TSTP Solution File: ALG437-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG437-1 : 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 : 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 : Wed Aug 30 16:07:45 EDT 2023
% Result : Unsatisfiable 123.96s 124.19s
% Output : CNFRefutation 123.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 159
% Syntax : Number of formulae : 249 ( 50 unt; 116 typ; 0 def)
% Number of atoms : 243 ( 153 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 204 ( 94 ~; 110 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 179 ( 106 >; 73 *; 0 +; 0 <<)
% Number of predicates : 59 ( 57 usr; 1 prp; 0-5 aty)
% Number of functors : 59 ( 59 usr; 10 con; 0-5 aty)
% Number of variables : 214 ( 29 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_23,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_24,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_27,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_28,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_29,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_30,type,
class_HOL_Ozero: $i > $o ).
tff(decl_31,type,
class_HOL_Oeq: $i > $o ).
tff(decl_32,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_33,type,
c_HOL_Oeq__class_Oeq: $i > $i ).
tff(decl_34,type,
c_fequal: $i > $i ).
tff(decl_35,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_36,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_37,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_38,type,
hBOOL: $i > $o ).
tff(decl_39,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_41,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_42,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
c_Fun_Ofcomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_45,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_47,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_48,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_49,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_52,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(decl_53,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_56,type,
c_Polynomial_Ocoeff: ( $i * $i ) > $i ).
tff(decl_57,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_58,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_59,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_60,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_61,type,
c_Polynomial_OAbs__poly: ( $i * $i ) > $i ).
tff(decl_62,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
tc_nat: $i ).
tff(decl_64,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_65,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_66,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_67,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_69,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_71,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(decl_72,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
class_SEQ_Obanach: $i > $o ).
tff(decl_74,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(decl_75,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_76,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_78,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_79,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
tff(decl_80,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_81,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_83,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_84,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
c_OrderedGroup_Olordered__ab__group__add__class_Opprt: ( $i * $i ) > $i ).
tff(decl_86,type,
c_OrderedGroup_Olordered__ab__group__add__class_Onprt: ( $i * $i ) > $i ).
tff(decl_87,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_89,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_90,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_93,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_94,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_95,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_96,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_97,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_98,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
tff(decl_99,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(decl_100,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_101,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_102,type,
c_Fun_Oid: $i > $i ).
tff(decl_103,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_104,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(decl_105,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_106,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_107,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_108,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_109,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_111,type,
c_Complex_Ocnj: $i > $i ).
tff(decl_112,type,
c_Complex_Oii: $i ).
tff(decl_113,type,
tc_Complex_Ocomplex: $i ).
tff(decl_114,type,
t_a: $i ).
tff(decl_115,type,
v_x: $i ).
tff(decl_116,type,
t_b: $i ).
tff(decl_117,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_118,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_119,type,
c_Polynomial_Osynthetic__divmod: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2: $i > $i ).
tff(decl_123,type,
c_Polynomial_Osko__Polynomial__XpCons__induct__1__2: ( $i * $i ) > $i ).
tff(decl_124,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1: $i > $i ).
tff(decl_125,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2: $i > $i ).
tff(decl_126,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1: $i > $i ).
tff(decl_127,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1: $i > $i ).
tff(decl_128,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1: $i > $i ).
tff(decl_129,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv2__1: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2: $i > $i ).
tff(decl_131,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__4__1: $i ).
tff(decl_132,type,
v_p: $i ).
tff(decl_133,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_134,type,
tc_RealDef_Oreal: $i ).
tff(decl_135,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_136,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_137,type,
tc_bool: $i ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(cls_right__inverse__eq_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(cls_minus__divide__left_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
cnf(cls_minus__mult__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
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_poly__eq__iff_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__eq__iff_0) ).
cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
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_divide__eq__eq_0,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_order__root_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Oorder(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Polynomial_Opoly(X3,X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__root_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X1) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_order__root_2,axiom,
( hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_HOL_Ozero__class_Ozero(X1)
| c_Polynomial_Oorder(X3,X2,X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__root_2) ).
cnf(cls_divide__1_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
cnf(cls_poly__mult_0,axiom,
( hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X1),X4) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X2,X1),X4),hAPP(c_Polynomial_Opoly(X3,X1),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__mult_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_class__semiring_Osemiring__rules_I10_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
cnf(cls_minus__mult__commute_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
cnf(cls_class__ring_Oneg__mul_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
cnf(cls_poly__minus_0,axiom,
( hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X1),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X2,X1),X3),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__minus_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
cnf(cls_smult__eq__0__iff_1,axiom,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,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_1) ).
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_poly__pCons_0,axiom,
( hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X1),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,hAPP(c_Polynomial_Opoly(X3,X1),X4),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_synthetic__div__eq__0__iff_1,axiom,
( c_Polynomial_Osynthetic__div(X2,X3,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Odegree(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).
cnf(cls_synthetic__div__unique_1,axiom,
( X4 = c_Polynomial_Osynthetic__div(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_1) ).
cnf(cls_constant__degree_0,axiom,
( c_Polynomial_Odegree(X2,X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X2,X1),X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_constant__degree_0) ).
cnf(cls_fundamental__theorem__of__algebra_0,axiom,
( hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X1)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra_0) ).
cnf(cls_complex__cnj__one_0,axiom,
c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__one_0) ).
cnf(cls_conjecture_0,negated_conjecture,
( hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),v_x) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_mpoly__base__conv_I1_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mpoly__base__conv_I1_J_0) ).
cnf(c_0_43,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
cls_zero__neq__one_0 ).
cnf(c_0_44,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one ).
cnf(c_0_45,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_right__inverse__eq_1 ).
cnf(c_0_46,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_47,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
( c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_minus__divide__left_0 ).
