%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA026-1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:09:20 PM UTC 2026
% Result : Unsatisfiable 62.27s 36.26s
% Output : CNFRefutation 62.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 38
% Syntax : Number of clauses : 131 ( 12 unt; 3 nHn; 96 RR)
% Number of literals : 329 ( 61 equ; 217 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 212 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oneg__equal__0__iff__equal_0,axiom,
( X2 = c_0
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X2,X1) != c_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( c_uminus(c_uminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__minus_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_4) ).
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_Oneg__0__equal__iff__equal_1,axiom,
( c_0 = c_uminus(c_0,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
cnf(cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0,axiom,
( c_plus(c_uminus(X2,X1),X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( c_plus(X2,c_uminus(X2,X1),X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oright__minus_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__11_1,axiom,
( X2 = c_minus(c_plus(X2,X3,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__11_1) ).
cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__left_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonpos_0,axiom,
( c_HOL_Oabs(X2,X1) = c_uminus(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X2,c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonpos_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
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(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_37) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0,axiom,
( c_minus(X2,X3,X1) = c_plus(X2,c_uminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( c_HOL_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( c_lessequals(X2,c_minus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_0,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
( c_lessequals(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_minus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
cnf(cls_OrderedGroup_Oneg__0__le__iff__le_1,axiom,
( c_lessequals(c_0,c_uminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
cnf(cls_OrderedGroup_Odiff__0__right_0,axiom,
( c_minus(X2,c_0,X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__0__right_0) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( c_lessequals(X4,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,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_1) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_10,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
cnf(cls_OrderedGroup_Oadd__le__cancel__left_1,axiom,
( c_lessequals(c_plus(X4,X2,X1),c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
cnf(cls_OrderedGroup_Ocompare__rls__10_0,axiom,
( X2 = c_plus(c_minus(X2,X3,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_0) ).
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(clsrel_OrderedGroup_Opordered__ab__group__add_12,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( c_plus(c_0,X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_Orderings_Olinorder__not__le_0,axiom,
( c_less(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(c_0_38,axiom,
( X2 = c_0
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X2,X1) != c_0 ),
cls_OrderedGroup_Oneg__equal__0__iff__equal_0 ).
cnf(c_0_39,axiom,
( c_uminus(c_uminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ominus__minus_0 ).
cnf(c_0_40,plain,
( c_uminus(X1,X2) = c_0
| X1 != c_0
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_4 ).
cnf(c_0_42,plain,
( c_uminus(X1,X2) = c_0
| X1 != c_0
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_44,axiom,
( c_0 = c_uminus(c_0,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Oneg__0__equal__iff__equal_1 ).
cnf(c_0_45,axiom,
( c_plus(c_uminus(X2,X1),X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0 ).
cnf(c_0_46,negated_conjecture,
( c_uminus(X1,t_b) = c_0
| X1 != c_0 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
( c_uminus(c_0,X1) = c_0
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( c_plus(c_0,X1,t_b) = c_0
| X1 != c_0
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,axiom,
( c_plus(X2,c_uminus(X2,X1),X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Oright__minus_0 ).
cnf(c_0_50,negated_conjecture,
c_uminus(c_0,t_b) = c_0,
inference(spm,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_51,axiom,
( X2 = c_minus(c_plus(X2,X3,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__11_1 ).
cnf(c_0_52,negated_conjecture,
( c_plus(c_0,X1,t_b) = c_0
| X1 != c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_41]),c_0_43])]) ).
cnf(c_0_53,negated_conjecture,
( c_plus(c_0,c_0,t_b) = c_0
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,axiom,
( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Odiff__minus__eq__add_0 ).
cnf(c_0_55,negated_conjecture,
( c_minus(c_0,X1,t_b) = c_0
| X1 != c_0
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,axiom,
( c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X2,X4,X1),X1) ),
cls_OrderedGroup_Oadd__le__cancel__left_0 ).
