#--------------------------------------------------------------------------
# File     : LCL051-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Logic Calculi (Implication/Negation 2 valued sentential)
# Problem  : CN-22 depends on the Lukasiewicz system
# 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-22 depends on the short Lukasiewicz system.

# Refs     : [LM92]  Lusk & McCune (1992), Experiments with ROO, a Parallel
#          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
#          : [McC92] McCune (1992), Email to G. Sutcliffe
# Source   : [McC92]
# Names    : CD-12 [LM92]
#          : CN-12 [MW92]

# Status   : unsatisfiable
# Rating   : 0.78 v2.1.0, 0.88 v2.0.0
# Syntax   : Number of clauses    :    5 (   0 non-Horn;   4 unit;   2 RR)
#            Number of literals   :    7 (   0 equality)
#            Maximal clause size  :    3 (   1 average)
#            Number of predicates :    1 (   0 propositional; 1-1 arity)
#            Number of functors   :    5 (   3 constant; 0-2 arity)
#            Number of variables  :    8 (   1 singleton)
#            Maximal term depth   :    4 (   2 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp LCL051-1.p 
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# condensed_detachment, axiom.
is_a_theorem(Y) <- 
    is_a_theorem(implies(X, Y)),
    is_a_theorem(X).

# cn_1, axiom.
is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) <- .

# cn_2, axiom.
is_a_theorem(implies(implies(not(X), X), X)) <- .

# cn_3, axiom.
is_a_theorem(implies(X, implies(not(X), Y))) <- .

# prove_cn_22, conjecture.
 <- is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))).

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