%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA026-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:02:48 PM UTC 2026
% Result : Unsatisfiable 236.38s 54.88s
% Output : CNFRefutation 236.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 46
% Syntax : Number of clauses : 239 ( 49 unt; 45 nHn; 175 RR)
% Number of literals : 501 ( 140 equ; 223 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 353 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_OrderedGroup_Oabs__0__eq_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__0__eq_1) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(cls_OrderedGroup_Oabs__le__zero__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__le__zero__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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(cls_OrderedGroup_Oneg__le__iff__le_1,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_uminus(X3,X1),c_uminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__le__iff__le_1) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Orderings_Olinorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_less(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(clsrel_Orderings_Olinorder_4,axiom,
( ~ class_Orderings_Olinorder(X1)
| class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Orderings_Olinorder_4) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Omax(X2,X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1,axiom,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_53,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_53) ).
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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(cls_OrderedGroup_Opprt__eq__id_0,axiom,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Opprt__eq__id_0) ).
cnf(cls_OrderedGroup_Odiff__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(c_0,X2,X1) = c_uminus(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__0_0) ).
cnf(cls_OrderedGroup_Oabs__le__zero__iff_0,axiom,
( ~ c_lessequals(c_HOL_Oabs(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| X2 = c_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
cnf(cls_OrderedGroup_Opprt__eq__0_0,axiom,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X2,X1) = c_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Opprt__eq__0_0) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_minus(X2,X3,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
cnf(cls_Orderings_Olinorder__not__le_1,axiom,
( ~ c_lessequals(X3,X2,X1)
| ~ c_less(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
cnf(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__minus__cancel_0) ).
cnf(cls_OrderedGroup_Oabs__0__eq_0,axiom,
( c_0 != c_HOL_Oabs(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| X2 = c_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__0__eq_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
( ~ c_lessequals(X2,c_minus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_plus(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( ~ c_lessequals(c_plus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,c_minus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__3_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
cnf(cls_OrderedGroup_Odiff__self_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,X2,X1) = c_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__self_0) ).
cnf(cls_OrderedGroup_Oadd__0__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__0__right_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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonpos_0) ).
cnf(cls_OrderedGroup_Odiff__eq__0__iff__eq_0,axiom,
( c_minus(X2,X3,X1) != c_0
| ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
cnf(cls_OrderedGroup_Onprt__eq__0_0,axiom,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X2,X1) = c_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Onprt__eq__0_0) ).
cnf(cls_OrderedGroup_Onprt__eq__id_0,axiom,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Onprt__eq__id_0) ).
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/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
cnf(c_0_46,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_47,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__0__eq_1]) ).
cnf(c_0_48,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_46 ).
cnf(c_0_49,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_50,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c_0_51,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
c_0_47 ).
cnf(c_0_52,negated_conjecture,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
cnf(c_0_54,plain,
( ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2]) ).
cnf(c_0_55,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
c_0_50 ).
cnf(c_0_56,negated_conjecture,
c_HOL_Oabs(c_0,t_b) = c_0,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
c_0_53 ).
cnf(c_0_58,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
cnf(c_0_59,plain,
( ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1) ),
c_0_54 ).
cnf(c_0_60,negated_conjecture,
c_lessequals(c_0,c_0,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52])]) ).
cnf(c_0_61,negated_conjecture,
class_Orderings_Olinorder(t_b),
inference(spm,[status(thm)],[c_0_57,c_0_49]) ).
cnf(c_0_62,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__le__zero__iff_1]) ).
cnf(c_0_63,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_64,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
c_0_58 ).
cnf(c_0_65,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_54]) ).
cnf(c_0_66,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
cnf(c_0_67,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_uminus(X3,X1),c_uminus(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oneg__le__iff__le_1]) ).
cnf(c_0_68,negated_conjecture,
( ~ c_lessequals(X1,c_0,t_b)
| c_lessequals(c_Orderings_Omax(c_0,X1,t_b),c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_69,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
c_0_62 ).
