TSTP Solution File: SWW204+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW204+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 : n014.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 00:16:30 EDT 2023

% Result   : Theorem 1.26s 1.51s
% Output   : CNFRefutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  214
% Syntax   : Number of formulae    :  247 (  20 unt; 202 typ;   0 def)
%            Number of atoms       :   93 (   7 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   86 (  38   ~;  32   |;   4   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  309 ( 181   >; 128   *;   0   +;   0  <<)
%            Number of predicates  :   75 (  73 usr;   1 prp; 0-3 aty)
%            Number of functors    :  129 ( 129 usr;  21 con; 0-5 aty)
%            Number of variables   :   63 (   8 sgn;  37   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_23,type,
    v_ga____: $i ).

tff(decl_24,type,
    c_SEQ_Osubseq: $i > $o ).

tff(decl_25,type,
    class_Orderings_Opreorder: $i > $o ).

tff(decl_26,type,
    c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).

tff(decl_27,type,
    hBOOL: $i > $o ).

tff(decl_28,type,
    tc_RealDef_Oreal: $i ).

tff(decl_29,type,
    tc_Complex_Ocomplex: $i ).

tff(decl_30,type,
    v_s: $i ).

tff(decl_31,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

tff(decl_32,type,
    v_r: $i ).

tff(decl_33,type,
    tc_Nat_Onat: $i ).

tff(decl_34,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

tff(decl_35,type,
    v_f____: $i ).

tff(decl_36,type,
    class_Orderings_Oord: $i > $o ).

tff(decl_37,type,
    tc_fun: ( $i * $i ) > $i ).

tff(decl_38,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_39,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_40,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(decl_41,type,
    class_Groups_Ozero: $i > $o ).

tff(decl_42,type,
    c_RealDef_Oreal: ( $i * $i ) > $i ).

tff(decl_43,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

tff(decl_44,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

tff(decl_45,type,
    class_Groups_Oab__semigroup__mult: $i > $o ).

tff(decl_46,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(decl_47,type,
    class_Rings_Olinordered__ring: $i > $o ).

tff(decl_48,type,
    class_Rings_Olinordered__ring__strict: $i > $o ).

tff(decl_49,type,
    class_Rings_Oordered__cancel__semiring: $i > $o ).

tff(decl_50,type,
    class_Rings_Oordered__ring: $i > $o ).

tff(decl_51,type,
    class_Rings_Oordered__semiring: $i > $o ).

tff(decl_52,type,
    class_Rings_Oordered__comm__semiring: $i > $o ).

tff(decl_53,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

tff(decl_54,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

tff(decl_55,type,
    class_Rings_Omult__zero: $i > $o ).

tff(decl_56,type,
    c_SEQ_Odecseq: ( $i * $i ) > $o ).

tff(decl_57,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff(decl_58,type,
    c_SEQ_Oincseq: ( $i * $i ) > $o ).

tff(decl_59,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).

tff(decl_60,type,
    tc_Polynomial_Opoly: $i > $i ).

tff(decl_61,type,
    c_RComplete_Onatfloor: $i > $i ).

tff(decl_62,type,
    c_SEQ_Omonoseq: ( $i * $i ) > $o ).

tff(decl_63,type,
    c_RComplete_Onatceiling: $i > $i ).

tff(decl_64,type,
    class_Lattices_Oab__semigroup__idem__mult: $i > $o ).

tff(decl_65,type,
    class_Rings_Ocomm__semiring__0: $i > $o ).

tff(decl_66,type,
    c_Complex_OIm: $i ).

tff(decl_67,type,
    c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_68,type,
    c_Orderings_Oord__class_Oless: ( $i * $i ) > $i ).

tff(decl_69,type,
    c_Complex_ORe: $i ).

tff(decl_70,type,
    class_Rings_Olinordered__idom: $i > $o ).

tff(decl_71,type,
    class_Rings_Olinordered__semiring__strict: $i > $o ).

tff(decl_72,type,
    class_Rings_Olinordered__comm__semiring__strict: $i > $o ).

tff(decl_73,type,
    class_Rings_Olinordered__semiring: $i > $o ).

tff(decl_74,type,
    c_SEQ_OBseq: ( $i * $i ) > $o ).

tff(decl_75,type,
    c_Nat_OSuc: $i > $i ).

