TSTP Solution File: SWW189+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW189+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 : Fri Sep 1 00:16:25 EDT 2023
% Result : Theorem 4.99s 5.13s
% Output : CNFRefutation 5.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 157
% Syntax : Number of formulae : 201 ( 21 unt; 142 typ; 0 def)
% Number of atoms : 119 ( 79 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 42 ~; 41 |; 6 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 234 ( 137 >; 97 *; 0 +; 0 <<)
% Number of predicates : 83 ( 81 usr; 1 prp; 0-5 aty)
% Number of functors : 61 ( 61 usr; 5 con; 0-5 aty)
% Number of variables : 101 ( 9 sgn; 59 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_24,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_25,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_27,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_29,type,
class_Rings_Oidom: $i > $o ).
tff(decl_30,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_31,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_32,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_33,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_34,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_36,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_38,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_39,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
c_Polynomial_Ocoeff: ( $i * $i ) > $i ).
tff(decl_41,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Groups_Osemigroup: ( $i * $i ) > $o ).
tff(decl_43,type,
c_Groups_Ocomm__monoid: ( $i * $i * $i ) > $o ).
tff(decl_44,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_45,type,
class_Groups_Ozero: $i > $o ).
tff(decl_46,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_47,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_48,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_49,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
tc_Nat_Onat: $i ).
tff(decl_52,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_55,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_57,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_58,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_59,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_60,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_61,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_62,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_63,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_64,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_65,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_66,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_67,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_68,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_69,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_70,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_71,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_72,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_73,type,
hBOOL: $i > $o ).
tff(decl_74,type,
c_Nat_Onat_Onat__case: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_76,type,
class_Fields_Ofield: $i > $o ).
tff(decl_77,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_78,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_79,type,
c_Polynomial_OAbs__poly: ( $i * $i ) > $i ).
tff(decl_80,type,
c_Nat_OSuc: $i > $i ).
tff(decl_81,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_82,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_83,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_84,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_85,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_86,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_87,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_88,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_89,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_90,type,
class_Orderings_Oord: $i > $o ).
tff(decl_91,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_92,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_93,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_94,type,
c_Nat_Onat_Onat__size: $i > $i ).
tff(decl_95,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_97,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_98,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_99,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_100,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_101,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_102,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_103,type,
class_Groups_Oone: $i > $o ).
tff(decl_104,type,
class_Rings_Oring: $i > $o ).
tff(decl_105,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_106,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_107,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_108,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_109,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_110,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_111,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_112,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_113,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_114,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_115,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_116,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_117,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_118,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_119,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_121,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_122,type,
class_Groups_Ominus: $i > $o ).
tff(decl_123,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_124,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_125,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_126,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_127,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_129,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_130,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_131,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_132,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_133,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_134,type,
class_Rings_Odvd: $i > $o ).
tff(decl_135,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_136,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_137,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_138,type,
tc_Complex_Ocomplex: $i ).
tff(decl_139,type,
tc_HOL_Obool: $i ).
tff(decl_140,type,
v_p: $i ).
tff(decl_141,type,
v_a: $i ).
tff(decl_142,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_144,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_146,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk6_1: $i > $i ).
tff(decl_148,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_151,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_152,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_157,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_158,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_160,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk21_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_163,type,
esk22_1: $i > $i ).
fof(conj_0,conjecture,
? [X79] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X79) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p)
& ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X79),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_poly__offset__poly,axiom,
! [X4,X8,X6,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> hAPP(c_Polynomial_Opoly(X7,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X7,X6,X8)),X4) = hAPP(c_Polynomial_Opoly(X7,X6),c_Groups_Oplus__class_Oplus(X7,X8,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
fof(fact_psize__def,axiom,
! [X6,X7] :
( class_Groups_Ozero(X7)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X7,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X7,X6) = c_Nat_OSuc(c_Polynomial_Odegree(X7,X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__def) ).
fof(fact_Suc__eq__plus1,axiom,
! [X18] : c_Nat_OSuc(X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(fact_nat__add__commute,axiom,
! [X18,X25] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(fact_degree__offset__poly,axiom,
! [X8,X6,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> c_Polynomial_Odegree(X7,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X7,X6,X8)) = c_Polynomial_Odegree(X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
fof(fact_smult__0__left,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> c_Polynomial_Osmult(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X12,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Otimes__class_Otimes(X7,c_Groups_Ozero__class_Ozero(X7),X12) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_smult__pCons,axiom,
! [X6,X14,X12,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> c_Polynomial_Osmult(X7,X12,c_Polynomial_OpCons(X7,X14,X6)) = c_Polynomial_OpCons(X7,c_Groups_Otimes__class_Otimes(X7,X12,X14),c_Polynomial_Osmult(X7,X12,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_psize__eq__0__iff,axiom,
! [X10,X7] :
( class_Groups_Ozero(X7)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X7,X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X10 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_offset__poly__eq__0__iff,axiom,
! [X20,X10,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X7,X10,X20) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
<=> X10 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(fact_offset__poly__single,axiom,
! [X8,X12,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X7,c_Polynomial_OpCons(X7,X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))),X8) = c_Polynomial_OpCons(X7,X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(c_0_15,negated_conjecture,
~ ? [X79] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X79) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p)
& ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X79),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,X3)) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_16,negated_conjecture,
! [X3175] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X3175) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3175),esk22_1(X3175)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,esk22_1(X3175))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_17,plain,
! [X92,X93,X94,X95] :
( ~ class_Rings_Ocomm__semiring__0(X95)
| hAPP(c_Polynomial_Opoly(X95,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X95,X94,X93)),X92) = hAPP(c_Polynomial_Opoly(X95,X94),c_Groups_Oplus__class_Oplus(X95,X93,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__offset__poly])]) ).
