TSTP Solution File: SWW207+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW207+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 : n021.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 00:16:31 EDT 2023

% Result   : Theorem 1.66s 1.74s
% Output   : CNFRefutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  221
% Syntax   : Number of formulae    :  266 (  33 unt; 206 typ;   0 def)
%            Number of atoms       :  101 (  30 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   76 (  35   ~;  27   |;   7   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  312 ( 187   >; 125   *;   0   +;   0  <<)
%            Number of predicates  :   80 (  78 usr;   1 prp; 0-3 aty)
%            Number of functors    :  128 ( 128 usr;  19 con; 0-5 aty)
%            Number of variables   :   56 (   4 sgn;  30   !;   2   ?;   0   :)

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

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

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

tff(decl_25,type,
    v_ga____: $i ).

tff(decl_26,type,
    tc_RealDef_Oreal: $i ).

tff(decl_27,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

tff(decl_28,type,
    c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).

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

tff(decl_30,type,
    hBOOL: $i > $o ).

tff(decl_31,type,
    class_Groups_Oordered__ab__group__add__abs: $i > $o ).

tff(decl_32,type,
    c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(decl_33,type,
    c_Orderings_Oord__class_Oless: ( $i * $i ) > $i ).

tff(decl_34,type,
    class_Orderings_Opreorder: $i > $o ).

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

tff(decl_36,type,
    v_s: $i ).

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

tff(decl_38,type,
    tc_Nat_Onat: $i ).

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

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

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

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

tff(decl_43,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_44,type,
    c_Complex_OIm: $i ).

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

tff(decl_46,type,
    c_Groups_Oplus__class_Oplus: $i > $i ).

tff(decl_47,type,
    c_Groups_Oone__class_Oone: $i > $i ).

tff(decl_48,type,
    c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).

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

tff(decl_50,type,
    c_Complex_ORe: $i ).

tff(decl_51,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

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

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

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

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

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

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

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

tff(decl_59,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_60,type,
    class_Groups_Oordered__ab__semigroup__add: $i > $o ).

tff(decl_61,type,
    class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).

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

tff(decl_63,type,
    class_Rings_Olinordered__semidom: $i > $o ).

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

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

tff(decl_66,type,
    c_SEQ_Oconvergent: ( $i * $i ) > $o ).

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

tff(decl_68,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(decl_69,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

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

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

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

tff(decl_73,type,
    c_COMBK: ( $i * $i * $i ) > $i ).

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

tff(decl_75,type,
    c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_76,type,
    c_Complex_Oexpi: $i > $i ).

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

tff(decl_78,type,
    class_Groups_Osgn__if: $i > $o ).

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

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

tff(decl_81,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).

tff(decl_82,type,
    tc_Polynomial_Opoly: $i > $i ).

tff(decl_83,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

tff(decl_84,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

tff(decl_85,type,
    c_Power_Opower__class_Opower: $i > $i ).

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

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

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

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

tff(decl_90,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

tff(decl_91,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

tff(decl_92,type,
    class_Rings_Osemiring: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(decl_107,type,
    tc_Int_Oint: $i ).

tff(decl_108,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

tff(decl_109,type,
    class_Power_Opower: $i > $o ).

tff(decl_110,type,
    class_Rings_Osemiring__0: $i > $o ).

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

tff(decl_112,type,
    c_RealDef_Oreal: ( $i * $i ) > $i ).

tff(decl_113,type,
    c_Complex_Orcis: ( $i * $i ) > $i ).

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

tff(decl_115,type,
    c_Complex_Ocis: $i > $i ).

tff(decl_116,type,
    c_Transcendental_Oln: $i > $i ).

tff(decl_117,type,
    c_Transcendental_Ocos: $i > $i ).

tff(decl_118,type,
    c_Transcendental_Osin: $i > $i ).

tff(decl_119,type,
    c_Transcendental_Oarccos: $i > $i ).

tff(decl_120,type,
    c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

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

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

tff(decl_123,type,
    class_Groups_Oab__group__add: $i > $o ).

tff(decl_124,type,
    class_Rings_Oring: $i > $o ).

tff(decl_125,type,
    class_Rings_Oring__1: $i > $o ).

tff(decl_126,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

tff(decl_127,type,
    c_Complex_Oii: $i ).

tff(decl_128,type,
    c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).

tff(decl_129,type,
    c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).

tff(decl_130,type,
    class_Divides_Osemiring__div: $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__rec: ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

tff(decl_144,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

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

tff(decl_146,type,
    class_Rings_Oidom: $i > $o ).

tff(decl_147,type,
    class_Groups_Ocancel__comm__monoid__add: $i > $o ).

tff(decl_148,type,
    class_Rings_Ocomm__semiring__0: $i > $o ).

tff(decl_149,type,
    class_Rings_Ocomm__ring: $i > $o ).

tff(decl_150,type,
    tc_HOL_Obool: $i ).

