some horn+equality problems

[helm.git] / helm / software / matita / contribs / TPTP / HEQ / CAT018-4.ma

diff --git a/helm/software/matita/contribs/TPTP/HEQ/CAT018-4.ma b/helm/software/matita/contribs/TPTP/HEQ/CAT018-4.ma
new file mode 100644 (file)
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+++ b/helm/software/matita/contribs/TPTP/HEQ/CAT018-4.ma
@@ -0,0 +1,122 @@
+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.
+
+(* -------------------------------------------------------------------------- *)