%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG365-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:44 AM UTC 2026
% Result : Unsatisfiable 14.37s 4.68s
% Output : Refutation 15.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 474
% Syntax : Number of formulae : 949 ( 235 unt; 0 typ; 0 def)
% Number of atoms : 2289 ( 558 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 14098 (1292 ~;1340 |; 0 &;11466 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 84 usr; 11 con; 0-5 aty)
% Number of variables : 2472 ( 0 ^;2472 !; 0 ?;2472 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(c_SEQ_OLIMSEQ_decl,type,
c_SEQ_OLIMSEQ: $i > $i > $i > $o ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_Complex_OIm_decl,type,
c_Complex_OIm: $i ).
thf(v_s_decl,type,
v_s: $i ).
thf(v_f_____decl,type,
v_f____: $i ).
thf(v_ga_____decl,type,
v_ga____: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Odivision__ring_decl,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_decl,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(c_HOL_Oinverse__class_Oinverse_decl,type,
c_HOL_Oinverse__class_Oinverse: $i > $i ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_Series_Osummable_decl,type,
c_Series_Osummable: $i > $i > $o ).
thf(c_Series_Osums_decl,type,
c_Series_Osums: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(class_RealVector_Oreal__vector_decl,type,
class_RealVector_Oreal__vector: $i > $o ).
thf(c_RealVector_OscaleR__class_OscaleR_decl,type,
c_RealVector_OscaleR__class_OscaleR: $i > $i ).
thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_RealVector_Ometric__space_decl,type,
class_RealVector_Ometric__space: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(c_Lim_OLIM_decl,type,
c_Lim_OLIM: $i > $i > $i > $i > $i > $o ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__algebra__1_decl,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
thf(c_RealVector_Oof__real_decl,type,
c_RealVector_Oof__real: $i > $i ).
thf(c_Lim_OisUCont_decl,type,
c_Lim_OisUCont: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(c_Lim_OisCont_decl,type,
c_Lim_OisCont: $i > $i > $i > $i > $o ).
thf(c_RealVector_Obounded__linear_decl,type,
c_RealVector_Obounded__linear: $i > $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Series_Osuminf_decl,type,
c_Series_Osuminf: $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_RealVector_Oreal__algebra_decl,type,
class_RealVector_Oreal__algebra: $i > $o ).
thf(c_Suc_decl,type,
c_Suc: $i ).
thf(class_SEQ_Ocomplete__space_decl,type,
class_SEQ_Ocomplete__space: $i > $o ).
thf(c_SEQ_Oconvergent_decl,type,
c_SEQ_Oconvergent: $i > $i > $o ).
thf(c_SEQ_OCauchy_decl,type,
c_SEQ_OCauchy: $i > $i > $o ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_Finite__Set_Osetsum_decl,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_decl,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(c_Complex_Ocomplex_OComplex_decl,type,
c_Complex_Ocomplex_OComplex: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_HOL_Ozero_decl,type,
class_HOL_Ozero: $i > $o ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(c_Deriv_Odifferentiable_decl,type,
c_Deriv_Odifferentiable: $i > $i > $i > $o ).
thf(class_RealVector_Otopological__space_decl,type,
class_RealVector_Otopological__space: $i > $o ).
thf(c_Limits_Otendsto_decl,type,
c_Limits_Otendsto: $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Lattices_Oboolean__algebra_decl,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_decl,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(c_Limits_OZfun_decl,type,
c_Limits_OZfun: $i > $i > $i > $i > $o ).
thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(c_Complex_ORe_decl,type,
c_Complex_ORe: $i ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_RealVector_Onorm__class_Onorm_decl,type,
c_RealVector_Onorm__class_Onorm: $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_SEQ_OZseq_decl,type,
c_SEQ_OZseq: $i > $i > $o ).
thf(class_SEQ_Obanach_decl,type,
class_SEQ_Obanach: $i > $o ).
