%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA014-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:02:45 PM UTC 2026
% Result : Unsatisfiable 73.52s 19.90s
% Output : CNFRefutation 73.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 50
% Syntax : Number of clauses : 186 ( 55 unt; 13 nHn; 106 RR)
% Number of literals : 354 ( 126 equ; 172 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 278 ( 35 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__left_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_0,X2,X1) = c_times(c_0,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
cnf(cls_Ring__and__Field_Ofield__mult__cancel__right_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(X2,c_0,X1) = c_times(X3,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
cnf(clsrel_Ring__and__Field_Oordered__field_24,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_24) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_HOL_Oinverse(X2,X1),X2,X1) = c_1
| X2 = c_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_34) ).
cnf(cls_Ring__and__Field_Omult__cancel__left1_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 = c_times(X2,c_1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__left1_2) ).
cnf(cls_SetInterval_OgreaterThan__subset__iff_0,axiom,
( ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OgreaterThan__subset__iff_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_41,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_41) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_Osubset__refl_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_6) ).
cnf(cls_IntDef_Oint__0__neq__1_0,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__0__neq__1_0) ).
cnf(cls_Ring__and__Field_Omult__minus__left_0,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X2,X1),X3,X1) = c_uminus(c_times(X2,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Omult__minus__left_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_7) ).
cnf(cls_Numeral_Omult__minus1_0,axiom,
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Numeral_Omult__minus1_0) ).
cnf(cls_IntDiv_Ozdiv__1_0,axiom,
c_div(X1,c_1,tc_IntDef_Oint) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__1_0) ).
cnf(cls_IntDiv_Ozdiv__zmult__self1_0,axiom,
( c_div(c_times(X2,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2
| X1 = c_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__zmult__self1_0) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__minus_0) ).
cnf(clsarity_IntDef__Oint_60,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_60) ).
cnf(cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(c_uminus(X2,X1),X2,X1) = c_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
cnf(cls_IntDiv_Ozdiv__zminus__zminus_0,axiom,
c_div(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X1,X2,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
cnf(cls_IntDiv_Ozdiv__minus1__right_0,axiom,
c_div(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDiv_Ozdiv__minus1__right_0) ).
cnf(cls_Ring__and__Field_Omult__eq__0__iff_0,axiom,
( c_times(X2,X3,X1) != c_0
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| X2 = c_0
| X3 = c_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_47,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_47) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(cls_IntDef_Oof__int__0__le__iff_1,axiom,
( ~ c_lessequals(c_0,X2,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_IntDef_Oof__int(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oof__int__0__le__iff_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_0,axiom,
( ~ c_lessequals(c_minus(X2,X3,X1),c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
cnf(cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0,axiom,
c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
cnf(clsarity_IntDef__Oint_17,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_17) ).
cnf(cls_IntDef_Oint__le__0__conv_1,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__le__0__conv_1) ).
cnf(cls_IntDef_Oint__eq__0__conv_1,axiom,
c_IntDef_Oint(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oint__eq__0__conv_1) ).
cnf(cls_IntDef_Oof__int__0__eq__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oof__int__0__eq__iff_1) ).
cnf(clsarity_IntDef__Oint_47,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_IntDef__Oint_47) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonpos_0,axiom,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = c_uminus(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonpos_0) ).
cnf(cls_IntDef_Oof__int__le__0__iff_1,axiom,
( ~ c_lessequals(X2,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_IntDef_Oof__int(X2,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_IntDef_Oof__int__le__0__iff_1) ).
cnf(cls_OrderedGroup_Oneg__0__equal__iff__equal_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_25,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_25) ).
cnf(cls_OrderedGroup_Oadd__0__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__0__right_0) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 = c_times(c_1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Omult__cancel__right1_2) ).
cnf(cls_Ring__and__Field_Omult__minus__right_0,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X2,c_uminus(X3,X1),X1) = c_uminus(c_times(X2,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Omult__minus__right_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_3) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Ofield_21) ).
cnf(cls_conjecture_0,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_50,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),t_a),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_51,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_0,X2,X1) = c_times(c_0,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Ofield__mult__cancel__left_1]) ).
