;-------------------------------------------------------------------------- ; 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))))) ;--------------------------------------------------------------------------