thf(c_SEQ_Olim_decl,type,
c_SEQ_Olim: $i > $i > $i ).
thf(c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1_decl,type,
c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1: $i > $i > $i > $i ).
thf(c_SEQ_Omonoseq_decl,type,
c_SEQ_Omonoseq: $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(v_sko__CHAINED__1_decl,type,
v_sko__CHAINED__1: $i > $i > $i > $i ).
thf(c_SEQ_Osubseq_decl,type,
c_SEQ_Osubseq: $i > $o ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) )
= ( A @ ( C @ c_Series_Osuminf ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_suminf__mult_0) ).
thf(1322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) )
= ( A @ ( C @ c_Series_Osuminf ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(202,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OZseq ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OZseq_0) ).
thf(1036,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OZseq ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(459,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1501,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__const_0) ).
thf(1369,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(277,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(1168,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OscaleR_0) ).
thf(893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(229,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( F @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( ( B @ ( F @ ( D @ c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 ) ) @ ( D @ hAPP ) )
= F )
| ~ ( B @ ( F @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( E @ ( tc_nat @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__SEQ__conv1_0) ).
thf(1083,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( F @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( ( B @ ( F @ ( D @ c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 ) ) @ ( D @ hAPP ) )
= F )
| ~ ( B @ ( F @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( E @ ( tc_nat @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( E @ ( D @ c_Series_Osums ) ) )
| ( B @ ( E @ ( C @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_Osums_0) ).
thf(1110,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( E @ ( D @ c_Series_Osums ) ) )
| ( B @ ( E @ ( C @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Series_Osums ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__mult_0) ).
thf(1024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Series_Osums ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( A @ c_Limits_Otendsto ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( D @ ( C @ ( c_Complex_OIm @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Otendsto_0) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( A @ c_Limits_Otendsto ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( D @ ( C @ ( c_Complex_OIm @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(241,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( F @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( D @ ( F @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_OLIM_0) ).
thf(1105,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( F @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( D @ ( F @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(199,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( F @ ( E @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( F @ ( D @ ( E @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_Otendsto_0) ).
thf(1031,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( F @ ( E @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( F @ ( D @ ( E @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OZfun__right_0) ).
thf(1200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__const__iff_1) ).
thf(1211,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(405,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OCauchy ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OCauchy_0) ).
thf(1406,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OCauchy ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__left_0) ).
thf(1522,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__LIMSEQ__zero_0) ).
thf(1443,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ ( C @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ( B = C )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__unique_0) ).
thf(1401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ ( C @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ( B = C )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(223,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
thf(1073,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(272,axiom,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Ozero_0) ).
thf(1158,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_OCauchy ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_SEQ_Ocomplete__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cauchy__convergent__iff_0) ).
thf(582,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_OCauchy ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_SEQ_Ocomplete__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).
thf(762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(449,axiom,
v_f____ @ c_SEQ_Osubseq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_f_I1_J_0) ).
thf(1486,plain,
v_f____ @ c_SEQ_Osubseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(456,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(1497,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__def_1) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).
thf(715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_SEQ_Obanach ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__norm__cancel_0) ).
thf(1327,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_SEQ_Obanach ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(218,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( tc_RealDef_Oreal @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_Osetsum_0) ).
thf(1063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( tc_RealDef_Oreal @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(275,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OZfun_0) ).
thf(1164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(114,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(797,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
thf(1354,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) )
!= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( ( A @ ( C @ c_Series_Osuminf ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Osuminf_0) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( ( A @ ( C @ c_Series_Osuminf ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(306,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1222,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(829,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_convergentI_0) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OisCont_0) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(256,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
thf(1127,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(397,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
thf(1391,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__norm_0) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(709,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(379,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( E @ ( D @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tendsto__inverse_0) ).
thf(1359,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( E @ ( D @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(394,axiom,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(1386,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(324,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1254,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_Ocont_0) ).
thf(565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Osetsum_0) ).
