%------------------------------------------------------------------------------
% File     : ANA045-2 : TPTP v8.2.0. Released v3.2.0.
% Domain   : Analysis
% Problem  : Problem about Big-O notation
% Version  : [Pau06] axioms : Reduced > Especial.
% English  :

% Refs     : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source   : [Pau06]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.1.0, 0.14 v5.0.0, 0.29 v4.1.0, 0.22 v4.0.1, 0.33 v3.7.0, 0.17 v3.3.0, 0.29 v3.2.0
% Syntax   : Number of clauses     :    5 (   2 unt;   0 nHn;   3 RR)
%            Number of literals    :    8 (   1 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 1-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :    6 (   1 sgn)
% SPC      : CNF_UNS_RFO_SEQ_HRN

% Comments : The problems in the [Pau06] collection each have very many axioms,
%            of which only a small selection are required for the refutation.
%            The mission is to find those few axioms, after which a refutation
%            can be quite easily found. This version has only the necessary
%            axioms.
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
    ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b) ).

cnf(tfree_tcs,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b) ).

cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
    | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).

cnf(cls_Ring__and__Field_Omult__cancel__right1_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | V_c = c_times(c_1,V_c,T_a) ) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T)
    | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).

%------------------------------------------------------------------------------