TSTP Solution File: SWW255+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW255+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 3.27s 3.39s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 212
% Syntax : Number of formulae : 269 ( 41 unt; 192 typ; 0 def)
% Number of atoms : 117 ( 80 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 30 ~; 23 |; 6 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 293 ( 171 >; 122 *; 0 +; 0 <<)
% Number of predicates : 79 ( 77 usr; 1 prp; 0-3 aty)
% Number of functors : 115 ( 115 usr; 21 con; 0-5 aty)
% Number of variables : 122 ( 7 sgn; 63 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_s____: $i ).
tff(decl_24,type,
tc_Complex_Ocomplex: $i ).
tff(decl_25,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_26,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_27,type,
v_a____: $i ).
tff(decl_28,type,
v_p: $i ).
tff(decl_29,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_30,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
v_q____: $i ).
tff(decl_32,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_33,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_35,type,
v_k____: $i ).
tff(decl_36,type,
tc_Nat_Onat: $i ).
tff(decl_37,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_38,type,
v_w____: $i ).
tff(decl_39,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_40,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_43,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_44,type,
class_Fields_Ofield: $i > $o ).
tff(decl_45,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_46,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_47,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_48,type,
tc_RealDef_Oreal: $i ).
tff(decl_49,type,
v_pa____: $i ).
tff(decl_50,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_51,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_52,type,
class_Groups_Ozero: $i > $o ).
tff(decl_53,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_54,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_55,type,
class_Rings_Oidom: $i > $o ).
tff(decl_56,type,
class_Power_Opower: $i > $o ).
tff(decl_57,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_58,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_59,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_60,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_61,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_62,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_63,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_64,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_65,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_66,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_67,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_68,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_69,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_70,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_71,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_72,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_73,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_74,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
v_c____: $i ).
tff(decl_77,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_78,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_79,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_80,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_81,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_82,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_83,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_84,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_85,type,
hBOOL: $i > $o ).
tff(decl_86,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_87,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_88,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_89,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_90,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_91,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_92,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_93,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_94,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_95,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_96,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_97,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_98,type,
class_Groups_Oone: $i > $o ).
tff(decl_99,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_100,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_101,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_102,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_103,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_104,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_105,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_106,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_108,type,
class_Orderings_Oord: $i > $o ).
tff(decl_109,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_110,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_111,type,
tc_Int_Oint: $i ).
tff(decl_112,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_113,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_114,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_115,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_116,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_117,type,
class_Rings_Oring: $i > $o ).
tff(decl_118,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_119,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_120,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_121,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_122,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_123,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_124,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_125,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_126,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_127,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
class_Rings_Odvd: $i > $o ).
tff(decl_129,type,
c_Nat_OSuc: $i > $i ).
tff(decl_130,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_131,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_132,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_133,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_134,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff(decl_135,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_136,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_137,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(decl_138,type,
c_Transcendental_Oln: $i > $i ).
tff(decl_139,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(decl_140,type,
c_Complex_Ocis: $i > $i ).
tff(decl_141,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_142,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_143,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_144,type,
tc_HOL_Obool: $i ).
tff(decl_145,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_146,type,
esk2_0: $i ).
tff(decl_147,type,
esk3_0: $i ).
tff(decl_148,type,
esk4_1: $i > $i ).
tff(decl_149,type,
esk5_1: $i > $i ).
tff(decl_150,type,
esk6_0: $i ).
tff(decl_151,type,
esk7_0: $i ).
tff(decl_152,type,
esk8_0: $i ).
tff(decl_153,type,
esk9_0: $i ).
tff(decl_154,type,
esk10_0: $i ).
tff(decl_155,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk12_1: $i > $i ).
tff(decl_157,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_160,type,
esk16_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_161,type,
esk17_0: $i ).
tff(decl_162,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk20_1: $i > $i ).
tff(decl_165,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk23_3: ( $i * $i * $i ) > $i ).
tff(decl_168,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_169,type,
esk25_1: $i > $i ).
tff(decl_170,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_171,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_172,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_173,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_174,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_175,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_176,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_178,type,
esk34_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk35_1: $i > $i ).
tff(decl_180,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_181,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_182,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_183,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_184,type,
esk40_3: ( $i * $i * $i ) > $i ).