cnf(c_0_57,negated_conjecture,
c_plus(c_0,c_0,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_43])]) ).
cnf(c_0_58,negated_conjecture,
( c_plus(c_0,X1,t_b) = c_0
| c_uminus(X1,t_b) != c_0
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,axiom,
( c_HOL_Oabs(X2,X1) = c_uminus(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X2,c_0,X1) ),
cls_OrderedGroup_Oabs__of__nonpos_0 ).
cnf(c_0_60,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_50 ).
cnf(c_0_61,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(c_0,c_plus(c_0,X1,t_b),t_b) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( c_plus(c_0,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_58,c_0_41]),c_0_43])]) ).
cnf(c_0_63,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),
cls_conjecture_2 ).
cnf(c_0_64,plain,
( c_HOL_Oabs(X1,X2) = c_uminus(X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(X1,c_0,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| c_uminus(X1,t_b) != c_0
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(c_0,c_0,t_b) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_37 ).
cnf(c_0_67,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_Orderings_Oorder__class_Oaxioms__1_0 ).
cnf(c_0_68,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_44 ).
cnf(c_0_69,negated_conjecture,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_uminus(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_43])]) ).
cnf(c_0_70,axiom,
( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ominus__diff__eq_0 ).
cnf(c_0_71,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| c_uminus(X1,t_b) != c_0
| ~ c_lessequals(c_0,c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_43])]) ).
cnf(c_0_72,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,axiom,
( c_minus(X2,X3,X1) = c_plus(X2,c_uminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0 ).
cnf(c_0_74,axiom,
( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2 ).
cnf(c_0_75,axiom,
( c_HOL_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X2,X1) ),
cls_OrderedGroup_Oabs__of__nonneg_0 ).
cnf(c_0_76,negated_conjecture,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_minus(v_g(v_x),v_f(v_x),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,axiom,
( c_lessequals(X2,c_minus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),X4,X1) ),
cls_OrderedGroup_Ocompare__rls__9_1 ).
cnf(c_0_78,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
clsrel_OrderedGroup_Opordered__ab__group__add_0 ).
cnf(c_0_79,axiom,
( c_lessequals(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_minus(X3,X4,X1),X1) ),
cls_OrderedGroup_Ocompare__rls__9_0 ).
cnf(c_0_80,axiom,
( c_lessequals(c_0,c_uminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_0,X1) ),
cls_OrderedGroup_Oneg__0__le__iff__le_1 ).
cnf(c_0_81,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| c_uminus(X1,t_b) != c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_43])]) ).
cnf(c_0_82,axiom,
( c_minus(X2,c_0,X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Odiff__0__right_0 ).
cnf(c_0_83,negated_conjecture,
( c_minus(X1,c_0,t_b) = c_plus(X1,c_0,t_b)
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_73,c_0_50]) ).
cnf(c_0_84,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_63,c_0_74]) ).
cnf(c_0_85,plain,
( c_HOL_Oabs(X1,X2) = X1
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(c_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_60]) ).
cnf(c_0_86,axiom,
( c_lessequals(X4,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_Orderings_Oorder__class_Oorder__trans_0 ).
cnf(c_0_87,axiom,
( c_lessequals(c_minus(X2,X3,X1),c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_OrderedGroup_Odiff__le__0__iff__le_1 ).
cnf(c_0_88,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
clsrel_OrderedGroup_Opordered__ab__group__add_10 ).
cnf(c_0_89,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),v_f(v_x),t_b),v_g(v_x),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_90,plain,
( c_lessequals(c_plus(c_Orderings_Omax(X1,X2,X3),X4,X3),X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,c_minus(X5,X4,X3),X3)
| ~ c_lessequals(X2,c_minus(X5,X4,X3),X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_74]) ).
cnf(c_0_91,plain,
( c_lessequals(c_0,c_minus(X1,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_minus(X2,X1,X3),c_0,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_70]),c_0_78]) ).
