%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA026-2 : 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 : n002.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 92.41s 55.02s
% Output : CNFRefutation 92.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 30
% Syntax : Number of clauses : 119 ( 22 unt; 8 nHn; 69 RR)
% Number of literals : 271 ( 36 equ; 169 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 229 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
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/theBenchmark.p',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/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
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/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(cls_Orderings_Olinorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
cnf(cls_OrderedGroup_Ocompare__rls__6_0,axiom,
( c_less(X2,c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_minus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__6_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__10_1,axiom,
( c_minus(c_plus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_1) ).
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/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
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/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_OrderedGroup_Ocompare__rls__4_0,axiom,
( c_minus(c_minus(X2,X3,X1),X4,X1) = c_minus(X2,c_plus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__4_0) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
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_OrderedGroup_Odiff__self_0,axiom,
( c_minus(X2,X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_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(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
( c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
cnf(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
( c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
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(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( class_Orderings_Oorder(X1)
| ~ class_LOrder_Ojoin__semilorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( class_LOrder_Ojoin__semilorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
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_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_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/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
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/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_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/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_1,axiom,
( c_lessequals(c_minus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_plus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
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/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
cnf(cls_OrderedGroup_Ocompare__rls__3_0,axiom,
( c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_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_Olordered__ab__group__abs_6,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
cnf(c_0_30,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_31,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_23 ).
cnf(c_0_32,plain,
( c_plus(c_0,X1,X2) = X1
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_34,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_4 ).
cnf(c_0_35,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_Orderings_Olinorder__not__le_1 ).
cnf(c_0_36,axiom,
( c_less(X2,c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_minus(X2,X3,X1),X4,X1) ),
cls_OrderedGroup_Ocompare__rls__6_0 ).
cnf(c_0_37,axiom,
( c_minus(c_plus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__10_1 ).
cnf(c_0_38,negated_conjecture,
c_plus(c_0,X1,t_b) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_40,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(c_minus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_plus(X4,X3,X1),X2,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
c_minus(X1,X1,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ c_less(c_0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(X1,X2,t_b),X2,t_b) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_33 ).
cnf(c_0_44,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_45,axiom,
( c_minus(c_minus(X2,X3,X1),X4,X1) = c_minus(X2,c_plus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__4_0 ).
cnf(c_0_46,negated_conjecture,
( ~ c_less(c_0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(X1,X2,t_b),X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_33])]) ).
cnf(c_0_47,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_1 ).
cnf(c_0_48,negated_conjecture,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(spm,[status(thm)],[c_0_44,c_0_33]) ).
cnf(c_0_49,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_50,axiom,
( c_minus(X2,X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Odiff__self_0 ).
cnf(c_0_51,negated_conjecture,
c_minus(c_minus(X1,c_0,t_b),X2,t_b) = c_minus(X1,X2,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_38]),c_0_39])]) ).
cnf(c_0_52,negated_conjecture,
( ~ c_less(c_0,X1,t_b)
| ~ c_lessequals(c_plus(X1,X2,t_b),X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_53,negated_conjecture,
c_uminus(X1,t_b) = c_minus(c_0,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_49]),c_0_39])]) ).
cnf(c_0_54,negated_conjecture,
c_minus(X1,c_minus(X1,c_0,t_b),t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_39])]) ).
cnf(c_0_55,axiom,
( c_less(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Orderings_Olinorder__not__le_0 ).
cnf(c_0_56,plain,
( c_minus(c_minus(X1,X2,X3),c_uminus(X2,X3),X3) = X1
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( ~ c_less(c_0,X1,t_b)
| ~ c_lessequals(c_minus(X1,X2,t_b),c_minus(c_0,X2,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_49]),c_0_53]),c_0_39])]) ).
cnf(c_0_58,axiom,
( c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__2_0 ).
cnf(c_0_59,negated_conjecture,
c_minus(c_plus(X1,c_0,t_b),X1,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_37]),c_0_39])]) ).
cnf(c_0_60,axiom,
( c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__minus__cancel_0 ).
cnf(c_0_61,plain,
( c_less(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_43]) ).
cnf(c_0_62,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ c_lessequals(c_plus(X3,c_uminus(X4,X1),X1),c_minus(X2,X4,X1),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
c_plus(X1,c_minus(c_0,X2,t_b),t_b) = c_minus(X1,X2,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_53]),c_0_39])]) ).
cnf(c_0_64,negated_conjecture,
( ~ c_less(c_0,c_plus(X1,X2,t_b),t_b)
| ~ c_lessequals(X1,c_minus(c_0,X2,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_37]),c_0_39])]) ).
cnf(c_0_65,negated_conjecture,
c_plus(X1,c_minus(c_0,X1,t_b),t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_39])]) ).
cnf(c_0_66,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__ge__zero_0 ).
cnf(c_0_67,negated_conjecture,
c_HOL_Oabs(c_minus(c_0,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_60,c_0_53]),c_0_48])]) ).
cnf(c_0_68,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_69,negated_conjecture,
( c_less(X1,X2,t_b)
| c_lessequals(X2,X1,t_b) ),
inference(spm,[status(thm)],[c_0_61,c_0_33]) ).
cnf(c_0_70,axiom,
( class_Orderings_Oorder(X1)
| ~ class_LOrder_Ojoin__semilorder(X1) ),
clsrel_LOrder_Ojoin__semilorder_1 ).
cnf(c_0_71,axiom,
( class_LOrder_Ojoin__semilorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_35 ).
cnf(c_0_72,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ c_less(X1,X2,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_minus(X2,X1,t_b),c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_41]),c_0_39]),c_0_53]),c_0_63])]) ).