cnf(c_0_70,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
c_0_63 ).
cnf(c_0_71,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_64,c_0_49]) ).
cnf(c_0_72,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_65 ).
cnf(c_0_73,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_74,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_less(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Olinorder__not__le_0]) ).
cnf(c_0_75,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c_0_76,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
c_0_66 ).
cnf(c_0_77,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_uminus(X3,X1),c_uminus(X2,X1),X1) ),
c_0_67 ).
cnf(c_0_78,negated_conjecture,
c_lessequals(c_Orderings_Omax(c_0,c_0,t_b),c_0,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_56]),c_0_52])]) ).
cnf(c_0_79,negated_conjecture,
c_uminus(c_0,t_b) = c_0,
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(spm,[status(thm)],[c_0_72,c_0_49]) ).
cnf(c_0_81,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0]) ).
cnf(c_0_82,plain,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
cnf(c_0_83,plain,
( ~ class_Orderings_Olinorder(X1)
| class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Orderings_Olinorder_4]) ).
cnf(c_0_84,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Omax(X2,X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0]) ).
cnf(c_0_85,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(c_0_86,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
c_0_73 ).
cnf(c_0_87,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_less(X2,X3,X1) ),
c_0_74 ).
cnf(c_0_88,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
c_0_75 ).
cnf(c_0_89,negated_conjecture,
class_Orderings_Oorder(t_b),
inference(spm,[status(thm)],[c_0_76,c_0_49]) ).
cnf(c_0_90,negated_conjecture,
c_lessequals(c_0,c_uminus(c_Orderings_Omax(c_0,c_0,t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_80])]) ).
cnf(c_0_91,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,X4,X1) ),
c_0_81 ).
cnf(c_0_92,plain,
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X2,X1) ),
c_0_82 ).
cnf(c_0_93,plain,
( ~ class_Orderings_Olinorder(X1)
| class_Orderings_Oorder(X1) ),
c_0_83 ).
cnf(c_0_94,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Omax(X2,X2,X1) = X2 ),
c_0_84 ).
cnf(c_0_95,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
c_0_85 ).
cnf(c_0_96,negated_conjecture,
c_less(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_61])]) ).
cnf(c_0_97,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1]) ).
cnf(c_0_98,negated_conjecture,
( ~ c_lessequals(c_0,X1,t_b)
| c_lessequals(c_Orderings_Omax(c_0,c_0,t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_78]),c_0_89])]) ).
cnf(c_0_99,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_53]) ).
cnf(c_0_100,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_101,negated_conjecture,
( ~ c_lessequals(c_uminus(c_Orderings_Omax(c_0,c_0,t_b),t_b),X1,t_b)
| c_lessequals(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_90]),c_0_89])]) ).
cnf(c_0_102,plain,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X1,c_Orderings_Omax(X1,X2,X3),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
cnf(c_0_103,negated_conjecture,
c_Orderings_Omax(X1,X1,t_b) = X1,
inference(spm,[status(thm)],[c_0_94,c_0_61]) ).
cnf(c_0_104,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_89])]) ).
cnf(c_0_105,plain,
( ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X4,X1) ),
c_0_97 ).
cnf(c_0_106,negated_conjecture,
( c_lessequals(c_Orderings_Omax(c_0,X1,t_b),c_0,t_b)
| c_less(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_87]),c_0_61])]) ).
cnf(c_0_107,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Opprt__eq__id_0]) ).
cnf(c_0_108,negated_conjecture,
c_lessequals(c_Orderings_Omax(c_0,c_0,t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_55]),c_0_52])]) ).
cnf(c_0_109,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group(X1) ),
c_0_99 ).
cnf(c_0_110,negated_conjecture,
c_lessequals(c_Orderings_Omax(c_0,c_Orderings_Omax(c_0,c_0,t_b),t_b),c_0,t_b),
inference(spm,[status(thm)],[c_0_68,c_0_78]) ).
