#--------------------------------------------------------------------------
# File     : LCL115-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Logic Calculi (Many valued sentential)
# Problem  : MV-39 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 39 depends 
#            on the Meredith system.

# Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
#          : [McC92] McCune (1992), Email to G. Sutcliffe
# Source   : [McC92]
# Names    : MV-61 [MW92]

# Status   : unsatisfiable
# Rating   : 0.56 v2.1.0, 0.63 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 setheo:sign -t rm_equality:rstfp LCL115-1.p 
#--------------------------------------------------------------------------
# condensed_detachment, axiom.
is_a_theorem(Y) <- 
    is_a_theorem(implies(X, Y)),
    is_a_theorem(X).

# mv_1, axiom.
is_a_theorem(implies(X, implies(Y, X))) <- .

# mv_2, axiom.
is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) <- .

# mv_3, axiom.
is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) <- .

# mv_5, axiom.
is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) <- .

# prove_mv_39, conjecture.
 <- is_a_theorem(implies(not(implies(a, b)), not(b))).

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