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53 lines
2.4 KiB
Text
53 lines
2.4 KiB
Text
;--------------------------------------------------------------------------
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; File : COL003-1 : TPTP v2.2.0. Released v1.0.0.
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; Domain : Combinatory Logic
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; Problem : Strong fixed point for B and W
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; Version : [WM88] (equality) axioms.
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; English : The strong fixed point property holds for the set
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; P consisting of the combinators B and W alone, where ((Bx)y)z
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; = x(yz) and (Wx)y = (xy)y.
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; Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
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; : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
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; : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
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; : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
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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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; : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
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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 : [WM88]
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; Names : C2 [WM88]
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; : Test Problem 17 [Wos88]
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; : Sages and Combinatory Logic [Wos88]
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; : CADE-11 Competition Eq-8 [Ove90]
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; : CL2 [LW92]
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; : THEOREM EQ-8 [LM93]
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; : Question 3 [Wos93]
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; : Question 5 [Wos93]
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; : PROBLEM 8 [Zha93]
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; Status : unknown
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; Rating : 1.00 v2.0.0
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; Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR)
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; Number of literals : 3 ( 3 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; 0-2 arity)
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; Number of variables : 6 ( 0 singleton)
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; Maximal term depth : 4 ( 3 average)
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; Comments :
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; : tptp2X -f kif -t rm_equality:rstfp COL003-1.p
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;--------------------------------------------------------------------------
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; b_definition, axiom.
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(or (= (apply (apply (apply b ?A) ?B) ?C) (apply ?A (apply ?B ?C))))
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; w_definition, axiom.
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(or (= (apply (apply w ?A) ?B) (apply (apply ?A ?B) ?B)))
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; prove_strong_fixed_point, conjecture.
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(or (/= (apply ?A (f ?A)) (apply (f ?A) (apply ?A (f ?A)))))
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;--------------------------------------------------------------------------
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