2 include "logic/equality.ma".
3 (* Inclusion of: LCL114-2.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : LCL114-2 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Logic Calculi (Many valued sentential) *)
7 (* Problem : MV-36 depends on the Meredith system *)
8 (* Version : [LW92] axioms. *)
9 (* Theorem formulation : Wajsberg algebra formulation *)
10 (* English : An axiomatisation of the many valued sentential calculus *)
11 (* is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented *)
12 (* an equality axiomatisation. Show that MV-36 depends on the *)
13 (* Wajsberg axiomatisation. *)
14 (* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
15 (* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
16 (* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
18 (* Names : MV3 [LW92] *)
19 (* Status : Unsatisfiable *)
20 (* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
21 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *)
22 (* Number of atoms : 5 ( 5 equality) *)
23 (* Maximal clause size : 1 ( 1 average) *)
24 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
25 (* Number of functors : 5 ( 3 constant; 0-2 arity) *)
26 (* Number of variables : 8 ( 0 singleton) *)
27 (* Maximal term depth : 4 ( 2 average) *)
29 (* -------------------------------------------------------------------------- *)
30 (* ----Include Wajsberg algebra axioms *)
31 (* Inclusion of: Axioms/LCL001-0.ax *)
32 (* -------------------------------------------------------------------------- *)
33 (* File : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
34 (* Domain : Logic Calculi (Wajsberg Algebras) *)
35 (* Axioms : Wajsberg algebra axioms *)
36 (* Version : [Bon91] (equality) axioms. *)
38 (* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
39 (* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
40 (* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
42 (* Names : MV Sentential Calculus [MW92] *)
44 (* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
45 (* Number of literals : 4 ( 4 equality) *)
46 (* Maximal clause size : 1 ( 1 average) *)
47 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
48 (* Number of functors : 3 ( 1 constant; 0-2 arity) *)
49 (* Number of variables : 8 ( 0 singleton) *)
50 (* Maximal term depth : 4 ( 2 average) *)
52 (* -------------------------------------------------------------------------- *)
53 (* -------------------------------------------------------------------------- *)
54 (* -------------------------------------------------------------------------- *)
57 \forall implies:\forall _:Univ.\forall _:Univ.Univ.
58 \forall not:\forall _:Univ.Univ.
62 \forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
63 \forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
64 \forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
65 \forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (not y) (not x))) truth
68 autobatch paramodulation timeout=100;
72 (* -------------------------------------------------------------------------- *)