fof(c_0_18,plain,
! [X797,X798] :
( ( X797 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X798))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X798,X797) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X798) )
& ( X797 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X798))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X798,X797) = c_Nat_OSuc(c_Polynomial_Odegree(X798,X797))
| ~ class_Groups_Ozero(X798) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__def])])]) ).
fof(c_0_19,plain,
! [X1791] : c_Nat_OSuc(X1791) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1791,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
cnf(c_0_20,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X1) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),esk22_1(X1)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,esk22_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3)),X4) = hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(c_0_23,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X666,X667] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X667,X666) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X666,X667),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_26,negated_conjecture,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,esk22_1(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2)))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,esk22_1(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2))))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Groups_Ozero(X2) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_a)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
fof(c_0_32,plain,
! [X741,X742,X743] :
( ~ class_Rings_Ocomm__semiring__0(X743)
| c_Polynomial_Odegree(X743,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X743,X742,X741)) = c_Polynomial_Odegree(X743,X742) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__offset__poly])]) ).
fof(c_0_33,plain,
! [X195,X196] :
( ~ class_Rings_Ocomm__semiring__0(X196)
| c_Polynomial_Osmult(X196,c_Groups_Ozero__class_Ozero(X196),X195) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X196)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
fof(c_0_34,plain,
! [X366,X367] :
( ~ class_Rings_Ocomm__semiring__1(X367)
| c_Groups_Otimes__class_Otimes(X367,c_Groups_Ozero__class_Ozero(X367),X366) = c_Groups_Ozero__class_Ozero(X367) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
cnf(c_0_35,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_a) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_a))) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_36,plain,
( c_Polynomial_Odegree(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3)) = c_Polynomial_Odegree(X1,X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X462,X463,X464,X465] :
( ~ class_Rings_Ocomm__semiring__0(X465)
| c_Polynomial_Osmult(X465,X464,c_Polynomial_OpCons(X465,X463,X462)) = c_Polynomial_OpCons(X465,c_Groups_Otimes__class_Otimes(X465,X464,X463),c_Polynomial_Osmult(X465,X464,X462)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])]) ).
cnf(c_0_38,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_41,plain,
! [X485,X486] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X486,X485) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X485 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X486))
| ~ class_Groups_Ozero(X486) )
& ( X485 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X486))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X486,X485) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X486) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(c_0_42,plain,
! [X182,X183,X184] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X184,X183,X182) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X184))
| X183 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X184))
| ~ class_Rings_Ocomm__semiring__0(X184) )
& ( X183 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X184))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X184,X183,X182) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X184))
| ~ class_Rings_Ocomm__semiring__0(X184) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff])])]) ).
cnf(c_0_43,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_a) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_22])]) ).
fof(c_0_44,plain,
! [X243,X244,X245] :
( ~ class_Rings_Ocomm__semiring__0(X245)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X245,c_Polynomial_OpCons(X245,X244,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X245))),X243) = c_Polynomial_OpCons(X245,X244,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X245))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__single])]) ).
cnf(c_0_45,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) = c_Polynomial_OpCons(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_47,plain,
c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_a) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_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_43,c_0_30]),c_0_31])]) ).
cnf(c_0_51,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) = c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(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_45,c_0_46]),c_0_47]),c_0_46]),c_0_22])]) ).
cnf(c_0_53,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
c_Groups_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_49,c_0_50]),c_0_22])]) ).
cnf(c_0_55,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_22])]) ).
cnf(c_0_56,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_31])]) ).
cnf(c_0_57,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,X1) = v_p,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54]),c_0_54]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_56]),c_0_57]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW189+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 22:16:25 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 4.99/5.13 % Version : CSE_E---1.5
% 4.99/5.13 % Problem : theBenchmark.p
% 4.99/5.13 % Proof found
% 4.99/5.13 % SZS status Theorem for theBenchmark.p
% 4.99/5.13 % SZS output start Proof
% See solution above
% 5.13/5.15 % Total time : 4.521000 s
% 5.13/5.15 % SZS output end Proof
% 5.13/5.15 % Total time : 4.560000 s
%------------------------------------------------------------------------------