1 include "logic/equality.ma".
3 (* Inclusion of: BOO005-4.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO005-4 : TPTP v3.7.0. Bugfixed v1.2.1. *)
9 (* Domain : Boolean Algebra *)
11 (* Problem : Addition is bounded (X + 1 = 1) *)
13 (* Version : [Ver94] (equality) axioms. *)
17 (* Refs : [Ver94] Veroff (1994), Problem Set *)
19 (* Source : [Ver94] *)
21 (* Names : TB [Ver94] *)
23 (* Status : Unsatisfiable *)
25 (* Rating : 0.00 v2.0.0 *)
27 (* Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 1 RR) *)
29 (* Number of atoms : 9 ( 9 equality) *)
31 (* Maximal clause size : 1 ( 1 average) *)
33 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
35 (* Number of functors : 6 ( 3 constant; 0-2 arity) *)
37 (* Number of variables : 14 ( 0 singleton) *)
39 (* Maximal term depth : 3 ( 2 average) *)
43 (* Bugfixes : v1.2.1 - Clause prove_a_plus_1_is_a fixed. *)
45 (* -------------------------------------------------------------------------- *)
47 (* ----Include boolean algebra axioms for equality formulation *)
49 (* Inclusion of: Axioms/BOO004-0.ax *)
51 (* -------------------------------------------------------------------------- *)
53 (* File : BOO004-0 : TPTP v3.7.0. Released v1.0.0. *)
55 (* Domain : Boolean Algebra *)
57 (* Axioms : Boolean algebra (equality) axioms *)
59 (* Version : [Ver94] (equality) axioms. *)
63 (* Refs : [Ver94] Veroff (1994), Problem Set *)
65 (* Source : [Ver94] *)
71 (* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
73 (* Number of atoms : 8 ( 8 equality) *)
75 (* Maximal clause size : 1 ( 1 average) *)
77 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
79 (* Number of functors : 5 ( 2 constant; 0-2 arity) *)
81 (* Number of variables : 14 ( 0 singleton) *)
83 (* Maximal term depth : 3 ( 2 average) *)
87 (* -------------------------------------------------------------------------- *)
89 (* -------------------------------------------------------------------------- *)
91 (* -------------------------------------------------------------------------- *)
92 ntheorem prove_a_plus_1_is_a:
93 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
95 ∀add:∀_:Univ.∀_:Univ.Univ.
96 ∀additive_identity:Univ.
97 ∀inverse:∀_:Univ.Univ.
98 ∀multiplicative_identity:Univ.
99 ∀multiply:∀_:Univ.∀_:Univ.Univ.
100 ∀H0:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
101 ∀H1:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
102 ∀H2:∀X:Univ.eq Univ (multiply X multiplicative_identity) X.
103 ∀H3:∀X:Univ.eq Univ (add X additive_identity) X.
104 ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
105 ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
106 ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X).
107 ∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity)
115 #additive_identity ##.
117 #multiplicative_identity ##.
127 nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##;
128 ntry (nassumption) ##;
131 (* -------------------------------------------------------------------------- *)