TSTP Solution File: SWW178+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW178+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 : n019.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 00:16:21 EDT 2023
% Result : Theorem 38.39s 38.47s
% Output : CNFRefutation 38.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 196
% Syntax : Number of formulae : 243 ( 38 unt; 178 typ; 0 def)
% Number of atoms : 98 ( 42 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 60 ( 27 ~; 23 |; 1 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 285 ( 164 >; 121 *; 0 +; 0 <<)
% Number of predicates : 74 ( 72 usr; 1 prp; 0-4 aty)
% Number of functors : 106 ( 106 usr; 14 con; 0-4 aty)
% Number of variables : 104 ( 0 sgn; 54 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_RealDef_Oreal: $i ).
tff(decl_24,type,
tc_Complex_Ocomplex: $i ).
tff(decl_25,type,
v_w: $i ).
tff(decl_26,type,
v_z: $i ).
tff(decl_27,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_29,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_30,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_33,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_34,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_35,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_36,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_37,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_38,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_39,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_40,type,
class_Orderings_Oord: $i > $o ).
tff(decl_41,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_42,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_43,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_44,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_45,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_46,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_47,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_48,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_49,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_50,type,
class_Groups_Ominus: $i > $o ).
tff(decl_51,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_52,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_53,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(decl_54,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_55,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
c_Complex_OIm: $i > $i ).
tff(decl_57,type,
c_Complex_ORe: $i > $i ).
tff(decl_58,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
c_RealVector_Obounded__bilinear: ( $i * $i * $i * $i ) > $o ).
tff(decl_60,type,
c_RealVector_Odist__class_Odist: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_62,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_63,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(decl_64,type,
class_RealVector_Ometric__space: $i > $o ).
tff(decl_65,type,
class_Groups_Ozero: $i > $o ).
tff(decl_66,type,
class_Groups_Oabs__if: $i > $o ).
tff(decl_67,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_68,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_69,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_70,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_71,type,
class_RealVector_Odist__norm: $i > $o ).
tff(decl_72,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_73,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_74,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(decl_75,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
tff(decl_76,type,
tc_Nat_Onat: $i ).
tff(decl_77,type,
c_Complex_Ocomplex_Ocomplex__rec: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
c_Complex_Ocomplex_Ocomplex__case: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_80,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_81,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_82,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_83,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_84,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_85,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_86,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_87,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_88,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_89,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_90,type,
class_Rings_Oring: $i > $o ).
tff(decl_91,type,
class_Rings_Oidom: $i > $o ).
tff(decl_92,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(decl_93,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_94,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_95,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_96,type,
class_Rings_Oordered__ring: $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_Olinordered__semiring__strict: $i > $o ).
tff(decl_100,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_101,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_102,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_103,type,
hBOOL: $i > $o ).
tff(decl_104,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_105,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_106,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_107,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_108,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_109,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_110,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_111,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_112,type,
class_Groups_Oone: $i > $o ).
tff(decl_113,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_114,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_115,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_116,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_117,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_118,type,
c_Complex_Oii: $i ).
tff(decl_119,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_120,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_121,type,
class_Power_Opower: $i > $o ).
tff(decl_122,type,
tc_Int_Oint: $i ).
tff(decl_123,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_124,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_125,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_126,type,
c_Transcendental_Oln: $i > $i ).
tff(decl_127,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff(decl_128,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(decl_129,type,
c_Nat_OSuc: $i > $i ).
tff(decl_130,type,
tc_HOL_Obool: $i ).
tff(decl_131,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_133,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_134,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_135,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_136,type,
esk6_0: $i ).
tff(decl_137,type,
esk7_0: $i ).
tff(decl_138,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk9_1: $i > $i ).
tff(decl_140,type,
esk10_0: $i ).
tff(decl_141,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_144,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk15_0: $i ).
tff(decl_146,type,
esk16_1: $i > $i ).
tff(decl_147,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk18_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_149,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk20_1: $i > $i ).
tff(decl_151,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk23_0: $i ).
