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%--------------------------------------------------------------------------
% File : COL042-8 : TPTP v6.4.0. Released v2.1.0.
% Domain : Combinatory Logic
% Problem : Strong fixed point for B and W1
% Version : [WM88] (equality) axioms.
% Theorem formulation : The fixed point is provided and checked.
% English : The strong fixed point property holds for the set
% P consisting of the combinators B and W1, where ((Bx)y)z
% = x(yz), (W1x)y = (yx)x.
% Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
% Source : [TPTP]
% Names :
% Status : Unsatisfiable
% Rating : 0.26 v6.4.0, 0.32 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.31 v6.0.0, 0.48 v5.5.0, 0.47 v5.4.0, 0.40 v5.3.0, 0.33 v5.2.0, 0.36 v5.1.0, 0.33 v5.0.0, 0.43 v4.1.0, 0.36 v4.0.0, 0.31 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0, 0.00 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.50 v2.2.0, 0.80 v2.1.0
% Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 2 RR)
% Number of atoms : 4 ( 4 equality)
% Maximal clause size : 1 ( 1 average)
% Number of predicates : 1 ( 0 propositional; 2-2 arity)
% Number of functors : 5 ( 4 constant; 0-2 arity)
% Number of variables : 5 ( 0 singleton)
% Maximal term depth : 7 ( 3 average)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments :
%--------------------------------------------------------------------------
cnf(b_definition,axiom,
( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )).
cnf(w1_definition,axiom,
( apply(apply(w1,X),Y) = apply(apply(Y,X),X) )).
cnf(strong_fixed_point,axiom,
( strong_fixed_point = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b) )).
cnf(prove_strong_fixed_point,negated_conjecture,
( apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) )).
%--------------------------------------------------------------------------
|
