1 include "logic/equality.ma".
3 (* Inclusion of: BOO002-2.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO002-2 : TPTP v3.7.0. Released v1.1.0. *)
9 (* Domain : Boolean Algebra (Ternary) *)
11 (* Problem : In B3 algebra, X * X^-1 * Y = Y *)
13 (* Version : [OTTER] (equality) axioms : Reduced & Augmented > Incomplete. *)
17 (* Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
19 (* Source : [Wos88] *)
21 (* Names : Test Problem 13 [Wos88] *)
23 (* : Lemma for Axiom Independence [Wos88] *)
25 (* Status : Unsatisfiable *)
27 (* Rating : 0.00 v2.7.0, 0.09 v2.6.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.38 v2.0.0 *)
29 (* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR) *)
31 (* Number of atoms : 6 ( 6 equality) *)
33 (* Maximal clause size : 1 ( 1 average) *)
35 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
37 (* Number of functors : 4 ( 2 constant; 0-3 arity) *)
39 (* Number of variables : 13 ( 3 singleton) *)
41 (* Maximal term depth : 3 ( 2 average) *)
43 (* Comments : This version contains an extra lemma *)
45 (* -------------------------------------------------------------------------- *)
47 (* ----Don't include ternary Boolean algebra axioms, as one is omitted *)
49 (* include('axioms/BOO001-0.ax'). *)
51 (* -------------------------------------------------------------------------- *)
53 (* ----This axiom is omitted *)
55 (* input_clause(right_inverse,axiom, *)
57 (* [++equal(multiply(X,Y,inverse(Y)),X)]). *)
58 ntheorem prove_equation:
59 (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
62 ∀inverse:∀_:Univ.Univ.
63 ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
64 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y X) X.
65 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
66 ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
67 ∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
68 ∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b)
85 nauto by H0,H1,H2,H3,H4 ##;
86 ntry (nassumption) ##;
89 (* -------------------------------------------------------------------------- *)