TSTP Solution File: ALG426-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG426-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 16:07:43 EDT 2023
% Result : Unsatisfiable 20.61s 20.79s
% Output : CNFRefutation 20.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 168
% Syntax : Number of formulae : 332 ( 79 unt; 102 typ; 0 def)
% Number of atoms : 448 ( 242 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 440 ( 222 ~; 218 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 154 ( 95 >; 59 *; 0 +; 0 <<)
% Number of predicates : 61 ( 59 usr; 1 prp; 0-5 aty)
% Number of functors : 43 ( 43 usr; 7 con; 0-4 aty)
% Number of variables : 421 ( 57 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_23,type,
class_Power_Opower: $i > $o ).
tff(decl_24,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_25,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
tc_nat: $i ).
tff(decl_27,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_28,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_33,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_34,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_35,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_36,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_37,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_38,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
class_HOL_Ozero: $i > $o ).
tff(decl_40,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
class_HOL_Oeq: $i > $o ).
tff(decl_42,type,
c_HOL_Oeq__class_Oeq: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_44,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_45,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_48,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_49,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_50,type,
c_OrderedGroup_Olordered__ab__group__add__class_Opprt: ( $i * $i ) > $i ).
tff(decl_51,type,
c_OrderedGroup_Olordered__ab__group__add__class_Onprt: ( $i * $i ) > $i ).
tff(decl_52,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_53,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_54,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_56,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_57,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_58,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_59,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_60,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_62,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_65,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_66,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_67,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_68,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_69,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_70,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_71,type,
c_Polynomial_Ocoeff: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_73,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_74,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_75,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_78,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_79,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_80,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(decl_81,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_83,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_84,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_85,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
class_SEQ_Obanach: $i > $o ).
tff(decl_90,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(decl_91,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_92,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_93,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_94,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_95,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_96,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_97,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(decl_98,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_99,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_101,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_102,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
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,
c_Complex_Ocnj: $i > $i ).
tff(decl_107,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_108,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_109,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_110,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_111,type,
c_Polynomial_Osynthetic__divmod: ( $i * $i * $i ) > $i ).
tff(decl_112,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
c_Complex_Oii: $i ).
tff(decl_114,type,
tc_Complex_Ocomplex: $i ).
tff(decl_115,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1: $i > $i ).
tff(decl_116,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2: $i > $i ).
tff(decl_117,type,
v_p: $i ).
tff(decl_118,type,
t_a: $i ).
tff(decl_119,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2: $i > $i ).
tff(decl_120,type,
v_q: $i ).
tff(decl_121,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_122,type,
tc_RealDef_Oreal: $i ).
tff(decl_123,type,
tc_prod: ( $i * $i ) > $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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(cls_inverse__inverse__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(cls_divide__inverse_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
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_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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(cls_dvd__refl_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
cnf(cls_dvd__minus__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
cnf(cls_dvd__mult__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
cnf(cls_inverse__minus__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_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/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
cnf(cls_dvd__0__left_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
cnf(cls_inverse__zero__imp__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
cnf(cls_dvd__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
cnf(cls_inverse__eq__1__iff_0,axiom,
( X2 = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_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/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
cnf(cls_inverse__eq__1__iff_1,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
cnf(cls_dvd__mult__cancel__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
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_dvd__0__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
cnf(cls_minus__divide__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
cnf(cls_dvd__mult_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
cnf(cls_inverse__mult__distrib_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
cnf(cls_mult__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
cnf(cls_poly__add_0,axiom,
( c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).
cnf(cls_add__poly__code_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_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_pe_0,axiom,
v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pe_0) ).
cnf(cls_order__root_1,axiom,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
cnf(cls_inverse__1_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
cnf(cls_mult__1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(cls_inverse__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_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_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_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/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
cnf(cls_frac__eq__eq_0,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Otimes__class_Otimes(X2,X5,X1) = c_HOL_Otimes__class_Otimes(X4,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oinverse__class_Odivide(X4,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
cnf(cls_smult__pCons_0,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_OpCons(X3,X4,X1),X1) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
cnf(cls_mult__frac__num_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
cnf(cls_power__one__over_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
cnf(cls_eq__divide__imp_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
cnf(cls_power__one_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_nonzero__minus__divide__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
cnf(cls_field__inverse_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
cnf(cls_fundamental__theorem__of__algebra__alt_1,axiom,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_1) ).
