TPTP Problem File: ANA018-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ANA018-2 : 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 : 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v3.3.0, 0.14 v3.2.0
% Syntax : Number of clauses : 13 ( 5 unt; 0 nHn; 10 RR)
% Number of literals : 26 ( 1 equ; 14 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 0 prp; 1-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 21 ( 0 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_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
c_less(c_0,v_ca,t_b) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
cnf(cls_OrderedGroup_Omult__ac__1_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_Orderings_Oorder__class_Oorder__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,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(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_LOrder_Ojoin__semilorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ) ).
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