tff(decl_185,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_186,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_187,type,
esk43_3: ( $i * $i * $i ) > $i ).
tff(decl_188,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_189,type,
esk45_3: ( $i * $i * $i ) > $i ).
tff(decl_190,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_191,type,
esk47_3: ( $i * $i * $i ) > $i ).
tff(decl_192,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_193,type,
esk49_3: ( $i * $i * $i ) > $i ).
tff(decl_194,type,
esk50_2: ( $i * $i ) > $i ).
tff(decl_195,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_196,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_197,type,
esk53_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_198,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_199,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_200,type,
esk56_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_201,type,
esk57_2: ( $i * $i ) > $i ).
tff(decl_202,type,
esk58_2: ( $i * $i ) > $i ).
tff(decl_203,type,
esk59_3: ( $i * $i * $i ) > $i ).
tff(decl_204,type,
esk60_1: $i > $i ).
tff(decl_205,type,
esk61_1: $i > $i ).
tff(decl_206,type,
esk62_2: ( $i * $i ) > $i ).
tff(decl_207,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_208,type,
esk64_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_209,type,
esk65_2: ( $i * $i ) > $i ).
tff(decl_210,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_211,type,
esk67_1: $i > $i ).
tff(decl_212,type,
esk68_2: ( $i * $i ) > $i ).
tff(decl_213,type,
esk69_2: ( $i * $i ) > $i ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_poly__0,axiom,
! [X9,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> hAPP(c_Polynomial_Opoly(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))),X9) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
fof(fact_kas_I4_J,axiom,
! [X4] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X4) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X4),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I4_J) ).
fof(fact_s0,axiom,
v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__diff__cancel,axiom,
! [X8,X6,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X8),X8) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X17,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X6,X17) = c_Groups_Oplus__class_Oplus(X7,X17,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_pqc0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pqc0) ).
fof(fact_r01,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r01) ).
fof(fact_poly__pCons,axiom,
! [X9,X10,X6,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> hAPP(c_Polynomial_Opoly(X7,c_Polynomial_OpCons(X7,X6,X10)),X9) = c_Groups_Oplus__class_Oplus(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X9),hAPP(c_Polynomial_Opoly(X7,X10),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X8,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X8) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X8),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096,axiom,
? [X32,X33] :
( X33 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& X32 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X34] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X34),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
& ! [X4] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X4) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X4),X32)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X33,X34)),X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096) ).
fof(fact_minus__add__cancel,axiom,
! [X8,X6,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Oplus__class_Oplus(X7,X6,X8)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_add__minus__cancel,axiom,
! [X8,X6,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X8)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(conj_0,conjecture,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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),v_w____),v_k____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(c_0_20,plain,
! [X616,X617] :
( ~ class_Rings_Ocomm__semiring__1(X617)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X617),c_Groups_Ozero__class_Ozero(X617)),X616) = c_Groups_Ozero__class_Ozero(X617) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(c_0_21,plain,
! [X95,X96] :
( hAPP(X96,esk1_2(X95,X96)) != hAPP(X95,esk1_2(X95,X96))
| X96 = X95 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
cnf(c_0_22,plain,
( hAPP(hAPP(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_20]) ).
cnf(c_0_23,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_24,plain,
! [X313,X314] :
( ~ class_Rings_Ocomm__semiring__0(X314)
| hAPP(c_Polynomial_Opoly(X314,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X314))),X313) = c_Groups_Ozero__class_Ozero(X314) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(c_0_25,plain,
! [X99] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X99) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X99),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X99))),
inference(variable_rename,[status(thm)],[fact_kas_I4_J]) ).
cnf(c_0_26,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
hAPP(hAPP(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_22,c_0_23]) ).
cnf(c_0_28,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_s0]) ).