cnf(c_0_92,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| c_uminus(c_plus(c_0,X1,t_b),t_b) != c_0
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(spm,[status(thm)],[c_0_61,c_0_81]) ).
cnf(c_0_93,negated_conjecture,
( c_plus(X1,c_0,t_b) = X1
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_94,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ 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_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_43])]) ).
cnf(c_0_95,axiom,
( c_lessequals(c_plus(X4,X2,X1),c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_OrderedGroup_Oadd__le__cancel__left_1 ).
cnf(c_0_96,axiom,
( X2 = c_plus(c_minus(X2,X3,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__10_0 ).
cnf(c_0_97,plain,
( c_lessequals(c_minus(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_0,X4,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_98,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_g(v_x),v_f(v_x),t_b),t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_99,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| c_uminus(c_plus(c_0,X1,t_b),t_b) != c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_66]),c_0_43])]) ).
cnf(c_0_100,negated_conjecture,
c_plus(X1,c_0,t_b) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_41]),c_0_43])]) ).
cnf(c_0_101,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_plus(c_minus(v_f(v_x),v_k(v_x),t_b),v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_94,c_0_77]) ).
cnf(c_0_102,plain,
( c_lessequals(c_plus(c_minus(X1,X2,X3),X4,X3),X1,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Oab__group__add(X3)
| ~ c_lessequals(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
cls_conjecture_1 ).
cnf(c_0_104,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
clsrel_OrderedGroup_Opordered__ab__group__add_12 ).
cnf(c_0_105,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_94,c_0_97]) ).
cnf(c_0_106,axiom,
( c_plus(c_0,X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 ).
cnf(c_0_107,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_23 ).
cnf(c_0_108,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_97]),c_0_91]) ).
cnf(c_0_109,negated_conjecture,
c_lessequals(c_0,c_0,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_50])]) ).
cnf(c_0_110,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
cls_Orderings_Oorder__less__imp__le_0 ).
cnf(c_0_111,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]),c_0_78]),c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_105,c_0_77]) ).
cnf(c_0_113,plain,
( c_plus(c_0,X1,X2) = X1
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,axiom,
( c_less(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Orderings_Olinorder__not__le_0 ).
cnf(c_0_115,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_33 ).
cnf(c_0_116,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b)
| ~ c_lessequals(v_f(v_x),v_g(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_97]),c_0_109])]) ).
cnf(c_0_117,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_110,c_0_68]) ).
cnf(c_0_118,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_111,c_0_77]) ).
cnf(c_0_119,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(v_g(v_x),v_f(v_x),t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_43])]) ).
cnf(c_0_120,plain,
( c_less(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_less(v_f(v_x),v_g(v_x),t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_43])]) ).
cnf(c_0_122,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_113]),c_0_43])]) ).
cnf(c_0_123,negated_conjecture,
( c_lessequals(v_g(X1),X2,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_k(X1),X2,t_b) ),
inference(spm,[status(thm)],[c_0_86,c_0_103]) ).
cnf(c_0_124,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_43])]),c_0_121]) ).
cnf(c_0_125,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_88]) ).
cnf(c_0_126,negated_conjecture,
( c_less(v_k(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_120]),c_0_43])]) ).
cnf(c_0_127,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_117]),c_0_43])]),c_0_126]) ).
cnf(c_0_128,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_54 ).
cnf(c_0_129,negated_conjecture,
~ class_Orderings_Olinorder(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_43])]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_115]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA026-1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:35:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 62.27/36.26 % Version : CSE_E---1.7
% 62.27/36.26 % Problem : theBenchmark.p
% 62.27/36.26 % SZS status Unsatisfiable for theBenchmark.p
% 62.27/36.26 % SZS output start CNFRefutation
% See solution above
% 62.47/36.48 % Total time : 27.645s
%------------------------------------------------------------------------------