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53 lines
2.3 KiB
Text
53 lines
2.3 KiB
Text
;--------------------------------------------------------------------------
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; File : GRP002-3 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Group Theory
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; Problem : Commutator equals identity in groups of order 3
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; Version : [Ove90] (equality) axioms : Incomplete.
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; English : In a group, if (for all x) the cube of x is the identity
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; (i.e. a group of order 3), then the equation [[x,y],y]=
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; identity holds, where [x,y] is the product of x, y, the
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; inverse of x and the inverse of y (i.e. the commutator
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; of x and y).
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; Refs : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
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; : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal
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; : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11
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; : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in
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; Source : [Ove90]
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; Names : CADE-11 Competition Eq-1 [Ove90]
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; : THEOREM EQ-1 [LM93]
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; : PROBLEM 1 [Zha93]
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; : comm.in [OTTER]
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; Status : unsatisfiable
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; Rating : 0.33 v2.2.0, 0.43 v2.1.0, 0.25 v2.0.0
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; Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR)
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; Number of literals : 6 ( 6 equality)
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; Maximal clause size : 1 ( 1 average)
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; Number of predicates : 1 ( 0 propositional; 2-2 arity)
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; Number of functors : 6 ( 3 constant; 0-2 arity)
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; Number of variables : 8 ( 0 singleton)
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; Maximal term depth : 5 ( 2 average)
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; Comments : Uses an explicit formulation of the commutator.
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; : tptp2X -f kif -t rm_equality:rstfp GRP002-3.p
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;--------------------------------------------------------------------------
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; left_identity, axiom.
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(or (= (multiply identity ?A) ?A))
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; left_inverse, axiom.
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(or (= (multiply (inverse ?A) ?A) identity))
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; associativity, axiom.
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(or (= (multiply (multiply ?A ?B) ?C) (multiply ?A (multiply ?B ?C))))
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; commutator, axiom.
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(or (= (commutator ?A ?B) (multiply ?A (multiply ?B (multiply (inverse ?A) (inverse ?B))))))
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; x_cubed_is_identity, hypothesis.
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(or (= (multiply ?A (multiply ?A ?A)) identity))
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; prove_commutator, conjecture.
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(or (/= (commutator (commutator a b) b) identity))
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;--------------------------------------------------------------------------
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