TPTP Problem File: ANA015-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ANA015-2 : 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 : 0.08 v9.0.0, 0.12 v8.2.0, 0.08 v8.1.0, 0.00 v7.5.0, 0.10 v7.4.0, 0.22 v7.3.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.14 v6.3.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.17 v3.3.0, 0.29 v3.2.0
% Syntax : Number of clauses : 12 ( 3 unt; 0 nHn; 8 RR)
% Number of literals : 23 ( 2 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 0 prp; 1-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 20 ( 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_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_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_g(V_U),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U)),t_a),t_a),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ).
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_34,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Oordered__idom(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_46,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Opordered__semiring(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(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a) ).
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