cnf(c_0_52,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),t_a),
c_0_50 ).
cnf(c_0_53,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_0,X2,X1) = c_times(c_0,X3,X1) ),
c_0_51 ).
cnf(c_0_54,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(X2,c_0,X1) = c_times(X3,c_0,X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Ofield__mult__cancel__right_1]) ).
cnf(c_0_55,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_24]) ).
cnf(c_0_56,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_0)),t_a),c_times(c_0,X1,t_a),t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(X2,c_0,X1) = c_times(X3,c_0,X1) ),
c_0_54 ).
cnf(c_0_58,plain,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]) ).
cnf(c_0_59,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
c_0_55 ).
cnf(c_0_60,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
tfree_tcs ).
cnf(c_0_61,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_0)),t_a),c_times(X1,c_0,t_a),t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
c_0_58 ).
cnf(c_0_63,negated_conjecture,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_0)),t_a),c_times(X1,c_times(X2,c_0,t_a),t_a),t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_65,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_HOL_Oinverse(X2,X1),X2,X1) = c_1
| X2 = c_0 ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Ofield__class_Oaxioms__1_0]) ).
cnf(c_0_66,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__idom(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_34]) ).
cnf(c_0_67,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_0)),t_a),c_times(X1,c_times(X2,c_times(X3,c_0,t_a),t_a),t_a),t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_62]),c_0_63])]) ).
cnf(c_0_68,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_HOL_Oinverse(X2,X1),X2,X1) = c_1
| X2 = c_0 ),
c_0_65 ).
cnf(c_0_69,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 = c_times(X2,c_1,X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Omult__cancel__left1_2]) ).
cnf(c_0_70,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__idom(X1) ),
c_0_66 ).
cnf(c_0_71,plain,
( ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OgreaterThan__subset__iff_0]) ).
cnf(c_0_72,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Orderings_Olinorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_41]) ).
cnf(c_0_73,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_0)),t_a),c_times(X2,c_1,t_a),t_a)
| ~ class_Ring__and__Field_Ofield(t_a)
| c_times(X1,c_0,t_a) = c_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 = c_times(X2,c_1,X1) ),
c_0_69 ).
cnf(c_0_75,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
inference(spm,[status(thm)],[c_0_70,c_0_60]) ).
cnf(c_0_76,plain,
( ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1) ),
c_0_71 ).
cnf(c_0_77,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_78,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Orderings_Olinorder(X1) ),
c_0_72 ).
cnf(c_0_79,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oring(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_6]) ).
cnf(c_0_80,plain,
c_0 != c_1,
inference(fof_simplification,[status(thm)],[cls_IntDef_Oint__0__neq__1_0]) ).
cnf(c_0_81,plain,
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X2,X1),X3,X1) = c_uminus(c_times(X2,X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Omult__minus__left_0]) ).
cnf(c_0_82,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_0)),t_a),X2,t_a)
| ~ class_Ring__and__Field_Ofield(t_a)
| c_times(X1,c_0,t_a) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_83,plain,
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
class_Orderings_Olinorder(t_a),
inference(spm,[status(thm)],[c_0_78,c_0_60]) ).
cnf(c_0_85,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oring(X1) ),
c_0_79 ).
cnf(c_0_86,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_7]) ).
cnf(c_0_87,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_Numeral_Omult__minus1_0]) ).
cnf(c_0_88,axiom,
c_div(X1,c_1,tc_IntDef_Oint) = X1,
cls_IntDiv_Ozdiv__1_0 ).
cnf(c_0_89,axiom,
( c_div(c_times(X2,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2
| X1 = c_0 ),
cls_IntDiv_Ozdiv__zmult__self1_0 ).
cnf(c_0_90,plain,
c_0 != c_1,
c_0_80 ).
cnf(c_0_91,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ominus__minus_0]) ).
cnf(c_0_92,plain,
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X2,X1),X3,X1) = c_uminus(c_times(X2,X3,X1),X1) ),
c_0_81 ).
cnf(c_0_93,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_times(X1,c_0,t_a) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_94,negated_conjecture,
class_Ring__and__Field_Oring(t_a),
inference(spm,[status(thm)],[c_0_85,c_0_60]) ).
