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60 lines
2.4 KiB
Text
60 lines
2.4 KiB
Text
;--------------------------------------------------------------------------
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; File : RNG009-5 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Ring Theory
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; Problem : If X*X*X = X then the ring is commutative
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; Version : [Peterson & Stickel,1981] (equality) axioms :
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; Reduced > Incomplete.
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; English : Given a ring in which for all x, x * x * x = x, prove that
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; for all x and y, x * y = y * x.
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; Refs : [PS81] Peterson & Stickel (1981), Complete Sets of Reductions
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; : [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-7 [Ove90]
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; : THEOREM EQ-7 [LM93]
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; : PROBLEM 7 [Zha93]
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; Status : unsatisfiable
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; Rating : 0.67 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0
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; Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 1 RR)
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; Number of literals : 9 ( 9 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 : 17 ( 0 singleton)
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; Maximal term depth : 3 ( 2 average)
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; Comments :
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; : tptp2X -f kif -t rm_equality:rstfp RNG009-5.p
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;--------------------------------------------------------------------------
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; right_identity, axiom.
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(or (= (add ?A additive_identity) ?A))
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; right_additive_inverse, axiom.
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(or (= (add ?A (additive_inverse ?A)) additive_identity))
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; distribute1, axiom.
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(or (= (multiply ?A (add ?B ?C)) (add (multiply ?A ?B) (multiply ?A ?C))))
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; distribute2, axiom.
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(or (= (multiply (add ?A ?B) ?C) (add (multiply ?A ?C) (multiply ?B ?C))))
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; associative_addition, axiom.
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(or (= (add (add ?A ?B) ?C) (add ?A (add ?B ?C))))
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; commutative_addition, axiom.
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(or (= (add ?A ?B) (add ?B ?A)))
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; associative_multiplication, axiom.
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(or (= (multiply (multiply ?A ?B) ?C) (multiply ?A (multiply ?B ?C))))
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; x_cubed_is_x, hypothesis.
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(or (= (multiply ?A (multiply ?A ?A)) ?A))
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; prove_commutativity, conjecture.
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(or (/= (multiply a b) (multiply b a)))
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;--------------------------------------------------------------------------
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