y).∀H10:∀X:Univ.∀Y:Univ.eq Univ (big_p term6 X Y) (plus Y X).∀H11:∀X:Univ.∀Y:Univ.eq Univ (big_p term5 X Y) (plus X Y).∀H12:∀X:Univ.∀Y:Univ.eq Univ (big_p term4 X Y) (times Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (big_p term3 X Y) (times X Y).∀H14:∀X:Univ.∀Y:Univ.eq Univ (big_p term2 X Y) Y.∀H15:∀X:Univ.∀Y:Univ.eq Univ (big_p term1 X Y) X.eq Univ (times a (plus b (times d (times c e)))) (times a (plus b (times (plus b c) (times d (times c e)))))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL109-4".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL109-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL109-4 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : A theorem in the lattice structure of Wajsberg algebras *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* Theorem formulation : Wajsberg algebras lattice structure. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : Lattice structure theorem 8 [Bon91] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 v2.2.1, 0.89 v2.2.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 9 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra axioms *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
+
+(* Source : [MW92] *)
+
+(* Names : MV Sentential Calculus [MW92] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra lattice structure axioms *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra lattice structure definitions *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 4 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat *)
+
+(* ----Definition of partial order *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_mv_4:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (big_V (implies x y) (implies y x)) truth
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL147-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL147-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL147-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : A theorem in the lattice structure of Wajsberg algebras *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : Lattice structure theorem 6 [Bon91] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 9 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra axioms *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
+
+(* Source : [MW92] *)
+
+(* Names : MV Sentential Calculus [MW92] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra lattice structure axioms *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra lattice structure definitions *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 4 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat *)
+
+(* ----Definition of partial order *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_theorem:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_V x y) z) (big_hat (implies x z) (implies y z))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL148-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL148-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL148-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : A theorem in the lattice structure of Wajsberg algebras *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : Lattice structure theorem 7 [Bon91] *)
+
+(* Status : Unknown *)
+
+(* Rating : 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 9 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra axioms *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
+
+(* Source : [MW92] *)
+
+(* Names : MV Sentential Calculus [MW92] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra lattice structure axioms *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra lattice structure definitions *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 4 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat *)
+
+(* ----Definition of partial order *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_theorem:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (big_hat y z)) (big_hat (implies x y) (implies x z))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL149-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL149-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL149-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : A theorem in the lattice structure of Wajsberg algebras *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : Lattice structure theorem 9 [Bon91] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.2.0, 0.71 v3.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 9 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra axioms *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
+
+(* Source : [MW92] *)
+
+(* Names : MV Sentential Calculus [MW92] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra lattice structure axioms *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra lattice structure definitions *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 4 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat *)
+
+(* ----Definition of partial order *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_theorem:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (big_V y z)) (big_V (implies x y) (implies x z))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL150-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL150-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL150-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : A theorem in the lattice structure of Wajsberg algebras *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : Lattice structure theorem 10 [Bon91] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.2.0, 0.71 v3.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 9 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra axioms *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
+
+(* Source : [MW92] *)
+
+(* Names : MV Sentential Calculus [MW92] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra lattice structure axioms *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra lattice structure definitions *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 4 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat *)
+
+(* ----Definition of partial order *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_theorem:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_hat x y) z) (big_V (implies x z) (implies y z))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL151-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL151-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL151-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : A theorem in the lattice structure of Wajsberg algebras *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : Lattice structure theorem 11 [Bon91] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 9 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra axioms *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
+
+(* Source : [MW92] *)
+
+(* Names : MV Sentential Calculus [MW92] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra lattice structure axioms *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra lattice structure definitions *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 4 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat *)
+
+(* ----Definition of partial order *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_theorem:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (big_V (big_hat x y) z) (big_hat (big_V x z) (big_V y z))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL152-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL152-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL152-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : A theorem in the lattice structure of Wajsberg algebras *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : Lattice structure theorem 12 [Bon91] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.86 v2.5.0, 0.80 v2.4.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 9 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra axioms *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
+
+(* Source : [MW92] *)
+
+(* Names : MV Sentential Calculus [MW92] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 3 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra lattice structure axioms *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Wajsberg algebra lattice structure definitions *)
+
+(* Version : [Bon91] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(* Source : [Bon91] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *)
+
+(* Number of literals : 6 ( 4 equality) *)
+
+(* Maximal clause size : 2 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat *)
+
+(* ----Definition of partial order *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_theorem:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_hat x y) z) (implies (implies x y) (implies x z))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL174-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL174-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL174-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.06 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [Wr27] *)
+
+(* Names : Problem 2.06 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0, 0.14 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.00 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p q) (implies (implies q r) (implies p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL181-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL181-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL181-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.15 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.15 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.57 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (not p) q) (implies (not q) p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL182-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL182-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL182-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.16 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.16 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0, 0.14 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.57 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p q) (implies (not q) (not p)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL183-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL183-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL183-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.17 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.17 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0, 0.00 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (not q) (not p)) (implies p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL191-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL191-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL191-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.31 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [Wr27] *)
+
+(* Names : Problem 2.31 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.56 v2.7.0, 0.50 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.33 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p (or q r)) (or (or p q) r))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL192-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL192-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL192-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.32 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.32 [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, 0.40 v2.4.0, 0.33 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or (or p q) r) (or p (or q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL193-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL193-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL193-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.36 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [Wr27] *)
+
+(* Names : Problem 2.36 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.33 v2.6.0, 0.29 v2.5.0, 0.00 v2.4.0, 0.33 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 r) (implies (or p q) (or r p)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL194-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL194-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL194-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.37 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.37 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 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 : 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 r) (implies (or q p) (or p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL195-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL195-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL195-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.38 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.38 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 r) (implies (or q p) (or r p)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL198-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL198-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL198-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.42 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.42 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or (not p) (implies p q)) (implies p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL201-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL201-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL201-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.47 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.47 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (not (or p q)) (or (not p) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL206-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL206-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL206-3 : TPTP v3.2.0. Bugfixed v2.4.1. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.52 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.52 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.50 v2.5.0 *)
+
+(* 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : *)
+
+(* Bugfixes : v2.4.1 - Fixed clause prove_this. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (not (implies p q)) (implies (not p) (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL208-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL208-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL208-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.53 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.53 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.57 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p q) (implies (not p) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL213-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL213-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL213-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.61 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.61 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.60 v2.4.0, 0.67 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 : 5 ( 2 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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p q) (implies (implies (not p) q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL214-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL214-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL214-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.61 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.62 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.86 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.57 v2.5.0, 0.20 v2.4.0, 0.33 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p q) (implies (implies p q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL215-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL215-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL215-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.621 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.621 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p q) (implies (or p q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL216-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL216-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL216-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.64 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.64 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.56 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 : 5 ( 2 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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p q) (implies (or p (not q)) p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL217-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL217-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL217-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.65 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.65 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 : 5 ( 2 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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p q) (implies (implies p (not q)) (not p)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL218-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL218-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL218-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.67 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.67 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0, 0.14 v3.1.0, 0.33 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p q) q) (implies p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL219-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL219-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL219-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.68 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.68 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0, 0.00 v3.1.0, 0.33 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) q) (or p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL220-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL220-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL220-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.69 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.69 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.60 v2.4.0, 0.67 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) q) (implies (implies q p) p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL221-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL221-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL221-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.73 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.73 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.89 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 : 6 ( 3 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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p q) (implies (or (or p q) r) (or q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL222-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL222-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL222-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.74 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.74 [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 : 6 ( 3 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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p) (implies (or (or p q) r) (or p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL223-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL223-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL223-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.75 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.75 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 : 6 ( 3 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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p q) (implies (or p (implies q r)) (or p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL224-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL224-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL224-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.76 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.76 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.78 v2.7.0, 1.00 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p (implies q r)) (implies (or p q) (or p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL225-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL225-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL225-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.77 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.77 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p (implies q r)) (implies (implies p q) (implies p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL226-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL226-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL226-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.8 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.8 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0, 0.14 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.20 v2.4.0, 0.00 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 : 6 ( 3 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.