tff(decl_154,type,
esk24_0: $i ).
tff(decl_155,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk26_1: $i > $i ).
tff(decl_157,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_158,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk29_1: $i > $i ).
tff(decl_160,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk32_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_163,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk34_1: $i > $i ).
tff(decl_165,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk37_1: $i > $i ).
tff(decl_168,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_169,type,
esk39_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_170,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_171,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_172,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_173,type,
esk43_3: ( $i * $i * $i ) > $i ).
tff(decl_174,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_175,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_176,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk47_3: ( $i * $i * $i ) > $i ).
tff(decl_178,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_180,type,
esk50_2: ( $i * $i ) > $i ).
tff(decl_181,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_182,type,
esk52_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_183,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_184,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_185,type,
esk55_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_186,type,
esk56_2: ( $i * $i ) > $i ).
tff(decl_187,type,
esk57_3: ( $i * $i * $i ) > $i ).
tff(decl_188,type,
esk58_3: ( $i * $i * $i ) > $i ).
tff(decl_189,type,
esk59_3: ( $i * $i * $i ) > $i ).
tff(decl_190,type,
esk60_3: ( $i * $i * $i ) > $i ).
tff(decl_191,type,
esk61_3: ( $i * $i * $i ) > $i ).
tff(decl_192,type,
esk62_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_193,type,
esk63_3: ( $i * $i * $i ) > $i ).
tff(decl_194,type,
esk64_2: ( $i * $i ) > $i ).
tff(decl_195,type,
esk65_3: ( $i * $i * $i ) > $i ).
tff(decl_196,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_197,type,
esk67_2: ( $i * $i ) > $i ).
tff(decl_198,type,
esk68_1: $i > $i ).
tff(decl_199,type,
esk69_2: ( $i * $i ) > $i ).
fof(fact_equation__minus__iff,axiom,
! [X8,X10,X6] :
( class_Groups_Ogroup__add(X6)
=> ( X10 = c_Groups_Ouminus__class_Ouminus(X6,X8)
<=> X8 = c_Groups_Ouminus__class_Ouminus(X6,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_minus__real__def,axiom,
! [X4,X5] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X4) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_minus__diff__eq,axiom,
! [X12,X13,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ominus__class_Ominus(X6,X13,X12)) = c_Groups_Ominus__class_Ominus(X6,X12,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_complex__diff__def,axiom,
! [X4,X5] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5,X4) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X5,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__diff__def) ).
fof(fact_norm__minus__cancel,axiom,
! [X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ouminus__class_Ouminus(X6,X5)) = c_RealVector_Onorm__class_Onorm(X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X11,X13,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X13,X11) = c_Groups_Oplus__class_Oplus(X6,X11,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_real__add__left__mono,axiom,
! [X7,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,X5),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_add__minus__cancel,axiom,
! [X12,X13,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X13,c_Groups_Oplus__class_Oplus(X6,c_Groups_Ouminus__class_Ouminus(X6,X13),X12)) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [X12,X13,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Ouminus__class_Ouminus(X6,X13),c_Groups_Ouminus__class_Ouminus(X6,X12)) = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ominus__class_Ominus(X6,X13,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(fact__096cmod_A_Iw_A_L_Az_A_L_A_N_Az_J_A_N_Acmod_A_Iw_A_L_Az_J_A_060_061_Acmod_A_I_N_Az_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A_Iw_A_L_Az_A_L_A_N_Az_J_A_N_Acmod_A_Iw_A_L_Az_J_A_060_061_Acmod_A_I_N_Az_J_096) ).
