TSTP Solution File: SWW208+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW208+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 : n007.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 2.63s 2.73s
% Output : CNFRefutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 238
% Syntax : Number of formulae : 324 ( 67 unt; 206 typ; 0 def)
% Number of atoms : 215 ( 44 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 168 ( 71 ~; 65 |; 10 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 311 ( 186 >; 125 *; 0 +; 0 <<)
% Number of predicates : 80 ( 78 usr; 1 prp; 0-3 aty)
% Number of functors : 128 ( 128 usr; 20 con; 0-5 aty)
% Number of variables : 152 ( 17 sgn; 84 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_RealDef_Oreal: $i ).
tff(decl_24,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_25,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).
tff(decl_26,type,
v_r: $i ).
tff(decl_27,type,
hBOOL: $i > $o ).
tff(decl_28,type,
v_f____: $i ).
tff(decl_29,type,
c_SEQ_Osubseq: $i > $o ).
tff(decl_30,type,
c_Complex_OIm: $i ).
tff(decl_31,type,
v_s: $i ).
tff(decl_32,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_33,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
tff(decl_34,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_35,type,
v_ga____: $i ).
tff(decl_36,type,
tc_Complex_Ocomplex: $i ).
tff(decl_37,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_38,type,
c_Orderings_Oord__class_Oless: ( $i * $i ) > $i ).
tff(decl_39,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_40,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_41,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_42,type,
tc_Nat_Onat: $i ).
tff(decl_43,type,
class_Groups_Ozero: $i > $o ).
tff(decl_44,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_45,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_46,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_47,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_48,type,
class_Groups_Oone: $i > $o ).
tff(decl_49,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_50,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_51,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_52,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_53,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_54,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_55,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_56,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_57,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_58,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_59,type,
class_Orderings_Oord: $i > $o ).
tff(decl_60,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_61,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_62,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_63,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_64,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_65,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_66,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_67,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_68,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_69,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_70,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_71,type,
c_SEQ_Omonoseq: ( $i * $i ) > $o ).
tff(decl_72,type,
c_Complex_ORe: $i ).
tff(decl_73,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_74,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_75,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_76,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_77,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_78,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_79,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_80,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_81,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_82,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_83,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_84,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_85,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_86,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_87,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_88,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_89,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_90,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_91,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_92,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_93,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_94,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_95,type,
c_SEQ_Oconvergent: ( $i * $i ) > $o ).
tff(decl_96,type,
class_RealVector_Ometric__space: $i > $o ).
tff(decl_97,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_101,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff(decl_102,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(decl_103,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_104,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_105,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_106,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_107,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_108,type,
c_Nat_OSuc: $i > $i ).
tff(decl_109,type,
tc_Int_Oint: $i ).
tff(decl_110,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_111,type,
class_Power_Opower: $i > $o ).
tff(decl_112,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_113,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
c_Complex_Orcis: ( $i * $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_Oordered__ab__group__add: $i > $o ).
tff(decl_122,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_123,type,
class_Rings_Oring: $i > $o ).
tff(decl_124,type,
class_Groups_Oab__group__add: $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_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_139,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_140,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_141,type,
class_Fields_Ofield: $i > $o ).
tff(decl_142,type,
class_Fields_Ofield__inverse__zero: $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_2: ( $i * $i ) > $i ).
tff(decl_155,type,
esk4_0: $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_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk10_1: $i > $i ).
tff(decl_162,type,
esk11_1: $i > $i ).
tff(decl_163,type,
esk12_0: $i ).
tff(decl_164,type,
esk13_0: $i ).
tff(decl_165,type,
esk14_0: $i ).
tff(decl_166,type,
esk15_0: $i ).
tff(decl_167,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk17_1: $i > $i ).
tff(decl_169,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk19_0: $i ).
tff(decl_171,type,
esk20_0: $i ).
tff(decl_172,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_173,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_174,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_175,type,
esk24_1: $i > $i ).
tff(decl_176,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_178,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_180,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_181,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_182,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_183,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_184,type,
esk33_1: $i > $i ).
tff(decl_185,type,
esk34_1: $i > $i ).
tff(decl_186,type,
esk35_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_187,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_188,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_189,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_190,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_191,type,
esk40_3: ( $i * $i * $i ) > $i ).
tff(decl_192,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_193,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_194,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_195,type,
esk44_1: $i > $i ).
tff(decl_196,type,
esk45_2: ( $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_3: ( $i * $i * $i ) > $i ).
tff(decl_203,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_204,type,
esk53_3: ( $i * $i * $i ) > $i ).
tff(decl_205,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_206,type,
esk55_1: $i > $i ).