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or q r) (implies (or (not r) s) (or q s)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+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 X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL229-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL229-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL229-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.83 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.83 [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 X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 p (implies q r)) (implies (implies p (implies r s)) (implies p (implies q s))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL230-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL230-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL230-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.85 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.85 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p q) (or p r)) (or p (implies q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL231-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL231-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL231-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.86 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.86 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 : 6 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) (implies p r)) (implies p (implies q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL234-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL234-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL234-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.2 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.2 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 6 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀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 (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies p (implies q (myand p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL237-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL237-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL237-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.21 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.21 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 6 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀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 (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies q (implies p (myand p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL242-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL242-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL242-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.3 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.3 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.40 v2.4.0, 0.67 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (myand p q) r) (implies p (implies q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL243-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL243-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL243-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.31 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.31 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p (implies q r)) (implies (myand p q) r))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL245-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL245-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL245-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.34 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.34 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies q r) (implies p q)) (implies p r))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL246-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL246-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL246-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.35 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.35 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 6 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀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 (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand p (implies p q)) q)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL247-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL247-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL247-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.37 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.37 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies (myand p q) r) (implies (myand p (not r)) (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL249-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL249-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL249-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.41 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.41 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.56 v2.7.0, 0.17 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p r) (implies (myand p q) r))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL250-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL250-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL250-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.42 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.42 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.2.0, 0.14 v3.1.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies q r) (implies (myand p q) r))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL251-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL251-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL251-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.43 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.43 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p q) (implies p r)) (implies p (myand q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL252-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL252-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL252-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.44 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.44 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies q p) (implies r p)) (implies (or q r) p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL253-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL253-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL253-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.45 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.45 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 1.00 v2.4.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (implies p q) (implies (myand p r) (myand q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL254-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL254-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL254-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.47 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.47 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p r) (implies q s)) (implies (myand p q) (myand r s)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL255-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL255-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL255-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.48 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [SE94] *)
+
+(* Names : Problem 3.48 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 8 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀s:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand (implies p r) (implies q s)) (implies (or p q) (or r s)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL260-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL260-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL260-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 2.63 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 2.63 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.86 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.57 v2.5.0, 0.20 v2.4.0, 0.33 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 : 5 ( 2 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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or p q) (implies (or (not p) q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL261-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL261-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL261-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 3.12 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 3.12 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 6 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀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 (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (or (not p) (or (not q) (myand p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL262-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL262-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL262-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.10 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.1 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.67 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) (implies (not q) (not p)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL263-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL263-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL263-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.11 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.11 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (equivalent p q) (equivalent (not p) (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL264-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL264-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL264-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.12 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.12 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (equivalent p q) (equivalent (not p) (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL265-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL265-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL265-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.13 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.13 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.44 v2.7.0, 0.50 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.00 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 : 6 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (not (not p)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL266-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL266-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL266-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.14 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.14 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand p (implies q r)) (myand p (implies (not r) (not q))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL269-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL269-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL269-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.21 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.21 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.56 v2.7.0, 0.67 v2.6.0, 0.57 v2.5.0, 0.20 v2.4.0, 0.67 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (equivalent p q) (equivalent q p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL270-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL270-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL270-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.22 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.22 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (myand (equivalent p q) (equivalent q r)) (equivalent p r))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL271-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL271-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL271-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.24 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.24 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.00 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 : 6 ( 1 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.∀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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (myand p p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL272-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL272-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL272-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.25 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.25 [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, 0.00 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 : 6 ( 1 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.∀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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (or p p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL273-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL273-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL273-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.3 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.3 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.56 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.20 v2.4.0, 0.67 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand p q) (myand q p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL275-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL275-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL275-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.32 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.32 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand r (myand p q)) (myand p (myand q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL276-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL276-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL276-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.33 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.33 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 r (or p q)) (or p (or q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL277-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL277-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL277-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.36 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.36 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (equivalent p q) (equivalent (myand p r) (myand q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL278-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL278-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL278-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.37 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.37 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (equivalent p q) (equivalent (or p r) (or q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL281-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL281-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL281-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.4 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.4 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand p (or q r)) (or (myand p q) (myand p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL282-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL282-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL282-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.41 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.41 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand q r)) (myand (or p q) (or p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL283-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL283-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL283-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.42 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.42 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (or (myand p q) (myand p (not q))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL284-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL284-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL284-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.43 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.43 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (myand (or p q) (or p (not q))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL285-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL285-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL285-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.44 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.44 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (or p (myand p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL286-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL286-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL286-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.45 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.45 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (myand p (or p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL289-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL289-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL289-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.53 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.53 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.67 v2.6.0, 0.57 v2.5.0, 0.60 v2.4.0, 0.67 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (myand p (not q))) (or (not p) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL293-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL293-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL293-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.57 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.57 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 v2.4.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (myand (not p) (not q))) (or p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL295-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL295-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL295-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.61 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.61 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.67 v2.7.0, 0.83 v2.6.0, 0.57 v2.5.0, 0.60 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (implies p q)) (myand p (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL298-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL298-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL298-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.51 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.51 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (myand p q)) (or (not p) (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL299-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL299-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL299-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.65 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.65 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (implies (not p) q)) (myand (not p) (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL300-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL300-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL300-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.66 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.66 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.60 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (not p) (not q)) (or p (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL302-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL302-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL302-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.7 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.7 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) (implies p (myand p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL303-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL303-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL303-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.71 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.71 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) (equivalent q (or p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL304-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL304-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL304-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.72 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.72 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) (equivalent q (or p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL305-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL305-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL305-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.73 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.73 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 v2.5.0, 0.80 v2.4.