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_conjecture_0,negated_conjecture,
c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_1) ).
cnf(cls_conjecture_1,negated_conjecture,
v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_66,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_67,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one ).
cnf(c_0_68,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__inverse__eq_0 ).
cnf(c_0_69,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_70,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_71,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,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_73,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_74,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__inverse_0 ).
cnf(c_0_75,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_76,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_77,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_78,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_79,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_80,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__refl_0 ).
cnf(c_0_81,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_82,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_73])]) ).
cnf(c_0_83,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_76,c_0_77]) ).
cnf(c_0_84,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
cls_dvd__minus__iff_0 ).
cnf(c_0_85,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_78,c_0_79]) ).
cnf(c_0_86,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1 ).
cnf(c_0_87,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_dvd__mult__left_0 ).
cnf(c_0_88,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_80,c_0_77]) ).
cnf(c_0_89,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__minus__eq_0 ).
cnf(c_0_90,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(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_81,c_0_82]),c_0_83]) ).
cnf(c_0_91,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_92,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring ).
cnf(c_0_93,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_dvd__0__left_0 ).
cnf(c_0_94,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
cnf(c_0_95,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_77])]) ).
cnf(c_0_96,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_inverse__zero__imp__zero_0 ).
cnf(c_0_97,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_69]),c_0_70])]) ).
cnf(c_0_98,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(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_90,c_0_75]),c_0_83]) ).
cnf(c_0_99,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_91,c_0_92]) ).
cnf(c_0_100,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_77])]) ).
cnf(c_0_101,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__trans_0 ).
cnf(c_0_102,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_74]),c_0_73])]) ).
cnf(c_0_103,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_Oinverse(X1,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_96,c_0_97]),c_0_69])]) ).
cnf(c_0_104,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_97]),c_0_85]) ).
cnf(c_0_105,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_83]),c_0_73])]) ).
cnf(c_0_106,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_94]),c_0_85]) ).
cnf(c_0_107,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oinverse__class_Odivide(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_77])]) ).
cnf(c_0_108,axiom,
( X2 = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oone__class_Oone(X1) ),
cls_inverse__eq__1__iff_0 ).
cnf(c_0_109,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_110,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_103,c_0_75]) ).
cnf(c_0_111,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_75]) ).
cnf(c_0_112,plain,
( c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_97]),c_0_70]),c_0_73])]) ).
cnf(c_0_114,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_115,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber__ring ).
cnf(c_0_116,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__eq__1__iff_1 ).
cnf(c_0_117,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X1,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_109,c_0_110]),c_0_79])]) ).
cnf(c_0_118,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_113,c_0_75]) ).
cnf(c_0_120,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_dvd__mult__cancel__left_0 ).
cnf(c_0_121,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_122,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_123,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_70]),c_0_73])]),c_0_71]) ).
cnf(c_0_124,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__0__right_0 ).
cnf(c_0_125,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_71]) ).
cnf(c_0_126,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_minus__divide__right_0 ).
cnf(c_0_127,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]),c_0_121])]),c_0_123]) ).
cnf(c_0_128,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_124,c_0_77]) ).
cnf(c_0_129,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_125,c_0_107]) ).
cnf(c_0_130,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_70]),c_0_73])]) ).
cnf(c_0_131,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X2,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_127,c_0_110]),c_0_128])]) ).
cnf(c_0_132,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_neg__0__equal__iff__equal_1 ).
cnf(c_0_133,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mult_0 ).
cnf(c_0_134,plain,
( c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_85]) ).
cnf(c_0_135,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_131,c_0_75]) ).
cnf(c_0_136,plain,
c_HOL_Ouminus__class_Ouminus(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_132,c_0_79]) ).
cnf(c_0_137,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_133,c_0_77]) ).
cnf(c_0_138,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_134,c_0_82]) ).
cnf(c_0_139,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X2,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_135,c_0_117]),c_0_136])]) ).
cnf(c_0_140,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_106,c_0_137]) ).
cnf(c_0_141,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_142,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__mult__distrib_0 ).
cnf(c_0_143,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_140,c_0_131]) ).
cnf(c_0_144,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_mult__1_0 ).
cnf(c_0_145,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult ).
cnf(c_0_146,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_141,c_0_105]) ).
cnf(c_0_147,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_70]),c_0_73])]) ).
cnf(c_0_148,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_149,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__neg__iff__add__eq__0_1 ).
cnf(c_0_150,axiom,
( c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__add_0 ).
cnf(c_0_151,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_add__poly__code_I1_J_0 ).
cnf(c_0_152,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_153,axiom,
v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_pe_0 ).
cnf(c_0_154,axiom,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_order__root_1 ).
cnf(c_0_155,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_inverse__1_0 ).
cnf(c_0_156,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__right_0 ).
cnf(c_0_157,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_158,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X3,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_146,c_0_147]),c_0_136])]) ).
cnf(c_0_159,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_74]),c_0_73])]) ).
cnf(c_0_160,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X2,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__divide_0 ).
cnf(c_0_161,plain,
( c_Polynomial_Opoly(X1,X2,X3) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X4,X2,X3),X3)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,X4,tc_Polynomial_Opoly(X3)),X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_162,plain,
c_HOL_Oplus__class_Oplus(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_163,plain,
c_Polynomial_Opoly(v_p,X1,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_154,c_0_153]),c_0_122])]) ).
cnf(c_0_164,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_165,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_166,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_167,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_155,c_0_69]) ).
cnf(c_0_168,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_169,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_170,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_82,c_0_75]) ).
cnf(c_0_171,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_70]),c_0_73])]) ).
cnf(c_0_172,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_97]),c_0_85]) ).
cnf(c_0_173,plain,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]),c_0_164]),c_0_79])]) ).