tff(decl_76,type,
    c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_77,type,
    c_COMBK: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    c_NthRoot_Oroot: ( $i * $i ) > $i ).

tff(decl_79,type,
    c_Groups_Oone__class_Oone: $i > $i ).

tff(decl_80,type,
    c_Power_Opower__class_Opower: $i > $i ).

tff(decl_81,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

tff(decl_82,type,
    class_Groups_Oone: $i > $o ).

tff(decl_83,type,
    class_Rings_Ozero__neq__one: $i > $o ).

tff(decl_84,type,
    class_Groups_Ocomm__monoid__mult: $i > $o ).

tff(decl_85,type,
    class_Groups_Omonoid__mult: $i > $o ).

tff(decl_86,type,
    class_Rings_Olinordered__semidom: $i > $o ).

tff(decl_87,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

tff(decl_88,type,
    class_Power_Opower: $i > $o ).

tff(decl_89,type,
    class_Rings_Osemiring__0: $i > $o ).

tff(decl_90,type,
    c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    c_Groups_Oplus__class_Oplus: $i > $i ).

tff(decl_92,type,
    c_Transcendental_Oln: $i > $i ).

tff(decl_93,type,
    class_Groups_Oab__semigroup__add: $i > $o ).

tff(decl_94,type,
    class_Groups_Ocancel__semigroup__add: $i > $o ).

tff(decl_95,type,
    class_Groups_Ocancel__ab__semigroup__add: $i > $o ).

tff(decl_96,type,
    class_Rings_Ocomm__semiring: $i > $o ).

tff(decl_97,type,
    class_Rings_Osemiring: $i > $o ).

tff(decl_98,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(decl_99,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_100,type,
    class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_101,type,
    class_Groups_Oordered__ab__semigroup__add: $i > $o ).

tff(decl_102,type,
    class_Groups_Ocomm__monoid__add: $i > $o ).

tff(decl_103,type,
    class_Groups_Omonoid__add: $i > $o ).

tff(decl_104,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

tff(decl_105,type,
    class_Groups_Oordered__comm__monoid__add: $i > $o ).

tff(decl_106,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

tff(decl_107,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

tff(decl_108,type,
    tc_Int_Oint: $i ).

tff(decl_109,type,
    c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_110,type,
    c_Complex_Ocis: $i > $i ).

tff(decl_111,type,
    c_Complex_Orcis: ( $i * $i ) > $i ).

tff(decl_112,type,
    c_Complex_Oexpi: $i > $i ).

tff(decl_113,type,
    c_Transcendental_Ocos: $i > $i ).

tff(decl_114,type,
    c_Transcendental_Osin: $i > $i ).

tff(decl_115,type,
    c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(decl_116,type,
    class_Groups_Oordered__ab__group__add: $i > $o ).

tff(decl_117,type,
    class_Groups_Ominus: $i > $o ).

tff(decl_118,type,
    class_Groups_Oab__group__add: $i > $o ).

tff(decl_119,type,
    class_Groups_Ogroup__add: $i > $o ).

tff(decl_120,type,
    class_Rings_Oring: $i > $o ).

tff(decl_121,type,
    class_Rings_Oring__1: $i > $o ).

tff(decl_122,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

tff(decl_123,type,
    c_Complex_Oii: $i ).

tff(decl_124,type,
    c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).

tff(decl_125,type,
    class_Divides_Osemiring__div: $i > $o ).

tff(decl_126,type,
    c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(decl_127,type,
    c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).

tff(decl_128,type,
    class_Groups_Oordered__ab__group__add__abs: $i > $o ).

tff(decl_129,type,
    class_Fields_Ofield: $i > $o ).

tff(decl_130,type,
    class_Rings_Oordered__ring__abs: $i > $o ).

tff(decl_131,type,
    c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).

tff(decl_132,type,
    c_Complex_Ocomplex_Ocomplex__size: $i > $i ).

tff(decl_133,type,
    c_Complex_Oarg: $i > $i ).

tff(decl_134,type,
    c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).

tff(decl_135,type,
    c_Complex_Ocomplex_Ocomplex__case: ( $i * $i * $i ) > $i ).

tff(decl_136,type,
    c_Complex_Ocomplex_Ocomplex__rec: ( $i * $i * $i ) > $i ).

