1 include "logic/equality.ma".
3 (* Inclusion of: BOO015-2.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : BOO015-2 : TPTP v3.7.0. Bugfixed v1.0.1. *)
9 (* Domain : Boolean Algebra *)
11 (* Problem : DeMorgan for inverse and sum (X^-1 + Y^-1) = (X * Y)^-1 *)
13 (* Version : [ANL] (equality) axioms. *)
21 (* Names : prob10.ver2.in [ANL] *)
23 (* Status : Unsatisfiable *)
25 (* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.62 v2.0.0 *)
27 (* Syntax : Number of clauses : 17 ( 0 non-Horn; 17 unit; 3 RR) *)
29 (* Number of atoms : 17 ( 17 equality) *)
31 (* Maximal clause size : 1 ( 1 average) *)
33 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
35 (* Number of functors : 9 ( 6 constant; 0-2 arity) *)
37 (* Number of variables : 24 ( 0 singleton) *)
39 (* Maximal term depth : 3 ( 2 average) *)
43 (* Bugfixes : v1.0.1 - Clause a_inverse_plus_b_inverse_is_d fixed. *)
45 (* -------------------------------------------------------------------------- *)
47 (* ----Include boolean algebra axioms for equality formulation *)
49 (* Inclusion of: Axioms/BOO003-0.ax *)
51 (* -------------------------------------------------------------------------- *)
53 (* File : BOO003-0 : TPTP v3.7.0. Released v1.0.0. *)
55 (* Domain : Boolean Algebra *)
57 (* Axioms : Boolean algebra (equality) axioms *)
59 (* Version : [ANL] (equality) axioms. *)
71 (* Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 0 RR) *)
73 (* Number of atoms : 14 ( 14 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 : 24 ( 0 singleton) *)
83 (* Maximal term depth : 3 ( 2 average) *)
87 (* -------------------------------------------------------------------------- *)
89 (* -------------------------------------------------------------------------- *)
91 (* -------------------------------------------------------------------------- *)
92 ntheorem prove_c_inverse_is_d:
93 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
95 ∀add:∀_:Univ.∀_:Univ.Univ.
96 ∀additive_identity:Univ.
100 ∀inverse:∀_:Univ.Univ.
101 ∀multiplicative_identity:Univ.
102 ∀multiply:∀_:Univ.∀_:Univ.Univ.
103 ∀H0:eq Univ (add (inverse a) (inverse b)) d.
104 ∀H1:eq Univ (multiply a b) c.
105 ∀H2:∀X:Univ.eq Univ (add additive_identity X) X.
106 ∀H3:∀X:Univ.eq Univ (add X additive_identity) X.
107 ∀H4:∀X:Univ.eq Univ (multiply multiplicative_identity X) X.
108 ∀H5:∀X:Univ.eq Univ (multiply X multiplicative_identity) X.
109 ∀H6:∀X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
110 ∀H7:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
111 ∀H8:∀X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
112 ∀H9:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
113 ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
114 ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
115 ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
116 ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
117 ∀H14:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X).
118 ∀H15:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse c) d)
126 #additive_identity ##.
131 #multiplicative_identity ##.
149 nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##;
150 ntry (nassumption) ##;
153 (* -------------------------------------------------------------------------- *)