1 include "logic/equality.ma".
3 (* Inclusion of: LCL111-2.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : LCL111-2 : TPTP v3.7.0. Released v1.0.0. *)
9 (* Domain : Logic Calculi (Many valued sentential) *)
11 (* Problem : MV-25 depends on the Meredith system *)
13 (* Version : [Bon91] (equality) axioms. *)
15 (* Theorem formulation : Wajsberg algebra formulation *)
17 (* English : An axiomatisation of the many valued sentential calculus *)
19 (* is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented *)
21 (* an equality axiomatisation. Show that MV-25 depends on the *)
23 (* Wajsberg axiomatisation. *)
25 (* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
27 (* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
29 (* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
31 (* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
33 (* Source : [Bon91] *)
35 (* Names : Lemma 6 [Bon91] *)
39 (* Status : Unsatisfiable *)
41 (* Rating : 0.00 v3.4.0, 0.12 v3.3.0, 0.07 v3.1.0, 0.22 v2.7.0, 0.00 v2.4.0, 0.33 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.50 v2.0.0 *)
43 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *)
45 (* Number of atoms : 5 ( 5 equality) *)
47 (* Maximal clause size : 1 ( 1 average) *)
49 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
51 (* Number of functors : 6 ( 4 constant; 0-2 arity) *)
53 (* Number of variables : 8 ( 0 singleton) *)
55 (* Maximal term depth : 4 ( 2 average) *)
59 (* -------------------------------------------------------------------------- *)
61 (* ----Include Wajsberg algebra axioms *)
63 (* Inclusion of: Axioms/LCL001-0.ax *)
65 (* -------------------------------------------------------------------------- *)
67 (* File : LCL001-0 : TPTP v3.7.0. Released v1.0.0. *)
69 (* Domain : Logic Calculi (Wajsberg Algebras) *)
71 (* Axioms : Wajsberg algebra axioms *)
73 (* Version : [Bon91] (equality) axioms. *)
77 (* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
79 (* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
81 (* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
85 (* Names : MV Sentential Calculus [MW92] *)
89 (* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
91 (* Number of atoms : 4 ( 4 equality) *)
93 (* Maximal clause size : 1 ( 1 average) *)
95 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
97 (* Number of functors : 3 ( 1 constant; 0-2 arity) *)
99 (* Number of variables : 8 ( 0 singleton) *)
101 (* Maximal term depth : 4 ( 2 average) *)
105 (* -------------------------------------------------------------------------- *)
107 (* -------------------------------------------------------------------------- *)
109 (* -------------------------------------------------------------------------- *)
110 ntheorem prove_mv_25:
111 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
112 ∀implies:∀_:Univ.∀_:Univ.Univ.
118 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
119 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
120 ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
121 ∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (implies z x) (implies z y))) truth)
137 nauto by H0,H1,H2,H3 ##;
138 ntry (nassumption) ##;
141 (* -------------------------------------------------------------------------- *)