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# File     : LCL009-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Logic Calculi (Equivalential)
# Problem  : EC-5 depends on YQL
# Version  : [McC92] axioms.
# English  : An axiomatisation of the equivalential calculus is {EC-4, 
#            EC-5} by Wajsburg. Show that EC-5 can be derived from the 
#            single Lukasiewicz axiom YQL.

# Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
#          : [McC92] McCune (1992), Email to G. Sutcliffe
# Source   : [McC92]
# Names    : EC-72 [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  :    5 (   0 singleton)
#            Maximal term depth   :    4 (   2 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp LCL009-1.p 
#--------------------------------------------------------------------------
# condensed_detachment, axiom.
is_a_theorem(Y) <- 
    is_a_theorem(equivalent(X, Y)),
    is_a_theorem(X).

# yql, axiom.
is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))) <- .

# prove_ec_5, conjecture.
 <- is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))).

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