tff(decl_151,type,
    epred1_3: ( $i * $i * $i ) > $o ).

tff(decl_152,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_153,type,
    esk2_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_154,type,
    esk3_1: $i > $i ).

tff(decl_155,type,
    esk4_1: $i > $i ).

tff(decl_156,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_158,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_159,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_160,type,
    esk9_0: $i ).

tff(decl_161,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_162,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_163,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_164,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_165,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_166,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_167,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_168,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_169,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_170,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_171,type,
    esk20_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_172,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_173,type,
    esk22_1: $i > $i ).

tff(decl_174,type,
    esk23_1: $i > $i ).

tff(decl_175,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_176,type,
    esk25_0: $i ).

tff(decl_177,type,
    esk26_0: $i ).

tff(decl_178,type,
    esk27_0: $i ).

tff(decl_179,type,
    esk28_0: $i ).

tff(decl_180,type,
    esk29_1: $i > $i ).

tff(decl_181,type,
    esk30_2: ( $i * $i ) > $i ).

tff(decl_182,type,
    esk31_2: ( $i * $i ) > $i ).

tff(decl_183,type,
    esk32_0: $i ).

tff(decl_184,type,
    esk33_0: $i ).

tff(decl_185,type,
    esk34_2: ( $i * $i ) > $i ).

tff(decl_186,type,
    esk35_2: ( $i * $i ) > $i ).

tff(decl_187,type,
    esk36_1: $i > $i ).

tff(decl_188,type,
    esk37_2: ( $i * $i ) > $i ).

tff(decl_189,type,
    esk38_2: ( $i * $i ) > $i ).

tff(decl_190,type,
    esk39_3: ( $i * $i * $i ) > $i ).

tff(decl_191,type,
    esk40_2: ( $i * $i ) > $i ).

tff(decl_192,type,
    esk41_3: ( $i * $i * $i ) > $i ).

tff(decl_193,type,
    esk42_2: ( $i * $i ) > $i ).

tff(decl_194,type,
    esk43_3: ( $i * $i * $i ) > $i ).

tff(decl_195,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_196,type,
    esk45_3: ( $i * $i * $i ) > $i ).

tff(decl_197,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_198,type,
    esk47_2: ( $i * $i ) > $i ).

tff(decl_199,type,
    esk48_2: ( $i * $i ) > $i ).

tff(decl_200,type,
    esk49_1: $i > $i ).

tff(decl_201,type,
    esk50_2: ( $i * $i ) > $i ).

tff(decl_202,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_203,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_204,type,
    esk53_1: $i > $i ).

tff(decl_205,type,
    esk54_2: ( $i * $i ) > $i ).

tff(decl_206,type,
    esk55_3: ( $i * $i * $i ) > $i ).

tff(decl_207,type,
    esk56_2: ( $i * $i ) > $i ).

tff(decl_208,type,
    esk57_3: ( $i * $i * $i ) > $i ).

tff(decl_209,type,
    esk58_1: $i > $i ).

tff(decl_210,type,
    esk59_2: ( $i * $i ) > $i ).

tff(decl_211,type,
    esk60_2: ( $i * $i ) > $i ).

tff(decl_212,type,
    esk61_2: ( $i * $i ) > $i ).

tff(decl_213,type,
    esk62_1: $i > $i ).

tff(decl_214,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_215,type,
    esk64_3: ( $i * $i * $i ) > $i ).

tff(decl_216,type,
    esk65_3: ( $i * $i * $i ) > $i ).

tff(decl_217,type,
    esk66_1: $i > $i ).

tff(decl_218,type,
    esk67_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_219,type,
    esk68_3: ( $i * $i * $i ) > $i ).

tff(decl_220,type,
    esk69_3: ( $i * $i * $i ) > $i ).

tff(decl_221,type,
    esk70_3: ( $i * $i * $i ) > $i ).

tff(decl_222,type,
    esk71_3: ( $i * $i * $i ) > $i ).

tff(decl_223,type,
    esk72_1: $i > $i ).

tff(decl_224,type,
    esk73_3: ( $i * $i * $i ) > $i ).

tff(decl_225,type,
    esk74_3: ( $i * $i * $i ) > $i ).

tff(decl_226,type,
    esk75_3: ( $i * $i * $i ) > $i ).

tff(decl_227,type,
    esk76_3: ( $i * $i * $i ) > $i ).

fof(fact_not__real__square__gt__zero,axiom,
    ! [X10] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X10)))
    <=> X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

fof(conj_0,conjecture,
    ? [X37] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
      & ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X8)))))),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_real__le__trans,axiom,
    ! [X17,X18,X19] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X18))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).

fof(fact_assms,axiom,
    ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X8))),v_r)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).

fof(fact_abs__Im__le__cmod,axiom,
    ! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__Im__le__cmod) ).

fof(fact_real__norm__def,axiom,
    ! [X23] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X23) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).

