TSTP Solution File: ALG385-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG385-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 : Wed Aug 30 16:07:34 EDT 2023
% Result : Unsatisfiable 11.18s 11.21s
% Output : CNFRefutation 11.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 137
% Syntax : Number of formulae : 186 ( 38 unt; 113 typ; 0 def)
% Number of atoms : 122 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 102 ( 53 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 153 ( 106 >; 47 *; 0 +; 0 <<)
% Number of predicates : 77 ( 75 usr; 1 prp; 0-3 aty)
% Number of functors : 38 ( 38 usr; 7 con; 0-4 aty)
% Number of variables : 122 ( 16 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_23,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_24,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_27,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_28,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_30,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_31,type,
tc_RealDef_Oreal: $i ).
tff(decl_32,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_33,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_34,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_35,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_37,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_38,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_39,type,
class_Power_Opower: $i > $o ).
tff(decl_40,type,
class_HOL_Ozero: $i > $o ).
tff(decl_41,type,
class_HOL_Oeq: $i > $o ).
tff(decl_42,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_43,type,
c_HOL_Oeq__class_Oeq: ( $i * $i * $i ) > $o ).
tff(decl_44,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_46,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_47,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_49,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_50,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_51,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(decl_53,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_54,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_56,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_57,type,
c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_59,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_60,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_61,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_62,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_63,type,
c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(decl_65,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_66,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_67,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_68,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_69,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_70,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_71,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_72,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_73,type,
tc_Complex_Ocomplex: $i ).
tff(decl_74,type,
c_Complex_Ocnj: $i > $i ).
tff(decl_75,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_79,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_80,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_81,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
c_Complex_ORe: $i > $i ).
tff(decl_83,type,
c_Complex_OIm: $i > $i ).
tff(decl_84,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_87,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_88,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_89,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_90,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_91,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_92,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_93,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_94,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_95,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_96,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_97,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_98,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_99,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_100,type,
class_SEQ_Obanach: $i > $o ).
tff(decl_101,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_103,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_104,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_105,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_106,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_108,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_109,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
tff(decl_110,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_111,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
tff(decl_112,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_113,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_114,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_115,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_116,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_117,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_118,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_119,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_120,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_121,type,
class_Orderings_Obot: $i > $o ).
tff(decl_122,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_123,type,
v_da____: $i ).
tff(decl_124,type,
v_cs____: $i ).
tff(decl_125,type,
v_c____: $i ).
tff(decl_126,type,
v_z____: $i ).
tff(decl_127,type,
v_aa____: $i ).
tff(decl_128,type,
v_sko__local__XpCons__1__1: ( $i * $i * $i ) > $i ).
tff(decl_129,type,
v_sko__local__XpCons__Xhyps__1: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1: ( $i * $i ) > $i ).
tff(decl_131,type,
v_sko__unknown__thm__re6__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_132,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_133,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_134,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
cnf(cls_min__max_Oinf__le2_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
cnf(cls_min__max_Ole__iff__inf_0,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
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/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_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_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_30,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder ).
cnf(c_0_31,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_min__max_Osup__absorb1_0 ).
cnf(c_0_32,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__le2_0 ).
cnf(c_0_33,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_34,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_35,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_36,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_37,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
cls_real__less__def_1 ).
cnf(c_0_38,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_29,c_0_30]) ).
cnf(c_0_39,plain,
( c_Orderings_Oord__class_Omax(X1,X2,tc_RealDef_Oreal) = X1
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_40,plain,
c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_41,axiom,
( c_Orderings_Oord__class_Omin(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_min__max_Ole__iff__inf_0 ).
cnf(c_0_42,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_43,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_34,c_0_35]) ).
cnf(c_0_44,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_34,c_0_36]) ).
cnf(c_0_45,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_46,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_47,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_48,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_49,axiom,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_cs0_0 ).
cnf(c_0_50,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_51,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_52,plain,
~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_53,plain,
c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_54,plain,
( c_Orderings_Oord__class_Omin(X1,X2,tc_RealDef_Oreal) = X1
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_41,c_0_30]) ).
cnf(c_0_55,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_56,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_57,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_58,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_59,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_42,c_0_43]) ).
cnf(c_0_60,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_44,c_0_43]) ).
cnf(c_0_61,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_62,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_45,c_0_46]) ).
cnf(c_0_63,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_47,c_0_48]),c_0_49]),c_0_49]) ).
cnf(c_0_64,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_50,c_0_51]),c_0_49]) ).
cnf(c_0_65,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_66,plain,
c_Orderings_Oord__class_Omin(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) = v_da____,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,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_56,c_0_57]) ).
cnf(c_0_68,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_58,c_0_59]),c_0_60]) ).
cnf(c_0_69,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_61,c_0_46]) ).
cnf(c_0_70,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_62,c_0_63]),c_0_64])]) ).
cnf(c_0_71,plain,
~ c_HOL_Oord__class_Oless(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),v_da____,tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_67]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG385-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 02:30:20 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.61/0.62 start to proof: theBenchmark
% 11.18/11.21 % Version : CSE_E---1.5
% 11.18/11.21 % Problem : theBenchmark.p
% 11.18/11.21 % Proof found
% 11.18/11.21 % SZS status Theorem for theBenchmark.p
% 11.18/11.21 % SZS output start Proof
% See solution above
% 11.18/11.22 % Total time : 10.557000 s
% 11.18/11.22 % SZS output end Proof
% 11.18/11.22 % Total time : 10.588000 s
%------------------------------------------------------------------------------