tff(decl_207,type,
esk56_2: ( $i * $i ) > $i ).
tff(decl_208,type,
esk57_2: ( $i * $i ) > $i ).
tff(decl_209,type,
esk58_2: ( $i * $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_2: ( $i * $i ) > $i ).
tff(decl_214,type,
esk63_1: $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_0: $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_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/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_assms,axiom,
! [X4] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X4))),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).
fof(fact_abs__Im__le__cmod,axiom,
! [X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X5))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5))),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_norm__ge__zero,axiom,
! [X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X6,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_real__le__antisym,axiom,
! [X12,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11))
=> X11 = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
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_less__le__not__le,axiom,
! [X21,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X13),X21))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(conj_0,conjecture,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& ! [X4] : 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____,X4)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_Im__cis,axiom,
! [X8] : hAPP(c_Complex_OIm,c_Complex_Ocis(X8)) = c_Transcendental_Osin(X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__cis) ).
fof(fact_cis__rcis__eq,axiom,
! [X8] : c_Complex_Ocis(X8) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__rcis__eq) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_abs__norm__cancel,axiom,
! [X8,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X8)) = c_RealVector_Onorm__class_Onorm(X6,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_less__eq__real__def,axiom,
! [X21,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13),X21))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13),X21))
| X13 = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_th,axiom,
! [X4] : 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,X4)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th) ).
fof(fact_sin__le__one,axiom,
! [X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X5)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__le__one) ).
fof(fact_complex__Im__i,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__i) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__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(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X9,X8,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X8),X9) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X9),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_linorder__not__less,axiom,
! [X21,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_cis__zero,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__zero) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_complex__Im__one,axiom,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__one) ).
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_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X8,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X8),c_Groups_Ozero__class_Ozero(X6)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_xt1_I7_J,axiom,
! [X11,X5,X14,X6] :
( class_Orderings_Oorder(X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X14),X5))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X11),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X11),X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_add__less__cancel__left,axiom,
! [X16,X10,X15,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X15),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X15),X16)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X10),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
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(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_32,plain,
! [X180,X181,X182] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X182),X181))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X181),X180))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X182),X180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(c_0_33,plain,
! [X114] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X114))),v_r)),
inference(variable_rename,[status(thm)],[fact_assms]) ).
fof(c_0_34,plain,
! [X336] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X336))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X336))),
inference(variable_rename,[status(thm)],[fact_abs__Im__le__cmod]) ).
fof(c_0_35,plain,
! [X361] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X361) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X361),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
cnf(c_0_36,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_32]) ).
cnf(c_0_37,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_33]) ).
cnf(c_0_38,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_34]) ).
cnf(c_0_39,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_35]) ).
fof(c_0_40,plain,
! [X352,X353] :
( ~ class_RealVector_Oreal__normed__vector(X353)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X353,X352))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(c_0_41,plain,
! [X178,X179] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X179),X178))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X178),X179))
| X179 = X178 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
cnf(c_0_42,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_36,c_0_37]) ).
cnf(c_0_43,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_38,c_0_39]) ).
cnf(c_0_44,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_40]) ).
cnf(c_0_45,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_46,plain,
! [X21,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X13),X21))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_47,negated_conjecture,
~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& ! [X4] : 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____,X4)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_48,plain,
! [X1979] : hAPP(c_Complex_OIm,c_Complex_Ocis(X1979)) = c_Transcendental_Osin(X1979),
inference(variable_rename,[status(thm)],[fact_Im__cis]) ).
fof(c_0_49,plain,
! [X1963] : c_Complex_Ocis(X1963) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1963),
inference(variable_rename,[status(thm)],[fact_cis__rcis__eq]) ).
fof(c_0_50,plain,
! [X115] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X115)))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(c_0_51,plain,
! [X560,X561] :
( ~ class_RealVector_Oreal__normed__vector(X561)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X561,X560)) = c_RealVector_Onorm__class_Onorm(X561,X560) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
fof(c_0_52,plain,
! [X266,X267] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X267),X266))
| X267 = X266 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X267),X266))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266)) )
& ( X267 != X266
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
cnf(c_0_53,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_41]) ).
cnf(c_0_54,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_42,c_0_43]) ).
cnf(c_0_55,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_44,c_0_45]) ).
fof(c_0_56,plain,
! [X503,X504,X505] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X504),X503))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
| ~ class_Orderings_Opreorder(X505) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X503),X504))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
| ~ class_Orderings_Opreorder(X505) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X504),X503))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X503),X504))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
| ~ class_Orderings_Opreorder(X505) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
fof(c_0_57,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ 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_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
fof(c_0_58,plain,
! [X113] : 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,X113)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[fact_th]) ).