cnf(c_0_95,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
c_0_86 ).
cnf(c_0_96,plain,
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
c_0_87 ).
cnf(c_0_97,plain,
c_times(X1,c_1,tc_IntDef_Oint) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_98,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
clsarity_IntDef__Oint_60 ).
cnf(c_0_99,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X2,X1),X1) = X2 ),
c_0_91 ).
cnf(c_0_100,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_uminus(c_times(X1,c_0,t_a),t_a) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).
cnf(c_0_101,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_a),
inference(spm,[status(thm)],[c_0_95,c_0_60]) ).
cnf(c_0_102,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(c_uminus(X2,X1),X2,X1) = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0]) ).
cnf(c_0_103,axiom,
c_div(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X1,X2,tc_IntDef_Oint),
cls_IntDiv_Ozdiv__zminus__zminus_0 ).
cnf(c_0_104,plain,
c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]) ).
cnf(c_0_105,axiom,
c_div(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X1,tc_IntDef_Oint),
cls_IntDiv_Ozdiv__minus1__right_0 ).
cnf(c_0_106,plain,
( c_times(X2,X3,X1) != c_0
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| X2 = c_0
| X3 = c_0 ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Omult__eq__0__iff_0]) ).
cnf(c_0_107,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]) ).
cnf(c_0_108,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_47]) ).
cnf(c_0_109,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_times(X1,c_0,t_a) = c_uminus(c_0,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101])]) ).
cnf(c_0_110,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_0]) ).
cnf(c_0_111,plain,
( ~ c_lessequals(c_0,X2,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_IntDef_Oof__int(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_IntDef_Oof__int__0__le__iff_1]) ).
cnf(c_0_112,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(c_0_113,plain,
( ~ c_lessequals(c_minus(X2,X3,X1),c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Odiff__le__0__iff__le_0]) ).
cnf(c_0_114,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(c_uminus(X2,X1),X2,X1) = c_0 ),
c_0_102 ).
cnf(c_0_115,plain,
c_uminus(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]),c_0_88]) ).
cnf(c_0_116,axiom,
c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0 ).
cnf(c_0_117,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
clsarity_IntDef__Oint_17 ).
cnf(c_0_118,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
cls_IntDef_Oint__le__0__conv_1 ).
cnf(c_0_119,axiom,
c_IntDef_Oint(c_0) = c_0,
cls_IntDef_Oint__eq__0__conv_1 ).
cnf(c_0_120,plain,
( c_times(X2,X3,X1) != c_0
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| X2 = c_0
| X3 = c_0 ),
c_0_106 ).
cnf(c_0_121,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
c_0_107 ).
cnf(c_0_122,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_108 ).
cnf(c_0_123,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_times(X1,c_times(X2,c_0,t_a),t_a) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_93]),c_0_63])]) ).
cnf(c_0_124,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_times(c_0,X1,t_a) = c_uminus(c_0,t_a) ),
inference(spm,[status(thm)],[c_0_53,c_0_109]) ).
cnf(c_0_125,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
c_0_110 ).
cnf(c_0_126,plain,
( ~ c_lessequals(c_0,X2,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_IntDef_Oof__int(X2,X1),X1) ),
c_0_111 ).
cnf(c_0_127,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_112 ).
cnf(c_0_128,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
inference(fof_simplification,[status(thm)],[cls_IntDef_Oof__int__0__eq__iff_1]) ).
cnf(c_0_129,plain,
( ~ c_lessequals(c_minus(X2,X3,X1),c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,X3,X1) ),
c_0_113 ).
cnf(c_0_130,plain,
c_minus(X1,X1,tc_IntDef_Oint) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),c_0_117])]) ).
cnf(c_0_131,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
clsarity_IntDef__Oint_47 ).
cnf(c_0_132,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(rw,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_133,plain,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Oabs(c_times(X3,X1,X2),X2) != c_0
| c_HOL_Oabs(X3,X2) = c_0
| c_HOL_Oabs(X1,X2) = c_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]) ).