cnf(c_0_50,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_49,c_0_46]) ).
cnf(c_0_52,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0 ).
cnf(c_0_53,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring ).
cnf(c_0_54,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1 ).
cnf(c_0_57,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_58,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_59,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_60,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X3,X1) ),
cls_poly__eq__iff_0 ).
cnf(c_0_61,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Oring__char__0 ).
cnf(c_0_62,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_63,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_64,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_0 ).
cnf(c_0_66,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
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_58,c_0_59]) ).
cnf(c_0_68,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Oorder(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Polynomial_Opoly(X3,X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_order__root_0 ).
cnf(c_0_69,negated_conjecture,
( c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X1) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
cls_conjecture_1 ).
cnf(c_0_70,plain,
( X1 = X2
| c_Polynomial_Opoly(X1,tc_Complex_Ocomplex) != c_Polynomial_Opoly(X2,tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_71,axiom,
( hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_HOL_Ozero__class_Ozero(X1)
| c_Polynomial_Oorder(X3,X2,X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_order__root_2 ).
cnf(c_0_72,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_73,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X2
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_46])]),c_0_67]) ).
cnf(c_0_74,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__1_0 ).
cnf(c_0_75,axiom,
( hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X1),X4) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X2,X1),X4),hAPP(c_Polynomial_Opoly(X3,X1),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__mult_0 ).
cnf(c_0_76,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_77,negated_conjecture,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Oorder(X1,v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_62])]),c_0_70]) ).
cnf(c_0_78,plain,
( hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Oorder(X2,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(spm,[status(thm)],[c_0_71,c_0_62]) ).
cnf(c_0_79,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I10_J_0 ).
cnf(c_0_80,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
clsarity_Polynomial__Opoly__Int_Onumber__ring ).
cnf(c_0_81,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1 ).
cnf(c_0_82,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X2 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_46]) ).
cnf(c_0_84,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0 ).
cnf(c_0_85,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_neg__equal__0__iff__equal_0 ).
cnf(c_0_86,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0 ).
cnf(c_0_87,plain,
c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X3,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_88,negated_conjecture,
( hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X1) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_89,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_79,c_0_59]) ).
cnf(c_0_90,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Oneg__mul_0 ).
cnf(c_0_91,plain,
class_Int_Onumber__ring(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_92,axiom,
( hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X1),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X2,X1),X3),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_poly__minus_0 ).
cnf(c_0_93,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring ).
cnf(c_0_94,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_55]),c_0_64]),c_0_47]) ).
cnf(c_0_95,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_84,c_0_59]) ).
cnf(c_0_96,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_55]),c_0_57])]) ).
cnf(c_0_97,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_86,c_0_53]) ).
cnf(c_0_98,negated_conjecture,
( hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
cnf(c_0_99,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,plain,
hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_101,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_67]),c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_104,axiom,
( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_smult__eq__0__iff_1 ).
cnf(c_0_105,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_106,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_107,axiom,
( hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X1),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,hAPP(c_Polynomial_Opoly(X3,X1),X4),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__pCons_0 ).
cnf(c_0_108,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_101,c_0_67]) ).
cnf(c_0_109,negated_conjecture,
( c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X1),X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_89])]) ).
cnf(c_0_110,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0 ).
cnf(c_0_111,axiom,
( c_Polynomial_Osynthetic__div(X2,X3,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Odegree(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_synthetic__div__eq__0__iff_1 ).
cnf(c_0_112,axiom,
( X4 = c_Polynomial_Osynthetic__div(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_1 ).
cnf(c_0_113,plain,
c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_104,c_0_62]) ).
cnf(c_0_114,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_115,axiom,
( c_Polynomial_Odegree(X2,X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X2,X1),X1,X1) ),
cls_constant__degree_0 ).
cnf(c_0_116,axiom,
( hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X1)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ),
cls_fundamental__theorem__of__algebra_0 ).
cnf(c_0_117,plain,
hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,hAPP(c_Polynomial_Opoly(X2,tc_Complex_Ocomplex),X3),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_107,c_0_76]) ).
cnf(c_0_118,negated_conjecture,
( c_HOL_Otimes__class_Otimes(X1,hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_119,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_110,c_0_59]) ).
cnf(c_0_120,plain,
( c_Polynomial_Osynthetic__div(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(spm,[status(thm)],[c_0_111,c_0_76]) ).
cnf(c_0_121,plain,
c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X2,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]),c_0_76])])]) ).
cnf(c_0_122,plain,
( hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X1)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_61]),c_0_62])]) ).
cnf(c_0_123,negated_conjecture,
( hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]) ).
cnf(c_0_124,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(c_Polynomial_OpCons(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,axiom,
c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_complex__cnj__one_0 ).
cnf(c_0_126,negated_conjecture,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
cnf(c_0_127,negated_conjecture,
( hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),v_x) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
cls_conjecture_0 ).
cnf(c_0_128,negated_conjecture,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_47]) ).
cnf(c_0_129,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1),
cls_mpoly__base__conv_I1_J_0 ).
cnf(c_0_130,negated_conjecture,
hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),v_x) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128])]) ).
cnf(c_0_131,negated_conjecture,
hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X1) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_129,c_0_128]) ).
cnf(c_0_132,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG437-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 03:06:19 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.56 start to proof: theBenchmark
% 123.96/124.19 % Version : CSE_E---1.5
% 123.96/124.19 % Problem : theBenchmark.p
% 123.96/124.19 % Proof found
% 123.96/124.19 % SZS status Theorem for theBenchmark.p
% 123.96/124.19 % SZS output start Proof
% See solution above
% 123.96/124.20 % Total time : 123.580000 s
% 123.96/124.20 % SZS output end Proof
% 123.96/124.20 % Total time : 123.603000 s
%------------------------------------------------------------------------------