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53 lines
2.3 KiB
Text
53 lines
2.3 KiB
Text
;--------------------------------------------------------------------------
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; File : ROB005-1 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Robbins Algebra
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; Problem : c + c=c => Boolean
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; Version : [Win90] (equality) axioms.
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; English : If there is an element c such that c+c=c, then the algebra
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; is Boolean.
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; Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras
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; : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
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; : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
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; : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit
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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-2 [Ove90]
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; : Lemma 2.4 [Win90]
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; : RA3 [LW92]
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; : THEOREM EQ-2 [LM93]
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; : PROBLEM 2 [Zha93]
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; : robbins.occ.in [OTTER]
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; Status : unsatisfiable
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; Rating : 0.67 v2.2.0, 0.71 v2.1.0, 0.88 v2.0.0
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; Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR)
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; Number of literals : 5 ( 5 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 : 5 ( 3 constant; 0-2 arity)
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; Number of variables : 7 ( 0 singleton)
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; Maximal term depth : 6 ( 2 average)
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; Comments : Commutativity, associativity, and Huntington's axiom
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; axiomatize Boolean algebra.
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; : tptp2X -f kif -t rm_equality:rstfp ROB005-1.p
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;--------------------------------------------------------------------------
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; commutativity_of_add, axiom.
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(or (= (add ?A ?B) (add ?B ?A)))
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; associativity_of_add, axiom.
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(or (= (add (add ?A ?B) ?C) (add ?A (add ?B ?C))))
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; robbins_axiom, axiom.
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(or (= (negate (add (negate (add ?A ?B)) (negate (add ?A (negate ?B))))) ?A))
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; idempotence, hypothesis.
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(or (= (add c c) c))
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; prove_huntingtons_axiom, conjecture.
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(or (/= (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b))
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;--------------------------------------------------------------------------
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