cnf(c_0_30,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(c_0_31,plain,
! [X618,X619] :
( ~ class_Rings_Ocomm__semiring__1(X619)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X619),X618),c_Groups_Ozero__class_Ozero(X619)) = c_Groups_Ozero__class_Ozero(X619) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(c_0_32,plain,
! [X622,X623] :
( ~ class_Rings_Ocomm__semiring__1(X623)
| c_Groups_Oplus__class_Oplus(X623,X622,c_Groups_Ozero__class_Ozero(X623)) = X622 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(c_0_33,plain,
! [X2791,X2792,X2793] :
( ~ class_Groups_Ogroup__add(X2793)
| c_Groups_Ominus__class_Ominus(X2793,c_Groups_Oplus__class_Oplus(X2793,X2792,X2791),X2791) = X2792 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(c_0_34,plain,
! [X583,X584,X585] :
( ~ class_Rings_Ocomm__semiring__1(X585)
| c_Groups_Oplus__class_Oplus(X585,X584,X583) = c_Groups_Oplus__class_Oplus(X585,X583,X584) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
cnf(c_0_35,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(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____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X1))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_pqc0]) ).
cnf(c_0_37,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_r01]) ).
fof(c_0_38,plain,
! [X206,X207,X208,X209] :
( ~ class_Rings_Ocomm__semiring__0(X209)
| hAPP(c_Polynomial_Opoly(X209,c_Polynomial_OpCons(X209,X208,X207)),X206) = c_Groups_Oplus__class_Oplus(X209,X208,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X209),X206),hAPP(c_Polynomial_Opoly(X209,X207),X206))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
cnf(c_0_39,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X1
| hAPP(X1,esk1_2(X1,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_40,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_41,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_43,plain,
! [X549,X550,X551] :
( ~ class_Rings_Ocomm__semiring__1(X551)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X551),X550),X549) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X551),X549),X550) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
cnf(c_0_44,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(c_0_46,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_47,plain,
! [X384] :
( esk7_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& esk6_0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk8_0),esk6_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X384) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X384),esk6_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk7_0,esk8_0)),X384))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096])])]) ).
fof(c_0_48,plain,
! [X1625,X1626,X1627] :
( ~ class_Groups_Ogroup__add(X1627)
| c_Groups_Oplus__class_Oplus(X1627,c_Groups_Ouminus__class_Ouminus(X1627,X1626),c_Groups_Oplus__class_Oplus(X1627,X1626,X1625)) = X1625 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
cnf(c_0_49,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(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____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_50,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_51,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_38]) ).
cnf(c_0_52,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_53,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_54,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_55,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_43]) ).
cnf(c_0_56,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_57,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
fof(c_0_58,plain,
! [X1622,X1623,X1624] :
( ~ class_Groups_Ogroup__add(X1624)
| c_Groups_Oplus__class_Oplus(X1624,X1623,c_Groups_Oplus__class_Oplus(X1624,c_Groups_Ouminus__class_Ouminus(X1624,X1623),X1622)) = X1622 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
cnf(c_0_59,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),esk6_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk7_0,esk8_0)),X1))),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),X1),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,v_s____)),X2) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_27]),c_0_53]),c_0_54]),c_0_30])]) ).
cnf(c_0_63,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_55,c_0_23]) ).
cnf(c_0_64,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),esk6_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk7_0,esk8_0)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_36]),c_0_36]) ).
cnf(c_0_67,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),X1)) = 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____)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_45])]),c_0_62]),c_0_63]) ).
cnf(c_0_68,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_45])]) ).
fof(c_0_69,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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),v_w____),v_k____)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_70,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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),esk6_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk7_0,esk8_0)),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),X1),
inference(rw,[status(thm)],[c_0_66,c_0_50]) ).
cnf(c_0_71,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),X1),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____)),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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),v_w____),v_k____)))),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_73,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),esk6_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk7_0,esk8_0)),X1)) = 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____)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_70]),c_0_45])]),c_0_68]),c_0_71]) ).
cnf(c_0_74,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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),v_w____),v_k____)))),
inference(rw,[status(thm)],[c_0_72,c_0_36]) ).
cnf(c_0_75,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),X1) = 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____))),
inference(rw,[status(thm)],[c_0_70,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW255+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 20:28:36 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 3.27/3.39 % Version : CSE_E---1.5
% 3.27/3.39 % Problem : theBenchmark.p
% 3.27/3.39 % Proof found
% 3.27/3.39 % SZS status Theorem for theBenchmark.p
% 3.27/3.39 % SZS output start Proof
% See solution above
% 3.27/3.41 % Total time : 2.784000 s
% 3.27/3.41 % SZS output end Proof
% 3.27/3.41 % Total time : 2.824000 s
%------------------------------------------------------------------------------