cnf(c_0_111,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(c_0,X2,X1) = c_uminus(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Odiff__0_0]) ).
cnf(c_0_112,plain,
( ~ c_lessequals(c_HOL_Oabs(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| X2 = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__le__zero__iff_0]) ).
cnf(c_0_113,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
c_0_100 ).
cnf(c_0_114,negated_conjecture,
c_lessequals(c_0,c_Orderings_Omax(c_0,X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_79]),c_0_61])]) ).
cnf(c_0_115,plain,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X2,X1) = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Opprt__eq__0_0]) ).
cnf(c_0_116,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),X1,t_b)
| c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_104]),c_0_89])]) ).
cnf(c_0_117,negated_conjecture,
( c_lessequals(X1,c_0,t_b)
| c_less(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_61])]) ).
cnf(c_0_118,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X2,X1) = X2 ),
c_0_107 ).
cnf(c_0_119,negated_conjecture,
c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_108]),c_0_61])]) ).
cnf(c_0_120,negated_conjecture,
class_OrderedGroup_Olordered__ab__group(t_b),
inference(spm,[status(thm)],[c_0_109,c_0_49]) ).
cnf(c_0_121,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_minus(X2,X3,X1),c_0,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Odiff__le__0__iff__le_1]) ).
cnf(c_0_122,negated_conjecture,
c_lessequals(c_Orderings_Omax(c_0,c_Orderings_Omax(c_0,c_Orderings_Omax(c_0,c_0,t_b),t_b),t_b),c_0,t_b),
inference(spm,[status(thm)],[c_0_68,c_0_110]) ).
cnf(c_0_123,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(c_0,X2,X1) = c_uminus(X2,X1) ),
c_0_111 ).
cnf(c_0_124,plain,
( ~ c_lessequals(c_HOL_Oabs(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| X2 = c_0 ),
c_0_112 ).
cnf(c_0_125,negated_conjecture,
c_HOL_Oabs(c_Orderings_Omax(c_0,X1,t_b),t_b) = c_Orderings_Omax(c_0,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_52])]) ).
cnf(c_0_126,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_less(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Olinorder__not__le_1]) ).
cnf(c_0_127,plain,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X2,X1) = c_0 ),
c_0_115 ).
cnf(c_0_128,negated_conjecture,
( c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_0,t_b)
| c_less(c_0,c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_129,negated_conjecture,
c_OrderedGroup_Opprt(c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120])]) ).
cnf(c_0_130,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_minus(X2,X3,X1),c_0,X1) ),
c_0_121 ).
cnf(c_0_131,negated_conjecture,
c_lessequals(c_0,c_uminus(c_Orderings_Omax(c_0,c_Orderings_Omax(c_0,c_Orderings_Omax(c_0,c_0,t_b),t_b),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_122]),c_0_79]),c_0_80])]) ).
cnf(c_0_132,negated_conjecture,
c_minus(c_0,X1,t_b) = c_uminus(X1,t_b),
inference(spm,[status(thm)],[c_0_123,c_0_71]) ).
cnf(c_0_133,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(c_0,X1,t_b),c_0,t_b)
| c_Orderings_Omax(c_0,X1,t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_52])]) ).
cnf(c_0_134,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_less(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_126 ).
cnf(c_0_135,negated_conjecture,
( c_less(c_0,c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b)
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]),c_0_120])]) ).
cnf(c_0_136,plain,
( ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Omax(X2,X4,X3),X1,X3)
| c_less(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_87]) ).
cnf(c_0_137,negated_conjecture,
c_lessequals(c_uminus(c_uminus(c_Orderings_Omax(c_0,c_Orderings_Omax(c_0,c_Orderings_Omax(c_0,c_0,t_b),t_b),t_b),t_b),t_b),c_0,t_b),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_80])]),c_0_132]) ).