tff(decl_137,type,
    c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

tff(decl_138,type,
    class_Rings_Odivision__ring: $i > $o ).

tff(decl_139,type,
    class_Fields_Ofield__inverse__zero: $i > $o ).

tff(decl_140,type,
    class_RealVector_Oreal__normed__field: $i > $o ).

tff(decl_141,type,
    class_Rings_Oidom: $i > $o ).

tff(decl_142,type,
    class_Groups_Ocancel__comm__monoid__add: $i > $o ).

tff(decl_143,type,
    class_Rings_Ocomm__ring: $i > $o ).

tff(decl_144,type,
    tc_HOL_Obool: $i ).

tff(decl_145,type,
    epred1_3: ( $i * $i * $i ) > $o ).

tff(decl_146,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_147,type,
    esk2_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_148,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_149,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_150,type,
    esk5_1: $i > $i ).

tff(decl_151,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_152,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_153,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_154,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_155,type,
    esk10_1: $i > $i ).

tff(decl_156,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_158,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_159,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_160,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_161,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_162,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_163,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_164,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_165,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_166,type,
    esk21_1: $i > $i ).

tff(decl_167,type,
    esk22_1: $i > $i ).

tff(decl_168,type,
    esk23_0: $i ).

tff(decl_169,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_170,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_171,type,
    esk26_1: $i > $i ).

tff(decl_172,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_173,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_174,type,
    esk29_0: $i ).

tff(decl_175,type,
    esk30_0: $i ).

tff(decl_176,type,
    esk31_0: $i ).

tff(decl_177,type,
    esk32_0: $i ).

tff(decl_178,type,
    esk33_0: $i ).

tff(decl_179,type,
    esk34_0: $i ).

tff(decl_180,type,
    esk35_2: ( $i * $i ) > $i ).

tff(decl_181,type,
    esk36_3: ( $i * $i * $i ) > $i ).

tff(decl_182,type,
    esk37_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_183,type,
    esk38_3: ( $i * $i * $i ) > $i ).

tff(decl_184,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_185,type,
    esk40_3: ( $i * $i * $i ) > $i ).

tff(decl_186,type,
    esk41_2: ( $i * $i ) > $i ).

tff(decl_187,type,
    esk42_3: ( $i * $i * $i ) > $i ).

tff(decl_188,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_189,type,
    esk44_3: ( $i * $i * $i ) > $i ).

tff(decl_190,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_191,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_192,type,
    esk47_0: $i ).

tff(decl_193,type,
    esk48_2: ( $i * $i ) > $i ).

tff(decl_194,type,
    esk49_1: $i > $i ).

tff(decl_195,type,
    esk50_2: ( $i * $i ) > $i ).

tff(decl_196,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_197,type,
    esk52_1: $i > $i ).

tff(decl_198,type,
    esk53_2: ( $i * $i ) > $i ).

tff(decl_199,type,
    esk54_3: ( $i * $i * $i ) > $i ).

tff(decl_200,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_201,type,
    esk56_3: ( $i * $i * $i ) > $i ).

tff(decl_202,type,
    esk57_0: $i ).

tff(decl_203,type,
    esk58_1: $i > $i ).

tff(decl_204,type,
    esk59_2: ( $i * $i ) > $i ).

tff(decl_205,type,
    esk60_2: ( $i * $i ) > $i ).

tff(decl_206,type,
    esk61_2: ( $i * $i ) > $i ).

tff(decl_207,type,
    esk62_2: ( $i * $i ) > $i ).

tff(decl_208,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_209,type,
    esk64_2: ( $i * $i ) > $i ).

tff(decl_210,type,
    esk65_2: ( $i * $i ) > $i ).

tff(decl_211,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_212,type,
    esk67_2: ( $i * $i ) > $i ).

tff(decl_213,type,
    esk68_3: ( $i * $i * $i ) > $i ).

tff(decl_214,type,
    esk69_3: ( $i * $i * $i ) > $i ).

tff(decl_215,type,
    esk70_1: $i > $i ).

tff(decl_216,type,
    esk71_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_217,type,
    esk72_3: ( $i * $i * $i ) > $i ).

tff(decl_218,type,
    esk73_3: ( $i * $i * $i ) > $i ).

