TPTP Problem File: COL057-1.p
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%--------------------------------------------------------------------------
% File : COL057-1 : TPTP v8.2.0. Released v1.0.0.
% Domain : Combinatory Logic
% Problem : Strong fixed point for S, B, C, and I
% Version : [WM88] (equality) axioms.
% English : The strong fixed point property holds for the set
% P consisting of the combinators S, B, C, and I, where
% ((Sx)y)z = (xz)(yz), ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y, and
% Ix = x.
% Refs : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit
% Source : [LW92]
% Names : CL5 [LW92]
% Status : Unsatisfiable
% Rating : 0.32 v8.2.0, 0.38 v8.1.0, 0.35 v7.5.0, 0.42 v7.4.0, 0.48 v7.3.0, 0.47 v7.1.0, 0.39 v7.0.0, 0.37 v6.4.0, 0.42 v6.3.0, 0.41 v6.2.0, 0.43 v6.1.0, 0.44 v6.0.0, 0.48 v5.5.0, 0.47 v5.4.0, 0.53 v5.3.0, 0.58 v5.2.0, 0.50 v5.1.0, 0.47 v5.0.0, 0.43 v4.1.0, 0.36 v4.0.1, 0.50 v4.0.0, 0.54 v3.7.0, 0.22 v3.4.0, 0.25 v3.3.0, 0.36 v3.1.0, 0.56 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.00 v2.1.0, 0.25 v2.0.0
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 RR)
% Number of literals : 5 ( 5 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 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(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(c_definition,axiom,
apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y) ).
cnf(i_definition,axiom,
apply(i,X) = X ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
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