Spectra/snark-20120808r02/examples/COL003-1+rm_eq_rstfp.kif

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;--------------------------------------------------------------------------
; File : COL003-1 : TPTP v2.2.0. Released v1.0.0.
; Domain : Combinatory Logic
; Problem : Strong fixed point for B and W
; Version : [WM88] (equality) axioms.
; English : The strong fixed point property holds for the set
; P consisting of the combinators B and W alone, where ((Bx)y)z
; = x(yz) and (Wx)y = (xy)y.
; Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
; : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
; : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
; : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
; : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
; : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit
; : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
; : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal
; : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11
; : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in
; Source : [WM88]
; Names : C2 [WM88]
; : Test Problem 17 [Wos88]
; : Sages and Combinatory Logic [Wos88]
; : CADE-11 Competition Eq-8 [Ove90]
; : CL2 [LW92]
; : THEOREM EQ-8 [LM93]
; : Question 3 [Wos93]
; : Question 5 [Wos93]
; : PROBLEM 8 [Zha93]
; Status : unknown
; Rating : 1.00 v2.0.0
; Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR)
; Number of literals : 3 ( 3 equality)
; Maximal clause size : 1 ( 1 average)
; Number of predicates : 1 ( 0 propositional; 2-2 arity)
; Number of functors : 4 ( 2 constant; 0-2 arity)
; Number of variables : 6 ( 0 singleton)
; Maximal term depth : 4 ( 3 average)
; Comments :
; : tptp2X -f kif -t rm_equality:rstfp COL003-1.p
;--------------------------------------------------------------------------
; b_definition, axiom.
(or (= (apply (apply (apply b ?A) ?B) ?C) (apply ?A (apply ?B ?C))))
; w_definition, axiom.
(or (= (apply (apply w ?A) ?B) (apply (apply ?A ?B) ?B)))
; prove_strong_fixed_point, conjecture.
(or (/= (apply ?A (f ?A)) (apply (f ?A) (apply ?A (f ?A)))))
;--------------------------------------------------------------------------