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
%------------------------------------------------------------------------------