TSTP Solution File: SWW233+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW233+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 : 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 00:16:40 EDT 2023
% Result : Theorem 1.83s 1.92s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 218
% Syntax : Number of formulae : 285 ( 35 unt; 195 typ; 0 def)
% Number of atoms : 192 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 168 ( 66 ~; 72 |; 6 &)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 337 ( 181 >; 156 *; 0 +; 0 <<)
% Number of predicates : 76 ( 74 usr; 1 prp; 0-3 aty)
% Number of functors : 121 ( 121 usr; 14 con; 0-5 aty)
% Number of variables : 140 ( 3 sgn; 78 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_p: $i ).
tff(decl_24,type,
tc_Complex_Ocomplex: $i ).
tff(decl_25,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_26,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_27,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_28,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
tc_RealDef_Oreal: $i ).
tff(decl_30,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_31,type,
v_r____: $i ).
tff(decl_32,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_33,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
v_z____: $i ).
tff(decl_35,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $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,
v_cs____: $i ).
tff(decl_41,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_42,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_43,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_44,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_45,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_46,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_47,type,
class_Groups_Ozero: $i > $o ).
tff(decl_48,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_49,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_50,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_51,type,
class_Groups_Oone: $i > $o ).
tff(decl_52,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_53,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_54,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_55,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_56,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_57,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_58,type,
v_c____: $i ).
tff(decl_59,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_61,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_62,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_63,type,
tc_Nat_Onat: $i ).
tff(decl_64,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_65,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_66,type,
v_da____: $i ).
tff(decl_67,type,
v_aa____: $i ).
tff(decl_68,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_69,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_70,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_71,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_73,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_74,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_75,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_76,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_77,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_78,type,
class_Rings_Oring: $i > $o ).
tff(decl_79,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_80,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_81,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_82,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_83,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_84,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_85,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_86,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_87,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_88,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_89,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_90,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_91,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_92,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_93,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_94,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_95,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_96,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_97,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_98,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_99,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_100,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_101,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_102,type,
class_Rings_Oidom: $i > $o ).
tff(decl_103,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_104,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_105,type,
hBOOL: $i > $o ).
tff(decl_106,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_108,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_109,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_110,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_111,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_112,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_113,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_114,type,
c_Complex_Oii: $i ).
tff(decl_115,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_116,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_117,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff(decl_118,type,
class_Power_Opower: $i > $o ).
tff(decl_119,type,
tc_Int_Oint: $i ).
tff(decl_120,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_121,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_122,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_124,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(decl_125,type,
c_Transcendental_Oln: $i > $i ).
tff(decl_126,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(decl_127,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_128,type,
c_Nat_OSuc: $i > $i ).
tff(decl_129,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_130,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_131,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_132,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_133,type,
class_Fields_Ofield: $i > $o ).
tff(decl_134,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_135,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_136,type,
c_Complex_Ocis: $i > $i ).
tff(decl_137,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_138,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_139,type,
tc_HOL_Obool: $i ).
tff(decl_140,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_141,type,
epred2_3: ( $i * $i * $i ) > $o ).
tff(decl_142,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_144,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk4_0: $i ).
tff(decl_146,type,
esk5_1: $i > $i ).
tff(decl_147,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_151,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk13_1: $i > $i ).
tff(decl_155,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_156,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk16_1: $i > $i ).
tff(decl_158,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk21_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_163,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk23_1: $i > $i ).
tff(decl_165,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_169,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_171,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_172,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_173,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_174,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_175,type,
esk34_2: ( $i * $i ) > $i ).
tff(decl_176,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_178,type,
esk37_3: ( $i * $i * $i ) > $i ).
tff(decl_179,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_180,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_181,type,
esk40_3: ( $i * $i * $i ) > $i ).
tff(decl_182,type,
esk41_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_183,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_184,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_185,type,
esk44_3: ( $i * $i * $i ) > $i ).
tff(decl_186,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_187,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_188,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_189,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_190,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_191,type,
esk50_2: ( $i * $i ) > $i ).
tff(decl_192,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_193,type,
esk52_1: $i > $i ).
tff(decl_194,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_195,type,
esk54_3: ( $i * $i * $i ) > $i ).
tff(decl_196,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_197,type,
esk56_3: ( $i * $i * $i ) > $i ).
tff(decl_198,type,
esk57_2: ( $i * $i ) > $i ).
