2 include "logic/equality.ma".
3 (* Inclusion of: LDA001-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : LDA001-1 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : LD-Algebras *)
7 (* Problem : Verify 3*2*U = UUU, where U = 2*2 *)
8 (* Version : [Jec93] (equality) axioms. *)
10 (* Refs : [Jec93] Jech (1993), LD-Algebras *)
11 (* Source : [Jec93] *)
12 (* Names : Problem 1 [Jec93] *)
13 (* Status : Unsatisfiable *)
14 (* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
15 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 4 RR) *)
16 (* Number of atoms : 5 ( 5 equality) *)
17 (* Maximal clause size : 1 ( 1 average) *)
18 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
19 (* Number of functors : 5 ( 4 constant; 0-2 arity) *)
20 (* Number of variables : 3 ( 0 singleton) *)
21 (* Maximal term depth : 3 ( 2 average) *)
23 (* -------------------------------------------------------------------------- *)
24 (* ----A1: x(yz)=xy(xz) *)
25 (* ----3*2*U = U*U*U *)
26 theorem prove_equation:
28 \forall f:\forall _:Univ.\forall _:Univ.Univ.
33 \forall H0:eq Univ u (f n2 n2).
34 \forall H1:eq Univ n3 (f n2 n1).
35 \forall H2:eq Univ n2 (f n1 n1).
36 \forall H3:\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 (f n3 n2) u) (f (f u u) u)
39 autobatch paramodulation timeout=100;
43 (* -------------------------------------------------------------------------- *)