#--------------------------------------------------------------------------
# File     : LCL135-1 : TPTP v2.1.0. Released v1.0.0.
# Domain   : Logic Calculi (Wajsberg Algebra)
# Problem  : A lemma in Wajsberg algebras
# Version  : [Bon91] (equality) axioms.
# English  : An axiomatisation of the many valued sentential calculus 
#            is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg provided 
#            a different axiomatisation. Show that MV-1 depends on the 
#            Wajsberg system.

# Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras
#          : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic
#          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
# Source   : [Bon91]
# Names    : Lemma 4 [Bon91]

# Status   : unsatisfiable
# Rating   : 0.33 v2.1.0, 0.25 v2.0.0
# Syntax   : Number of clauses    :    5 (   0 non-Horn;   5 unit;   1 RR)
#            Number of literals   :    5 (   5 equality)
#            Maximal clause size  :    1 (   1 average)
#            Number of predicates :    1 (   0 propositional; 2-2 arity)
#            Number of functors   :    5 (   3 constant; 0-2 arity)
#            Number of variables  :    8 (   0 singleton)
#            Maximal term depth   :    4 (   2 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp LCL135-1.p 
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# wajsberg_1, axiom.
equal(implies(true, X), X) <- .

# wajsberg_2, axiom.
equal(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))), true) <- .

# wajsberg_3, axiom.
equal(implies(implies(X, Y), Y), implies(implies(Y, X), X)) <- .

# wajsberg_4, axiom.
equal(implies(implies(not(X), not(Y)), implies(Y, X)), true) <- .

# prove_wajsberg_lemma, conjecture.
 <- equal(implies(x, implies(y, x)), true).

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