thf(1366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__minus_0) ).
thf(1287,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(587,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) )
!= ( D @ ( C @ c_Complex_Ocomplex_OComplex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex_Oinject_0) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) )
!= ( D @ ( C @ c_Complex_Ocomplex_OComplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(338,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OLIM__right__zero_0) ).
thf(1279,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__isCont__iff_1) ).
thf(1455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(169,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(949,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ hAPP ) @ ( B @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ ( D @ ( C @ c_Deriv_Odifferentiable ) ) )
| ( A @ ( D @ ( A @ ( A @ ( A @ ( C @ ( B @ c_COMBB ) ) ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_differentiable__compose_0) ).
thf(1055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ hAPP ) @ ( B @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ ( D @ ( C @ c_Deriv_Odifferentiable ) ) )
| ( A @ ( D @ ( A @ ( A @ ( A @ ( C @ ( B @ c_COMBB ) ) ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(407,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ hAPP ) @ ( A @ ( c_Complex_ORe @ c_Lim_OLIM ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ocont_0) ).
thf(1409,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ hAPP ) @ ( A @ ( c_Complex_ORe @ c_Lim_OLIM ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Obounded__linear__right_0) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(290,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_Lim_OisCont ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OisCont_0) ).
thf(1191,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_Lim_OisCont ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(437,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OZseq ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OZseq_0) ).
thf(1462,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OZseq ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(215,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(1059,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(559,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(638,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(390,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(1379,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_Series_Osummable ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_Osummable_0) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_Series_Osummable ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_RealDef_Oreal @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ ( D @ ( C @ ( D @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Osetsum_0) ).
thf(1147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_RealDef_Oreal @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ ( D @ ( C @ ( D @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(358,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
thf(1319,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zfun__minus_0) ).
thf(1398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(454,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
thf(1494,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( D @ ( C @ ( D @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( C @ ( B @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zfun__norm__iff_0) ).
thf(1362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( D @ ( C @ ( D @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( C @ ( B @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(237,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_RealVector_Obounded__linear ) ) )
| ~ ( B @ ( C @ ( B @ c_HOL_Ozero__class_Ozero @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( F @ ( C @ ( A @ ( B @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OLIM__zero_0) ).
thf(1100,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_RealVector_Obounded__linear ) ) )
| ~ ( B @ ( C @ ( B @ c_HOL_Ozero__class_Ozero @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( F @ ( C @ ( A @ ( B @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ ( B @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__ignore__initial__segment_0) ).
thf(1232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ ( B @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).
thf(969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(373,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(1347,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(475,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(430,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_OIm @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_0) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_OIm @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(412,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1418,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_OLIM__zero_0) ).
thf(1334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ~ ( A @ ( B @ ( E @ ( D @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__const__not__eq_0) ).
thf(514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ~ ( A @ ( B @ ( E @ ( D @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(340,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
thf(1283,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__zero_0) ).
thf(1051,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(451,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( F @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( F @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OLIM_0) ).
thf(1489,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( F @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( F @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(410,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1415,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Lim_OisUCont ) ) )
| ~ ( A @ ( D @ c_SEQ_OCauchy ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isUCont__Cauchy_0) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Lim_OisUCont ) ) )
| ~ ( A @ ( D @ c_SEQ_OCauchy ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(100,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(756,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OZseq ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__const__iff_0) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OZseq ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(244,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(1109,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__summable_0) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(261,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( F @ ( E @ ( C @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( D @ ( F @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Otendsto_0) ).
thf(1136,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( F @ ( E @ ( C @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( D @ ( F @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(388,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
thf(1377,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( A @ ( B @ ( B @ ( C @ ( B @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__minus_0) ).
thf(1447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( A @ ( B @ ( B @ ( C @ ( B @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(399,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OLIM__zero_0) ).
thf(1394,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(473,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__norm__zero_1) ).
thf(1526,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ c_Limits_OZfun ) ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( D @ ( C @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zfun__norm__iff_1) ).
