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# File     : GRP116-1 : TPTP v2.1.0. Released v1.2.0.
# Domain   : Group Theory
# Problem  : Derive left identity from a single axiom for groups order 3
# Version  : [Wos96] (equality) axioms.
# English  : 

# Refs     : [Wos96] Wos (1996), The Automation of Reasoning: An Experiment 
# Source   : [OTTER]
# Names    : groups.exp3.in part 2 [OTTER]

# Status   : unsatisfiable
# Rating   : 0.20 v2.1.0, 0.14 v2.0.0
# Syntax   : Number of clauses    :    2 (   0 non-Horn;   2 unit;   1 RR)
#            Number of literals   :    2 (   2 equality)
#            Maximal clause size  :    1 (   1 average)
#            Number of predicates :    1 (   0 propositional; 2-2 arity)
#            Number of functors   :    3 (   2 constant; 0-2 arity)
#            Number of variables  :    3 (   0 singleton)
#            Maximal term depth   :    6 (   2 average)

# Comments : 
#          : tptp2X -f setheo:sign -t rm_equality:rstfp GRP116-1.p 
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# single_axiom, axiom.
equal(multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Z)), multiply(identity, multiply(Z, Z)))), Y) <- .

# prove_order3, conjecture.
 <- equal(multiply(identity, a), a).

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