fof(c_0_59,plain,
! [X1978] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X1978)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_sin__le__one]) ).
cnf(c_0_60,plain,
hAPP(c_Complex_OIm,c_Complex_Ocis(X1)) = c_Transcendental_Osin(X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,plain,
c_Complex_Ocis(X1) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_63,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_64,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_65,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_66,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,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_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1))))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_67,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealVector_Onorm__class_Onorm(X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[c_0_36,c_0_55]) ).
cnf(c_0_68,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(c_0_69,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_70,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_71,plain,
! [X1138,X1139,X1140] :
( ~ class_Rings_Ocomm__semiring__1(X1140)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1140),X1139),X1138) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1140),X1138),X1139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
cnf(c_0_72,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ 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_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_73,plain,
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,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_74,plain,
! [X21,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
cnf(c_0_75,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_76,plain,
hAPP(c_Complex_OIm,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)) = c_Transcendental_Osin(X1),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_77,plain,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_cis__zero]) ).
cnf(c_0_78,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,c_Complex_Oii)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_45]),c_0_63]),c_0_39]) ).
cnf(c_0_79,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_39]) ).
cnf(c_0_80,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(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(spm,[status(thm)],[c_0_65,c_0_43]) ).
cnf(c_0_81,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1))) = v_r
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_82,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_37]),c_0_70])]) ).
cnf(c_0_83,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_84,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_85,negated_conjecture,
( ~ 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_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_45]),c_0_63]),c_0_63]) ).
cnf(c_0_86,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)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_39]),c_0_63]) ).
fof(c_0_87,plain,
! [X491,X492,X493] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X493,X492),X491))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X493,X491),X492))
| ~ class_Orderings_Olinorder(X493) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X493,X491),X492))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X493,X492),X491))
| ~ class_Orderings_Olinorder(X493) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])]) ).
cnf(c_0_88,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_89,plain,
c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_77,c_0_61]) ).
cnf(c_0_90,plain,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_complex__Im__one]) ).
cnf(c_0_91,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,c_Complex_Oii)),c_RealVector_Onorm__class_Onorm(X1,X2))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_92,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),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_93,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_94,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_95,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_39]),c_0_86])]) ).
cnf(c_0_96,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_97,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_98,plain,
! [X188,X189] :
( ~ class_Groups_Ocomm__monoid__add(X189)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X189),X188),c_Groups_Ozero__class_Ozero(X189)) = X188 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(c_0_99,plain,
! [X546,X547,X548,X549] :
( ~ class_Orderings_Oorder(X549)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X549,X548),X547))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X549,X546),X548))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X549,X546),X547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
cnf(c_0_100,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Orcis(hAPP(c_Complex_OIm,c_Complex_Oii),X1))),hAPP(c_Complex_OIm,c_Complex_Oii))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_63]),c_0_63]) ).
cnf(c_0_101,plain,
c_Complex_Orcis(hAPP(c_Complex_OIm,c_Complex_Oii),hAPP(c_Complex_ORe,c_Complex_Oii)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_63]),c_0_45]) ).
cnf(c_0_102,plain,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(c_Complex_ORe,c_Complex_Oii),
inference(rw,[status(thm)],[c_0_90,c_0_45]) ).
fof(c_0_103,plain,
! [X248,X249,X250,X251] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X251,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X251),X250),X249)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X251),X250),X248)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X251,X249),X248))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X251) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X251,X249),X248))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X251,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X251),X250),X249)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X251),X250),X248)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X251) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
cnf(c_0_104,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94])]),c_0_95]) ).
cnf(c_0_105,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_106,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_107,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
cnf(c_0_108,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X4),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_109,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(c_Complex_OIm,c_Complex_Oii))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_110,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_111,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,plain,
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_104,c_0_105]) ).
cnf(c_0_113,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),hAPP(c_Complex_ORe,c_Complex_Oii)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_45]) ).
cnf(c_0_114,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(c_0_115,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110])]) ).
cnf(c_0_116,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),v_r))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]),c_0_114])]) ).
cnf(c_0_117,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_93]),c_0_95]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 18:26:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 2.63/2.73 % Version : CSE_E---1.5
% 2.63/2.73 % Problem : theBenchmark.p
% 2.63/2.73 % Proof found
% 2.63/2.73 % SZS status Theorem for theBenchmark.p
% 2.63/2.73 % SZS output start Proof
% See solution above
% 2.63/2.76 % Total time : 2.095000 s
% 2.63/2.76 % SZS output end Proof
% 2.63/2.76 % Total time : 2.141000 s
%------------------------------------------------------------------------------