tff(decl_199,type,
esk58_1: $i > $i ).
tff(decl_200,type,
esk59_3: ( $i * $i * $i ) > $i ).
tff(decl_201,type,
esk60_3: ( $i * $i * $i ) > $i ).
tff(decl_202,type,
esk61_2: ( $i * $i ) > $i ).
tff(decl_203,type,
esk62_3: ( $i * $i * $i ) > $i ).
tff(decl_204,type,
esk63_3: ( $i * $i * $i ) > $i ).
tff(decl_205,type,
esk64_3: ( $i * $i * $i ) > $i ).
tff(decl_206,type,
esk65_3: ( $i * $i * $i ) > $i ).
tff(decl_207,type,
esk66_3: ( $i * $i * $i ) > $i ).
tff(decl_208,type,
esk67_2: ( $i * $i ) > $i ).
tff(decl_209,type,
esk68_3: ( $i * $i * $i ) > $i ).
tff(decl_210,type,
esk69_3: ( $i * $i * $i ) > $i ).
tff(decl_211,type,
esk70_3: ( $i * $i * $i ) > $i ).
tff(decl_212,type,
esk71_3: ( $i * $i * $i ) > $i ).
tff(decl_213,type,
esk72_3: ( $i * $i * $i ) > $i ).
tff(decl_214,type,
esk73_3: ( $i * $i * $i ) > $i ).
tff(decl_215,type,
esk74_3: ( $i * $i * $i ) > $i ).
tff(decl_216,type,
esk75_3: ( $i * $i * $i ) > $i ).
fof(fact_less__eq__real__def,axiom,
! [X13,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X13)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,X13)
| X14 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__le__linear,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X6)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_leI,axiom,
! [X12,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X12)
=> c_Orderings_Oord__class_Oless__eq(X5,X12,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_less__le__not__le,axiom,
! [X13,X14,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X14,X13)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X14,X13)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_real__norm__def,axiom,
! [X19] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X19) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_order__less__trans,axiom,
! [X7,X12,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X12)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X7)
=> c_Orderings_Oord__class_Oless(X5,X4,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_norm__ge__zero,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> 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(fact_abs__ge__self,axiom,
! [X16,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,X16,c_Groups_Oabs__class_Oabs(X5,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_h,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_h) ).
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_abs__add__one__gt__zero,axiom,
! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_order__trans,axiom,
! [X7,X12,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X7)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(fact_real__le__trans,axiom,
! [X8,X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
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_abs__norm__cancel,axiom,
! [X16,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X16)) = c_RealVector_Onorm__class_Onorm(X5,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
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(fact_abs__of__nonneg,axiom,
! [X16,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Groups_Oabs__class_Oabs(X5,X16) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_less__add__one,axiom,
! [X16,X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,X16,c_Groups_Oplus__class_Oplus(X5,X16,c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X15,X16,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X16,X15) = c_Groups_Oplus__class_Oplus(X5,X15,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
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(c_0_23,plain,
! [X899,X900] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X900,X899)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X900,X899)
| X900 = X899 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X900,X899)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X900,X899) )
& ( X900 != X899
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X900,X899) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(c_0_24,plain,
! [X104,X105] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X105,X104)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X104,X105) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_25,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_26,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,plain,
! [X12,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X12)
=> c_Orderings_Oord__class_Oless__eq(X5,X12,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(c_0_29,plain,
! [X13,X14,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X14,X13)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X14,X13)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X14) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_30,plain,
! [X199] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X199) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X199),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_31,plain,
! [X434,X435,X436,X437] :
( ~ class_Orderings_Opreorder(X437)
| ~ c_Orderings_Oord__class_Oless(X437,X436,X435)
| ~ c_Orderings_Oord__class_Oless(X437,X435,X434)
| c_Orderings_Oord__class_Oless(X437,X436,X434) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
cnf(c_0_32,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_34,plain,
! [X200,X201] :
( ~ class_RealVector_Oreal__normed__vector(X201)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X201,X200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(c_0_35,plain,
! [X281,X282] :
( ~ class_Groups_Oordered__ab__group__add__abs(X282)
| c_Orderings_Oord__class_Oless__eq(X282,X281,c_Groups_Oabs__class_Oabs(X282,X281)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(c_0_36,plain,
! [X783,X784,X785] :
( ~ class_Orderings_Olinorder(X785)
| c_Orderings_Oord__class_Oless(X785,X784,X783)
| c_Orderings_Oord__class_Oless__eq(X785,X783,X784) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
fof(c_0_37,plain,
! [X789,X790,X791] :
( ( c_Orderings_Oord__class_Oless__eq(X791,X790,X789)
| ~ c_Orderings_Oord__class_Oless(X791,X790,X789)
| ~ class_Orderings_Opreorder(X791) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X791,X789,X790)
| ~ c_Orderings_Oord__class_Oless(X791,X790,X789)
| ~ class_Orderings_Opreorder(X791) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X791,X790,X789)
| c_Orderings_Oord__class_Oless__eq(X791,X789,X790)
| c_Orderings_Oord__class_Oless(X791,X790,X789)
| ~ class_Orderings_Opreorder(X791) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_38,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[fact_h]) ).