cnf(c_0_134,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_times(X1,c_uminus(c_0,t_a),t_a) = c_0 ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_135,plain,
( ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Oabs(c_IntDef_Oof__int(X1,X2),X2) = c_IntDef_Oof__int(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_136,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
c_0_128 ).
cnf(c_0_137,plain,
c_lessequals(X1,X1,tc_IntDef_Oint),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_132])]) ).
cnf(c_0_138,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_HOL_Oabs(c_0,t_a) != c_0
| c_HOL_Oabs(X1,t_a) = c_0
| c_HOL_Oabs(c_uminus(c_0,t_a),t_a) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_75])]) ).
cnf(c_0_139,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_0,X1) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137])]) ).
cnf(c_0_140,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Ofield(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_0]) ).
cnf(c_0_141,plain,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = c_uminus(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__of__nonpos_0]) ).
cnf(c_0_142,plain,
( ~ c_lessequals(X2,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_IntDef_Oof__int(X2,X1),c_0,X1) ),
inference(fof_simplification,[status(thm)],[cls_IntDef_Oof__int__le__0__iff_1]) ).
cnf(c_0_143,negated_conjecture,
( ~ class_Ring__and__Field_Ofield(t_a)
| c_HOL_Oabs(X1,t_a) = c_0
| c_HOL_Oabs(c_uminus(c_0,t_a),t_a) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_75])]) ).
cnf(c_0_144,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Ofield(X1) ),
c_0_140 ).
cnf(c_0_145,plain,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = c_uminus(X2,X1) ),
c_0_141 ).
cnf(c_0_146,plain,
( ~ c_lessequals(X2,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_IntDef_Oof__int(X2,X1),c_0,X1) ),
c_0_142 ).
cnf(c_0_147,negated_conjecture,
( c_HOL_Oabs(X1,t_a) = c_0
| c_HOL_Oabs(c_uminus(c_0,t_a),t_a) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_60])]) ).
cnf(c_0_148,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oneg__0__equal__iff__equal_1]) ).
cnf(c_0_149,plain,
( ~ c_lessequals(X1,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Oabs(c_IntDef_Oof__int(X1,X2),X2) = c_uminus(c_IntDef_Oof__int(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_127]) ).
cnf(c_0_150,negated_conjecture,
c_HOL_Oabs(c_uminus(c_0,t_a),t_a) = c_0,
inference(ef,[status(thm)],[c_0_147]) ).
cnf(c_0_151,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
c_0_148 ).
cnf(c_0_152,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Odiff__minus__eq__add_0]) ).
cnf(c_0_153,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_0,X1) = c_uminus(c_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_136]),c_0_137])]) ).
cnf(c_0_154,negated_conjecture,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_101])]) ).
cnf(c_0_155,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_25]) ).
cnf(c_0_156,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oadd__0__right_0]) ).
cnf(c_0_157,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1) ),
c_0_152 ).
cnf(c_0_158,negated_conjecture,
c_uminus(c_0,t_a) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_75])]) ).
cnf(c_0_159,plain,
( ~ class_Ring__and__Field_Oordered__field(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_155 ).
cnf(c_0_160,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ominus__diff__eq_0]) ).
cnf(c_0_161,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
c_0_156 ).
cnf(c_0_162,negated_conjecture,
c_plus(X1,c_0,t_a) = c_minus(X1,c_0,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_101])]) ).
cnf(c_0_163,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(spm,[status(thm)],[c_0_159,c_0_60]) ).
cnf(c_0_164,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
c_0_160 ).
cnf(c_0_165,negated_conjecture,
c_minus(X1,c_0,t_a) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163])]) ).
cnf(c_0_166,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 = c_times(c_1,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Omult__cancel__right1_2]) ).
cnf(c_0_167,plain,
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X2,c_uminus(X3,X1),X1) = c_uminus(c_times(X2,X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Omult__minus__right_0]) ).
cnf(c_0_168,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oring(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_3]) ).
cnf(c_0_169,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Ofield_21]) ).
cnf(c_0_170,negated_conjecture,
c_minus(c_0,X1,t_a) = c_uminus(X1,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_101])]) ).
cnf(c_0_171,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 = c_times(c_1,X2,X1) ),
c_0_166 ).
