1 include "logic/equality.ma".
3 (* Inclusion of: LCL109-2.p *)
5 (* -------------------------------------------------------------------------- *)
7 (* File : LCL109-2 : TPTP v3.7.0. Released v1.0.0. *)
9 (* Domain : Logic Calculi (Many valued sentential) *)
11 (* Problem : MV-4 depends on the Merideth system *)
13 (* Version : [Ove90] 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 provided *)
21 (* a different axiomatisation. Show that MV-4 depends on the *)
23 (* Wajsberg system. *)
25 (* Refs : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 *)
27 (* : [LM92] Lusk & McCune (1992), Experiments with ROO, a Parallel *)
29 (* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
31 (* : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal *)
33 (* : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11 *)
35 (* : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in *)
37 (* Source : [Ove90] *)
39 (* Names : CADE-11 Competition Eq-5 [Ove90] *)
45 (* : THEOREM EQ-5 [LM93] *)
47 (* : PROBLEM 5 [Zha93] *)
49 (* Status : Unsatisfiable *)
51 (* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.33 v2.2.1, 0.56 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *)
53 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *)
55 (* Number of atoms : 5 ( 5 equality) *)
57 (* Maximal clause size : 1 ( 1 average) *)
59 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
61 (* Number of functors : 5 ( 3 constant; 0-2 arity) *)
63 (* Number of variables : 8 ( 0 singleton) *)
65 (* Maximal term depth : 4 ( 2 average) *)
69 (* -------------------------------------------------------------------------- *)
71 (* ----Include Wajsberg algebra axioms *)
73 (* Inclusion of: Axioms/LCL001-0.ax *)
75 (* -------------------------------------------------------------------------- *)
77 (* File : LCL001-0 : TPTP v3.7.0. Released v1.0.0. *)
79 (* Domain : Logic Calculi (Wajsberg Algebras) *)
81 (* Axioms : Wajsberg algebra axioms *)
83 (* Version : [Bon91] (equality) axioms. *)
87 (* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *)
89 (* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
91 (* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *)
95 (* Names : MV Sentential Calculus [MW92] *)
99 (* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
101 (* Number of atoms : 4 ( 4 equality) *)
103 (* Maximal clause size : 1 ( 1 average) *)
105 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
107 (* Number of functors : 3 ( 1 constant; 0-2 arity) *)
109 (* Number of variables : 8 ( 0 singleton) *)
111 (* Maximal term depth : 4 ( 2 average) *)
115 (* -------------------------------------------------------------------------- *)
117 (* -------------------------------------------------------------------------- *)
119 (* -------------------------------------------------------------------------- *)
120 ntheorem prove_wajsberg_mv_4:
121 (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
124 ∀implies:∀_:Univ.∀_:Univ.Univ.
127 ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
128 ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
129 ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
130 ∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (implies a b) (implies b a)) (implies b a)) truth)
145 nauto by H0,H1,H2,H3 ##;
146 ntry (nassumption) ##;
149 (* -------------------------------------------------------------------------- *)