cnf(c_0_73,negated_conjecture,
( ~ c_less(c_0,c_minus(X1,X2,t_b),t_b)
| ~ c_lessequals(X1,c_minus(c_0,c_minus(c_0,X2,t_b),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_49]),c_0_53]),c_0_39])]) ).
cnf(c_0_74,negated_conjecture,
c_minus(c_0,c_minus(c_0,X1,t_b),t_b) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_65]),c_0_39])]) ).
cnf(c_0_75,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_76,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_66,c_0_67]),c_0_48])]) ).
cnf(c_0_77,negated_conjecture,
( c_lessequals(X1,X2,t_b)
| c_lessequals(X2,X1,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,plain,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_79,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_80,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_81,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_82,negated_conjecture,
( ~ c_less(X1,X2,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_minus(X2,X1,t_b),c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_43]),c_0_33])]) ).
cnf(c_0_83,negated_conjecture,
( ~ c_less(c_0,c_minus(X1,X2,t_b),t_b)
| ~ c_lessequals(X1,X2,t_b) ),
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,negated_conjecture,
( c_lessequals(c_0,X1,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_HOL_Oabs(X2,t_b),X1,t_b) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,negated_conjecture,
( c_lessequals(X1,X2,t_b)
| c_lessequals(X2,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_33])]) ).
cnf(c_0_86,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) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_76])]) ).
cnf(c_0_87,plain,
( c_HOL_Oabs(c_minus(X1,X2,X3),X3) = c_HOL_Oabs(c_minus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_81]) ).
cnf(c_0_88,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_89,axiom,
( c_lessequals(c_minus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_plus(X3,X4,X1),X1) ),
cls_OrderedGroup_Ocompare__rls__8_1 ).
cnf(c_0_90,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_91,axiom,
( c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__3_0 ).
cnf(c_0_92,negated_conjecture,
( ~ c_less(X1,X2,t_b)
| ~ c_lessequals(c_minus(X2,X1,t_b),c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_47]),c_0_48])]) ).
cnf(c_0_93,negated_conjecture,
( c_lessequals(c_minus(X1,X2,t_b),c_0,t_b)
| ~ c_lessequals(X1,X2,t_b) ),
inference(spm,[status(thm)],[c_0_83,c_0_69]) ).
cnf(c_0_94,negated_conjecture,
c_minus(c_0,c_minus(X1,X2,t_b),t_b) = c_minus(X2,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_53]),c_0_39])]) ).
cnf(c_0_95,negated_conjecture,
( c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b)
| c_lessequals(c_0,X1,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_96,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_g(v_x),v_f(v_x),t_b),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_48]),c_0_39])]) ).
cnf(c_0_97,plain,
( c_HOL_Oabs(c_minus(X1,X2,X3),X3) = c_minus(X2,X1,X3)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ class_OrderedGroup_Oab__group__add(X3)
| ~ c_lessequals(c_minus(X1,X2,X3),c_0,X3) ),
inference(spm,[status(thm)],[c_0_88,c_0_81]) ).
cnf(c_0_98,plain,
( c_lessequals(c_minus(c_plus(X1,X2,X3),X4,X3),X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_99,plain,
( c_plus(c_minus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_91]) ).
cnf(c_0_100,negated_conjecture,
( c_lessequals(X1,X2,t_b)
| ~ c_lessequals(c_minus(X1,X2,t_b),c_0,t_b) ),
inference(spm,[status(thm)],[c_0_92,c_0_69]) ).
cnf(c_0_101,negated_conjecture,
( c_lessequals(c_minus(X1,X2,t_b),c_0,t_b)
| ~ c_lessequals(c_0,c_minus(X2,X1,t_b),t_b) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_102,negated_conjecture,
( c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b)
| c_lessequals(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_78]),c_0_33])]) ).
cnf(c_0_103,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_minus(v_g(v_x),v_f(v_x),t_b),c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_48]),c_0_39])]) ).
cnf(c_0_104,plain,
( c_lessequals(c_minus(X1,X2,X3),c_minus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(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_98,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
cls_conjecture_1 ).
cnf(c_0_106,negated_conjecture,
( c_lessequals(X1,X2,t_b)
| ~ c_lessequals(c_0,c_minus(X2,X1,t_b),t_b) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
( c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(spm,[status(thm)],[c_0_86,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(c_minus(v_g(v_x),v_f(v_x),t_b),c_0,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_39]),c_0_105])]) ).
cnf(c_0_109,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_75,c_0_105]) ).
cnf(c_0_110,negated_conjecture,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_108,c_0_93]) ).
cnf(c_0_112,negated_conjecture,
( c_lessequals(v_g(v_x),v_f(v_x),t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,negated_conjecture,
( ~ class_Orderings_Oorder(t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_114,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_78]),c_0_33])]) ).
cnf(c_0_115,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_47]),c_0_48])]) ).
cnf(c_0_116,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_6 ).
cnf(c_0_117,negated_conjecture,
~ class_Orderings_Olinorder(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_48])]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_43]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA026-2 : TPTP v9.2.1. Released v3.2.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 10:36:16 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.19/0.35 % start to proof: theBenchmark
% 92.41/55.02 % Version : CSE_E---1.7
% 92.41/55.02 % Problem : theBenchmark.p
% 92.41/55.02 % SZS status Unsatisfiable for theBenchmark.p
% 92.41/55.02 % SZS output start CNFRefutation
% See solution above
% 92.91/55.43 % Total time : 39.859s
%------------------------------------------------------------------------------