cnf(c_0_138,negated_conjecture,
( c_less(c_0,X1,t_b)
| c_Orderings_Omax(c_0,X1,t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_133,c_0_106]) ).
cnf(c_0_139,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__minus__cancel_0]) ).
cnf(c_0_140,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_0,t_b)
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_61])]) ).
cnf(c_0_141,negated_conjecture,
( c_lessequals(c_Orderings_Omax(X1,c_0,t_b),c_0,t_b)
| c_less(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_103]),c_0_103]),c_0_103]),c_0_79]),c_0_79]),c_0_61])]) ).
cnf(c_0_142,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| c_Orderings_Omax(c_0,X1,t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_138]),c_0_89])]) ).
cnf(c_0_143,plain,
( c_0 != c_HOL_Oabs(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| X2 = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__0__eq_0]) ).
cnf(c_0_144,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
c_0_139 ).
cnf(c_0_145,negated_conjecture,
( c_less(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_146,plain,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X1,c_Orderings_Omax(X2,X1,X3),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_92]),c_0_93]) ).
cnf(c_0_147,negated_conjecture,
( c_HOL_Oabs(X1,t_b) = X1
| c_Orderings_Omax(c_0,X1,t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_142]),c_0_52])]) ).
cnf(c_0_148,plain,
( c_0 != c_HOL_Oabs(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| X2 = c_0 ),
c_0_143 ).
cnf(c_0_149,negated_conjecture,
c_HOL_Oabs(c_uminus(X1,t_b),t_b) = c_HOL_Oabs(X1,t_b),
inference(spm,[status(thm)],[c_0_144,c_0_52]) ).
cnf(c_0_150,negated_conjecture,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_145]),c_0_61])]) ).
cnf(c_0_151,negated_conjecture,
( c_lessequals(X1,c_0,t_b)
| c_HOL_Oabs(X1,t_b) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_61])]) ).
cnf(c_0_152,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_23]) ).
cnf(c_0_153,negated_conjecture,
( c_HOL_Oabs(X1,t_b) != c_0
| c_uminus(X1,t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_52])]) ).
cnf(c_0_154,negated_conjecture,
( c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0
| c_HOL_Oabs(c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(v_f(v_x),v_k(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_155,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0]) ).
cnf(c_0_156,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_152 ).
cnf(c_0_157,plain,
( ~ c_lessequals(X2,c_minus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_plus(X2,X4,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_0]) ).
cnf(c_0_158,negated_conjecture,
( c_uminus(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0
| c_HOL_Oabs(c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_minus(v_f(v_x),v_k(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_159,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X2,X1) = X2 ),
c_0_155 ).
cnf(c_0_160,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(spm,[status(thm)],[c_0_156,c_0_49]) ).
cnf(c_0_161,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_162,plain,
( ~ c_lessequals(c_plus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,c_minus(X4,X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_1]) ).
cnf(c_0_163,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
cls_conjecture_1 ).
cnf(c_0_164,plain,
( ~ c_lessequals(X2,c_minus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_plus(X2,X4,X1),X3,X1) ),
c_0_157 ).
cnf(c_0_165,negated_conjecture,
( c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_uminus(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_158]),c_0_52])]) ).
cnf(c_0_166,negated_conjecture,
c_plus(c_0,X1,t_b) = X1,
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_167,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1) ),
c_0_161 ).
cnf(c_0_168,plain,
( ~ c_lessequals(c_plus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X2,c_minus(X4,X3,X1),X1) ),
c_0_162 ).
cnf(c_0_169,negated_conjecture,
( ~ c_lessequals(v_k(X1),X2,t_b)
| c_lessequals(v_g(X1),X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_163]),c_0_89])]) ).
cnf(c_0_170,negated_conjecture,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| c_uminus(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]),c_0_80])]) ).
cnf(c_0_171,negated_conjecture,
c_uminus(c_minus(X1,X2,t_b),t_b) = c_minus(X2,X1,t_b),
inference(spm,[status(thm)],[c_0_167,c_0_71]) ).
