#--------------------------------------------------------------------------
# File     : LCL033-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Logic Calculi (Implication/Falsehood 2 valued sentential)
# Problem  : C0-2 depends on the Merideth axiom
# Version  : [McC92] axioms.
# English  : Axiomatisations for the Implication/Falsehood 2 valued 
#            sentential calculus are {C0-1,C0-2,C0-3,C0-4} 
#            by Tarski-Bernays, {C0-2,C0-5,C0-6} by Church, and the single 
#            Meredith axioms. Show that C0-2 can be derived from the 
#            single Meredith axiom.

# Refs     : [Mer53] Meredith (1953), Single Axioms for the Systems (C,N), 
#          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
#          : [McC92] McCune (1992), Email to G. Sutcliffe
# Source   : [McC92]
# Names    : C0-45 [MW92]

# Status   : unsatisfiable
# Rating   : 0.33 v2.1.0, 0.13 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 (   3 constant; 0-2 arity)
#            Number of variables  :    7 (   2 singleton)
#            Maximal term depth   :    6 (   2 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp LCL033-1.p 
#--------------------------------------------------------------------------
# condensed_detachment, axiom.
is_a_theorem(Y) <- 
    is_a_theorem(implies(X, Y)),
    is_a_theorem(X).

# c0_CAMerideth, axiom.
is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), U), V), implies(implies(V, X), implies(Z, X)))) <- .

# prove_c0_2, conjecture.
 <- is_a_theorem(implies(a, implies(b, a))).

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