TSTP Solution File: SWW235+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW235+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 00:16:40 EDT 2023
% Result : Theorem 15.12s 15.21s
% Output : CNFRefutation 15.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 206
% Syntax : Number of formulae : 226 ( 17 unt; 196 typ; 0 def)
% Number of atoms : 50 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 340 ( 182 >; 158 *; 0 +; 0 <<)
% Number of predicates : 75 ( 73 usr; 1 prp; 0-3 aty)
% Number of functors : 123 ( 123 usr; 14 con; 0-5 aty)
% Number of variables : 51 ( 0 sgn; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_cs____: $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_c____: $i ).
tff(decl_28,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
tc_RealDef_Oreal: $i ).
tff(decl_30,type,
v_r____: $i ).
tff(decl_31,type,
v_z____: $i ).
tff(decl_32,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_33,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
v_da____: $i ).
tff(decl_35,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_36,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_37,type,
v_aa____: $i ).
tff(decl_38,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
v_p: $i ).
tff(decl_41,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_42,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_43,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_44,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_45,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_46,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_47,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_48,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_49,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_50,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_51,type,
class_Groups_Ozero: $i > $o ).
tff(decl_52,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_53,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_54,type,
class_Rings_Oidom: $i > $o ).
tff(decl_55,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_56,type,
class_Orderings_Oord: $i > $o ).
tff(decl_57,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_58,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_59,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_60,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_61,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_62,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_63,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_64,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_65,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_66,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_67,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_68,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_69,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_70,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_71,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_72,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_73,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_74,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_75,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_76,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_77,type,
class_Rings_Oring: $i > $o ).
tff(decl_78,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_79,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_81,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_82,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_83,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_84,type,
class_Groups_Oone: $i > $o ).
tff(decl_85,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_86,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_87,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_88,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_89,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_90,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_91,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_92,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_93,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_94,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_95,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
tc_Nat_Onat: $i ).
tff(decl_97,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_98,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_100,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_102,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_103,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_104,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_105,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_106,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_107,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_108,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_109,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_110,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_111,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_112,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_113,type,
hBOOL: $i > $o ).
tff(decl_114,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_115,type,
c_Complex_Oii: $i ).
tff(decl_116,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_117,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_118,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff(decl_119,type,
class_Power_Opower: $i > $o ).
tff(decl_120,type,
tc_Int_Oint: $i ).
tff(decl_121,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_122,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_123,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_125,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(decl_126,type,
c_Transcendental_Oln: $i > $i ).
tff(decl_127,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(decl_128,type,
c_Nat_OSuc: $i > $i ).
tff(decl_129,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_130,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_131,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_132,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_133,type,
class_Fields_Ofield: $i > $o ).
tff(decl_134,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_135,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_136,type,
c_Complex_Ocis: $i > $i ).
tff(decl_137,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_138,type,
tc_HOL_Obool: $i ).
tff(decl_139,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_140,type,
epred2_3: ( $i * $i * $i ) > $o ).
tff(decl_141,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_143,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk4_0: $i ).
tff(decl_145,type,
esk5_1: $i > $i ).
tff(decl_146,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk10_1: $i > $i ).
tff(decl_151,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk15_1: $i > $i ).
tff(decl_156,type,
esk16_1: $i > $i ).
tff(decl_157,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_160,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk23_3: ( $i * $i * $i ) > $i ).
tff(decl_164,type,
esk24_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_165,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_169,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_170,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_171,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_172,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_173,type,
esk33_3: ( $i * $i * $i ) > $i ).
tff(decl_174,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_175,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_176,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_178,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_180,type,
esk40_3: ( $i * $i * $i ) > $i ).
tff(decl_181,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_182,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_183,type,
esk43_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_184,type,
esk44_3: ( $i * $i * $i ) > $i ).
tff(decl_185,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_186,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_187,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_188,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_189,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_190,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_191,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_192,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_193,type,
esk53_1: $i > $i ).
tff(decl_194,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_195,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_196,type,
esk56_3: ( $i * $i * $i ) > $i ).
tff(decl_197,type,
esk57_2: ( $i * $i ) > $i ).
tff(decl_198,type,
esk58_3: ( $i * $i * $i ) > $i ).
tff(decl_199,type,
esk59_2: ( $i * $i ) > $i ).
tff(decl_200,type,
esk60_1: $i > $i ).
