2 include "logic/equality.ma".
3 (* Inclusion of: LDA007-3.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : LDA007-3 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : LD-Algebras (Embedding algebras) *)
7 (* Problem : Let g = cr(t). Show that t(tsg) = tt(ts)(tg) *)
8 (* Version : [Jec93] axioms : Incomplete > Reduced & Augmented > Incomplete. *)
10 (* Refs : [Jec93] Jech (1993), LD-Algebras *)
11 (* Source : [Jec93] *)
12 (* Names : Problem 8 [Jec93] *)
13 (* Status : Unsatisfiable *)
14 (* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *)
15 (* Syntax : Number of clauses : 7 ( 0 non-Horn; 7 unit; 6 RR) *)
16 (* Number of atoms : 7 ( 7 equality) *)
17 (* Maximal clause size : 1 ( 1 average) *)
18 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
19 (* Number of functors : 9 ( 8 constant; 0-2 arity) *)
20 (* Number of variables : 3 ( 0 singleton) *)
21 (* Maximal term depth : 3 ( 2 average) *)
23 (* -------------------------------------------------------------------------- *)
24 (* ----Include Embedding algebra axioms *)
25 (* include('Axioms/LDA001-0.ax'). *)
26 (* -------------------------------------------------------------------------- *)
27 (* ----t(tsk) = tt(ts)(tk), where k=crit(t) *)
28 theorem prove_equation:
30 \forall f:\forall _:Univ.\forall _:Univ.Univ.
39 \forall H0:eq Univ tsk (f ts k).
40 \forall H1:eq Univ tk (f t k).
41 \forall H2:eq Univ tt_ts (f tt ts).
42 \forall H3:eq Univ ts (f t s).
43 \forall H4:eq Univ tt (f t t).
44 \forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk)
47 autobatch paramodulation timeout=100;
51 (* -------------------------------------------------------------------------- *)