;--------------------------------------------------------------------------
; File     : LCL114-1 : TPTP v2.2.0. Released v1.0.0.
; Domain   : Logic Calculi (Many valued sentential)
; Problem  : MV-36 depnds on the Merideth system
; Version  : [McC92] axioms.
; English  : An axiomatisation of the many valued sentential calculus 
;            is {MV-1,MV-2,MV-3,MV-5} by Meredith. Show that 36 depends 
;            on the Meredith system.

; Refs     : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
;          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
;          : [McC92] McCune (1992), Email to G. Sutcliffe
;          : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal 
;          : [LM93]  Lusk & McCune (1993), Uniform Strategies: The CADE-11 
; Source   : [McC92]
; Names    : CADE-11 Competition 7 [Ove90]
;          : MV-60 [MW92]
;          : THEOREM 7 [LM93]

; Status   : unsatisfiable
; Rating   : 0.89 v2.1.0, 0.88 v2.0.0
; Syntax   : Number of clauses    :    6 (   0 non-Horn;   5 unit;   2 RR)
;            Number of literals   :    8 (   0 equality)
;            Maximal clause size  :    3 (   1 average)
;            Number of predicates :    1 (   0 propositional; 1-1 arity)
;            Number of functors   :    4 (   2 constant; 0-2 arity)
;            Number of variables  :   11 (   1 singleton)
;            Maximal term depth   :    4 (   2 average)

; Comments : 
;          : tptp2X -f kif -t rm_equality:rstfp LCL114-1.p 
;--------------------------------------------------------------------------
; condensed_detachment, axiom.
(or (not (is_a_theorem (implies ?A ?B)))
    (not (is_a_theorem ?A))
    (is_a_theorem ?B))

; mv_1, axiom.
(or (is_a_theorem (implies ?A (implies ?B ?A))))

; mv_2, axiom.
(or (is_a_theorem (implies (implies ?A ?B) (implies (implies ?B ?C) (implies ?A ?C)))))

; mv_3, axiom.
(or (is_a_theorem (implies (implies (implies ?A ?B) ?B) (implies (implies ?B ?A) ?A))))

; mv_5, axiom.
(or (is_a_theorem (implies (implies (not ?A) (not ?B)) (implies ?B ?A))))

; prove_mv_36, conjecture.
(or (not (is_a_theorem (implies (implies a b) (implies (not b) (not a))))))

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