tff(decl_201,type,
esk61_3: ( $i * $i * $i ) > $i ).
tff(decl_202,type,
esk62_3: ( $i * $i * $i ) > $i ).
tff(decl_203,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_204,type,
esk64_3: ( $i * $i * $i ) > $i ).
tff(decl_205,type,
esk65_3: ( $i * $i * $i ) > $i ).
tff(decl_206,type,
esk66_3: ( $i * $i * $i ) > $i ).
tff(decl_207,type,
esk67_3: ( $i * $i * $i ) > $i ).
tff(decl_208,type,
esk68_3: ( $i * $i * $i ) > $i ).
tff(decl_209,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_210,type,
esk70_3: ( $i * $i * $i ) > $i ).
tff(decl_211,type,
esk71_3: ( $i * $i * $i ) > $i ).
tff(decl_212,type,
esk72_3: ( $i * $i * $i ) > $i ).
tff(decl_213,type,
esk73_3: ( $i * $i * $i ) > $i ).
tff(decl_214,type,
esk74_3: ( $i * $i * $i ) > $i ).
tff(decl_215,type,
esk75_3: ( $i * $i * $i ) > $i ).
tff(decl_216,type,
esk76_3: ( $i * $i * $i ) > $i ).
tff(decl_217,type,
esk77_3: ( $i * $i * $i ) > $i ).
fof(fact_xt1_I6_J,axiom,
! [X19,X9,X8,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,X8)
=> c_Orderings_Oord__class_Oless__eq(X6,X19,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_norm__diff__ineq,axiom,
! [X4,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_RealVector_Onorm__class_Onorm(X6,X4)),c_RealVector_Onorm__class_Onorm(X6,c_Groups_Oplus__class_Oplus(X6,X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X22,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,X22) = c_Groups_Oplus__class_Oplus(X6,X22,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
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(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(fact_poly__pCons,axiom,
! [X9,X11,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Polynomial_OpCons(X6,X5,X11)),X9) = c_Groups_Oplus__class_Oplus(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X9),hAPP(c_Polynomial_Opoly(X6,X11),X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_real__le__refl,axiom,
! [X20] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
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(c_0_10,plain,
! [X211,X212,X213,X214] :
( ~ class_Orderings_Oorder(X214)
| ~ c_Orderings_Oord__class_Oless__eq(X214,X213,X212)
| ~ c_Orderings_Oord__class_Oless__eq(X214,X211,X213)
| c_Orderings_Oord__class_Oless__eq(X214,X211,X212) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(c_0_11,plain,
! [X196,X197,X198] :
( ~ class_RealVector_Oreal__normed__vector(X198)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X198,X197),c_RealVector_Onorm__class_Onorm(X198,X196)),c_RealVector_Onorm__class_Onorm(X198,c_Groups_Oplus__class_Oplus(X198,X197,X196))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])]) ).
fof(c_0_12,plain,
! [X768,X769,X770] :
( ~ class_Rings_Ocomm__semiring__1(X770)
| c_Groups_Oplus__class_Oplus(X770,X769,X768) = c_Groups_Oplus__class_Oplus(X770,X768,X769) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_13,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_14,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_17,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_12]) ).
cnf(c_0_18,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(c_0_19,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),X4)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_21,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_22,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_17,c_0_18]) ).
fof(c_0_23,plain,
! [X199,X200,X201,X202] :
( ~ class_Rings_Ocomm__semiring__0(X202)
| hAPP(c_Polynomial_Opoly(X202,c_Polynomial_OpCons(X202,X201,X200)),X199) = c_Groups_Oplus__class_Oplus(X202,X201,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X202),X199),hAPP(c_Polynomial_Opoly(X202,X200),X199))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(c_0_24,plain,
! [X376] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X376,X376),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
cnf(c_0_25,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_26,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_23]) ).
cnf(c_0_27,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW235+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 22:12:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 15.12/15.21 % Version : CSE_E---1.5
% 15.12/15.21 % Problem : theBenchmark.p
% 15.12/15.21 % Proof found
% 15.12/15.21 % SZS status Theorem for theBenchmark.p
% 15.12/15.21 % SZS output start Proof
% See solution above
% 15.12/15.22 % Total time : 14.571000 s
% 15.12/15.22 % SZS output end Proof
% 15.12/15.22 % Total time : 14.614000 s
%------------------------------------------------------------------------------