fof(fact_natceiling__le__eq__one,axiom,
    ! [X10] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).

fof(fact_natceiling__neg,axiom,
    ! [X7] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
     => c_RComplete_Onatceiling(X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).

fof(fact_real__mult__1,axiom,
    ! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X14) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).

fof(fact_complex__Im__i,axiom,
    hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__Im__i) ).

fof(fact_complex__Re__i,axiom,
    hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__Re__i) ).

fof(fact_le0,axiom,
    ! [X29] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_real__zero__not__eq__one,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).

fof(fact_real__less__def,axiom,
    ! [X9,X10] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10),X9))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10),X9))
        & X10 != X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).

fof(fact_rp,axiom,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp) ).

fof(c_0_15,plain,
    ! [X10] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X10)))
    <=> X10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).

fof(c_0_16,negated_conjecture,
    ~ ? [X37] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
        & ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X8)))))),X37)) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_17,plain,
    ! [X270,X271,X272] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X272),X271))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X271),X270))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X272),X270)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).

fof(c_0_18,plain,
    ! [X127] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X127))),v_r)),
    inference(variable_rename,[status(thm)],[fact_assms]) ).

fof(c_0_19,plain,
    ! [X348] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X348))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X348))),
    inference(variable_rename,[status(thm)],[fact_abs__Im__le__cmod]) ).

fof(c_0_20,plain,
    ! [X400] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X400) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X400),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

fof(c_0_21,plain,
    ! [X1343] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1343)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1343),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1343),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1343)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])]) ).

fof(c_0_22,plain,
    ! [X1260] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1260),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
      | c_RComplete_Onatceiling(X1260) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])]) ).

fof(c_0_23,plain,
    ! [X1630] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1630),X1630)))
        | X1630 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X1630 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1630),X1630))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).

fof(c_0_24,plain,
    ! [X1060] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1060) = X1060,
    inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).

fof(c_0_25,negated_conjecture,
    ! [X2833] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2833))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X2833))))))),X2833)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

cnf(c_0_26,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3))
    | ~ 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),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_27,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_18]) ).

cnf(c_0_28,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_29,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,plain,
    hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_complex__Im__i]) ).

cnf(c_0_32,plain,
    ( c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_33,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_34,plain,
    ! [X576] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X576)),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

cnf(c_0_35,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_36,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_37,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_real__zero__not__eq__one]) ).

fof(c_0_38,plain,
    ! [X128,X129] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X129),X128))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X129),X128)) )
      & ( X129 != X128
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X129),X128)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X129),X128))
        | X129 = X128
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X129),X128)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).

cnf(c_0_39,plain,
    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)],[fact_rp]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X1))))))),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_41,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X2)))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_42,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_43,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,c_Complex_Oii)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_44,plain,
    ( c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_45,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_46,plain,
    ( X1 = hAPP(c_Complex_ORe,c_Complex_Oii)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_33]),c_0_33]) ).

cnf(c_0_47,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,c_Complex_Oii)),X1) = X1,
    inference(rw,[status(thm)],[c_0_36,c_0_31]) ).

cnf(c_0_48,plain,
    hAPP(c_Complex_OIm,c_Complex_Oii) != hAPP(c_Complex_ORe,c_Complex_Oii),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_33]),c_0_31]) ).

cnf(c_0_49,plain,
    ( X1 = X2
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_50,plain,
    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_39,c_0_33]) ).

cnf(c_0_51,negated_conjecture,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X1))))))),X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_33]),c_0_29]) ).

cnf(c_0_52,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),v_r)),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_53,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,c_Complex_Oii)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_54,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(c_Complex_OIm,c_Complex_Oii))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_55,plain,
    ( hAPP(c_Complex_ORe,c_Complex_Oii) = v_r
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_56,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_57,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(hAPP(c_Complex_OIm,c_Complex_Oii)))))))),hAPP(c_Complex_ORe,c_Complex_Oii))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_53]),c_0_54])]) ).

cnf(c_0_58,plain,
    hAPP(c_Complex_ORe,c_Complex_Oii) = v_r,
    inference(sr,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_59,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_52])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16  % Problem    : SWW207+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.17  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.37  % Computer : n021.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit   : 300
% 0.17/0.37  % WCLimit    : 300
% 0.17/0.37  % DateTime   : Sun Aug 27 20:08:58 EDT 2023
% 0.17/0.37  % CPUTime  : 
% 0.23/0.61  start to proof: theBenchmark
% 1.66/1.74  % Version  : CSE_E---1.5
% 1.66/1.74  % Problem  : theBenchmark.p
% 1.66/1.74  % Proof found
% 1.66/1.74  % SZS status Theorem for theBenchmark.p
% 1.66/1.74  % SZS output start Proof
% See solution above
% 1.66/1.76  % Total time : 1.086000 s
% 1.66/1.76  % SZS output end Proof
% 1.66/1.76  % Total time : 1.131000 s
%------------------------------------------------------------------------------