TPTP Problem File: COL087-1.p
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%--------------------------------------------------------------------------
% File : COL087-1 : TPTP v9.0.0. Released v2.7.0.
% Domain : Combinatory Logic
% Problem : Strong fixed point for B and M
% Version : [Cla03] axioms.
% English : The strong fixed point property holds for the set with the
% combinators B and M as a basis, where Bxyz = x(yz) and
% Mx = xx.
% Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% : [Cla03] Claessen (2003), Email to G. Sutcliffe
% Source : [Cla03]
% Names :
% Status : Open
% Rating : 1.00 v2.7.0
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% Number of literals : 3 ( 3 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% SPC : CNF_OPN_RFO_PEQ_UEQ
% Comments :
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cnf(definition_B,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(definition_M,axiom,
apply(m,X) = apply(X,X) ).
cnf(strong_fixpoint,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
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