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies q (equivalent p (myand p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL306-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL306-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL306-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.74 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.74 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.67 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (not p) (equivalent q (or p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL307-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL307-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL307-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.76 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.76 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand (implies p q) (implies p r)) (implies p (myand q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL308-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL308-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL308-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.77 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.77 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand (implies q p) (implies r p)) (implies (or q r) p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL309-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL309-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL309-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.78 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.78 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p q) (implies p r)) (implies p (or q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL310-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL310-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL310-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.79 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.79 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies q p) (implies r p)) (implies (myand q r) p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL311-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL311-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL311-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.8 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.8 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.00 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 : 6 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p (not p)) (not p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL312-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL312-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL312-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.81 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.81 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 : 6 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (not p) p) p)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL313-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL313-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL313-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.82 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.82 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand (implies p q) (implies p (not q))) (not p))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL314-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL314-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL314-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.83 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.83 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand (implies p q) (implies (not p) q)) q)
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL315-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL315-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL315-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.84 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.84 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (equivalent p q) (equivalent (implies p r) (implies q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL316-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL316-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL316-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 4.85 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 4.85 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (equivalent p q) (equivalent (implies r p) (implies r q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL319-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL319-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL319-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.1 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.1 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.2.0, 0.57 v3.1.0, 0.56 v2.7.0, 0.67 v2.6.0, 1.00 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (myand p q) (equivalent p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL320-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL320-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL320-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.11 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.11 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.20 v2.4.0, 0.00 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 : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 16 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP 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 (or (implies p q) (implies (not p) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL324-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL324-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL324-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.16 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.16 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.89 v2.7.0, 0.83 v2.6.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (myand (equivalent p q) (equivalent p (not q))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL325-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL325-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL325-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.17 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.17 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand (or p q) (not (myand p q))) (equivalent p (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL326-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL326-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL326-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.19 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.19 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.33 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.40 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 : 6 ( 1 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (equivalent p (not p)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL327-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL327-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL327-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.21 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.21 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (myand (not p) (not q)) (equivalent p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL328-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL328-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL328-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.23 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.23 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (equivalent p q) (or (myand p q) (myand (not p) (not q))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL329-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL329-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL329-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.24 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.24 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 1.00 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 : 6 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (not (or (myand p q) (myand (not p) (not q)))) (or (myand p (not q)) (myand q (not p))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL330-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL330-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL330-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.25 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.25 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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) (implies (implies p q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL331-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL331-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL331-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.3 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.3 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (myand p q) r) (implies (myand p q) (myand p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL332-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL332-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL332-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.31 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.31 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 v2.3.0 *)
+
+(* Syntax : Number of clauses : 10 ( 0 non-Horn; 8 unit; 3 RR) *)
+
+(* Number of atoms : 13 ( 2 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 18 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+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.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀r:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀P:Univ.∀Q:Univ.eq Univ (myand P Q) (not (or (not P) (not Q))).∀H1:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H2:∀X:Univ.∀_:theoremP X.axiomP X.∀H3:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H6:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H7:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H8:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (myand r (implies p q)) (implies p (myand q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL334-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL334-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL334-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.33 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.33 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand p (implies q r)) (myand p (implies (myand p q) r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL335-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL335-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL335-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.35 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.35 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 4 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (myand (implies p q) (implies q r)) (implies p (equivalent q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL336-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL336-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL336-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.36 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.36 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand p (equivalent p q)) (myand q (equivalent p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL337-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL337-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL337-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.4 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.4 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.67 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p (implies p q)) (implies p q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL339-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL339-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL339-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.42 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.42 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p (implies q r)) (implies p (implies q (myand p r))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL340-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL340-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL340-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.44 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.44 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (implies p q) (equivalent (implies p r) (implies p (myand q r))))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL341-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL341-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL341-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.5 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.5 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.67 v2.6.0, 0.57 v2.5.0, 0.40 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p (equivalent (implies p q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL342-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL342-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL342-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.501 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.501 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies p (equivalent q (equivalent p q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL344-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL344-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL344-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.54 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.54 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (or (equivalent (myand p q) p) (equivalent (myand p q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL345-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL345-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL345-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.55 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.55 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (or (equivalent (or p q) p) (equivalent (or p q) q))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL346-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL346-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL346-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.6 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.6 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (myand p (not q)) r) (implies p (or q r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL347-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL347-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL347-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.61 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.61 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 1.00 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand (or p q) (not q)) (myand p (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL348-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL348-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL348-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.62 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.62 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.40 v2.4.0, 0.67 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 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (myand p q) (not q)) (or p (not q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL349-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL349-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL349-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.63 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.63 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 0.60 v2.4.0, 1.00 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 : 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 p (myand (not p) q)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL351-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL351-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL351-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.71 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.71 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (implies q (not r)) (equivalent (myand (or p q) r) (myand p r)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LCL353-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL353-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL353-3 : TPTP v3.2.0. Released v2.3.0. *)
+
+(* Domain : Logic Calculi (Propositional) *)
+
+(* Problem : Principia Mathematica 5.75 *)
+
+(* Version : [WR27] axioms. *)
+
+(* English : *)
+
+(* Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica *)
+
+(* Source : [WR27] *)
+
+(* Names : Problem 5.75 [WR27] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.1.0, 0.89 v2.7.0, 1.00 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 : 8 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 1 singleton) *)
+
+(* Maximal term depth : 6 ( 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))]). *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* 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.∀r: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 X.∀_:theoremP (implies Y X).theoremP Y.∀H3:∀X:Univ.∀_:theoremP X.axiomP 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 (implies (equivalent (myand (implies r (not q)) p) (or q r)) (equivalent (myand p (not q)) r))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LDA004-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LDA004-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LDA004-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : LD-Algebras (Left segments) *)
+
+(* Problem : Show that 3*2(U2) is a left segment of U1(U3) *)
+
+(* Version : [Jec93] axioms. *)
+
+(* English : *)
+
+(* Refs : [Jec93] Jech (1993), LD-Algebras *)
+
+(* Source : [Jec93] *)
+
+(* Names : Problem 4 [Jec93] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.50 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.67 v2.3.0, 0.83 v2.2.1, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 12 ( 0 non-Horn; 11 unit; 10 RR) *)
+
+(* Number of atoms : 14 ( 9 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 10 ( 9 constant; 0-2 arity) *)
+
+(* Number of variables : 8 ( 1 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----A1: x(yz)=xy(xz) *)
+
+(* ----x is a left segment of xy *)
+
+(* ----transitive *)
+
+(* ----3*2*U2 is a left segment of U1*U3 *)
+theorem prove_equation:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀f:∀_:Univ.∀_:Univ.Univ.∀left:∀_:Univ.∀_:Univ.Prop.∀n1:Univ.∀n2:Univ.∀n3:Univ.∀u:Univ.∀u1:Univ.∀u2:Univ.∀u3:Univ.∀H0:eq Univ b (f u1 u3).∀H1:eq Univ a (f (f n3 n2) u2).∀H2:eq Univ u3 (f u n3).∀H3:eq Univ u2 (f u n2).∀H4:eq Univ u1 (f u n1).∀H5:eq Univ u (f n2 n2).∀H6:eq Univ n3 (f n2 n1).∀H7:eq Univ n2 (f n1 n1).∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:left X Y.∀_:left Y Z.left X Z.∀H9:∀X:Univ.∀Y:Univ.left X (f X Y).∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).left a b
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/MGT011-1".
+include "logic/equality.ma".
+
+(* Inclusion of: MGT011-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : MGT011-1 : TPTP v3.2.0. Released v2.4.0. *)
+
+(* Domain : Management (Organisation Theory) *)
+
+(* Problem : Organizational size cannot decrease without reorganization *)
+
+(* Version : [PB+94] axioms. *)
+
+(* English : *)
+
+(* Refs : [PB+92] Peli et al. (1992), A Logical Approach to Formalizing *)
+
+(* : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing *)
+
+(* : [Kam94] Kamps (1994), Email to G. Sutcliffe *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.4.0 *)
+
+(* Syntax : Number of clauses : 14 ( 0 non-Horn; 7 unit; 14 RR) *)
+
+(* Number of atoms : 38 ( 2 equality) *)
+
+(* Maximal clause size : 10 ( 3 average) *)
+
+(* Number of predicates : 7 ( 0 propositional; 2-3 arity) *)
+
+(* Number of functors : 7 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 27 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Created with tptp2X -f tptp -t clausify:otter MGT011+1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/MGT012-1".
+include "logic/equality.ma".
