1 include "logic/equality.ma".
3 (* Inclusion of: BOO019-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO019-1 : TPTP v3.7.0. Released v1.2.0. *)
9 (* Domain : Boolean Algebra (Ternary) *)
11 (* Problem : Prove the independance of Ternary Boolean algebra axiom *)
13 (* Version : Especial. *)
17 (* Refs : [Win82] Winker (1982), Generation and Verification of Finite M *)
19 (* : [BCP94] Bourely et al. (1994), A Method for Building Models Au *)
21 (* : [Pel98] Peltier (1998), A New Method for Automated Finite Mode *)
23 (* Source : [BCP94] *)
25 (* Names : A1 [Win82] *)
27 (* : Example 4 [BCP94] *)
31 (* Status : Satisfiable *)
33 (* Rating : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.4.0, 0.67 v2.2.1, 0.75 v2.2.0, 0.67 v2.1.0, 1.00 v2.0.0 *)
35 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *)
37 (* Number of atoms : 5 ( 5 equality) *)
39 (* Maximal clause size : 1 ( 1 average) *)
41 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
43 (* Number of functors : 4 ( 2 constant; 0-3 arity) *)
45 (* Number of variables : 11 ( 1 singleton) *)
47 (* Maximal term depth : 3 ( 2 average) *)
49 (* Comments : Thought to be satisfiable. *)
51 (* -------------------------------------------------------------------------- *)
52 ntheorem prove_ternary_multiply_1_independant:
53 (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
54 ∀inverse:∀_:Univ.Univ.
55 ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
58 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y (inverse Y)) X.
59 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
60 ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
61 ∀H3:∀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 y x x) x)
77 nauto by H0,H1,H2,H3 ##;
78 ntry (nassumption) ##;
81 (* -------------------------------------------------------------------------- *)