2 include "logic/equality.ma".
3 (* Inclusion of: BOO012-2.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : BOO012-2 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Boolean Algebra *)
7 (* Problem : Inverse is an involution *)
8 (* Version : [ANL] (equality) axioms. *)
12 (* Names : prob8.ver2.in [ANL] *)
13 (* Status : Unsatisfiable *)
14 (* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.25 v2.0.0 *)
15 (* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 1 RR) *)
16 (* Number of atoms : 15 ( 15 equality) *)
17 (* Maximal clause size : 1 ( 1 average) *)
18 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
19 (* Number of functors : 6 ( 3 constant; 0-2 arity) *)
20 (* Number of variables : 24 ( 0 singleton) *)
21 (* Maximal term depth : 3 ( 2 average) *)
23 (* -------------------------------------------------------------------------- *)
24 (* ----Include boolean algebra axioms for equality formulation *)
25 (* Inclusion of: Axioms/BOO003-0.ax *)
26 (* -------------------------------------------------------------------------- *)
27 (* File : BOO003-0 : TPTP v3.1.1. Released v1.0.0. *)
28 (* Domain : Boolean Algebra *)
29 (* Axioms : Boolean algebra (equality) axioms *)
30 (* Version : [ANL] (equality) axioms. *)
36 (* Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 0 RR) *)
37 (* Number of literals : 14 ( 14 equality) *)
38 (* Maximal clause size : 1 ( 1 average) *)
39 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
40 (* Number of functors : 5 ( 2 constant; 0-2 arity) *)
41 (* Number of variables : 24 ( 0 singleton) *)
42 (* Maximal term depth : 3 ( 2 average) *)
44 (* -------------------------------------------------------------------------- *)
45 (* -------------------------------------------------------------------------- *)
46 (* -------------------------------------------------------------------------- *)
47 theorem prove_inverse_is_an_involution:
49 \forall add:\forall _:Univ.\forall _:Univ.Univ.
50 \forall additive_identity:Univ.
51 \forall inverse:\forall _:Univ.Univ.
52 \forall multiplicative_identity:Univ.
53 \forall multiply:\forall _:Univ.\forall _:Univ.Univ.
55 \forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
56 \forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
57 \forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
58 \forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
59 \forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
60 \forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
61 \forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
62 \forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
63 \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)).
64 \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)).
65 \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)).
66 \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)).
67 \forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
68 \forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x
71 autobatch paramodulation timeout=100;
75 (* -------------------------------------------------------------------------- *)