TSTP Solution File: SWW260+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW260+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 : n001.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 00:16:46 EDT 2023
% Result : Theorem 2.23s 2.37s
% Output : CNFRefutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 176
% Syntax : Number of formulae : 212 ( 36 unt; 161 typ; 0 def)
% Number of atoms : 66 ( 42 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 10 |; 0 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 197 ( 131 >; 66 *; 0 +; 0 <<)
% Number of predicates : 81 ( 79 usr; 1 prp; 0-3 aty)
% Number of functors : 82 ( 82 usr; 30 con; 0-4 aty)
% Number of variables : 52 ( 0 sgn; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_Complex_Ocomplex: $i ).
tff(decl_24,type,
v_p: $i ).
tff(decl_25,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_26,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
v_k____: $i ).
tff(decl_28,type,
tc_Nat_Onat: $i ).
tff(decl_29,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_30,type,
tc_RealDef_Oreal: $i ).
tff(decl_31,type,
v_t____: $i ).
tff(decl_32,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_33,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_35,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(decl_36,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_37,type,
v_w____: $i ).
tff(decl_38,type,
v_a____: $i ).
tff(decl_39,type,
v_s____: $i ).
tff(decl_40,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_42,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_43,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(decl_45,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_46,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_47,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_48,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_49,type,
v_pa____: $i ).
tff(decl_50,type,
class_Groups_Ozero: $i > $o ).
tff(decl_51,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_52,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_53,type,
class_Power_Opower: $i > $o ).
tff(decl_54,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_55,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_56,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_57,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_58,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_59,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_60,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_61,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_62,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_63,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_64,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_65,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_66,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_67,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_68,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_69,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_70,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_71,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_72,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_73,type,
class_Groups_Oone: $i > $o ).
tff(decl_74,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_75,type,
class_Rings_Oring: $i > $o ).
tff(decl_76,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_77,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_78,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_79,type,
v_m____: $i ).
tff(decl_80,type,
v_c____: $i ).
tff(decl_81,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_82,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_83,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_84,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_85,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_86,type,
class_Rings_Oidom: $i > $o ).
tff(decl_87,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_88,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_89,type,
hBOOL: $i > $o ).
tff(decl_90,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_91,type,
v_q____: $i ).
tff(decl_92,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_93,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_94,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_95,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_96,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_97,type,
class_RealVector_Oreal__div__algebra: $i > $o ).
tff(decl_98,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_99,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_100,type,
class_Fields_Ofield: $i > $o ).
tff(decl_101,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_102,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_103,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_105,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_106,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_107,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_108,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_109,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_110,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_111,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_112,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_114,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_116,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_117,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_119,type,
tc_Int_Oint: $i ).
tff(decl_120,type,
c_Complex_Oii: $i ).
tff(decl_121,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_123,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
class_Orderings_Oord: $i > $o ).
tff(decl_125,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_126,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_127,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_128,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_129,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_130,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_131,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_132,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_133,type,
class_Groups_Ominus: $i > $o ).
tff(decl_134,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_135,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_136,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_137,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_138,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_139,type,
class_Rings_Odvd: $i > $o ).
tff(decl_140,type,
c_Nat_OSuc: $i > $i ).
tff(decl_141,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_142,type,
tc_HOL_Obool: $i ).
tff(decl_143,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk2_1: $i > $i ).
tff(decl_145,type,
esk3_1: $i > $i ).
tff(decl_146,type,
esk4_0: $i ).
tff(decl_147,type,
esk5_1: $i > $i ).
tff(decl_148,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_149,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk8_1: $i > $i ).
tff(decl_151,type,
esk9_0: $i ).
tff(decl_152,type,
esk10_0: $i ).
tff(decl_153,type,
esk11_0: $i ).
tff(decl_154,type,
esk12_0: $i ).
tff(decl_155,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk15_0: $i ).
tff(decl_158,type,
esk16_0: $i ).
tff(decl_159,type,
esk17_0: $i ).
tff(decl_160,type,
esk18_0: $i ).
tff(decl_161,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk20_0: $i ).
tff(decl_163,type,
esk21_0: $i ).
tff(decl_164,type,
esk22_0: $i ).
tff(decl_165,type,
esk23_0: $i ).
tff(decl_166,type,
esk24_1: $i > $i ).
tff(decl_167,type,
esk25_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_168,type,
esk26_1: $i > $i ).
tff(decl_169,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_170,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_171,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_172,type,
esk30_1: $i > $i ).