+
+(* Inclusion of: MGT012-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : MGT012-1 : TPTP v3.2.0. Released v2.4.0. *)
+
+(* Domain : Management (Organisation Theory) *)
+
+(* Problem : Complexity of an organization cannot get smaller by age *)
+
+(* Version : [PB+94] axioms. *)
+
+(* English : Complexity of an organization cannot get smaller by age in *)
+
+(* lack of reorganization. *)
+
+(* Refs : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing *)
+
+(* : [Kam94] Kamps (1994), Email to G. Sutcliffe *)
+
+(* : [Kam95] Kamps (1995), Email to G. Sutcliffe *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.4.0 *)
+
+(* Syntax : Number of clauses : 14 ( 0 non-Horn; 7 unit; 14 RR) *)
+
+(* Number of atoms : 38 ( 2 equality) *)
+
+(* Maximal clause size : 10 ( 3 average) *)
+
+(* Number of predicates : 7 ( 0 propositional; 2-3 arity) *)
+
+(* Number of functors : 7 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 27 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : "Not published due to publication constraints." [Kam95]. *)
+
+(* : Created with tptp2X -f tptp -t clausify:otter MGT012+1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/NLP251-1".
+include "logic/equality.ma".
+
+(* Inclusion of: NLP251-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : NLP251-1 : TPTP v3.2.0. Released v2.4.0. *)
+
+(* Domain : Natural Language Processing *)
+
+(* Problem : Vincent believes that every man smokes, problem 32 *)
+
+(* Version : [Bos00b] axioms. *)
+
+(* English : Eliminating non-informative interpretations in the statement *)
+
+(* "Vincent believes that every man smokes. Jules is a man. *)
+
+(* Vincent believes that jules smokes." *)
+
+(* Refs : [Bos00a] Bos (2000), DORIS: Discourse Oriented Representation a *)
+
+(* [Bos00b] Bos (2000), Applied Theorem Proving - Natural Language *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.5.0, 0.40 v2.4.0 *)
+
+(* Syntax : Number of clauses : 95 ( 0 non-Horn; 18 unit; 92 RR) *)
+
+(* Number of atoms : 292 ( 3 equality) *)
+
+(* Maximal clause size : 41 ( 3 average) *)
+
+(* Number of predicates : 37 ( 0 propositional; 1-4 arity) *)
+
+(* Number of functors : 10 ( 8 constant; 0-1 arity) *)
+
+(* Number of variables : 227 ( 8 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Created from NLP251+1.p using FLOTTER *)
+
+(* -------------------------------------------------------------------------- *)
+theorem clause95:
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X10:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀X9:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀X9:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:accessible_world U V.∀_:think_believe_consider U W.∀_:present U W.∀_:event U W.∀_:theme U W V.∀_:vincent_forename U X.∀_:forename U X.∀_:agent U W Y.∀_:man U Y.∀_:of U X Y.∀_:state U Z.∀_:man U X1.∀_:be U Z X1 X1.∀_:forename U X2.∀_:jules_forename U X2.∀_:of U X2 X1.∀_:accessible_world U X3.∀_:proposition U X3.∀_:jules_forename U X4.∀_:forename U X4.∀_:smoke X3 X5.∀_:present X3 X5.∀_:agent X3 X5 X6.∀_:event X3 X5.∀_:man U X6.∀_:of U X4 X6.∀_:vincent_forename U X7.∀_:forename U X7.∀_:agent U X8 X9.∀_:man U X9.∀_:of U X7 X9.∀_:theme U X8 X3.∀_:event U X8.∀_:present U X8.∀_:think_believe_consider U X8.∀_:actual_world U.man V (skf4 V).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X10:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃X9:Univ.∃Y:Univ.∃Z:Univ.And (proposition U V) (And (accessible_world U V) (And (smoke V W) (And (present V W) (And (agent V W (skf4 V)) (And (event V W) (And (think_believe_consider U X) (And (present U X) (And (event U X) (And (theme U X V) (And (vincent_forename U Y) (And (forename U Y) (And (agent U X Z) (And (man U Z) (And (of U Y Z) (And (state U X1) (And (man U X2) (And (be U X1 X2 X2) (And (forename U X3) (And (jules_forename U X3) (And (of U X3 X2) (And (accessible_world U X4) (And (proposition U X4) (And (jules_forename U X5) (And (forename U X5) (And (smoke X4 X6) (And (present X4 X6) (And (agent X4 X6 X7) (And (event X4 X6) (And (man U X7) (And (of U X5 X7) (And (vincent_forename U X8) (And (forename U X8) (And (agent U X9 X10) (And (man U X10) (And (of U X8 X10) (And (theme U X9 X4) (And (event U X9) (And (present U X9) (And (think_believe_consider U X9) (actual_world U))))))))))))))))))))))))))))))))))))))))
+.
+intros.
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/NLP252-1".
+include "logic/equality.ma".
+
+(* Inclusion of: NLP252-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : NLP252-1 : TPTP v3.2.0. Released v2.4.0. *)
+
+(* Domain : Natural Language Processing *)
+
+(* Problem : Vincent believes that every man smokes, problem 33 *)
+
+(* Version : [Bos00b] axioms. *)
+
+(* English : Eliminating non-informative interpretations in the statement *)
+
+(* "Vincent believes that every man smokes. Jules is a man. *)
+
+(* Vincent believes that jules smokes." *)
+
+(* Refs : [Bos00a] Bos (2000), DORIS: Discourse Oriented Representation a *)
+
+(* [Bos00b] Bos (2000), Applied Theorem Proving - Natural Language *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.5.0, 0.40 v2.4.0 *)
+
+(* Syntax : Number of clauses : 95 ( 0 non-Horn; 18 unit; 92 RR) *)
+
+(* Number of atoms : 284 ( 3 equality) *)
+
+(* Maximal clause size : 37 ( 3 average) *)
+
+(* Number of predicates : 37 ( 0 propositional; 1-4 arity) *)
+
+(* Number of functors : 10 ( 8 constant; 0-1 arity) *)
+
+(* Number of variables : 223 ( 8 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Created from NLP252+1.p using FLOTTER *)
+
+(* -------------------------------------------------------------------------- *)
+theorem clause95:
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀Y:Univ.∀Z:Univ.∀_:accessible_world U V.∀_:proposition U V.∀_:theme U W V.∀_:event U W.∀_:present U W.∀_:think_believe_consider U W.∀_:forename U X.∀_:vincent_forename U X.∀_:of U X Y.∀_:man U Y.∀_:agent U W Y.∀_:state U Z.∀_:smoke X1 X2.∀_:present X1 X2.∀_:agent X1 X2 X3.∀_:event X1 X2.∀_:be U Z X3 X3.∀_:man U X3.∀_:of U X4 X3.∀_:jules_forename U X4.∀_:forename U X4.∀_:proposition U X1.∀_:accessible_world U X1.∀_:think_believe_consider U X5.∀_:present U X5.∀_:event U X5.∀_:theme U X5 X1.∀_:vincent_forename U X6.∀_:forename U X6.∀_:agent U X5 X7.∀_:man U X7.∀_:of U X6 X7.∀_:actual_world U.man V (skf4 V).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃Y:Univ.∃Z:Univ.And (smoke U V) (And (present U V) (And (agent U V (skf4 U)) (And (event U V) (And (accessible_world W U) (And (proposition W U) (And (theme W X U) (And (event W X) (And (present W X) (And (think_believe_consider W X) (And (forename W Y) (And (vincent_forename W Y) (And (of W Y Z) (And (man W Z) (And (agent W X Z) (And (state W X1) (And (smoke X2 X3) (And (present X2 X3) (And (agent X2 X3 X4) (And (event X2 X3) (And (be W X1 X4 X4) (And (man W X4) (And (of W X5 X4) (And (jules_forename W X5) (And (forename W X5) (And (proposition W X2) (And (accessible_world W X2) (And (think_believe_consider W X6) (And (present W X6) (And (event W X6) (And (theme W X6 X2) (And (vincent_forename W X7) (And (forename W X7) (And (agent W X6 X8) (And (man W X8) (And (of W X7 X8) (actual_world W))))))))))))))))))))))))))))))))))))
+.
