1 include "logic/equality.ma".
3 (* Inclusion of: BOO002-1.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO002-1 : TPTP v3.7.0. Released v1.0.0. *)
9 (* Domain : Boolean Algebra (Ternary) *)
11 (* Problem : In B3 algebra, X * X^-1 * Y = Y *)
13 (* Version : [OTTER] (equality) axioms : Reduced > Incomplete. *)
17 (* Refs : [LO85] Lusk & Overbeek (1985), Reasoning about Equality *)
19 (* : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 *)
21 (* : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal *)
23 (* : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11 *)
25 (* : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in *)
27 (* Source : [Ove90] *)
29 (* Names : Problem 5 [LO85] *)
31 (* : CADE-11 Competition Eq-3 [Ove90] *)
33 (* : THEOREM EQ-3 [LM93] *)
35 (* : PROBLEM 3 [Zha93] *)
37 (* Status : Unsatisfiable *)
39 (* Rating : 0.00 v3.3.0, 0.07 v3.1.0, 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 *)
41 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *)
43 (* Number of atoms : 5 ( 5 equality) *)
45 (* Maximal clause size : 1 ( 1 average) *)
47 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
49 (* Number of functors : 4 ( 2 constant; 0-3 arity) *)
51 (* Number of variables : 11 ( 2 singleton) *)
53 (* Maximal term depth : 3 ( 2 average) *)
57 (* -------------------------------------------------------------------------- *)
59 (* ----Don't include ternary Boolean algebra axioms, as one is omitted *)
61 (* include('axioms/BOO001-0.ax'). *)
63 (* -------------------------------------------------------------------------- *)
65 (* ----This axiom is omitted *)
67 (* input_clause(right_inverse,axiom, *)
69 (* [++equal(multiply(X,Y,inverse(Y)),X)]). *)
70 ntheorem prove_equation:
71 (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
74 ∀inverse:∀_:Univ.Univ.
75 ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
76 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
77 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
78 ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
79 ∀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 a (inverse a) b) b)
95 nauto by H0,H1,H2,H3 ##;
96 ntry (nassumption) ##;
99 (* -------------------------------------------------------------------------- *)