cnf(c_0_172,negated_conjecture,
( ~ c_lessequals(X2,X1,t_b)
| c_lessequals(c_0,c_minus(X1,X2,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_166]),c_0_80])]) ).
cnf(c_0_173,negated_conjecture,
( c_lessequals(v_g(v_x),v_f(v_x),t_b)
| c_uminus(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_174,plain,
( ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3)
| c_lessequals(c_Orderings_Omax(X1,X2,X3),X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_92]),c_0_93]) ).
cnf(c_0_175,negated_conjecture,
( c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(rw,[status(thm)],[c_0_165,c_0_171]) ).
cnf(c_0_176,negated_conjecture,
( c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| c_uminus(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_177,negated_conjecture,
( c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_61])]) ).
cnf(c_0_178,negated_conjecture,
( c_uminus(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_0
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_minus(v_f(v_x),v_g(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_176]),c_0_52])]) ).
cnf(c_0_179,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__2_0]) ).
cnf(c_0_180,negated_conjecture,
( c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_116,c_0_177]) ).
cnf(c_0_181,negated_conjecture,
( c_minus(v_g(v_x),v_f(v_x),t_b) = c_0
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_minus(v_f(v_x),v_g(v_x),t_b) ),
inference(rw,[status(thm)],[c_0_178,c_0_171]) ).
cnf(c_0_182,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Ocompare__rls__3_0]) ).
cnf(c_0_183,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1) ),
c_0_179 ).
cnf(c_0_184,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,X2,X1) = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Odiff__self_0]) ).
cnf(c_0_185,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_186,negated_conjecture,
( c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_187,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1) ),
c_0_182 ).
cnf(c_0_188,negated_conjecture,
c_minus(c_plus(X1,X2,t_b),X3,t_b) = c_plus(X1,c_minus(X2,X3,t_b),t_b),
inference(spm,[status(thm)],[c_0_183,c_0_71]) ).
cnf(c_0_189,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X2,X2,X1) = c_0 ),
c_0_184 ).
cnf(c_0_190,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X2,c_0,X1) = X2 ),
c_0_185 ).
cnf(c_0_191,negated_conjecture,
( c_less(c_0,c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_128]),c_0_52])]) ).
cnf(c_0_192,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(X2,t_b),X1,t_b)
| c_lessequals(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_119]),c_0_89])]) ).
cnf(c_0_193,negated_conjecture,
( c_lessequals(c_minus(v_k(v_x),v_f(v_x),t_b),c_minus(v_g(v_x),v_f(v_x),t_b),t_b)
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_186]),c_0_171]),c_0_171]),c_0_80])]) ).
cnf(c_0_194,negated_conjecture,
c_plus(c_minus(X1,X2,t_b),X3,t_b) = c_plus(X1,c_minus(X3,X2,t_b),t_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_71]),c_0_188]) ).
cnf(c_0_195,negated_conjecture,
c_minus(X1,X1,t_b) = c_0,
inference(spm,[status(thm)],[c_0_189,c_0_71]) ).
cnf(c_0_196,negated_conjecture,
c_plus(X1,c_0,t_b) = X1,
inference(spm,[status(thm)],[c_0_190,c_0_160]) ).
cnf(c_0_197,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_0,t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_191]),c_0_61])]) ).
cnf(c_0_198,negated_conjecture,
c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b),
inference(spm,[status(thm)],[c_0_192,c_0_104]) ).
cnf(c_0_199,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_200,negated_conjecture,
( c_lessequals(v_k(v_x),v_g(v_x),t_b)
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_193]),c_0_194]),c_0_195]),c_0_196]),c_0_80])]) ).
cnf(c_0_201,negated_conjecture,
( c_less(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_197,c_0_141]) ).
