X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FCOL050-1.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FCOL050-1.p.ma;h=e8383c1b14ad4d2546880c330afe8cfd46f90687;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/COL050-1.p.ma b/matita/tests/TPTP/Veloci/COL050-1.p.ma new file mode 100644 index 000000000..e8383c1b1 --- /dev/null +++ b/matita/tests/TPTP/Veloci/COL050-1.p.ma @@ -0,0 +1,56 @@ + +include "logic/equality.ma". +(* Inclusion of: COL050-1.p *) +(* -------------------------------------------------------------------------- *) +(* File : COL050-1 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Combinatory Logic *) +(* Problem : The Significance of the Mockingbird *) +(* Version : Especial. *) +(* English : There exists a mocking bird. For all birds x and y, there *) +(* exists a bird z that composes x with y for all birds w. Prove *) +(* that every bird is fond of at least one other bird. *) +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) +(* Source : [ANL] *) +(* Names : bird1.ver1.in [ANL] *) +(* Status : Unsatisfiable *) +(* Rating : 0.00 v2.0.0 *) +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) +(* Number of atoms : 3 ( 3 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) +(* Number of variables : 5 ( 0 singleton) *) +(* Maximal term depth : 3 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ---- There exists a mocking bird (Mock). *) +(* ---- TEx FAy [response(x,y) = response(y,y)]. *) +(* ---- response(Mock,y) = response(y,y). *) +(* ---- For all birds x and y, there exists a bird z that composes *) +(* ---- x with y for all birds w. *) +(* ---- FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))] *) +(* ---- response(comp(x,y),w) = response(x,response(y,w)). *) +(* ---- Hypothesis: Every bird is fond of at least one other bird. *) +(* ---- -FAx TEy [response(x,y) = y]. *) +(* ---- TEx FAy -[response(x,y) = y]. *) +(* ---- Letting A = x, *) +(* ---- -[response(A,y) = y]. *) +theorem prove_all_fond_of_another: + \forall Univ:Set. +\forall a:Univ. +\forall compose:\forall _:Univ.\forall _:Univ.Univ. +\forall mocking_bird:Univ. +\forall response:\forall _:Univ.\forall _:Univ.Univ. +\forall H0:\forall W:Univ.\forall X:Univ.\forall Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)). +\forall H1:\forall Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).\exist Y:Univ.eq Univ (response a Y) Y +. +intros. +exists[ +2: +autobatch paramodulation timeout=100; +try assumption. +| +skip] +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)