X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLCL215-3.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLCL215-3.ma;h=bc00e9df389b0dd800bbc524320df2b1a0de33cc;hb=36326bac6e833046698176f50fdbb4517f6705a5;hp=0000000000000000000000000000000000000000;hpb=0910d4f494486273e3a22fbfbb2290b48f5786b7;p=helm.git diff --git a/helm/software/matita/contribs/TPTP/HEQ/LCL215-3.ma b/helm/software/matita/contribs/TPTP/HEQ/LCL215-3.ma new file mode 100644 index 000000000..bc00e9df3 --- /dev/null +++ b/helm/software/matita/contribs/TPTP/HEQ/LCL215-3.ma @@ -0,0 +1,112 @@ +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. + +(* -------------------------------------------------------------------------- *)