2 include "logic/equality.ma".
3 (* Inclusion of: BOO011-2.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : BOO011-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
6 (* Domain : Boolean Algebra *)
7 (* Problem : Inverse of additive identity = Multiplicative identity *)
8 (* Version : [ANL] (equality) axioms. *)
9 (* English : The inverse of the additive identity is the multiplicative *)
13 (* Names : prob7.ver2.in [ANL] *)
14 (* Status : Unsatisfiable *)
15 (* Rating : 0.00 v2.0.0 *)
16 (* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 1 RR) *)
17 (* Number of atoms : 15 ( 15 equality) *)
18 (* Maximal clause size : 1 ( 1 average) *)
19 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
20 (* Number of functors : 5 ( 2 constant; 0-2 arity) *)
21 (* Number of variables : 24 ( 0 singleton) *)
22 (* Maximal term depth : 3 ( 2 average) *)
24 (* Bugfixes : v1.2.1 - Clause prove_inverse_of_1_is_0 fixed. *)
25 (* -------------------------------------------------------------------------- *)
26 (* ----Include boolean algebra axioms for equality formulation *)
27 (* Inclusion of: Axioms/BOO003-0.ax *)
28 (* -------------------------------------------------------------------------- *)
29 (* File : BOO003-0 : TPTP v3.1.1. Released v1.0.0. *)
30 (* Domain : Boolean Algebra *)
31 (* Axioms : Boolean algebra (equality) axioms *)
32 (* Version : [ANL] (equality) axioms. *)
38 (* Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 0 RR) *)
39 (* Number of literals : 14 ( 14 equality) *)
40 (* Maximal clause size : 1 ( 1 average) *)
41 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
42 (* Number of functors : 5 ( 2 constant; 0-2 arity) *)
43 (* Number of variables : 24 ( 0 singleton) *)
44 (* Maximal term depth : 3 ( 2 average) *)
46 (* -------------------------------------------------------------------------- *)
47 (* -------------------------------------------------------------------------- *)
48 (* -------------------------------------------------------------------------- *)
49 theorem prove_inverse_of_1_is_0:
51 \forall add:\forall _:Univ.\forall _:Univ.Univ.
52 \forall additive_identity:Univ.
53 \forall inverse:\forall _:Univ.Univ.
54 \forall multiplicative_identity:Univ.
55 \forall multiply:\forall _:Univ.\forall _:Univ.Univ.
56 \forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
57 \forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
58 \forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
59 \forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
60 \forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
61 \forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
62 \forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
63 \forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
64 \forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
65 \forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
66 \forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
67 \forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
68 \forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
69 \forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity
72 autobatch paramodulation timeout=100;
76 (* -------------------------------------------------------------------------- *)