tff(decl_219,type,
    esk74_3: ( $i * $i * $i ) > $i ).

tff(decl_220,type,
    esk75_3: ( $i * $i * $i ) > $i ).

tff(decl_221,type,
    esk76_3: ( $i * $i * $i ) > $i ).

tff(decl_222,type,
    esk77_3: ( $i * $i * $i ) > $i ).

tff(decl_223,type,
    esk78_3: ( $i * $i * $i ) > $i ).

fof(conj_0,conjecture,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(fact_complex__Re__i,axiom,
    hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__i) ).

fof(fact_real__le__linear,axiom,
    ! [X7,X8] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),X7))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).

fof(fact_xt1_I6_J,axiom,
    ! [X8,X4,X13,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X8),X13))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X8),X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_norm__ge__zero,axiom,
    ! [X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X5,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).

fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

fof(fact_norm__not__less__zero,axiom,
    ! [X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).

fof(fact_real__le__antisym,axiom,
    ! [X7,X8] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),X7))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X8))
       => X8 = X7 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).

fof(fact_assms,axiom,
    ! [X6] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X6))),v_r)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).

fof(fact_less__le__not__le,axiom,
    ! [X14,X15,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X14))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X14))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(c_0_12,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

cnf(c_0_13,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_14,plain,
    hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_complex__Re__i]) ).

fof(c_0_15,plain,
    ! [X128,X129] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X129),X128))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X128),X129)) ),
    inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).

fof(c_0_16,plain,
    ! [X158,X159,X160,X161] :
      ( ~ class_Orderings_Oorder(X161)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X161,X160),X159))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X161,X158),X160))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X161,X158),X159)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

cnf(c_0_17,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_19,plain,
    ! [X198,X199] :
      ( ~ class_RealVector_Oreal__normed__vector(X199)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X199,X198))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).

cnf(c_0_20,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),hAPP(c_Complex_ORe,c_Complex_Oii))),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).

cnf(c_0_23,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X1,X2)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_24,plain,
    ! [X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).

fof(c_0_25,plain,
    ! [X133,X134] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X134),X133))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X133),X134))
      | X134 = X133 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).

fof(c_0_26,plain,
    ! [X126] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X126))),v_r)),
    inference(variable_rename,[status(thm)],[fact_assms]) ).

cnf(c_0_27,negated_conjecture,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).

cnf(c_0_28,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),c_RealVector_Onorm__class_Onorm(X1,X2)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(rw,[status(thm)],[c_0_23,c_0_14]) ).

fof(c_0_29,plain,
    ! [X14,X15,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X15),X14))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X14))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X14),X15)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(c_0_30,plain,
    ! [X779,X780] :
      ( ~ class_RealVector_Oreal__normed__vector(X780)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X780,X779)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).

cnf(c_0_31,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1))),v_r)),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(X1,X2)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

fof(c_0_35,plain,
    ! [X608,X609,X610] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X610,X609),X608))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X610,X609),X608))
        | ~ class_Orderings_Opreorder(X610) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X610,X608),X609))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X610,X609),X608))
        | ~ class_Orderings_Opreorder(X610) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X610,X609),X608))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X610,X608),X609))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X610,X609),X608))
        | ~ class_Orderings_Opreorder(X610) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).

cnf(c_0_36,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_37,plain,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1)) = v_r
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1)))) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_38,negated_conjecture,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

cnf(c_0_41,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
    inference(rw,[status(thm)],[c_0_36,c_0_14]) ).

cnf(c_0_42,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1)) = v_r,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).

cnf(c_0_43,negated_conjecture,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(c_Complex_ORe,c_Complex_Oii))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_21]),c_0_40])]),c_0_17]) ).

cnf(c_0_44,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_34]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW204+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
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun Aug 27 17:49:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 1.26/1.51  % Version  : CSE_E---1.5
% 1.26/1.51  % Problem  : theBenchmark.p
% 1.26/1.51  % Proof found
% 1.26/1.51  % SZS status Theorem for theBenchmark.p
% 1.26/1.51  % SZS output start Proof
% See solution above
% 1.26/1.52  % Total time : 0.894000 s
% 1.26/1.52  % SZS output end Proof
% 1.26/1.52  % Total time : 0.940000 s
%------------------------------------------------------------------------------