TSTP Solution File: SWW236+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW236+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 : n017.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 00:16:41 EDT 2023
% Result : Theorem 6.09s 6.18s
% Output : CNFRefutation 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 190
% Syntax : Number of formulae : 229 ( 33 unt; 174 typ; 0 def)
% Number of atoms : 169 ( 18 equ)
% Maximal formula atoms : 62 ( 3 avg)
% Number of connectives : 185 ( 71 ~; 73 |; 19 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 276 ( 161 >; 115 *; 0 +; 0 <<)
% Number of predicates : 77 ( 75 usr; 1 prp; 0-3 aty)
% Number of functors : 99 ( 99 usr; 13 con; 0-5 aty)
% Number of variables : 81 ( 0 sgn; 51 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_c____: $i ).
tff(decl_24,type,
tc_Complex_Ocomplex: $i ).
tff(decl_25,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
tc_RealDef_Oreal: $i ).
tff(decl_27,type,
v_da____: $i ).
tff(decl_28,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_29,type,
v_aa____: $i ).
tff(decl_30,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_31,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
v_z____: $i ).
tff(decl_34,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
v_p: $i ).
tff(decl_36,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_37,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_38,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_39,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_40,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_41,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_42,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_43,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_44,type,
v_cs____: $i ).
tff(decl_45,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_46,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_47,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_48,type,
class_Groups_Ozero: $i > $o ).
tff(decl_49,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_50,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_51,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_52,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_53,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_54,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_55,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_56,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_57,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_58,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_59,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_60,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_61,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_62,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_63,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_64,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_65,type,
class_Orderings_Oord: $i > $o ).
tff(decl_66,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_67,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_68,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_69,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_70,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_71,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_72,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_73,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_74,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_75,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_76,type,
class_Fields_Ofield: $i > $o ).
tff(decl_77,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_78,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_80,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_81,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_82,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_83,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_84,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_85,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_86,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_87,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_88,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_89,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_90,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_91,type,
class_Rings_Oidom: $i > $o ).
tff(decl_92,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_93,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
tc_Nat_Onat: $i ).
tff(decl_95,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_97,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_98,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_100,type,
hBOOL: $i > $o ).
tff(decl_101,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_102,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_103,type,
c_NthRoot_Oroot: ( $i * $i ) > $i ).
tff(decl_104,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_105,type,
class_Groups_Oone: $i > $o ).
tff(decl_106,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_107,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_108,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_109,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_110,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_111,type,
tc_Int_Oint: $i ).
tff(decl_112,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_113,type,
class_Power_Opower: $i > $o ).
tff(decl_114,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_115,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_117,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_118,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_119,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_120,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_121,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_122,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_123,type,
class_Rings_Oring: $i > $o ).
tff(decl_124,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_125,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_126,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_127,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_128,type,
c_Complex_Oii: $i ).
tff(decl_129,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
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_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_133,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(decl_134,type,
c_Nat_OSuc: $i > $i ).
tff(decl_135,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_136,type,
c_Transcendental_Oln: $i > $i ).
tff(decl_137,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_143,type,
esk3_0: $i ).
tff(decl_144,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_146,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk7_1: $i > $i ).
tff(decl_148,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_151,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk14_1: $i > $i ).
tff(decl_155,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk19_1: $i > $i ).
tff(decl_160,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_165,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_167,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_168,type,
esk28_1: $i > $i ).
tff(decl_169,type,
esk29_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_170,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_171,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_172,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_173,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_174,type,
esk34_2: ( $i * $i ) > $i ).
tff(decl_175,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_176,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_177,type,
esk37_3: ( $i * $i * $i ) > $i ).
tff(decl_178,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk39_1: $i > $i ).
tff(decl_180,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_181,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_182,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_183,type,
esk43_3: ( $i * $i * $i ) > $i ).
tff(decl_184,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_185,type,
esk45_3: ( $i * $i * $i ) > $i ).
tff(decl_186,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_187,type,
esk47_3: ( $i * $i * $i ) > $i ).
tff(decl_188,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_189,type,
esk49_3: ( $i * $i * $i ) > $i ).
tff(decl_190,type,
esk50_2: ( $i * $i ) > $i ).
tff(decl_191,type,
esk51_1: $i > $i ).
tff(decl_192,type,
esk52_3: ( $i * $i * $i ) > $i ).