cnf(c_0_174,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_175,plain,
c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = v_p,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_122]),c_0_153]) ).
cnf(c_0_176,plain,
c_HOL_Oplus__class_Oplus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_152]),c_0_153]) ).
cnf(c_0_177,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Otimes__class_Otimes(X2,X5,X1) = c_HOL_Otimes__class_Otimes(X4,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oinverse__class_Odivide(X4,X5,X1) ),
cls_frac__eq__eq_0 ).
cnf(c_0_178,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_167]),c_0_168]),c_0_73])]) ).
cnf(c_0_179,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171]) ).
cnf(c_0_180,plain,
( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,X2,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_172,c_0_173]),c_0_88])]) ).
cnf(c_0_181,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_176]),c_0_164])])]) ).
cnf(c_0_182,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_OpCons(X3,X4,X1),X1) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_smult__pCons_0 ).
cnf(c_0_183,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__frac__num_0 ).
cnf(c_0_184,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_168]),c_0_73])]),c_0_71])]) ).
cnf(c_0_185,plain,
( c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,X2,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_179,c_0_180]),c_0_136])]) ).
cnf(c_0_186,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_164])]) ).
cnf(c_0_187,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X3,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_70]),c_0_73])]) ).
cnf(c_0_188,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)],[c_0_184,c_0_83]) ).
cnf(c_0_189,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_187]) ).
cnf(c_0_190,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__mul_0 ).
cnf(c_0_191,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__one__over_0 ).
cnf(c_0_192,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_121]),c_0_123]) ).
cnf(c_0_193,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_189,c_0_83]) ).
cnf(c_0_194,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X4,X2,X3),X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X4,X3),X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_195,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_eq__divide__imp_0 ).
cnf(c_0_196,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_85,c_0_192]) ).
cnf(c_0_197,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(X1,X3,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_159]),c_0_170]),c_0_148]),c_0_70]),c_0_73]),c_0_77])]) ).
cnf(c_0_198,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_73])]),c_0_123]) ).
cnf(c_0_199,plain,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(X1,X3,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_197,c_0_82]) ).
cnf(c_0_200,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_85,c_0_198]) ).
cnf(c_0_201,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__one_0 ).
cnf(c_0_202,plain,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_203,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_201,c_0_157]) ).
cnf(c_0_204,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_159]),c_0_159]),c_0_70]),c_0_73])]) ).
cnf(c_0_205,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_206,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_207,plain,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_119]),c_0_203]),c_0_204])]) ).
cnf(c_0_208,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__minus__divide__right_0 ).
cnf(c_0_209,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_field__inverse_0 ).
cnf(c_0_210,axiom,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
cls_fundamental__theorem__of__algebra__alt_1 ).
cnf(c_0_211,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_212,negated_conjecture,
c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_conjecture_0 ).
cnf(c_0_213,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_205,c_0_77]) ).
cnf(c_0_214,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_206,c_0_77]) ).
cnf(c_0_215,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_191]),c_0_159]),c_0_75]),c_0_159]),c_0_70]),c_0_73])]) ).
cnf(c_0_216,plain,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1),X3,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(spm,[status(thm)],[c_0_191,c_0_208]) ).
cnf(c_0_217,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_209]) ).
cnf(c_0_218,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_219,plain,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),v_p,tc_Complex_Ocomplex) = X1 ),
inference(rw,[status(thm)],[c_0_210,c_0_153]) ).
cnf(c_0_220,negated_conjecture,
c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_q,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_213]),c_0_214]),c_0_164])]) ).
cnf(c_0_221,negated_conjecture,
v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_conjecture_1 ).
cnf(c_0_222,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_159]),c_0_97]),c_0_75]),c_0_85]),c_0_159]),c_0_70]),c_0_73])])]),c_0_71]) ).
cnf(c_0_223,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_112]),c_0_73]),c_0_75])]),c_0_71]) ).
cnf(c_0_224,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_218,c_0_175]),c_0_176]),c_0_164])])]) ).
cnf(c_0_225,negated_conjecture,
( c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X1,v_q,tc_Complex_Ocomplex)),v_p,tc_Complex_Ocomplex) = c_Polynomial_OpCons(X1,v_q,tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_226,negated_conjecture,
v_p != v_q,
inference(rw,[status(thm)],[c_0_221,c_0_153]) ).
cnf(c_0_227,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_228,negated_conjecture,
X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_224]),c_0_226]) ).
cnf(c_0_229,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_227,c_0_228]),c_0_228]),c_0_228]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG426-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 03:10:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 20.61/20.79 % Version : CSE_E---1.5
% 20.61/20.79 % Problem : theBenchmark.p
% 20.61/20.79 % Proof found
% 20.61/20.79 % SZS status Theorem for theBenchmark.p
% 20.61/20.79 % SZS output start Proof
% See solution above
% 20.61/20.81 % Total time : 20.208000 s
% 20.61/20.81 % SZS output end Proof
% 20.61/20.81 % Total time : 20.229000 s
%------------------------------------------------------------------------------