TSTP Solution File: SWW229+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 00:16:38 EDT 2023
% Result : Theorem 15.45s 15.65s
% Output : CNFRefutation 15.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 167
% Syntax : Number of formulae : 186 ( 19 unt; 160 typ; 0 def)
% Number of atoms : 33 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 190 ( 131 >; 59 *; 0 +; 0 <<)
% Number of predicates : 73 ( 71 usr; 1 prp; 0-3 aty)
% Number of functors : 89 ( 89 usr; 29 con; 0-4 aty)
% Number of variables : 38 ( 0 sgn; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_f____: $i ).
tff(decl_24,type,
c_SEQ_Osubseq: $i > $o ).
tff(decl_25,type,
tc_RealDef_Oreal: $i ).
tff(decl_26,type,
tc_Complex_Ocomplex: $i ).
tff(decl_27,type,
v_g____: $i > $i ).
tff(decl_28,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_29,type,
v_r: $i ).
tff(decl_30,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
v_w____: $i ).
tff(decl_32,type,
tc_Nat_Onat: $i ).
tff(decl_33,type,
v_N1____: $i ).
tff(decl_34,type,
v_N2____: $i ).
tff(decl_35,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_37,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_39,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_40,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_41,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_42,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_43,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_44,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_45,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_46,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_47,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_48,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_49,type,
v_z____: $i ).
tff(decl_50,type,
v_d____: $i ).
tff(decl_51,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_53,type,
v_s____: $i ).
tff(decl_54,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_55,type,
v_p: $i ).
tff(decl_56,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_57,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_58,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_59,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_60,type,
class_Groups_Oabs__if: $i > $o ).
tff(decl_61,type,
class_Groups_Ozero: $i > $o ).
tff(decl_62,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_63,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_64,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_65,type,
class_Orderings_Oord: $i > $o ).
tff(decl_66,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_67,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_68,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_69,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_70,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_71,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_72,type,
class_Rings_Oidom: $i > $o ).
tff(decl_73,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_74,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_75,type,
class_Groups_Oone: $i > $o ).
tff(decl_76,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_77,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_78,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_79,type,
hBOOL: $i > $o ).
tff(decl_80,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_81,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_82,type,
c_Nat_OSuc: $i > $i ).
tff(decl_83,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_84,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_86,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_87,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_88,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_89,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_90,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_91,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_92,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_93,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_94,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
c_Complex_Oii: $i ).
tff(decl_96,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_97,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_99,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_100,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_101,type,
class_Fields_Ofield: $i > $o ).
tff(decl_102,type,
class_Groups_Ominus: $i > $o ).
tff(decl_103,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_104,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_105,type,
c_Int_OPls: $i ).
tff(decl_106,type,
c_Int_OBit1: $i > $i ).
tff(decl_107,type,
c_Int_OBit0: $i > $i ).
tff(decl_108,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_109,type,
tc_Int_Oint: $i ).
tff(decl_110,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_111,type,
class_Int_Onumber: $i > $o ).
tff(decl_112,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_113,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_114,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_116,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_117,type,
class_Rings_Oring: $i > $o ).
tff(decl_118,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_119,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_120,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_121,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_122,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_123,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_124,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_125,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_126,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_127,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_128,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_129,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_130,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_131,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_132,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_133,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_134,type,
tc_HOL_Obool: $i ).
tff(decl_135,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_136,type,
esk2_1: $i > $i ).
tff(decl_137,type,
esk3_1: $i > $i ).
tff(decl_138,type,
esk4_1: $i > $i ).
tff(decl_139,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_140,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk7_0: $i ).
tff(decl_142,type,
esk8_1: $i > $i ).
tff(decl_143,type,
esk9_1: $i > $i ).
tff(decl_144,type,
esk10_0: $i ).
tff(decl_145,type,
esk11_0: $i ).
tff(decl_146,type,
esk12_0: $i ).
tff(decl_147,type,
esk13_0: $i ).
tff(decl_148,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_149,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk16_1: $i > $i ).
tff(decl_151,type,
esk17_1: $i > $i ).
tff(decl_152,type,
esk18_0: $i ).
tff(decl_153,type,
esk19_1: $i > $i ).
tff(decl_154,type,
esk20_1: $i > $i ).
tff(decl_155,type,
esk21_0: $i ).
tff(decl_156,type,
esk22_0: $i ).
tff(decl_157,type,
esk23_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_158,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk25_1: $i > $i ).
tff(decl_160,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk27_1: $i > $i ).
tff(decl_162,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_163,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_165,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_167,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_169,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk36_1: $i > $i ).
tff(decl_171,type,
esk37_0: $i ).
tff(decl_172,type,
esk38_1: $i > $i ).
tff(decl_173,type,
esk39_0: $i ).
tff(decl_174,type,
esk40_1: $i > $i ).
tff(decl_175,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_176,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_178,type,
esk44_3: ( $i * $i * $i ) > $i ).
tff(decl_179,type,
esk45_0: $i ).
tff(decl_180,type,
esk46_0: $i ).
tff(decl_181,type,
esk47_0: $i ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_real__norm__def,axiom,
! [X13] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X13) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X10,X11] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_minus__real__def,axiom,
! [X10,X11] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,X10) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(fact_norm__minus__commute,axiom,
! [X5,X6,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)) = c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_norm__triangle__ineq3,axiom,
! [X5,X6,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6),c_RealVector_Onorm__class_Onorm(X7,X5))),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(c_0_7,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_8,plain,
! [X133] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X133) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X133),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_9,plain,
! [X644,X645] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X645,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X644))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X644,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X645))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(c_0_10,plain,
! [X640,X641] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X641,X640) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X641,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X640)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_11,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,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_8]) ).
cnf(c_0_13,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,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_10]) ).
cnf(c_0_15,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_12]),c_0_14]),c_0_12]) ).
fof(c_0_17,plain,
! [X218,X219,X220] :
( ~ class_RealVector_Oreal__normed__vector(X220)
| c_RealVector_Onorm__class_Onorm(X220,c_Groups_Ominus__class_Ominus(X220,X219,X218)) = c_RealVector_Onorm__class_Onorm(X220,c_Groups_Ominus__class_Ominus(X220,X218,X219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).
fof(c_0_18,plain,
! [X95,X96,X97] :
( ~ class_RealVector_Oreal__normed__vector(X97)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X97,X96),c_RealVector_Onorm__class_Onorm(X97,X95))),c_RealVector_Onorm__class_Onorm(X97,c_Groups_Ominus__class_Ominus(X97,X96,X95))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3])]) ).
cnf(c_0_19,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_22,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(rw,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n011.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 21:29:25 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 15.45/15.65 % Version : CSE_E---1.5
% 15.45/15.65 % Problem : theBenchmark.p
% 15.45/15.65 % Proof found
% 15.45/15.65 % SZS status Theorem for theBenchmark.p
% 15.45/15.65 % SZS output start Proof
% See solution above
% 15.48/15.66 % Total time : 15.034000 s
% 15.48/15.66 % SZS output end Proof
% 15.48/15.66 % Total time : 15.073000 s
%------------------------------------------------------------------------------