TPTP Problem File: ANA030-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ANA030-1 : TPTP v9.0.0. Released v3.2.0.
% Domain : Analysis
% Problem : Problem about Big-O notation
% Version : [Pau06] axioms : Especial.
% English :
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names : BigO__bigo_lesso5 [Pau06]
% Status : Unsatisfiable
% Rating : 0.85 v8.2.0, 0.86 v8.1.0, 0.74 v7.5.0, 0.95 v7.4.0, 0.94 v7.3.0, 0.83 v7.0.0, 0.87 v6.3.0, 0.91 v6.2.0, 0.90 v6.1.0, 0.93 v6.0.0, 0.90 v5.5.0, 1.00 v5.4.0, 0.95 v5.3.0, 1.00 v5.2.0, 0.94 v5.0.0, 0.93 v4.1.0, 0.92 v4.0.1, 1.00 v3.2.0
% Syntax : Number of clauses : 2807 ( 648 unt; 248 nHn;1984 RR)
% Number of literals : 6168 (1291 equ;3172 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 87 ( 86 usr; 0 prp; 1-3 aty)
% Number of functors : 240 ( 240 usr; 46 con; 0-18 aty)
% Number of variables : 5877 (1184 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.
%------------------------------------------------------------------------------
include('Axioms/ANA003-0.ax').
include('Axioms/MSC001-1.ax').
include('Axioms/MSC001-0.ax').
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Ocompare__rls__10_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| V_a = c_plus(c_minus(V_a,V_b,T_a),V_b,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__10_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(c_plus(V_c,V_b,T_a),V_b,T_a) = V_c ) ).
cnf(cls_OrderedGroup_Ocompare__rls__11_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(c_minus(V_c,V_b,T_a),V_b,T_a) = V_c ) ).
cnf(cls_OrderedGroup_Ocompare__rls__11_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| V_a = c_minus(c_plus(V_a,V_b,T_a),V_b,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__1_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__3_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__4_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(V_a,c_plus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__5_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__6_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_minus(V_a,V_b,T_a),V_c,T_a)
| c_less(V_a,c_plus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__6_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(V_a,c_plus(V_c,V_b,T_a),T_a)
| c_less(c_minus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__7_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_less(c_plus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__7_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_less(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_less(V_a,c_minus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_SetsAndFunctions_Oset__one__times_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
| c_SetsAndFunctions_Oelt__set__times(c_1,V_y,T_a) = V_y ) ).
cnf(cls_SetsAndFunctions_Oset__zero__plus_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_SetsAndFunctions_Oelt__set__plus(c_0,V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Oadd__ac__1_0,axiom,
( ~ class_OrderedGroup_Osemigroup__add(T_a)
| c_plus(c_plus(V_a,V_b,T_a),V_c,T_a) = c_plus(V_a,c_plus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oadd__ac__2_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
| c_plus(V_a,V_b,T_a) = c_plus(V_b,V_a,T_a) ) ).
cnf(cls_OrderedGroup_Oadd__ac__3_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
| c_plus(V_a,c_plus(V_b,V_c,T_a),T_a) = c_plus(V_b,c_plus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_Orderings_Ole__maxI2_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_less(c_0,v_c,t_b) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
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