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_add__diff__cancel,axiom,
! [X12,X13,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Oplus__class_Oplus(X6,X13,X12),X12) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
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_18,plain,
! [X157,X158,X159] :
( ( X158 != c_Groups_Ouminus__class_Ouminus(X159,X157)
| X157 = c_Groups_Ouminus__class_Ouminus(X159,X158)
| ~ class_Groups_Ogroup__add(X159) )
& ( X157 != c_Groups_Ouminus__class_Ouminus(X159,X158)
| X158 = c_Groups_Ouminus__class_Ouminus(X159,X157)
| ~ class_Groups_Ogroup__add(X159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
cnf(c_0_19,plain,
( X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_20,plain,
! [X410,X411] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X411,X410) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X411,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X410)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_21,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(c_0_23,plain,
! [X145,X146,X147] :
( ~ class_Groups_Oab__group__add(X147)
| c_Groups_Ouminus__class_Ouminus(X147,c_Groups_Ominus__class_Ominus(X147,X146,X145)) = c_Groups_Ominus__class_Ominus(X147,X145,X146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
fof(c_0_24,plain,
! [X385,X386] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X386,X385) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X386,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X385)),
inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).
fof(c_0_25,plain,
! [X209,X210] :
( ~ class_RealVector_Oreal__normed__vector(X210)
| c_RealVector_Onorm__class_Onorm(X210,c_Groups_Ouminus__class_Ouminus(X210,X209)) = c_RealVector_Onorm__class_Onorm(X210,X209) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).
cnf(c_0_26,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
fof(c_0_27,plain,
! [X422,X423,X424] :
( ~ class_Rings_Ocomm__semiring__1(X424)
| c_Groups_Oplus__class_Oplus(X424,X423,X422) = c_Groups_Oplus__class_Oplus(X424,X422,X423) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_28,plain,
! [X110,X111,X112] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X112,X111)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X110,X112),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X110,X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
fof(c_0_29,plain,
! [X197,X198,X199] :
( ~ class_Groups_Ogroup__add(X199)
| c_Groups_Oplus__class_Oplus(X199,X198,c_Groups_Oplus__class_Oplus(X199,c_Groups_Ouminus__class_Ouminus(X199,X198),X197)) = X197 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(c_0_30,plain,
! [X322,X323,X324] :
( ~ class_Groups_Oab__group__add(X324)
| c_Groups_Ominus__class_Ominus(X324,c_Groups_Ouminus__class_Ouminus(X324,X323),c_Groups_Ouminus__class_Ouminus(X324,X322)) = c_Groups_Ouminus__class_Ouminus(X324,c_Groups_Ominus__class_Ominus(X324,X323,X322)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])]) ).
cnf(c_0_31,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_33,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).
cnf(c_0_35,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),
inference(split_conjunct,[status(thm)],[fact__096cmod_A_Iw_A_L_Az_A_L_A_N_Az_J_A_N_Acmod_A_Iw_A_L_Az_J_A_060_061_Acmod_A_I_N_Az_J_096]) ).
cnf(c_0_36,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_39,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(c_0_40,plain,
! [X188,X189,X190] :
( ~ class_Groups_Ogroup__add(X190)
| c_Groups_Ominus__class_Ominus(X190,c_Groups_Oplus__class_Oplus(X190,X189,X188),X188) = X189 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(c_0_41,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),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_42,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_27]) ).
cnf(c_0_43,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(c_0_44,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_45,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_46,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_47,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_48,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_49,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_50,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_51,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_54,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_55,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X1),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_22])]) ).
cnf(c_0_56,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_47]),c_0_48]) ).
cnf(c_0_57,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z)),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_26]) ).
cnf(c_0_59,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,v_w)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,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_42,c_0_54]) ).
cnf(c_0_61,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),X3) ),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,v_w))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_53]) ).
cnf(c_0_63,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,v_w)))),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_60]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW178+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 18:27:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 38.39/38.47 % Version : CSE_E---1.5
% 38.39/38.47 % Problem : theBenchmark.p
% 38.39/38.47 % Proof found
% 38.39/38.47 % SZS status Theorem for theBenchmark.p
% 38.39/38.47 % SZS output start Proof
% See solution above
% 38.45/38.48 % Total time : 37.855000 s
% 38.45/38.48 % SZS output end Proof
% 38.45/38.48 % Total time : 37.896000 s
%------------------------------------------------------------------------------