cnf(c_0_202,negated_conjecture,
( ~ c_lessequals(X1,c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b)
| c_lessequals(c_Orderings_Omax(c_0,X1,t_b),c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_198]),c_0_61])]) ).
cnf(c_0_203,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_199 ).
cnf(c_0_204,negated_conjecture,
( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_200]),c_0_80])]) ).
cnf(c_0_205,negated_conjecture,
( c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_201]),c_0_89])]) ).
cnf(c_0_206,negated_conjecture,
c_lessequals(c_Orderings_Omax(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_102]),c_0_61])]) ).
cnf(c_0_207,plain,
( c_minus(X2,X3,X1) != c_0
| ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Odiff__eq__0__iff__eq_0]) ).
cnf(c_0_208,negated_conjecture,
( c_minus(v_g(v_x),v_f(v_x),t_b) = c_0
| c_HOL_Oabs(c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = c_minus(v_g(v_x),v_k(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_171]),c_0_52])]) ).
cnf(c_0_209,negated_conjecture,
c_lessequals(c_minus(v_g(X1),v_k(X1),t_b),c_0,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_163]),c_0_80])]) ).
cnf(c_0_210,negated_conjecture,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_205]),c_0_166]),c_0_80])]) ).
cnf(c_0_211,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X2,X1) = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Onprt__eq__0_0]) ).
cnf(c_0_212,negated_conjecture,
c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_206]),c_0_61])]) ).
cnf(c_0_213,plain,
( c_minus(X2,X3,X1) != c_0
| ~ class_OrderedGroup_Oab__group__add(X1)
| X2 = X3 ),
c_0_207 ).
cnf(c_0_214,negated_conjecture,
( c_minus(v_k(v_x),v_g(v_x),t_b) = c_0
| c_minus(v_g(v_x),v_f(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_208]),c_0_52]),c_0_209])]) ).
cnf(c_0_215,negated_conjecture,
( c_lessequals(v_g(v_x),v_f(v_x),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_169,c_0_210]) ).
cnf(c_0_216,plain,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Onprt__eq__id_0]) ).
cnf(c_0_217,negated_conjecture,
( c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_205]),c_0_61])]) ).
cnf(c_0_218,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X2,X1) = c_0 ),
c_0_211 ).
cnf(c_0_219,negated_conjecture,
c_lessequals(c_0,c_minus(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),t_b),
inference(spm,[status(thm)],[c_0_172,c_0_212]) ).
cnf(c_0_220,negated_conjecture,
( v_f(v_x) = v_g(v_x)
| c_minus(v_k(v_x),v_g(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_71])]) ).
cnf(c_0_221,negated_conjecture,
( c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_172,c_0_215]) ).
cnf(c_0_222,plain,
( ~ c_lessequals(X2,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X2,X1) = X2 ),
c_0_216 ).
cnf(c_0_223,negated_conjecture,
( c_lessequals(c_minus(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),c_0,t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_217]),c_0_80])]) ).
cnf(c_0_224,negated_conjecture,
c_OrderedGroup_Onprt(c_minus(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_120])]) ).
cnf(c_0_225,negated_conjecture,
( v_g(v_x) = v_k(v_x)
| v_f(v_x) = v_g(v_x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_220]),c_0_71])]) ).
cnf(c_0_226,negated_conjecture,
( c_minus(v_f(v_x),v_g(v_x),t_b) = c_0
| c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_minus(v_f(v_x),v_g(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_221]),c_0_52])]) ).
cnf(c_0_227,negated_conjecture,
( c_minus(v_f(v_x),v_g(v_x),t_b) = c_0
| c_minus(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_224]),c_0_120])]) ).
cnf(c_0_228,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_g(v_x),v_k(v_x),t_b),c_0,t_b),c_0,t_b)
| v_g(v_x) = v_k(v_x) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_225]),c_0_195]),c_0_56]) ).
cnf(c_0_229,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_230,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_86,c_0_226]) ).
