1 include "logic/equality.ma".
3 (* Inclusion of: BOO034-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO034-1 : TPTP v3.7.0. Released v2.2.0. *)
9 (* Domain : Boolean Algebra (Ternary) *)
11 (* Problem : Ternary Boolean Algebra Single axiom is sound. *)
13 (* Version : [MP96] (equality) axioms. *)
15 (* English : We show that that an equation (which turns out to be a single *)
17 (* axiom for TBA) can be derived from the axioms of TBA. *)
19 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
21 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
23 (* Source : [McC98] *)
25 (* Names : TBA-1-a [MP96] *)
27 (* Status : Unsatisfiable *)
29 (* Rating : 0.44 v3.4.0, 0.50 v3.3.0, 0.29 v3.2.0, 0.21 v3.1.0, 0.11 v2.7.0, 0.27 v2.6.0, 0.33 v2.5.0, 0.00 v2.2.1 *)
31 (* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR) *)
33 (* Number of atoms : 6 ( 6 equality) *)
35 (* Maximal clause size : 1 ( 1 average) *)
37 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
39 (* Number of functors : 9 ( 7 constant; 0-3 arity) *)
41 (* Number of variables : 13 ( 2 singleton) *)
43 (* Maximal term depth : 5 ( 2 average) *)
47 (* -------------------------------------------------------------------------- *)
49 (* ----Include ternary Boolean algebra axioms *)
51 (* Inclusion of: Axioms/BOO001-0.ax *)
53 (* -------------------------------------------------------------------------- *)
55 (* File : BOO001-0 : TPTP v3.7.0. Released v1.0.0. *)
57 (* Domain : Algebra (Ternary Boolean) *)
59 (* Axioms : Ternary Boolean algebra (equality) axioms *)
61 (* Version : [OTTER] (equality) axioms. *)
65 (* Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
67 (* : [Win82] Winker (1982), Generation and Verification of Finite M *)
69 (* Source : [OTTER] *)
75 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 0 RR) *)
77 (* Number of atoms : 5 ( 5 equality) *)
79 (* Maximal clause size : 1 ( 1 average) *)
81 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
83 (* Number of functors : 2 ( 0 constant; 1-3 arity) *)
85 (* Number of variables : 13 ( 2 singleton) *)
87 (* Maximal term depth : 3 ( 2 average) *)
89 (* Comments : These axioms appear in [Win82], in which ternary_multiply_1 is *)
91 (* shown to be independant. *)
93 (* : These axioms are also used in [Wos88], p.222. *)
95 (* -------------------------------------------------------------------------- *)
97 (* -------------------------------------------------------------------------- *)
99 (* -------------------------------------------------------------------------- *)
101 (* ----Denial of single axiom: *)
102 ntheorem prove_single_axiom:
103 (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
111 ∀inverse:∀_:Univ.Univ.
112 ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
113 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y (inverse Y)) X.
114 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
115 ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
116 ∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
117 ∀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 (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c)) b)
139 nauto by H0,H1,H2,H3,H4 ##;
140 ntry (nassumption) ##;
143 (* -------------------------------------------------------------------------- *)