#--------------------------------------------------------------------------
# File     : LCL075-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Logic Calculi (Implication/Negation 2 valued sentential)
# Problem  : CN-3 depends on the single Merideth axiom
# Version  : [McC92] axioms.
# English  : Axiomatisations of the Implication/Negation 2 valued 
#            sentential calculus are {CN-1,CN-2,CN-3} by Lukasiewicz, 
#            {CN-18,CN-21,CN-35,CN-39,CN-39,CN-40,CN-46} by Frege, 
#            {CN-3,CN-18,CN-21,CN-22,CN-30,CN-54} by Hilbert, {CN-18, 
#            CN-35,CN-49} by Church, {CN-19,CN-37,CN-59} by Lukasiewicz, 
#            {CN-19,CN-37,CN-60} by Wos, and the single Meredith axiom. 
#            Show that CN-3 depends on the single Meredith axiom.

# Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
#          : [McC92] McCune (1992), Email to G. Sutcliffe
# Source   : [McC92]
# Names    : CN-36 [MW92]

# Status   : unsatisfiable
# Rating   : 0.56 v2.1.0, 0.38 v2.0.0
# Syntax   : Number of clauses    :    3 (   0 non-Horn;   2 unit;   2 RR)
#            Number of literals   :    5 (   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  :    7 (   1 singleton)
#            Maximal term depth   :    7 (   3 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp LCL075-1.p 
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# condensed_detachment, axiom.
is_a_theorem(Y) <- 
    is_a_theorem(implies(X, Y)),
    is_a_theorem(X).

# cn_CAMerideth, axiom.
is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(not(Z), not(U))), Z), V), implies(implies(V, X), implies(U, X)))) <- .

# prove_cn_3, conjecture.
 <- is_a_theorem(implies(a, implies(not(a), b))).

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