cnf(c_0_231,negated_conjecture,
( c_minus(v_f(v_x),v_g(v_x),t_b) = c_0
| c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) = c_minus(v_f(v_x),v_k(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_227]),c_0_71])]) ).
cnf(c_0_232,negated_conjecture,
( c_less(c_0,c_minus(v_g(v_x),v_k(v_x),t_b),t_b)
| v_g(v_x) = v_k(v_x) ),
inference(spm,[status(thm)],[c_0_228,c_0_141]) ).
cnf(c_0_233,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_229 ).
cnf(c_0_234,negated_conjecture,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| c_minus(v_f(v_x),v_g(v_x),t_b) = c_0 ),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_235,negated_conjecture,
v_g(v_x) = v_k(v_x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_232]),c_0_61]),c_0_209])]) ).
cnf(c_0_236,negated_conjecture,
c_lessequals(X1,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_195]),c_0_80]),c_0_60])]) ).
cnf(c_0_237,negated_conjecture,
c_minus(v_f(v_x),v_k(v_x),t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_234,c_0_235]),c_0_235]),c_0_236])]) ).
cnf(c_0_238,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_237]),c_0_103]),c_0_235]),c_0_237]),c_0_56]),c_0_236])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA026-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/20.43 % Computer : n016.cluster.edu
% 0.14/20.43 % Model : x86_64 x86_64
% 0.14/20.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/20.43 % Memory : 8046.5625MB
% 0.14/20.43 % OS : Linux 6.8.0-71-generic
% 0.14/20.43 % CPULimit : 300
% 0.14/20.43 % WCLimit : 300
% 0.14/20.43 % DateTime : Mon Sep 21 13:29:45 UTC 2026
% 0.14/20.43 % CPUTime :
% 0.14/20.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/20.50 Running first-order theorem proving
% 0.14/20.50 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 236.38/54.88 % Version: 3.5.1
% 236.38/54.88 % Preprocessing class: FMLMSMSMSSSNFFN.
% 236.38/54.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 236.38/54.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 236.38/54.88 % Starting new_bool_3 with 300s (1) cores
% 236.38/54.88 % Starting new_bool_1 with 300s (1) cores
% 236.38/54.88 % Starting sh5l with 300s (1) cores
% 236.38/54.88 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2519416 completed with status 0
% 236.38/54.88 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 236.38/54.88 % Preprocessing class: FMLMSMSMSSSNFFN.
% 236.38/54.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 236.38/54.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 236.38/54.88 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 236.38/54.88 % No SInE strategy applied
% 236.38/54.88 % Search class: FGHSM-SMLM32-DFFFFFNN
% 236.38/54.88 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 236.38/54.88 % Starting SubtermCWHack with 136s (1) cores
% 236.38/54.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 236.38/54.88 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 236.38/54.88 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 236.38/54.88 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 236.38/54.88 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 2519425 completed with status 0
% 236.38/54.88 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 236.38/54.88 % Preprocessing class: FMLMSMSMSSSNFFN.
% 236.38/54.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 236.38/54.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 236.38/54.88 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 236.38/54.88 % No SInE strategy applied
% 236.38/54.88 % Search class: FGHSM-SMLM32-DFFFFFNN
% 236.38/54.88 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 236.38/54.88 % Starting SubtermCWHack with 136s (1) cores
% 236.38/54.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 236.38/54.88 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 236.38/54.88 % Preprocessing time : 0.041 s
% 236.38/54.88
% 236.38/54.88 % Proof found!
