mirror of
https://github.com/RAIRLab/Spectra.git
synced 2024-11-09 11:10:34 -05:00
52 lines
2.4 KiB
Text
52 lines
2.4 KiB
Text
;--------------------------------------------------------------------------
|
|
; File : COL049-1 : TPTP v2.2.0. Released v1.0.0.
|
|
; Domain : Combinatory Logic
|
|
; Problem : Strong fixed point for B, W, and M
|
|
; Version : [WM88] (equality) axioms.
|
|
; English : The strong fixed point property holds for the set
|
|
; P consisting of the combinators B, W, and M, where ((Bx)y)z
|
|
; = x(yz), (Wx)y = (xy)y, Mx = xx.
|
|
|
|
; 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
|
|
; : [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 : [Ove90]
|
|
; Names : Problem 2 [WM88]
|
|
; : CADE-11 Competition Eq-6 [Ove90]
|
|
; : CL1 [LW92]
|
|
; : THEOREM EQ-6 [LM93]
|
|
; : Question 2 [Wos93]
|
|
; : PROBLEM 6 [Zha93]
|
|
|
|
; Status : unsatisfiable
|
|
; Rating : 0.22 v2.2.0, 0.14 v2.1.0, 0.62 v2.0.0
|
|
; Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR)
|
|
; Number of literals : 4 ( 4 equality)
|
|
; Maximal clause size : 1 ( 1 average)
|
|
; Number of predicates : 1 ( 0 propositional; 2-2 arity)
|
|
; Number of functors : 5 ( 3 constant; 0-2 arity)
|
|
; Number of variables : 7 ( 0 singleton)
|
|
; Maximal term depth : 4 ( 3 average)
|
|
|
|
; Comments :
|
|
; : tptp2X -f kif -t rm_equality:rstfp COL049-1.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)))
|
|
|
|
; m_definition, axiom.
|
|
(or (= (apply m ?A) (apply ?A ?A)))
|
|
|
|
; prove_strong_fixed_point, conjecture.
|
|
(or (/= (apply ?A (f ?A)) (apply (f ?A) (apply ?A (f ?A)))))
|
|
|
|
;--------------------------------------------------------------------------
|