;--------------------------------------------------------------------------
; File     : LCL109-2 : TPTP v2.2.0. Released v1.0.0.
; Domain   : Logic Calculi (Many valued sentential)
; Problem  : MV-4 depends on the Merideth system
; Version  : [Ove90] axioms.
;            Theorem formulation : Wajsberg algebra formulation.
; English  : An axiomatisation of the many valued sentential calculus 
;            is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg provided 
;            a different axiomatisation. Show that MV-4 depends on the 
;            Wajsberg system.

; Refs     : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
;          : [LM92]  Lusk & McCune (1992), Experiments with ROO, a Parallel
;          : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit
;          : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal 
;          : [LM93]  Lusk & McCune (1993), Uniform Strategies: The CADE-11 
;          : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in
; Source   : [Ove90]
; Names    : CADE-11 Competition Eq-5 [Ove90]
;          : Luka-5 [LM92]
;          : MV4 [LW92]
;          : THEOREM EQ-5 [LM93]
;          : PROBLEM 5 [Zha93]

; Status   : unsatisfiable
; Rating   : 0.56 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0
; Syntax   : Number of clauses    :    5 (   0 non-Horn;   5 unit;   1 RR)
;            Number of literals   :    5 (   5 equality)
;            Maximal clause size  :    1 (   1 average)
;            Number of predicates :    1 (   0 propositional; 2-2 arity)
;            Number of functors   :    5 (   3 constant; 0-2 arity)
;            Number of variables  :    8 (   0 singleton)
;            Maximal term depth   :    4 (   2 average)

; Comments : 
;          : tptp2X -f kif -t rm_equality:rstfp LCL109-2.p 
;          ; 'true' renamed to 'true0' - MES
;--------------------------------------------------------------------------
; wajsberg_1, axiom.
(or (= (implies true0 ?A) ?A))

; wajsberg_2, axiom.
(or (= (implies (implies ?A ?B) (implies (implies ?B ?C) (implies ?A ?C))) true0))

; wajsberg_3, axiom.
(or (= (implies (implies ?A ?B) ?B) (implies (implies ?B ?A) ?A)))

; wajsberg_4, axiom.
(or (= (implies (implies (not ?A) (not ?B)) (implies ?B ?A)) true0))

; prove_wajsberg_mv_4, conjecture.
(or (/= (implies (implies (implies a b) (implies b a)) (implies b a)) true0))

;--------------------------------------------------------------------------