1 include "logic/equality.ma".
3 (* Inclusion of: BOO023-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO023-1 : TPTP v3.7.0. Released v2.2.0. *)
9 (* Domain : Boolean Algebra *)
11 (* Problem : Half of Padmanabhan's 6-basis with Pixley, part 1. *)
13 (* Version : [MP96] (equality) axioms : Especial. *)
15 (* English : Part 1 (of 3) of the proof that half of Padmanaban's self-dual *)
17 (* independent 6-basis for Boolean Algebra, together with a Pixley *)
19 (* polynomial, is a basis for Boolean algebra. *)
21 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
23 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
25 (* Source : [McC98] *)
27 (* Names : DUAL-BA-2-a [MP96] *)
29 (* Status : Unsatisfiable *)
31 (* Rating : 0.44 v3.4.0, 0.50 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1 *)
33 (* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 1 RR) *)
35 (* Number of atoms : 8 ( 8 equality) *)
37 (* Maximal clause size : 1 ( 1 average) *)
39 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
41 (* Number of functors : 8 ( 4 constant; 0-3 arity) *)
43 (* Number of variables : 15 ( 2 singleton) *)
45 (* Maximal term depth : 5 ( 2 average) *)
49 (* -------------------------------------------------------------------------- *)
51 (* ----Half of Padmanabhan's self-dual independent 6-basis for Boolean Algebra: *)
53 (* ----pixley(X,Y,Z) is a Pixley polynomial: *)
55 (* ----Denial of conclusion: *)
56 ntheorem prove_add_multiply_property:
57 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
59 ∀add:∀_:Univ.∀_:Univ.Univ.
62 ∀inverse:∀_:Univ.Univ.
63 ∀multiply:∀_:Univ.∀_:Univ.Univ.
65 ∀pixley:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
66 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (pixley X Y X) X.
67 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (pixley X Y Y) X.
68 ∀H2:∀X:Univ.∀Y:Univ.eq Univ (pixley X X Y) Y.
69 ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (pixley X Y Z) (add (multiply X (inverse Y)) (add (multiply X Z) (multiply (inverse Y) Z))).
70 ∀H4:∀X:Univ.eq Univ (add X (inverse X)) n1.
71 ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).
72 ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (add a (multiply b c)) (multiply (add a b) (add a c)))
93 nauto by H0,H1,H2,H3,H4,H5,H6 ##;
94 ntry (nassumption) ##;
97 (* -------------------------------------------------------------------------- *)