+intros.
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/NLP257-1".
+include "logic/equality.ma".
+
+(* Inclusion of: NLP257-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : NLP257-1 : TPTP v3.2.0. Released v2.4.0. *)
+
+(* Domain : Natural Language Processing *)
+
+(* Problem : Vincent believes that every man smokes, problem 38 *)
+
+(* Version : [Bos00b] axioms. *)
+
+(* English : Eliminating non-informative interpretations in the statement *)
+
+(* "Vincent believes that every man smokes. Jules is a man. *)
+
+(* Vincent believes that jules smokes." *)
+
+(* Refs : [Bos00a] Bos (2000), DORIS: Discourse Oriented Representation a *)
+
+(* [Bos00b] Bos (2000), Applied Theorem Proving - Natural Language *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.5.0, 0.40 v2.4.0 *)
+
+(* Syntax : Number of clauses : 95 ( 0 non-Horn; 18 unit; 92 RR) *)
+
+(* Number of atoms : 284 ( 3 equality) *)
+
+(* Maximal clause size : 37 ( 3 average) *)
+
+(* Number of predicates : 37 ( 0 propositional; 1-4 arity) *)
+
+(* Number of functors : 10 ( 8 constant; 0-1 arity) *)
+
+(* Number of variables : 223 ( 8 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Created from NLP257+1.p using FLOTTER *)
+
+(* -------------------------------------------------------------------------- *)
+theorem clause95:
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀X8:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀X7:Univ.∀Y:Univ.∀Z:Univ.∀_:state U V.∀_:be U V W W.∀_:man U W.∀_:of U X W.∀_:jules_forename U X.∀_:forename U X.∀_:jules_forename U Y.∀_:forename U Y.∀_:smoke Z X1.∀_:present Z X1.∀_:agent Z X1 X2.∀_:event Z X1.∀_:man U X2.∀_:of U Y X2.∀_:proposition U Z.∀_:accessible_world U Z.∀_:accessible_world U X3.∀_:proposition U X3.∀_:theme U X4 X3.∀_:event U X4.∀_:present U X4.∀_:think_believe_consider U X4.∀_:man U X5.∀_:agent U X4 X5.∀_:agent U X6 X5.∀_:forename U X7.∀_:vincent_forename U X7.∀_:of U X7 X5.∀_:think_believe_consider U X6.∀_:present U X6.∀_:event U X6.∀_:theme U X6 Z.∀_:actual_world U.man X3 (skf4 X3).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃X7:Univ.∃X8:Univ.∃Y:Univ.∃Z:Univ.And (state U V) (And (be U V W W) (And (man U W) (And (of U X W) (And (jules_forename U X) (And (forename U X) (And (jules_forename U Y) (And (forename U Y) (And (smoke Z X1) (And (present Z X1) (And (agent Z X1 X2) (And (event Z X1) (And (man U X2) (And (of U Y X2) (And (proposition U Z) (And (accessible_world U Z) (And (smoke X3 X4) (And (present X3 X4) (And (agent X3 X4 (skf4 X3)) (And (event X3 X4) (And (accessible_world U X3) (And (proposition U X3) (And (theme U X5 X3) (And (event U X5) (And (present U X5) (And (think_believe_consider U X5) (And (man U X6) (And (agent U X5 X6) (And (agent U X7 X6) (And (forename U X8) (And (vincent_forename U X8) (And (of U X8 X6) (And (think_believe_consider U X7) (And (present U X7) (And (event U X7) (And (theme U X7 Z) (actual_world U))))))))))))))))))))))))))))))))))))
+.
+intros.
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/NLP258-1".
+include "logic/equality.ma".
+
+(* Inclusion of: NLP258-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : NLP258-1 : TPTP v3.2.0. Released v2.4.0. *)
+
+(* Domain : Natural Language Processing *)
+
+(* Problem : Vincent believes that every man smokes, problem 39 *)
+
+(* Version : [Bos00b] axioms. *)
+
+(* English : Eliminating non-informative interpretations in the statement *)
+
+(* "Vincent believes that every man smokes. Jules is a man. *)
+
+(* Vincent believes that jules smokes." *)
+
+(* Refs : [Bos00a] Bos (2000), DORIS: Discourse Oriented Representation a *)
+
+(* [Bos00b] Bos (2000), Applied Theorem Proving - Natural Language *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.5.0, 0.40 v2.4.0 *)
+
+(* Syntax : Number of clauses : 95 ( 0 non-Horn; 18 unit; 92 RR) *)
+
+(* Number of atoms : 276 ( 3 equality) *)
+
+(* Maximal clause size : 33 ( 3 average) *)
+
+(* Number of predicates : 37 ( 0 propositional; 1-4 arity) *)
+
+(* Number of functors : 10 ( 8 constant; 0-1 arity) *)
+
+(* Number of variables : 219 ( 8 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Created from NLP258+1.p using FLOTTER *)
+
+(* -------------------------------------------------------------------------- *)
+theorem clause95:
+ ∀Univ:Set.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀X6:Univ.∀Y:Univ.∀Z:Univ.∀abstraction:∀_:Univ.∀_:Univ.Prop.∀accessible_world:∀_:Univ.∀_:Univ.Prop.∀actual_world:∀_:Univ.Prop.∀agent:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀animate:∀_:Univ.∀_:Univ.Prop.∀be:∀_:Univ.∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀entity:∀_:Univ.∀_:Univ.Prop.∀event:∀_:Univ.∀_:Univ.Prop.∀eventuality:∀_:Univ.∀_:Univ.Prop.∀existent:∀_:Univ.∀_:Univ.Prop.∀forename:∀_:Univ.∀_:Univ.Prop.∀general:∀_:Univ.∀_:Univ.Prop.∀human:∀_:Univ.∀_:Univ.Prop.∀human_person:∀_:Univ.∀_:Univ.Prop.∀impartial:∀_:Univ.∀_:Univ.Prop.∀jules_forename:∀_:Univ.∀_:Univ.Prop.∀living:∀_:Univ.∀_:Univ.Prop.∀male:∀_:Univ.∀_:Univ.Prop.∀man:∀_:Univ.∀_:Univ.Prop.∀nonexistent:∀_:Univ.∀_:Univ.Prop.∀nonhuman:∀_:Univ.∀_:Univ.Prop.∀of:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀organism:∀_:Univ.∀_:Univ.Prop.∀present:∀_:Univ.∀_:Univ.Prop.∀proposition:∀_:Univ.∀_:Univ.Prop.∀relation:∀_:Univ.∀_:Univ.Prop.∀relname:∀_:Univ.∀_:Univ.Prop.∀singleton:∀_:Univ.∀_:Univ.Prop.∀skc10:Univ.∀skc11:Univ.∀skc12:Univ.∀skc13:Univ.∀skc14:Univ.∀skc15:Univ.∀skc8:Univ.∀skc9:Univ.∀skf2:∀_:Univ.Univ.∀skf4:∀_:Univ.Univ.∀smoke:∀_:Univ.∀_:Univ.Prop.∀specific:∀_:Univ.∀_:Univ.Prop.∀state:∀_:Univ.∀_:Univ.Prop.∀theme:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀thing:∀_:Univ.∀_:Univ.Prop.∀think_believe_consider:∀_:Univ.∀_:Univ.Prop.∀unisex:∀_:Univ.∀_:Univ.Prop.∀vincent_forename:∀_:Univ.∀_:Univ.Prop.∀H0:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀X1:Univ.∀X2:Univ.∀X3:Univ.∀X4:Univ.∀X5:Univ.∀Y:Univ.∀Z:Univ.∀_:state U V.∀_:man U W.∀_:be U V W W.∀_:smoke X Y.∀_:present X Y.∀_:agent X Y W.∀_:event X Y.∀_:forename U Z.∀_:jules_forename U Z.∀_:of U Z W.∀_:accessible_world U X.∀_:proposition U X.∀_:proposition U X1.∀_:accessible_world U X1.∀_:think_believe_consider U X2.∀_:present U X2.∀_:event U X2.∀_:theme U X2 X1.∀_:agent U X3 X4.∀_:agent U X2 X4.∀_:man U X4.∀_:of U X5 X4.∀_:vincent_forename U X5.∀_:forename U X5.∀_:theme U X3 X.∀_:event U X3.∀_:present U X3.∀_:think_believe_consider U X3.∀_:actual_world U.man X1 (skf4 X1).∀H1:∀U:Univ.∀_:man skc12 U.agent skc12 (skf2 U) U.∀H2:∀U:Univ.∀V:Univ.∀_:man skc12 U.event skc12 (skf2 V).∀H3:∀U:Univ.