1 include "logic/equality.ma".
3 (* Inclusion of: BOO029-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO029-1 : TPTP v3.7.0. Released v2.2.0. *)
9 (* Domain : Boolean Algebra *)
11 (* Problem : Self-dual 2-basis from majority reduction, part 3. *)
13 (* Version : [MP96] (equality) axioms : Especial. *)
15 (* English : This is part of a proof that there exists an independent *)
17 (* self-dual-2-basis for Boolean algebra by majority reduction. *)
19 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
21 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
23 (* Source : [McC98] *)
25 (* Names : DUAL-BA-5-c [MP96] *)
27 (* Status : Unsatisfiable *)
29 (* Rating : 0.00 v2.2.1 *)
31 (* Syntax : Number of clauses : 11 ( 0 non-Horn; 11 unit; 1 RR) *)
33 (* Number of atoms : 11 ( 11 equality) *)
35 (* Maximal clause size : 1 ( 1 average) *)
37 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
39 (* Number of functors : 5 ( 2 constant; 0-2 arity) *)
41 (* Number of variables : 26 ( 8 singleton) *)
43 (* Maximal term depth : 4 ( 3 average) *)
47 (* -------------------------------------------------------------------------- *)
49 (* ----Properties L1, L3, and B1 of Boolean Algebra: *)
51 (* ----The corresponding dual properties L2, L4, and B2. *)
53 (* ----Associativity and Commutativity of both operations: *)
55 (* ----Denial of conclusion: *)
56 ntheorem prove_equal_inverse:
57 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
59 ∀add:∀_:Univ.∀_:Univ.Univ.
61 ∀inverse:∀_:Univ.Univ.
62 ∀multiply:∀_:Univ.∀_:Univ.Univ.
63 ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
64 ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
65 ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X).
66 ∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).
67 ∀H4:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X Y) (multiply X (inverse Y))) X.
68 ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply (add X Y) (add Y Z)) Y) Y.
69 ∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (add X Z))) X.
70 ∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) (add X (inverse Y))) X.
71 ∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y.
72 ∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (add b (inverse b)) (add a (inverse a)))
93 nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##;
94 ntry (nassumption) ##;
97 (* -------------------------------------------------------------------------- *)