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38 lines
1.9 KiB
Text
38 lines
1.9 KiB
Text
;--------------------------------------------------------------------------
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; File : GRP014-1 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Group Theory
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; Problem : Product is associative in this group theory
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; Version : [Ove90] (equality) axioms : Incomplete.
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; English : The group theory specified by the axiom given implies the
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; associativity of multiply.
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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-4 [Ove90]
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; : THEOREM EQ-4 [LM93]
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; : PROBLEM 4 [Zha93]
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; Status : unsatisfiable
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; Rating : 0.33 v2.2.0, 0.43 v2.1.0, 0.50 v2.0.0
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; Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR)
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; Number of literals : 2 ( 2 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 : 4 ( 0 singleton)
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; Maximal term depth : 9 ( 4 average)
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; Comments : The group_axiom is in fact a single axiom for group theory
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; [LM93].
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; : tptp2X -f kif -t rm_equality:rstfp GRP014-1.p
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;--------------------------------------------------------------------------
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; group_axiom, axiom.
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(or (= (multiply ?A (inverse (multiply (multiply (inverse (multiply (inverse ?B) (multiply (inverse ?A) ?C))) ?D) (inverse (multiply ?B ?D))))) ?C))
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; prove_associativity, conjecture.
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(or (/= (multiply a (multiply b c)) (multiply (multiply a b) c)))
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;--------------------------------------------------------------------------
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