∀V:Univ.∀_:man skc12 U.present skc12 (skf2 V).∀H4:∀U:Univ.∀V:Univ.∀_:man skc12 U.smoke skc12 (skf2 V).∀H5:be skc8 skc9 skc10 skc10.∀H6:of skc8 skc11 skc10.∀H7:theme skc8 skc13 skc12.∀H8:agent skc8 skc13 skc15.∀H9:of skc8 skc14 skc15.∀H10:proposition skc8 skc12.∀H11:accessible_world skc8 skc12.∀H12:state skc8 skc9.∀H13:man skc8 skc10.∀H14:forename skc8 skc11.∀H15:jules_forename skc8 skc11.∀H16:think_believe_consider skc8 skc13.∀H17:present skc8 skc13.∀H18:event skc8 skc13.∀H19:vincent_forename skc8 skc14.∀H20:forename skc8 skc14.∀H21:man skc8 skc15.∀H22:actual_world skc8.∀H23:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:proposition U V.∀_:proposition U W.∀_:theme U X V.∀_:think_believe_consider U X.∀_:think_believe_consider U Y.∀_:theme U Y W.∀_:agent U Y Z.∀_:agent U X Z.eq Univ V W.∀H24:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:forename U V.∀_:of U W X.∀_:forename U W.∀_:of U V X.∀_:entity U X.eq Univ W V.∀H25:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀_:accessible_world U V.∀_:be U W X Y.be V W X Y.∀H26:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:of U W X.of V W X.∀H27:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:theme U W X.theme V W X.∀H28:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:accessible_world U V.∀_:agent U W X.agent V W X.∀H29:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:jules_forename U W.jules_forename V W.∀H30:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:vincent_forename U W.vincent_forename V W.∀H31:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relname U W.relname V W.∀H32:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:forename U W.forename V W.∀H33:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:male U W.male V W.∀H34:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:animate U W.animate V W.∀H35:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human U W.human V W.∀H36:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:living U W.living V W.∀H37:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:impartial U W.impartial V W.∀H38:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:existent U W.existent V W.∀H39:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:entity U W.entity V W.∀H40:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:organism U W.organism V W.∀H41:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:human_person U W.human_person V W.∀H42:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:man U W.man V W.∀H43:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:state U W.state V W.∀H44:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:general U W.general V W.∀H45:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonhuman U W.nonhuman V W.∀H46:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:abstraction U W.abstraction V W.∀H47:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:relation U W.relation V W.∀H48:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:proposition U W.proposition V W.∀H49:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:think_believe_consider U W.think_believe_consider V W.∀H50:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:present U W.present V W.∀H51:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:unisex U W.unisex V W.∀H52:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:nonexistent U W.nonexistent V W.∀H53:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:specific U W.specific V W.∀H54:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:singleton U W.singleton V W.∀H55:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:thing U W.thing V W.∀H56:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:eventuality U W.eventuality V W.∀H57:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:event U W.event V W.∀H58:∀U:Univ.∀V:Univ.∀W:Univ.∀_:accessible_world U V.∀_:smoke U W.smoke V W.∀H59:∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀_:be U V W X.eq Univ W X.∀H60:∀U:Univ.∀V:Univ.∀_:nonexistent U V.existent U V.∀H61:∀U:Univ.∀V:Univ.∀_:human U V.nonhuman U V.∀H62:∀U:Univ.∀V:Univ.∀_:general U V.specific U V.∀H63:∀U:Univ.∀V:Univ.∀_:male U V.unisex U V.∀H64:∀U:Univ.∀V:Univ.∀_:jules_forename U V.forename U V.∀H65:∀U:Univ.∀V:Univ.∀_:vincent_forename U V.forename U V.∀H66:∀U:Univ.∀V:Univ.∀_:relname U V.relation U V.∀H67:∀U:Univ.∀V:Univ.∀_:forename U V.relname U V.∀H68:∀U:Univ.∀V:Univ.∀_:man U V.male U V.∀H69:∀U:Univ.∀V:Univ.∀_:human_person U V.animate U V.∀H70:∀U:Univ.∀V:Univ.∀_:human_person U V.human U V.∀H71:∀U:Univ.∀V:Univ.∀_:organism U V.living U V.∀H72:∀U:Univ.∀V:Univ.∀_:organism U V.impartial U V.∀H73:∀U:Univ.∀V:Univ.∀_:entity U V.existent U V.∀H74:∀U:Univ.∀V:Univ.∀_:entity U V.specific U V.∀H75:∀U:Univ.∀V:Univ.∀_:entity U V.thing U V.∀H76:∀U:Univ.∀V:Univ.∀_:organism U V.entity U V.∀H77:∀U:Univ.∀V:Univ.∀_:human_person U V.organism U V.∀H78:∀U:Univ.∀V:Univ.∀_:man U V.human_person U V.∀H79:∀U:Univ.∀V:Univ.∀_:state U V.event U V.∀H80:∀U:Univ.∀V:Univ.∀_:state U V.eventuality U V.∀H81:∀U:Univ.∀V:Univ.∀_:abstraction U V.unisex U V.∀H82:∀U:Univ.∀V:Univ.∀_:abstraction U V.general U V.∀H83:∀U:Univ.∀V:Univ.∀_:abstraction U V.nonhuman U V.∀H84:∀U:Univ.∀V:Univ.∀_:abstraction U V.thing U V.∀H85:∀U:Univ.∀V:Univ.∀_:relation U V.abstraction U V.∀H86:∀U:Univ.∀V:Univ.∀_:proposition U V.relation U V.∀H87:∀U:Univ.∀V:Univ.∀_:eventuality U V.unisex U V.∀H88:∀U:Univ.∀V:Univ.∀_:eventuality U V.nonexistent U V.∀H89:∀U:Univ.∀V:Univ.∀_:eventuality U V.specific U V.∀H90:∀U:Univ.∀V:Univ.∀_:thing U V.singleton U V.∀H91:∀U:Univ.∀V:Univ.∀_:eventuality U V.thing U V.∀H92:∀U:Univ.∀V:Univ.∀_:event U V.eventuality U V.∀H93:∀U:Univ.∀V:Univ.∀_:smoke U V.event U V.∃U:Univ.∃V:Univ.∃W:Univ.∃X:Univ.∃X1:Univ.∃X2:Univ.∃X3:Univ.∃X4:Univ.∃X5:Univ.∃X6:Univ.∃Y:Univ.∃Z:Univ.And (state U V) (And (man U W) (And (be U V W W) (And (smoke X Y) (And (present X Y) (And (agent X Y W) (And (event X Y) (And (forename U Z) (And (jules_forename U Z) (And (of U Z W) (And (accessible_world U X) (And (proposition U X) (And (proposition U X1) (And (accessible_world U X1) (And (smoke X1 X2) (And (present X1 X2) (And (agent X1 X2 (skf4 X1)) (And (event X1 X2) (And (think_believe_consider U X3) (And (present U X3) (And (event U X3) (And (theme U X3 X1) (And (agent U X4 X5) (And (agent U X3 X5) (And (man U X5) (And (of U X6 X5) (And (vincent_forename U X6) (And (forename U X6) (And (theme U X4 X) (And (event U X4) (And (present U X4) (And (think_believe_consider U X4) (actual_world U))))))))))))))))))))))))))))))))
+.
