TPTP Problem File: COL020-1.p
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%--------------------------------------------------------------------------
% File : COL020-1 : TPTP v8.2.0. Released v1.0.0.
% Domain : Combinatory Logic
% Problem : Weak fixed point for B, S, and C
% Version : [WM88] (equality) axioms.
% English : The weak fixed point property holds for the set P consisting
% of the combinators B, S, and C, where ((Sx)y)z = (xz)(yz),
% ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y.
% 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
% : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% Source : [MW88]
% Names : - [MW88]
% Status : Unsatisfiable
% Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.25 v7.5.0, 0.29 v7.4.0, 0.35 v7.3.0, 0.37 v7.1.0, 0.28 v7.0.0, 0.26 v6.4.0, 0.37 v6.3.0, 0.41 v6.2.0, 0.43 v6.1.0, 0.12 v6.0.0, 0.19 v5.5.0, 0.16 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.21 v4.0.0, 0.23 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.33 v2.3.0, 0.00 v2.0.0
% Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR)
% Number of literals : 4 ( 4 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 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(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
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