cnf(c_0_172,plain,
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X2,c_uminus(X3,X1),X1) = c_uminus(c_times(X2,X3,X1),X1) ),
c_0_167 ).
cnf(c_0_173,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oring(X1) ),
c_0_168 ).
cnf(c_0_174,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_HOL_Oabs(c_times(v_c,v_f(v_x(X1)),t_a),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_121]),c_0_75])]) ).
cnf(c_0_175,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
c_0_169 ).
cnf(c_0_176,negated_conjecture,
c_uminus(c_uminus(X1,t_a),t_a) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_170]),c_0_165]),c_0_101])]) ).
cnf(c_0_177,plain,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_uminus(c_times(c_1,X1,X2),X2) = c_uminus(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173]) ).
cnf(c_0_178,negated_conjecture,
v_c != c_0,
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_179,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),c_HOL_Oabs(c_times(X1,c_times(v_c,v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_121]),c_0_75])]) ).
cnf(c_0_180,plain,
( ~ class_Ring__and__Field_Ofield(X2)
| X1 = c_0
| c_times(c_HOL_Oinverse(X1,X2),c_times(X1,X3,X2),X2) = c_times(c_1,X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_68]),c_0_175]) ).
cnf(c_0_181,negated_conjecture,
c_times(c_1,X1,t_a) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_176]),c_0_75])]) ).
cnf(c_0_182,negated_conjecture,
v_c != c_0,
c_0_178 ).
cnf(c_0_183,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]),c_0_182]) ).
cnf(c_0_184,negated_conjecture,
~ class_Ring__and__Field_Ofield(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_83]),c_0_84])]) ).
cnf(c_0_185,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_144]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA014-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/10.37 % Computer : n016.cluster.edu
% 0.12/10.37 % Model : x86_64 x86_64
% 0.12/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.37 % Memory : 8046.5625MB
% 0.12/10.37 % OS : Linux 6.8.0-71-generic
% 0.12/10.37 % CPULimit : 300
% 0.12/10.37 % WCLimit : 300
% 0.12/10.37 % DateTime : Mon Sep 21 13:28:49 UTC 2026
% 0.12/10.37 % CPUTime :
% 0.12/10.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/10.42 Running first-order theorem proving
% 0.16/10.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.52/19.90 % Version: 3.5.1
% 73.52/19.90 % Preprocessing class: FMLMSMSMSSSNFFN.
% 73.52/19.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.52/19.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.52/19.90 % Starting new_bool_3 with 300s (1) cores
% 73.52/19.90 % Starting new_bool_1 with 300s (1) cores
% 73.52/19.90 % Starting sh5l with 300s (1) cores
% 73.52/19.90 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2517772 completed with status 0
% 73.52/19.90 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 73.52/19.90 % Preprocessing class: FMLMSMSMSSSNFFN.
% 73.52/19.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.52/19.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.52/19.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.52/19.90 % No SInE strategy applied
% 73.52/19.90 % Search class: FGHSM-SMLM32-DFFFFFNN
% 73.52/19.90 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 73.52/19.90 % Starting SubtermCWHack with 136s (1) cores
% 73.52/19.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 73.52/19.90 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 73.52/19.90 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 73.52/19.90 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 73.52/19.90 % G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 2517782 completed with status 0
% 73.52/19.90 % Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 73.52/19.90 % Preprocessing class: FMLMSMSMSSSNFFN.
% 73.52/19.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.52/19.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.52/19.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.52/19.90 % No SInE strategy applied
% 73.52/19.90 % Search class: FGHSM-SMLM32-DFFFFFNN
% 73.52/19.90 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 73.52/19.90 % Starting SubtermCWHack with 136s (1) cores
% 73.52/19.90 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 73.52/19.90 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 73.52/19.90 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 73.52/19.90 % Preprocessing time : 0.030 s
% 73.52/19.90
% 73.52/19.90 % Proof found!