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_30]) ).
cnf(c_0_40,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____) = v_r____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_43,plain,
( 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_34]) ).
fof(c_0_44,plain,
! [X319] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X319))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(c_0_45,plain,
! [X149,X150,X151,X152] :
( ~ class_Orderings_Opreorder(X152)
| ~ c_Orderings_Oord__class_Oless__eq(X152,X151,X150)
| ~ c_Orderings_Oord__class_Oless__eq(X152,X150,X149)
| c_Orderings_Oord__class_Oless__eq(X152,X151,X149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
cnf(c_0_46,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
fof(c_0_48,plain,
! [X106,X107,X108] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X108,X107)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X107,X106)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X108,X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
cnf(c_0_49,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_51,plain,
! [X290,X291] :
( ~ class_RealVector_Oreal__normed__vector(X291)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X291,X290)) = c_RealVector_Onorm__class_Onorm(X291,X290) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
cnf(c_0_52,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_53,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_54,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____) = v_r____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_r____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_55,plain,
( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(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(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_56,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_57,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_44]) ).
fof(c_0_58,plain,
! [X188,X189] :
( ~ class_Groups_Oordered__ab__group__add__abs(X189)
| ~ c_Orderings_Oord__class_Oless__eq(X189,c_Groups_Ozero__class_Ozero(X189),X188)
| c_Groups_Oabs__class_Oabs(X189,X188) = X188 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
cnf(c_0_59,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_60,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_39]) ).
fof(c_0_61,plain,
! [X1043,X1044] :
( ~ class_Rings_Olinordered__semidom(X1044)
| c_Orderings_Oord__class_Oless(X1044,X1043,c_Groups_Oplus__class_Oplus(X1044,X1043,c_Groups_Oone__class_Oone(X1044))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
cnf(c_0_62,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_63,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_64,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_65,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_66,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_42])]) ).
cnf(c_0_67,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____) = v_r____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_68,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))),
inference(rw,[status(thm)],[c_0_57,c_0_39]) ).
cnf(c_0_69,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_42])]) ).
cnf(c_0_71,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c_0_73,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_74,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____),
inference(spm,[status(thm)],[c_0_32,c_0_64]) ).
cnf(c_0_75,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_65,c_0_39]) ).
cnf(c_0_76,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____) = v_r____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_77,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_63]),c_0_39]),c_0_47])]) ).
fof(c_0_78,plain,
! [X1109,X1110,X1111] :
( ~ class_Rings_Ocomm__semiring__1(X1111)
| c_Groups_Oplus__class_Oplus(X1111,X1110,X1109) = c_Groups_Oplus__class_Oplus(X1111,X1109,X1110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
cnf(c_0_79,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_70]),c_0_42])]) ).
cnf(c_0_80,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_81,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_r____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____) = v_r____,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_56])]),c_0_77]) ).
cnf(c_0_83,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
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,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____),v_r____),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_53]),c_0_82]) ).
cnf(c_0_87,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r____),
inference(spm,[status(thm)],[c_0_85,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW233+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
% 0.14/0.34 % Computer : n021.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 21:16:13 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.83/1.92 % Version : CSE_E---1.5
% 1.83/1.92 % Problem : theBenchmark.p
% 1.83/1.92 % Proof found
% 1.83/1.92 % SZS status Theorem for theBenchmark.p
% 1.83/1.92 % SZS output start Proof
% See solution above
% 1.83/1.93 % Total time : 1.305000 s
% 1.83/1.93 % SZS output end Proof
% 1.83/1.93 % Total time : 1.347000 s
%------------------------------------------------------------------------------