TPTP Problem File: ANA024-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ANA024-1 : TPTP v8.2.0. 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_lesso2_simpler_2 [Pau06]
% Status : Unsatisfiable
% Rating : 0.40 v8.2.0, 0.43 v8.1.0, 0.42 v7.5.0, 0.47 v7.4.0, 0.53 v7.3.0, 0.50 v7.2.0, 0.42 v7.1.0, 0.33 v7.0.0, 0.47 v6.4.0, 0.53 v6.3.0, 0.45 v6.2.0, 0.50 v6.1.0, 0.79 v6.0.0, 0.70 v5.5.0, 0.95 v5.4.0, 0.85 v5.3.0, 0.89 v5.2.0, 0.81 v5.1.0, 0.88 v5.0.0, 0.86 v4.1.0, 0.85 v4.0.1, 0.82 v3.7.0, 0.70 v3.5.0, 0.73 v3.4.0, 0.75 v3.3.0, 0.86 v3.2.0
% Syntax : Number of clauses : 2809 ( 649 unt; 249 nHn;1987 RR)
% Number of literals : 6176 (1289 equ;3178 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 : 239 ( 239 usr; 46 con; 0-18 aty)
% Number of variables : 5879 (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_Oab__group__add__class_Odiff__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_minus(V_a,V_b,T_a) = c_plus(V_a,c_uminus(V_b,T_a),T_a) ) ).
cnf(cls_Orderings_Olinorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_Orderings_Olinorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_less(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,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_conjecture_0,negated_conjecture,
c_lessequals(c_0,v_k(V_U),t_b) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_k(V_U),v_f(V_U),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
%------------------------------------------------------------------------------