tff(decl_173,type,
esk31_0: $i ).
tff(decl_174,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_175,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_176,type,
esk34_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk35_1: $i > $i ).
tff(decl_178,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_179,type,
esk37_3: ( $i * $i * $i ) > $i ).
tff(decl_180,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_181,type,
esk39_1: $i > $i ).
tff(decl_182,type,
esk40_2: ( $i * $i ) > $i ).
fof(conj_0,conjecture,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_wm1,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wm1) ).
fof(fact_i__mult__eq2,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_i__mult__eq2) ).
fof(fact_of__real__1,axiom,
! [X7] :
( class_RealVector_Oreal__algebra__1(X7)
=> c_RealVector_Oof__real(X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__1) ).
fof(fact_calculation,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).
fof(fact_of__real__diff,axiom,
! [X8,X5,X7] :
( class_RealVector_Oreal__algebra__1(X7)
=> c_RealVector_Oof__real(X7,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X8)) = c_Groups_Ominus__class_Ominus(X7,c_RealVector_Oof__real(X7,X5),c_RealVector_Oof__real(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__diff) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(fact_diff__0,axiom,
! [X6,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ominus__class_Ominus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_complex__of__real__power,axiom,
! [X4,X5] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X5)),X4) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__power) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X9,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X9),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X5,X7] :
( class_Rings_Ocomm__ring__1(X7)
=> c_Groups_Ouminus__class_Ouminus(X7,X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7))),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(fact_complex__diff__def,axiom,
! [X8,X5] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5,X8) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X5,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).
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(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(c_0_15,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_16,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_wm1]) ).
cnf(c_0_17,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_i__mult__eq2]) ).
fof(c_0_18,plain,
! [X110] :
( ~ class_RealVector_Oreal__algebra__1(X110)
| c_RealVector_Oof__real(X110,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__1])]) ).
cnf(c_0_19,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(split_conjunct,[status(thm)],[fact_calculation]) ).
cnf(c_0_21,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X101,X102,X103] :
( ~ class_RealVector_Oreal__algebra__1(X103)
| c_RealVector_Oof__real(X103,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X102,X101)) = c_Groups_Ominus__class_Ominus(X103,c_RealVector_Oof__real(X103,X102),c_RealVector_Oof__real(X103,X101)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__diff])]) ).
cnf(c_0_23,plain,
( c_RealVector_Oof__real(X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__algebra__1]) ).
fof(c_0_25,plain,
! [X329,X330] :
( ~ class_Groups_Ogroup__add(X330)
| c_Groups_Ominus__class_Ominus(X330,c_Groups_Ozero__class_Ozero(X330),X329) = c_Groups_Ouminus__class_Ouminus(X330,X329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
cnf(c_0_26,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(rw,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_27,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_30,plain,
! [X94,X95] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X95)),X94) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X95),X94)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__power]) ).
fof(c_0_31,plain,
! [X376,X377,X378] :
( ~ class_Rings_Ocomm__semiring__1(X378)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X376) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X376),X377) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(c_0_32,plain,
! [X591,X592] :
( ~ class_Rings_Ocomm__ring__1(X592)
| c_Groups_Ouminus__class_Ouminus(X592,X591) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X592),c_Groups_Ouminus__class_Ouminus(X592,c_Groups_Oone__class_Oone(X592))),X591) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
cnf(c_0_33,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
fof(c_0_35,plain,
! [X721,X722] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X722,X721) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X722,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X721)),
inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).
cnf(c_0_36,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24])]) ).
cnf(c_0_38,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),X2) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(c_0_41,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
cnf(c_0_43,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,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_35]) ).
cnf(c_0_45,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_46,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_39,c_0_40]) ).
cnf(c_0_47,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_17]),c_0_43]) ).
cnf(c_0_48,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),
inference(rw,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]) ).
cnf(c_0_50,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_46]),c_0_47]),c_0_48]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW260+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
% 0.13/0.34 % Computer : n001.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 19:51:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.53 start to proof: theBenchmark
% 2.23/2.37 % Version : CSE_E---1.5
% 2.23/2.37 % Problem : theBenchmark.p
% 2.23/2.37 % Proof found
% 2.23/2.37 % SZS status Theorem for theBenchmark.p
% 2.23/2.37 % SZS output start Proof
% See solution above
% 2.23/2.39 % Total time : 1.792000 s
% 2.23/2.39 % SZS output end Proof
% 2.23/2.39 % Total time : 1.833000 s
%------------------------------------------------------------------------------