% 73.52/19.90 % SZS status Unsatisfiable
% 73.52/19.90 % SZS output start CNFRefutation
% See solution above
% 73.52/19.90 % Parsed axioms : 2787
% 73.52/19.90 % Removed by relevancy pruning/SinE : 0
% 73.52/19.90 % Initial clauses : 2787
% 73.52/19.90 % Removed in clause preprocessing : 9
% 73.52/19.90 % Initial clauses in saturation : 2778
% 73.52/19.90 % Processed clauses : 51463
% 73.52/19.90 % ...of these trivial : 534
% 73.52/19.90 % ...subsumed : 43443
% 73.52/19.90 % ...remaining for further processing : 7486
% 73.52/19.90 % Other redundant clauses eliminated : 3082
% 73.52/19.90 % Clauses deleted for lack of memory : 0
% 73.52/19.90 % Backward-subsumed : 587
% 73.52/19.90 % Backward-rewritten : 479
% 73.52/19.90 % Generated clauses : 302050
% 73.52/19.90 % ...of the previous two non-redundant : 260940
% 73.52/19.90 % ...aggressively subsumed : 0
% 73.52/19.90 % Contextual simplify-reflections : 516
% 73.52/19.90 % Paramodulations : 298886
% 73.52/19.90 % Factorizations : 21
% 73.52/19.90 % NegExts : 0
% 73.52/19.90 % Equation resolutions : 3142
% 73.52/19.90 % Disequality decompositions : 0
% 73.52/19.90 % Total rewrite steps : 225501
% 73.52/19.90 % ...of those cached : 220025
% 73.52/19.90 % Propositional unsat checks : 1
% 73.52/19.90 % Propositional check models : 0
% 73.52/19.90 % Propositional check unsatisfiable : 0
% 73.52/19.90 % Propositional clauses : 0
% 73.52/19.90 % Propositional clauses after purity: 0
% 73.52/19.90 % Propositional unsat core size : 0
% 73.52/19.90 % Propositional preprocessing time : 0.000
% 73.52/19.90 % Propositional encoding time : 0.123
% 73.52/19.90 % Propositional solver time : 0.123
% 73.52/19.90 % Success case prop preproc time : 0.000
% 73.52/19.90 % Success case prop encoding time : 0.000
% 73.52/19.90 % Success case prop solver time : 0.000
% 73.52/19.90 % Current number of processed clauses : 6418
% 73.52/19.90 % Positive orientable unit clauses : 845
% 73.52/19.90 % Positive unorientable unit clauses: 16
% 73.52/19.90 % Negative unit clauses : 597
% 73.52/19.90 % Non-unit-clauses : 4960
% 73.52/19.90 % Current number of unprocessed clauses: 208825
% 73.52/19.90 % ...number of literals in the above : 779041
% 73.52/19.90 % Current number of archived formulas : 0
% 73.52/19.90 % Current number of archived clauses : 1075
% 73.52/19.90 % Clause-clause subsumption calls (NU) : 7666822
% 73.52/19.90 % Rec. Clause-clause subsumption calls : 4577016
% 73.52/19.90 % Non-unit clause-clause subsumptions : 18728
% 73.52/19.90 % Unit Clause-clause subsumption calls : 212263
% 73.52/19.90 % Rewrite failures with RHS unbound : 2
% 73.52/19.90 % BW rewrite match attempts : 1495
% 73.52/19.90 % BW rewrite match successes : 174
% 73.52/19.90 % Condensation attempts : 0
% 73.52/19.90 % Condensation successes : 0
% 73.52/19.90 % Termbank termtop insertions : 5239443
% 73.52/19.90 % Search garbage collected termcells : 4071
% 73.52/19.90
% 73.52/19.90 % -------------------------------------------------
% 73.52/19.90 % User time : 8.895 s
% 73.52/19.90 % System time : 0.222 s
% 73.52/19.90 % Total time : 9.117 s
% 73.52/19.90 % Maximum resident set size: 8504 pages
% 73.52/19.90
% 73.52/19.90 % -------------------------------------------------
% 73.52/19.90 % User time : 44.526 s
% 73.52/19.90 % System time : 1.135 s
% 73.52/19.90 % Total time : 45.661 s
% 73.52/19.90 % Maximum resident set size: 6400 pages
% 73.52/19.90 % E exiting
%------------------------------------------------------------------------------