+intros.
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/NUM017-2".
+include "logic/equality.ma".
+
+(* Inclusion of: NUM017-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : NUM017-2 : TPTP v3.2.0. Bugfixed v1.2.1. *)
+
+(* Domain : Number Theory *)
+
+(* Problem : Square root of this prime is irrational *)
+
+(* Version : [Rob63] axioms : Incomplete > Augmented > Complete. *)
+
+(* English : If a is prime, and a is not b^2/c^2, then the square root *)
+
+(* of a is irrational. *)
+
+(* Refs : [Rob63] Robinson (1963), Theorem Proving on the Computer *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v3.1.0, 0.22 v2.7.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.2.1, 0.38 v2.2.0, 0.50 v2.1.0, 0.33 v2.0.0 *)
+
+(* Syntax : Number of clauses : 15 ( 0 non-Horn; 5 unit; 14 RR) *)
+
+(* Number of atoms : 34 ( 2 equality) *)
+
+(* Maximal clause size : 4 ( 2 average) *)
+
+(* Number of predicates : 4 ( 0 propositional; 1-3 arity) *)
+
+(* Number of functors : 7 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 37 ( 1 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : *)
+
+(* Bugfixes : v1.2.1 - Clause primes_lemma1 fixed. *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_there_is_no_common_divisor:
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀a:Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀divides:∀_:Univ.∀_:Univ.Prop.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀prime:∀_:Univ.Prop.∀product:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀second_divided_by_1st:∀_:Univ.∀_:Univ.Univ.∀H0:product a e d.∀H1:product c c e.∀H2:product b b d.∀H3:prime a.∀H4:∀A:Univ.∀B:Univ.∀C:Univ.∀_:divides A B.∀_:product C C B.∀_:prime A.divides A C.∀H5:∀A:Univ.∀B:Univ.∀C:Univ.∀_:product A B C.divides A C.∀H6:∀A:Univ.∀B:Univ.∀_:divides A B.product A (second_divided_by_1st A B) B.∀H7:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀_:product A B C.∀_:product A B D.eq Univ D C.∀H8:∀A:Univ.∀B:Univ.∀C:Univ.∀_:divides A B.∀_:divides C A.divides C B.∀H9:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀_:product A B C.∀_:product A D C.eq Univ B D.∀H10:∀A:Univ.∀B:Univ.∀C:Univ.∀_:product A B C.product B A C.∀H11:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀_:product A B C.∀_:product D B E.∀_:product F D A.product F E C.∀H12:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀_:product A B C.∀_:product D E B.∀_:product A D F.product F E C.∀H13:∀A:Univ.∀B:Univ.product A B (multiply A B).∃A:Univ.And (divides A c) (divides A b)
+.
+intros.
+exists[
+2:
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /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.∀_:eq Univ (negate (add X Y)) (negate Y).∀_:positive_integer V2.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 paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ROB014-1".
+include "logic/equality.ma".
+
+(* Inclusion of: ROB014-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ROB014-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Robbins Algebra *)
+
+(* Problem : If -(-e + -(d + -e)) = d then -(e + k(d + -(d + -e))) = -e, k=1 *)
+
+(* Version : [Win90] (equality) axioms. *)
+
+(* English : This is the base step of an induction proof. *)
+
+(* Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(* Source : [Win90] *)
+
+(* Names : Lemma 3.6 [Win90] *)
+
+(* 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 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 4 RR) *)
+
+(* Number of atoms : 11 ( 7 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 11 ( 0 singleton) *)
+
+(* Maximal term depth : 8 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----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 numbers in Robbins algebras *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_base_step:
+ ∀Univ:Set.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀d:Univ.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (negate (add (negate e) (negate (add d (negate e))))) d.∀H1:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H2:positive_integer one.∀H3:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H4:∀X:Univ.eq Univ (multiply one X) X.∀H5:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add e (multiply one (add d (negate (add d (negate e))))))) (negate e)
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/ROB018-1".
+include "logic/equality.ma".
+
+(* Inclusion of: ROB018-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ROB018-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Robbins Algebra *)
+
+(* Problem : If -(d + e) = -e then e + 2(d + -(d + -e)) absorbs d + -(d + -e) *)
+
+(* Version : [Win90] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(* Source : [Win90] *)
+
+(* Names : Corollary 3.9 [Win90] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.57 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.86 v2.5.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 4 RR) *)
+
+(* Number of atoms : 11 ( 7 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 7 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 11 ( 0 singleton) *)
+
+(* Maximal term depth : 7 ( 3 average) *)
+
+(* Comments : This could be done with the second part, together *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----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 numbers in Robbins algebras *)
+
+(* 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_result:
+ ∀Univ:Set.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀d:Univ.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (negate (add d (negate e))) (negate e).∀H1:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H2:positive_integer one.∀H3:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H4:∀X:Univ.eq Univ (multiply one X) X.∀H5:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add e (multiply (successor (successor one)) (add d (negate (add d (negate e)))))) (add e (multiply (successor one) (add d (negate (add d (negate e))))))
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
--- /dev/null
+set "baseuri" "cic:/matita/TPTP/SWV251-2".
+include "logic/equality.ma".
