TPTP Problem File: COL006-1.p
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%--------------------------------------------------------------------------
% File : COL006-1 : TPTP v8.2.0. Released v1.0.0.
% Domain : Combinatory Logic
% Problem : Strong fixed point for S and K
% Version : [WM88] (equality) axioms.
% English : The strong fixed point property holds for the set
% P consisting of the combinators S and K alone, where
% ((Sx)y)z = (xz)(yz), (Kx)y = x.
% Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% Source : [WM88]
% Names : Problem 6 [WM88]
% Status : Unsatisfiable
% Rating : 0.64 v8.2.0, 0.71 v8.1.0, 0.70 v7.5.0, 0.71 v7.4.0, 0.65 v7.3.0, 0.58 v7.1.0, 0.50 v7.0.0, 0.53 v6.4.0, 0.63 v6.3.0, 0.65 v6.2.0, 0.57 v6.1.0, 0.69 v6.0.0, 0.86 v5.5.0, 0.84 v5.4.0, 0.80 v5.3.0, 0.75 v5.2.0, 0.79 v5.1.0, 0.80 v5.0.0, 0.79 v4.1.0, 0.64 v4.0.1, 0.71 v4.0.0, 0.77 v3.7.0, 0.56 v3.4.0, 0.50 v3.3.0, 0.57 v3.1.0, 0.78 v2.7.0, 0.64 v2.6.0, 0.67 v2.5.0, 0.50 v2.4.0, 0.67 v2.2.1, 0.67 v2.2.0, 0.57 v2.1.0, 1.00 v2.0.0
% 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 : 6 ( 1 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments :
%--------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
cnf(k_definition,axiom,
apply(apply(k,X),Y) = X ).
cnf(prove_fixed_point,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
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