1 include "logic/equality.ma".
3 (* Inclusion of: LDA001-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : LDA001-1 : TPTP v3.7.0. Released v1.0.0. *)
9 (* Domain : LD-Algebras *)
11 (* Problem : Verify 3*2*U = UUU, where U = 2*2 *)
13 (* Version : [Jec93] (equality) axioms. *)
17 (* Refs : [Jec93] Jech (1993), LD-Algebras *)
19 (* Source : [Jec93] *)
21 (* Names : Problem 1 [Jec93] *)
23 (* Status : Unsatisfiable *)
25 (* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
27 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 4 RR) *)
29 (* Number of atoms : 5 ( 5 equality) *)
31 (* Maximal clause size : 1 ( 1 average) *)
33 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
35 (* Number of functors : 5 ( 4 constant; 0-2 arity) *)
37 (* Number of variables : 3 ( 0 singleton) *)
39 (* Maximal term depth : 3 ( 2 average) *)
43 (* -------------------------------------------------------------------------- *)
45 (* ----A1: x(yz)=xy(xz) *)
47 (* ----3*2*U = U*U*U *)
48 ntheorem prove_equation:
49 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
50 ∀f:∀_:Univ.∀_:Univ.Univ.
55 ∀H0:eq Univ u (f n2 n2).
56 ∀H1:eq Univ n3 (f n2 n1).
57 ∀H2:eq Univ n2 (f n1 n1).
58 ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f (f n3 n2) u) (f (f u u) u))
73 nauto by H0,H1,H2,H3 ##;
74 ntry (nassumption) ##;
77 (* -------------------------------------------------------------------------- *)