2 include "logic/equality.ma".
3 (* Inclusion of: BOO001-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : BOO001-1 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Boolean Algebra (Ternary) *)
7 (* Problem : In B3 algebra, inverse is an involution *)
8 (* Version : [OTTER] (equality) axioms. *)
11 (* Source : [OTTER] *)
12 (* Names : tba_gg.in [OTTER] *)
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 : 6 ( 0 non-Horn; 6 unit; 1 RR) *)
16 (* Number of atoms : 6 ( 6 equality) *)
17 (* Maximal clause size : 1 ( 1 average) *)
18 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
19 (* Number of functors : 3 ( 1 constant; 0-3 arity) *)
20 (* Number of variables : 13 ( 2 singleton) *)
21 (* Maximal term depth : 3 ( 2 average) *)
23 (* -------------------------------------------------------------------------- *)
24 (* ----Include ternary Boolean algebra axioms *)
25 (* Inclusion of: Axioms/BOO001-0.ax *)
26 (* -------------------------------------------------------------------------- *)
27 (* File : BOO001-0 : TPTP v3.1.1. Released v1.0.0. *)
28 (* Domain : Algebra (Ternary Boolean) *)
29 (* Axioms : Ternary Boolean algebra (equality) axioms *)
30 (* Version : [OTTER] (equality) axioms. *)
32 (* Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
33 (* : [Win82] Winker (1982), Generation and Verification of Finite M *)
34 (* Source : [OTTER] *)
37 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 0 RR) *)
38 (* Number of literals : 5 ( 5 equality) *)
39 (* Maximal clause size : 1 ( 1 average) *)
40 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
41 (* Number of functors : 2 ( 0 constant; 1-3 arity) *)
42 (* Number of variables : 13 ( 2 singleton) *)
43 (* Maximal term depth : 3 ( 2 average) *)
44 (* Comments : These axioms appear in [Win82], in which ternary_multiply_1 is *)
45 (* shown to be independant. *)
46 (* : These axioms are also used in [Wos88], p.222. *)
47 (* -------------------------------------------------------------------------- *)
48 (* -------------------------------------------------------------------------- *)
49 (* -------------------------------------------------------------------------- *)
50 theorem prove_inverse_is_self_cancelling:
53 \forall inverse:\forall _:Univ.Univ.
54 \forall multiply:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
55 \forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y (inverse Y)) X.
56 \forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
57 \forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X X Y) X.
58 \forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply Y X X) X.
59 \forall H4:\forall V:Univ.\forall W:Univ.\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a
62 autobatch paramodulation timeout=100;
66 (* -------------------------------------------------------------------------- *)