X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLCL271-3.ma;fp=matitaB%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLCL271-3.ma;h=9f9b260f7a1ffcb5b5bd06d010ecfde4f7f5cdfb;hb=cacbe3c6493ddce76c4c13379ade271d8dd172e8;hp=0000000000000000000000000000000000000000;hpb=f04a064bb34aabaf91dc0c48e3b08b37ecd7b0a2;p=helm.git diff --git a/matitaB/matita/contribs/TPTP/HEQ/LCL271-3.ma b/matitaB/matita/contribs/TPTP/HEQ/LCL271-3.ma new file mode 100644 index 000000000..9f9b260f7 --- /dev/null +++ b/matitaB/matita/contribs/TPTP/HEQ/LCL271-3.ma @@ -0,0 +1,196 @@ +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 Y.∀_:theoremP (implies Y X).theoremP X.∀H3:∀X:Univ.∀_:axiomP X.theoremP X.∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H5:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H6:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H7:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H8:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H9:∀A:Univ.axiomP (implies (or A A) A).theoremP (equivalent p (myand p p)) +. +intros. +autobatch depth=5 width=5 size=20 timeout=10; +try assumption. +print proofterm. +qed. + +(* -------------------------------------------------------------------------- *)