TPTP Problem File: ANA012-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ANA012-2 : TPTP v9.0.0. 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 : 0.05 v9.0.0, 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.09 v6.2.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.00 v5.5.0, 0.05 v5.4.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.06 v5.0.0, 0.00 v4.1.0, 0.08 v4.0.1, 0.09 v4.0.0, 0.00 v3.3.0, 0.07 v3.2.0
% Syntax : Number of clauses : 9 ( 3 unt; 1 nHn; 7 RR)
% Number of literals : 17 ( 5 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 0 prp; 1-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 10 ( 1 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% 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,
v_c != c_0 ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a) ).
cnf(cls_OrderedGroup_Oabs__eq__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(V_a,T_a) != c_0
| V_a = c_0 ) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_47,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_58,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ) ).
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