TSTP Solution File: SWW257+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW257+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 : n006.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 00:16:45 EDT 2023
% Result : Theorem 249.44s 249.66s
% Output : CNFRefutation 249.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 154
% Syntax : Number of formulae : 183 ( 22 unt; 142 typ; 0 def)
% Number of atoms : 68 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 48 ( 21 ~; 17 |; 2 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 179 ( 117 >; 62 *; 0 +; 0 <<)
% Number of predicates : 75 ( 73 usr; 2 prp; 0-3 aty)
% Number of functors : 69 ( 69 usr; 24 con; 0-4 aty)
% Number of variables : 73 ( 3 sgn; 37 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_a____: $i ).
tff(decl_24,type,
tc_Complex_Ocomplex: $i ).
tff(decl_25,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
v_k____: $i ).
tff(decl_27,type,
tc_Nat_Onat: $i ).
tff(decl_28,type,
class_Power_Opower: $i > $o ).
tff(decl_29,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_30,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_31,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_32,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_33,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_35,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_36,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_37,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_39,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_40,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_41,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_42,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_43,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_44,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_45,type,
class_Rings_Oring: $i > $o ).
tff(decl_46,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_47,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_49,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_50,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_51,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_52,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_53,type,
class_Groups_Ozero: $i > $o ).
tff(decl_54,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_55,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_56,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_57,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_58,type,
class_Groups_Oone: $i > $o ).
tff(decl_59,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_60,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_61,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_62,type,
v_pa____: $i ).
tff(decl_63,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_64,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_65,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_66,type,
c_Nat_OSuc: $i > $i ).
tff(decl_67,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_70,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_71,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_72,type,
c_Fact_Ofact__class_Ofact: ( $i * $i ) > $i ).
tff(decl_73,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_74,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_75,type,
hBOOL: $i > $o ).
tff(decl_76,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_77,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_78,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_79,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_80,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_81,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_82,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_83,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_84,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_85,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_86,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_87,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_88,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_89,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_90,type,
tc_Int_Oint: $i ).
tff(decl_91,type,
v_q____: $i ).
tff(decl_92,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_93,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_94,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(decl_95,type,
v_p: $i ).
tff(decl_96,type,
v_c____: $i ).
tff(decl_97,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_98,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_99,type,
class_Rings_Oidom: $i > $o ).
tff(decl_100,type,
tc_RealDef_Oreal: $i ).
tff(decl_101,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_102,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_103,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
v_s____: $i ).
tff(decl_105,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_106,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_107,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_108,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_109,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_110,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_111,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_112,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_113,type,
class_Fields_Ofield: $i > $o ).
tff(decl_114,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_117,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_119,type,
class_Orderings_Oord: $i > $o ).
tff(decl_120,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_121,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_122,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_123,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_124,type,
class_Rings_Odvd: $i > $o ).
tff(decl_125,type,
c_Complex_Oii: $i ).
tff(decl_126,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_127,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_128,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_129,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_130,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_131,type,
tc_HOL_Obool: $i ).
tff(decl_132,type,
v_thesis____: $o ).
tff(decl_133,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk2_0: $i ).
tff(decl_135,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_136,type,
esk4_1: $i > $i ).
tff(decl_137,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_141,type,
esk9_0: $i ).
tff(decl_142,type,
esk10_1: $i > $i ).
tff(decl_143,type,
esk11_1: $i > $i ).
tff(decl_144,type,
esk12_1: $i > $i ).
tff(decl_145,type,
esk13_0: $i ).
tff(decl_146,type,
esk14_0: $i ).
tff(decl_147,type,
esk15_0: $i ).
tff(decl_148,type,
esk16_0: $i ).
tff(decl_149,type,
esk17_0: $i ).
tff(decl_150,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_151,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk20_0: $i ).
tff(decl_153,type,
esk21_0: $i ).
tff(decl_154,type,
esk22_0: $i ).
tff(decl_155,type,
esk23_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_156,type,
esk24_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_157,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_158,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_159,type,
esk27_0: $i ).
tff(decl_160,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk29_1: $i > $i ).
tff(decl_162,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk31_3: ( $i * $i * $i ) > $i ).
fof(fact_poly__pCons,axiom,
! [X17,X20,X7,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_OpCons(X5,X7,X20)),X17) = c_Groups_Oplus__class_Oplus(X5,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),hAPP(c_Polynomial_Opoly(X5,X20),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_poly__monom,axiom,
! [X17,X4,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_Omonom(X5,X7,X4)),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X21,X22,X24,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(conj_0,hypothesis,
( ? [X70] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X70),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X12,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096,axiom,
? [X14] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X14) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096) ).
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(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_realpow__num__eq__if,axiom,
! [X6,X4,X5] :
( class_Power_Opower(X5)
=> ( ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X4) = c_Groups_Oone__class_Oone(X5) )
& ( X4 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(fact_kas_I2_J,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I2_J) ).
fof(c_0_12,plain,
! [X1560,X1561,X1562,X1563] :
( ~ class_Rings_Ocomm__semiring__0(X1563)
| hAPP(c_Polynomial_Opoly(X1563,c_Polynomial_OpCons(X1563,X1562,X1561)),X1560) = c_Groups_Oplus__class_Oplus(X1563,X1562,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1563),X1560),hAPP(c_Polynomial_Opoly(X1563,X1561),X1560))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(c_0_13,plain,
! [X1564,X1565,X1566,X1567] :
( ~ class_Rings_Ocomm__semiring__1(X1567)
| hAPP(c_Polynomial_Opoly(X1567,c_Polynomial_Omonom(X1567,X1566,X1565)),X1564) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1567),X1566),hAPP(hAPP(c_Power_Opower__class_Opower(X1567),X1564),X1565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])]) ).
fof(c_0_14,plain,
! [X182,X183,X184,X185] :
( ~ class_Rings_Ocomm__semiring__1(X185)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X185),X184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X185),X183),X182)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X185),X183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X185),X184),X182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(c_0_15,hypothesis,
! [X2876] :
( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2876),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_thesis____ ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])]) ).
fof(c_0_16,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
fof(c_0_17,plain,
! [X186,X187,X188] :
( ~ class_Rings_Ocomm__semiring__1(X188)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X188),X187),X186) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X188),X186),X187) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(c_0_18,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),esk9_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096])]) ).
cnf(c_0_19,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(c_0_21,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(c_0_23,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_24,plain,
! [X253,X254,X255] :
( ( X254 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X255),X253),X254) = c_Groups_Oone__class_Oone(X255)
| ~ class_Power_Opower(X255) )
& ( X254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X255),X253),X254) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X255),X253),hAPP(hAPP(c_Power_Opower__class_Opower(X255),X253),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X254,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X255) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
cnf(c_0_25,hypothesis,
( v_thesis____
| c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),esk9_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_30,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_32,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
cnf(c_0_34,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_36,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),esk9_0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk9_0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_37,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_kas_I2_J]) ).
cnf(c_0_40,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : SWW257+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.16 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.38 % Computer : n006.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sun Aug 27 18:15:22 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.63 start to proof: theBenchmark
% 249.44/249.66 % Version : CSE_E---1.5
% 249.44/249.66 % Problem : theBenchmark.p
% 249.44/249.66 % Proof found
% 249.44/249.66 % SZS status Theorem for theBenchmark.p
% 249.44/249.66 % SZS output start Proof
% See solution above
% 249.44/249.67 % Total time : 248.752000 s
% 249.44/249.67 % SZS output end Proof
% 249.44/249.67 % Total time : 248.801000 s
%------------------------------------------------------------------------------