TSTP Solution File: SWW238+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW238+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 : n029.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 0.63s 1.51s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 188
% Syntax : Number of formulae : 222 ( 21 unt; 176 typ; 0 def)
% Number of atoms : 88 ( 14 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 71 ( 29 ~; 29 |; 2 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 295 ( 164 >; 131 *; 0 +; 0 <<)
% Number of predicates : 83 ( 81 usr; 1 prp; 0-3 aty)
% Number of functors : 95 ( 95 usr; 12 con; 0-5 aty)
% Number of variables : 75 ( 0 sgn; 41 !; 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,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_26,type,
v_z____: $i ).
tff(decl_27,type,
v_c____: $i ).
tff(decl_28,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_29,type,
v_aa____: $i ).
tff(decl_30,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
v_p: $i ).
tff(decl_33,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_34,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_35,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_36,type,
v_da____: $i ).
tff(decl_37,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_38,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_39,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_40,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_41,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_42,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_43,type,
v_cs____: $i ).
tff(decl_44,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_46,type,
class_Orderings_Oord: $i > $o ).
tff(decl_47,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_48,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_49,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_50,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_51,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_52,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_53,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_54,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_55,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_57,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_58,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_59,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_60,type,
class_Groups_Ozero: $i > $o ).
tff(decl_61,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_62,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_63,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_64,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_65,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_66,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_67,type,
class_Rings_Ono__zero__divisors: $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,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_71,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_72,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_73,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_74,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_75,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_76,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_77,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_78,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_79,type,
class_Fields_Ofield: $i > $o ).
tff(decl_80,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_81,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_82,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_83,type,
class_Fields_Olinordered__field__inverse__zero: $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,
class_Groups_Oone: $i > $o ).
tff(decl_104,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_105,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_106,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_107,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_108,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_109,type,
c_NthRoot_Oroot: ( $i * $i ) > $i ).
tff(decl_110,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_111,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_112,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_113,type,
tc_Int_Oint: $i ).
tff(decl_114,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_115,type,
class_Power_Opower: $i > $o ).
tff(decl_116,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_117,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_119,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_121,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_122,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff(decl_124,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(decl_125,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_126,type,
class_Rings_Odvd: $i > $o ).
tff(decl_127,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_129,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_130,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_131,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_132,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_133,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_134,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_135,type,
class_Rings_Oring: $i > $o ).
tff(decl_136,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_137,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_138,type,
tc_HOL_Obool: $i ).
tff(decl_139,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_140,type,
epred2_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_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk8_1: $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_1: $i > $i ).
tff(decl_154,type,
esk14_2: ( $i * $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_1: $i > $i ).
tff(decl_159,type,
esk19_2: ( $i * $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_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_168,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_169,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_171,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_172,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_173,type,
esk33_3: ( $i * $i * $i ) > $i ).
tff(decl_174,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_175,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_176,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_178,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_179,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_180,type,
esk40_3: ( $i * $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_2: ( $i * $i ) > $i ).
tff(decl_184,type,
esk44_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_185,type,
esk45_3: ( $i * $i * $i ) > $i ).
tff(decl_186,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_187,type,
esk47_3: ( $i * $i * $i ) > $i ).
tff(decl_188,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_189,type,
esk49_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_190,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_191,type,
esk51_3: ( $i * $i * $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 ).
tff(decl_196,type,
esk56_3: ( $i * $i * $i ) > $i ).
tff(decl_197,type,
esk57_3: ( $i * $i * $i ) > $i ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X26,X11,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X11,X26) = c_Groups_Oplus__class_Oplus(X8,X26,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_leI,axiom,
! [X6,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(X8,X6,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(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____)),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_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_real__le__trans,axiom,
! [X33,X34,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X35,X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X34,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X35,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_less__eq__real__def,axiom,
! [X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X28)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X28)
| X21 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_real__le__antisym,axiom,
! [X5,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X4)
=> X4 = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X5,X4)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_real__add__left__mono,axiom,
! [X4,X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X7),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_real__le__refl,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(c_0_12,plain,
! [X292,X293,X294] :
( ~ class_Rings_Ocomm__semiring__1(X294)
| c_Groups_Oplus__class_Oplus(X294,X293,X292) = c_Groups_Oplus__class_Oplus(X294,X292,X293) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_13,plain,
! [X6,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(X8,X6,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(c_0_14,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(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____)),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_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_15,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_12]) ).
cnf(c_0_16,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(c_0_17,plain,
! [X750,X751,X752] :
( ~ class_Orderings_Olinorder(X752)
| c_Orderings_Oord__class_Oless(X752,X751,X750)
| c_Orderings_Oord__class_Oless__eq(X752,X750,X751) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
fof(c_0_18,plain,
! [X297,X298,X299] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X299,X298)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X298,X297)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X299,X297) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(c_0_19,plain,
! [X800,X801] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X801,X800)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X801,X800)
| X801 = X800 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X801,X800)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X801,X800) )
& ( X801 != X800
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X801,X800) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
cnf(c_0_20,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(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____)),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_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,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_15,c_0_16]) ).
cnf(c_0_22,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_17]) ).
cnf(c_0_23,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_24,plain,
! [X295,X296] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X296,X295)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X295,X296)
| X296 = X295 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(c_0_25,plain,
! [X99,X100] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X100),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X100,X99)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X99))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
cnf(c_0_26,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_18]) ).
cnf(c_0_27,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_19]) ).
cnf(c_0_28,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(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____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))))),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,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_22,c_0_23]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ 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]) ).
cnf(c_0_31,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,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_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))),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_28,c_0_29]) ).
fof(c_0_34,plain,
! [X109,X110,X111] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X111,X110)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X109,X111),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X109,X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
cnf(c_0_35,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,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_34]) ).
cnf(c_0_38,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_39,plain,
! [X302] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X302,X302),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
cnf(c_0_40,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_21]),c_0_21]) ).
cnf(c_0_41,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_Complex_Ocomplex,v_aa____),X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,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_15,c_0_38]) ).
cnf(c_0_43,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_42]),c_0_43])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_44]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW238+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 18:21:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.63/1.51 % Version : CSE_E---1.5
% 0.63/1.51 % Problem : theBenchmark.p
% 0.63/1.51 % Proof found
% 0.63/1.51 % SZS status Theorem for theBenchmark.p
% 0.63/1.51 % SZS output start Proof
% See solution above
% 0.63/1.53 % Total time : 0.919000 s
% 0.63/1.53 % SZS output end Proof
% 0.63/1.53 % Total time : 0.945000 s
%------------------------------------------------------------------------------