tff(decl_193,type,
esk53_3: ( $i * $i * $i ) > $i ).
tff(decl_194,type,
esk54_3: ( $i * $i * $i ) > $i ).
tff(decl_195,type,
esk55_3: ( $i * $i * $i ) > $i ).
fof(fact_divide__le__eq,axiom,
! [X16,X17,X15,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Odivide(X6,X15,X17),X16)
<=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17)) )
& ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> ( ( c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17),X15) )
& ( ~ c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X16) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).
fof(fact_real__norm__def,axiom,
! [X20] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X20) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_h,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_h) ).
fof(fact_real__mult__commute,axiom,
! [X11,X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_xt1_I6_J,axiom,
! [X9,X5,X4,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X4,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X9,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X9,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact__0960_A_060_Acmod_Ac_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0960_A_060_Acmod_Ac_096) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(fact_leI,axiom,
! [X4,X5,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X5,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X7,X8,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X7),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
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(fact_norm__mult,axiom,
! [X4,X5,X6] :
( class_RealVector_Oreal__normed__div__algebra(X6)
=> c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X5)),c_RealVector_Onorm__class_Onorm(X6,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_real__less__def,axiom,
! [X22,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X22)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X22)
& X10 != X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(c_0_16,plain,
! [X16,X17,X15,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Odivide(X6,X15,X17),X16)
<=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17)) )
& ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> ( ( c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17),X15) )
& ( ~ c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X16) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).
fof(c_0_17,plain,
! [X211] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X211) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X211),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_18,plain,
! [X1155,X1156,X1157,X1158] :
( ( ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ class_Fields_Olinordered__field__inverse__zero(X1158) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_19,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[fact_h]) ).
cnf(c_0_20,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_17]) ).
fof(c_0_21,plain,
! [X142,X143] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X143),X142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X142),X143),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(c_0_22,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_23,plain,
! [X320,X321,X322,X323] :
( ~ class_Orderings_Oorder(X323)
| ~ c_Orderings_Oord__class_Oless__eq(X323,X322,X321)
| ~ c_Orderings_Oord__class_Oless__eq(X323,X320,X322)
| c_Orderings_Oord__class_Oless__eq(X323,X320,X321) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
cnf(c_0_24,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(split_conjunct,[status(thm)],[fact__0960_A_060_Acmod_Ac_096]) ).
cnf(c_0_27,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_28,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X4,X5,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X5,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X4,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
cnf(c_0_30,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,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,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_33,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(c_0_34,plain,
! [X714,X715,X716] :
( ~ class_Orderings_Olinorder(X716)
| c_Orderings_Oord__class_Oless(X716,X715,X714)
| c_Orderings_Oord__class_Oless__eq(X716,X714,X715) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
cnf(c_0_35,negated_conjecture,
~ 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,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(rw,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_36,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,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,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_34]) ).
cnf(c_0_38,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_39,plain,
! [X1096,X1097,X1098] :
( ~ class_Rings_Ocomm__semiring__1(X1098)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1098),X1097),X1096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1098),X1096),X1097) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
cnf(c_0_40,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,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_37,c_0_38]) ).
cnf(c_0_42,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
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]) ).
fof(c_0_44,plain,
! [X125,X126,X127] :
( ~ class_RealVector_Oreal__normed__div__algebra(X127)
| c_RealVector_Onorm__class_Onorm(X127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X127),X126),X125)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X127,X126)),c_RealVector_Onorm__class_Onorm(X127,X125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
fof(c_0_45,plain,
! [X766,X767] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X767,X766)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X767,X766) )
& ( X767 != X766
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X767,X766) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X767,X766)
| X767 = X766
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X767,X766) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
cnf(c_0_46,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
cnf(c_0_50,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_c____),v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW236+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.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 20:32:27 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 6.09/6.18 % Version : CSE_E---1.5
% 6.09/6.18 % Problem : theBenchmark.p
% 6.09/6.18 % Proof found
% 6.09/6.18 % SZS status Theorem for theBenchmark.p
% 6.09/6.18 % SZS output start Proof
% See solution above
% 6.09/6.19 % Total time : 5.543000 s
% 6.09/6.19 % SZS output end Proof
% 6.09/6.19 % Total time : 5.586000 s
%------------------------------------------------------------------------------