#--------------------------------------------------------------------------
# File     : LCL129-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Logic Calculi (Right group)
# Problem  : LG-2 depends on S-4
# Version  : [McC92b] axioms.
# English  : Kalman's axiomatisation of the right group calculus 
#            is {LG-1,LG-2,LG-3,LG-4,LG-5}. McCune has shown that LG-2 
#            is a single axiom. Other axiomatisations by McCune are 
#            {Q-2,Q-3}, {Q-3,Q-4}, S-2, S-3, S-4, P-4, S-6. Show that LG-2 
#            depends on S-4.

# Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
#          : [McC92a] McCune (1992), Automated Discovery of New Axiomatisat
#          : [McC92b] McCune (1992), Email to G. Sutcliffe
# Source   : [McC92b]
# Names    : RG-110 [MW92]

# Status   : unknown
# Rating   : 1.00 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   :    5 (   4 constant; 0-2 arity)
#            Number of variables  :    6 (   0 singleton)
#            Maximal term depth   :    6 (   3 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp LCL129-1.p 
#--------------------------------------------------------------------------
# condensed_detachment, axiom.
is_a_theorem(Y) <- 
    is_a_theorem(equivalent(X, Y)),
    is_a_theorem(X).

# s_4, axiom.
is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(U, Z)), equivalent(Y, U)))) <- .

# prove_lg_2, conjecture.
 <- is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))).

#--------------------------------------------------------------------------