%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG385-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 04:08:37 PM UTC 2026
% Result : Unsatisfiable 250.39s 188.63s
% Output : CNFRefutation 251.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of clauses : 74 ( 38 unt; 5 nHn; 47 RR)
% Number of literals : 124 ( 41 equ; 56 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 121 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf__absorb2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(clsarity_RealDef__Oreal__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
cnf(cls_real__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
cnf(cls_le__iff__inf_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_inf__le1_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(cls_less__max__iff__disj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
cnf(cls_real__less__def_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_min__max_Ole__iff__sup_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
cnf(cls_min__max_Osup__commute_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_synthetic__div__unique_0,axiom,
( X5 = c_Polynomial_Opoly(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(cls_smult__eq__0__iff_2,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(cls_cs0_0,axiom,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cs0_0) ).
cnf(cls_add__poly__code_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(cls_poly__pCons_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
cnf(cls_real__le__refl_0,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
cnf(c_0_24,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0 ).
cnf(c_0_25,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Lattices_Olower__semilattice ).
cnf(c_0_26,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal) = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0 ).
cnf(c_0_28,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_29,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le1_0 ).
cnf(c_0_30,negated_conjecture,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_conjecture_0 ).
cnf(c_0_31,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal) = X2
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal) != X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_33,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_linorder__not__less_1 ).
cnf(c_0_34,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder ).
cnf(c_0_35,axiom,
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_less__max__iff__disj_2 ).
cnf(c_0_36,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_37,negated_conjecture,
c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != v_da____,
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_39,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_41,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_2 ).
cnf(c_0_42,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != v_da____,
inference(rw,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_44,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__iff__sup_0 ).
cnf(c_0_45,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_47,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__commute_0 ).
cnf(c_0_48,plain,
( c_Orderings_Oord__class_Omax(X1,X2,tc_RealDef_Oreal) = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_49,axiom,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_CHAINED_0_01 ).
cnf(c_0_50,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0 ).
cnf(c_0_51,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_52,negated_conjecture,
~ c_lessequals(c_Orderings_Oord__class_Omax(X1,v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
c_Orderings_Oord__class_Omax(X1,X2,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(X2,X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_47,c_0_34]) ).
cnf(c_0_54,plain,
c_Orderings_Oord__class_Omax(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,axiom,
( X5 = c_Polynomial_Opoly(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1) ),
cls_synthetic__div__unique_0 ).
cnf(c_0_57,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_58,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_smult__eq__0__iff_2 ).
cnf(c_0_59,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_60,axiom,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_cs0_0 ).
cnf(c_0_61,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_add__poly__code_I2_J_0 ).
cnf(c_0_62,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_63,negated_conjecture,
~ c_lessequals(c_Orderings_Oord__class_Omax(v_da____,X1,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_64,plain,
c_Orderings_Oord__class_Omax(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_55]) ).
cnf(c_0_65,axiom,
( c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__pCons_0 ).
cnf(c_0_66,plain,
( X1 = c_Polynomial_Opoly(X2,X3,tc_Complex_Ocomplex)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Polynomial_OpCons(X1,X4,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,plain,
c_Polynomial_Osmult(X1,v_cs____,tc_Complex_Ocomplex) = v_cs____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_60]) ).
cnf(c_0_68,plain,
c_HOL_Oplus__class_Oplus(X1,v_cs____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_60]) ).
cnf(c_0_69,negated_conjecture,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_65,c_0_57]) ).
cnf(c_0_71,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_cs____,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = X1,
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_72,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0 ).
cnf(c_0_73,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_55]),c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG385-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:33:34 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 250.39/188.63 % Version : CSE_E---1.7
% 250.39/188.63 % Problem : theBenchmark.p
% 250.39/188.63 % SZS status Unsatisfiable for theBenchmark.p
% 250.39/188.63 % SZS output start CNFRefutation
% See solution above
% 251.00/189.26 % Total time : 162.745s
%------------------------------------------------------------------------------