% 236.38/54.88 % SZS status Unsatisfiable
% 236.38/54.88 % SZS output start CNFRefutation
% See solution above
% 236.38/54.88 % Parsed axioms : 2808
% 236.38/54.88 % Removed by relevancy pruning/SinE : 0
% 236.38/54.88 % Initial clauses : 2808
% 236.38/54.88 % Removed in clause preprocessing : 9
% 236.38/54.88 % Initial clauses in saturation : 2799
% 236.38/54.88 % Processed clauses : 104011
% 236.38/54.88 % ...of these trivial : 24092
% 236.38/54.88 % ...subsumed : 63930
% 236.38/54.88 % ...remaining for further processing : 15989
% 236.38/54.88 % Other redundant clauses eliminated : 741
% 236.38/54.88 % Clauses deleted for lack of memory : 0
% 236.38/54.88 % Backward-subsumed : 316
% 236.38/54.88 % Backward-rewritten : 3868
% 236.38/54.88 % Generated clauses : 1141474
% 236.38/54.88 % ...of the previous two non-redundant : 943563
% 236.38/54.88 % ...aggressively subsumed : 0
% 236.38/54.88 % Contextual simplify-reflections : 500
% 236.38/54.88 % Paramodulations : 1140500
% 236.38/54.88 % Factorizations : 78
% 236.38/54.88 % NegExts : 0
% 236.38/54.88 % Equation resolutions : 896
% 236.38/54.88 % Disequality decompositions : 0
% 236.38/54.88 % Total rewrite steps : 1855925
% 236.38/54.88 % ...of those cached : 1819760
% 236.38/54.88 % Propositional unsat checks : 0
% 236.38/54.88 % Propositional check models : 0
% 236.38/54.88 % Propositional check unsatisfiable : 0
% 236.38/54.88 % Propositional clauses : 0
% 236.38/54.88 % Propositional clauses after purity: 0
% 236.38/54.88 % Propositional unsat core size : 0
% 236.38/54.88 % Propositional preprocessing time : 0.000
% 236.38/54.88 % Propositional encoding time : 0.000
% 236.38/54.88 % Propositional solver time : 0.000
% 236.38/54.88 % Success case prop preproc time : 0.000
% 236.38/54.88 % Success case prop encoding time : 0.000
% 236.38/54.88 % Success case prop solver time : 0.000
% 236.38/54.88 % Current number of processed clauses : 11805
% 236.38/54.88 % Positive orientable unit clauses : 3525
% 236.38/54.88 % Positive unorientable unit clauses: 15
% 236.38/54.88 % Negative unit clauses : 128
% 236.38/54.88 % Non-unit-clauses : 8137
% 236.38/54.88 % Current number of unprocessed clauses: 834340
% 236.38/54.88 % ...number of literals in the above : 2311799
% 236.38/54.88 % Current number of archived formulas : 0
% 236.38/54.88 % Current number of archived clauses : 4192
% 236.38/54.88 % Clause-clause subsumption calls (NU) : 23189190
% 236.38/54.88 % Rec. Clause-clause subsumption calls : 16325242
% 236.38/54.88 % Non-unit clause-clause subsumptions : 62657
% 236.38/54.88 % Unit Clause-clause subsumption calls : 726600
% 236.38/54.88 % Rewrite failures with RHS unbound : 2
% 236.38/54.88 % BW rewrite match attempts : 121365
% 236.38/54.88 % BW rewrite match successes : 1384
% 236.38/54.88 % Condensation attempts : 0
% 236.38/54.88 % Condensation successes : 0
% 236.38/54.88 % Termbank termtop insertions : 33144544
% 236.38/54.88 % Search garbage collected termcells : 4116
% 236.38/54.88
% 236.38/54.88 % -------------------------------------------------
% 236.38/54.88 % User time : 33.051 s
% 236.38/54.88 % System time : 0.848 s
% 236.38/54.88 % Total time : 33.899 s
% 236.38/54.88 % Maximum resident set size: 8724 pages
% 236.38/54.88
% 236.38/54.88 % -------------------------------------------------
% 236.38/54.88 % User time : 164.563 s
% 236.38/54.88 % System time : 4.099 s
% 236.38/54.88 % Total time : 168.662 s
% 236.38/54.88 % Maximum resident set size: 6656 pages
% 236.38/54.88 % E exiting
%------------------------------------------------------------------------------