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47 lines
1.9 KiB
Text
47 lines
1.9 KiB
Text
;--------------------------------------------------------------------------
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; File : BOO002-1 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Boolean Algebra (Ternary)
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; Problem : In B3 algebra, X * X^-1 * Y = Y
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; Version : [OTTER] (equality) axioms : Reduced > Incomplete.
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; English :
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; Refs : [LO85] Lusk & Overbeek (1985), Reasoning about Equality
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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 : Problem 5 [LO85]
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; : CADE-11 Competition Eq-3 [Ove90]
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; : THEOREM EQ-3 [LM93]
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; : PROBLEM 3 [Zha93]
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; Status : unsatisfiable
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; Rating : 0.33 v2.2.0, 0.43 v2.1.0, 0.38 v2.0.0
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; Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 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 : 4 ( 2 constant; 0-3 arity)
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; Number of variables : 11 ( 2 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 BOO002-1.p
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;--------------------------------------------------------------------------
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; associativity, axiom.
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(or (= (multiply (multiply ?A ?B ?C) ?D (multiply ?A ?B ?E)) (multiply ?A ?B (multiply ?C ?D ?E))))
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; ternary_multiply_1, axiom.
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(or (= (multiply ?A ?B ?B) ?B))
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; ternary_multiply_2, axiom.
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(or (= (multiply ?A ?A ?B) ?A))
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; left_inverse, axiom.
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(or (= (multiply (inverse ?A) ?A ?B) ?B))
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; prove_equation, conjecture.
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(or (/= (multiply a (inverse a) b) b))
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;--------------------------------------------------------------------------
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