+
+(* Inclusion of: SWV251-2.p *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* File : SWV251-2 : TPTP v3.2.0. Released v3.2.0. *)
+
+(* Domain : Software Verification *)
+
+(* Problem : Cryptographic protocol problem for messages *)
+
+(* Version : [Pau06] axioms : Reduced > Especial. *)
+
+(* English : *)
+
+(* Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe *)
+
+(* Source : [Pau06] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0 *)
+
+(* Syntax : Number of clauses : 13 ( 0 non-Horn; 6 unit; 9 RR) *)
+
+(* Number of atoms : 23 ( 4 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 3 ( 0 propositional; 2-3 arity) *)
+
+(* Number of functors : 11 ( 5 constant; 0-3 arity) *)
+
+(* Number of variables : 60 ( 47 singleton) *)
+
+(* Maximal term depth : 5 ( 2 average) *)
+
+(* Comments : The problems in the [Pau06] collection each have very many axioms, *)
+
+(* of which only a small selection are required for the refutation. *)
+
+(* The mission is to find those few axioms, after which a refutation *)
+
+(* can be quite easily found. This version has only the necessary *)
+
+(* axioms. *)
+
+(* ------------------------------------------------------------------------------ *)
+theorem cls_conjecture_2:
+ ∀Univ:Set.∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀V_G:Univ.∀V_H:Univ.∀V_c:Univ.∀V_x:Univ.∀c_Message_Oanalz:∀_:Univ.Univ.∀c_Message_Osynth:∀_:Univ.Univ.∀c_in:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_insert:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c_lessequals:∀_:Univ.∀_:Univ.∀_:Univ.Prop.∀c_minus:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀c_union:∀_:Univ.∀_:Univ.∀_:Univ.Univ.∀tc_Message_Omsg:Univ.∀tc_set:∀_:Univ.Univ.∀v_G:Univ.∀v_H:Univ.∀v_X:Univ.∀v_x:Univ.∀H0:c_in v_x (c_Message_Oanalz (c_insert v_X v_H tc_Message_Omsg)) tc_Message_Omsg.∀H1:c_in v_X (c_Message_Osynth (c_Message_Oanalz v_G)) tc_Message_Omsg.∀H2:∀T_a:Univ.∀V_A:Univ.c_lessequals V_A V_A (tc_set T_a).∀H3:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀_:c_lessequals V_B V_A (tc_set T_a).∀_:c_lessequals V_A V_B (tc_set T_a).eq Univ V_A V_B.∀H4:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_c:Univ.∀_:c_in V_c V_A T_a.∀_:c_lessequals V_A V_B (tc_set T_a).c_in V_c V_B T_a.∀H5:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_x:Univ.∀_:c_in V_x V_B T_a.eq Univ (c_minus (c_insert V_x V_A T_a) V_B (tc_set T_a)) (c_minus V_A V_B (tc_set T_a)).∀H6:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals V_B V_C (tc_set T_a).∀_:c_lessequals V_A V_C (tc_set T_a).c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).∀H7:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).c_lessequals V_B V_C (tc_set T_a).∀H8:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.∀V_C:Univ.∀_:c_lessequals (c_union V_A V_B T_a) V_C (tc_set T_a).c_lessequals V_A V_C (tc_set T_a).∀H9:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.eq Univ (c_union V_A (c_minus V_B V_A (tc_set T_a)) T_a) (c_union V_A V_B T_a).∀H10:∀T_a:Univ.∀V_A:Univ.∀V_B:Univ.eq Univ (c_union (c_minus V_B V_A (tc_set T_a)) V_A T_a) (c_union V_B V_A T_a).∀H11:∀V_G:Univ.∀V_H:Univ.∀_:c_lessequals V_G V_H (tc_set tc_Message_Omsg).c_lessequals (c_Message_Oanalz V_G) (c_Message_Oanalz V_H) (tc_set tc_Message_Omsg).c_in v_x (c_Message_Oanalz (c_union (c_Message_Osynth (c_Message_Oanalz v_G)) v_H tc_Message_Omsg)) tc_Message_Omsg
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* ------------------------------------------------------------------------------ *)
--- /dev/null
+include ../Makefile.defs
+
+DIR=$(shell basename $$PWD)
+
+$(DIR) all:
+ $(BIN)matitac
+$(DIR).opt opt all.opt:
+ $(BIN)matitac.opt
+clean:
+ $(BIN)matitaclean
+clean.opt:
+ $(BIN)matitaclean.opt
+depend:
+ $(BIN)matitadep
+depend.opt:
+ $(BIN)matitadep.opt
--- /dev/null
+HEQ/LCL224-3.ma logic/equality.ma
+HEQ/LCL281-3.ma logic/equality.ma
+HEQ/LCL195-3.ma logic/equality.ma
+HEQ/LCL319-3.ma logic/equality.ma
+HEQ/LCL314-3.ma logic/equality.ma
+HEQ/HWC003-1.ma logic/equality.ma
+HEQ/LCL218-3.ma logic/equality.ma
+HEQ/LCL275-3.ma logic/equality.ma
+HEQ/LCL213-3.ma logic/equality.ma
+HEQ/LCL270-3.ma logic/equality.ma
+HEQ/LCL174-3.ma logic/equality.ma
+HEQ/LCL308-3.ma logic/equality.ma
+HEQ/LCL269-3.ma logic/equality.ma
+HEQ/LCL303-3.ma logic/equality.ma
+HEQ/LCL264-3.ma logic/equality.ma
+HEQ/COL003-6.ma logic/equality.ma
+HEQ/COL006-4.ma logic/equality.ma
+HEQ/LCL253-3.ma logic/equality.ma
+HEQ/LCL348-3.ma logic/equality.ma
+HEQ/HWV004-1.ma logic/equality.ma
+HEQ/LCL247-3.ma logic/equality.ma
+HEQ/ANA004-1.ma logic/equality.ma
+HEQ/LCL150-1.ma logic/equality.ma
+HEQ/LCL242-3.ma logic/equality.ma
+HEQ/LCL337-3.ma logic/equality.ma
+HEQ/COL042-5.ma logic/equality.ma
+HEQ/LCL298-3.ma logic/equality.ma
+HEQ/LCL332-3.ma logic/equality.ma
+HEQ/LCL149-1.ma logic/equality.ma
+HEQ/LCL293-3.ma logic/equality.ma
+HEQ/COL044-2.ma logic/equality.ma
+HEQ/LCL231-3.ma logic/equality.ma
+HEQ/LCL192-3.ma logic/equality.ma
+HEQ/LCL326-3.ma logic/equality.ma
+HEQ/LCL225-3.ma logic/equality.ma
+HEQ/ROB006-3.ma logic/equality.ma
+HEQ/LCL282-3.ma logic/equality.ma
+HEQ/LCL220-3.ma logic/equality.ma
+HEQ/LCL181-3.ma logic/equality.ma
+HEQ/ANA034-2.ma logic/equality.ma
+HEQ/LCL315-3.ma logic/equality.ma
+HEQ/LCL276-3.ma logic/equality.ma
+HEQ/LCL219-3.ma logic/equality.ma
+HEQ/LCL310-3.ma logic/equality.ma
+HEQ/LCL214-3.ma logic/equality.ma
+HEQ/LCL271-3.ma logic/equality.ma
+HEQ/LCL309-3.ma logic/equality.ma
+HEQ/LCL304-3.ma logic/equality.ma
+HEQ/LCL208-3.ma logic/equality.ma
+HEQ/LCL265-3.ma logic/equality.ma
+HEQ/LCL260-3.ma logic/equality.ma
+HEQ/COL003-5.ma logic/equality.ma
+HEQ/COL006-3.ma logic/equality.ma
+HEQ/LCL254-3.ma logic/equality.ma
+HEQ/LCL349-3.ma logic/equality.ma
+HEQ/LCL344-3.ma logic/equality.ma
+HEQ/ANA005-1.ma logic/equality.ma
+HEQ/LCL243-3.ma logic/equality.ma
+HEQ/LCL151-1.ma logic/equality.ma
+HEQ/COL042-4.ma logic/equality.ma
+HEQ/LCL299-3.ma logic/equality.ma
+HEQ/LCL237-3.ma logic/equality.ma
+HEQ/LCL193-3.ma logic/equality.ma
+HEQ/LCL327-3.ma logic/equality.ma
+HEQ/LCL226-3.ma logic/equality.ma
+HEQ/LCL283-3.ma logic/equality.ma
+HEQ/LCL221-3.ma logic/equality.ma
+HEQ/NLP251-1.ma logic/equality.ma
+HEQ/LCL182-3.ma logic/equality.ma
+HEQ/LCL316-3.ma logic/equality.ma
+HEQ/LCL277-3.ma logic/equality.ma
+HEQ/LCL311-3.ma logic/equality.ma
+HEQ/LCL215-3.ma logic/equality.ma
+HEQ/LCL272-3.ma logic/equality.ma
+HEQ/CAT018-4.ma logic/equality.ma
+HEQ/LAT001-1.ma logic/equality.ma
+HEQ/COL003-9.ma logic/equality.ma
+HEQ/LCL305-3.ma logic/equality.ma
+HEQ/LCL300-3.ma logic/equality.ma
+HEQ/LCL266-3.ma logic/equality.ma
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--- /dev/null
+baseuri=cic:/matita/TPTP
projects / helm.git / commitdiff