thf(1345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ c_Limits_OZfun ) ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( D @ ( C @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(240,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
thf(1104,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(470,axiom,
tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_f____ @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conv1_0) ).
thf(1521,plain,
tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_f____ @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) )
= ( A @ ( B @ c_Series_Osuminf ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_suminf__minus_0) ).
thf(1169,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) )
= ( A @ ( B @ c_Series_Osuminf ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Oadd_0) ).
thf(687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(251,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_Lim_OisCont ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OisCont_0) ).
thf(1119,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_Lim_OisCont ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OscaleR_0) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(224,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(1074,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(298,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
thf(1206,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Obounded__linear__left_0) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(925,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(352,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OZfun__left_0) ).
thf(1306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__norm__zero_0) ).
thf(1338,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(355,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
thf(1311,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) )
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__minus_0) ).
thf(1067,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ( A @ ( B @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__norm__iff_0) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ( A @ ( B @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(208,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
thf(1047,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( D @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__ignore__initial__segment_0) ).
thf(1057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( D @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(274,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
thf(1163,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(334,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(1274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(395,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OLIM__zero_0) ).
thf(1387,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OZseq__right_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__inverse_0) ).
thf(1091,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(1021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Suc @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__Suc__iff_0) ).
thf(1519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Suc @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(325,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_0) ).
thf(1255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(598,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Series_Osums ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_ORe @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osums_0) ).
thf(1502,plain,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Series_Osums ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_ORe @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__norm__zero__iff_0) ).
thf(1487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
thf(630,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(788,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_convergent__minus__iff_0) ).
thf(1238,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(415,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(1423,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(283,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ ( E @ c_Lim_OisCont ) ) ) )
| ~ ( B @ ( C @ ( F @ ( E @ hAPP ) @ ( D @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( F @ ( A @ ( B @ ( C @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__o2_0) ).
thf(1178,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ ( E @ c_Lim_OisCont ) ) ) )
| ~ ( B @ ( C @ ( F @ ( E @ hAPP ) @ ( D @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( F @ ( A @ ( B @ ( C @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_SEQ_OCauchy ) )
| ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_OCauchy_0) ).
thf(1457,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_SEQ_OCauchy ) )
| ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
thf(493,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(227,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( ( tc_Complex_Ocomplex @ ( A @ c_Series_Osuminf ) @ ( c_Complex_OIm @ hAPP ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osuminf_0) ).
thf(1079,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( ( tc_Complex_Ocomplex @ ( A @ c_Series_Osuminf ) @ ( c_Complex_OIm @ hAPP ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(257,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
thf(1128,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(339,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( B @ ( D @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__offset__zero__cancel_0) ).
thf(1281,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( B @ ( D @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ ( D @ ( C @ ( B @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( c_Complex_ORe @ hAPP ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OLIM_0) ).
thf(1392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ ( D @ ( C @ ( B @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( c_Complex_ORe @ hAPP ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
thf(842,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OCauchy ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OCauchy_0) ).
thf(1350,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OCauchy ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(96,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(742,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Osummable_0) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).
thf(650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__isCont__iff_0) ).
thf(1227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(457,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(1498,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_Series_Osummable ) )
| ( ( tc_RealDef_Oreal @ ( B @ c_Series_Osuminf ) @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Osuminf_0) ).
thf(1096,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_Series_Osummable ) )
| ( ( tc_RealDef_Oreal @ ( B @ c_Series_Osuminf ) @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( ( D @ ( C @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ( B @ ( A @ ( D @ ( A @ ( B @ ( B @ ( C @ ( B @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__div__algebra )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__inverse_0) ).
thf(1138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( ( D @ ( C @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ( B @ ( A @ ( D @ ( A @ ( B @ ( B @ ( C @ ( B @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__div__algebra )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( B @ ( A @ ( C @ c_Lim_OisUCont ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OisUCont_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( B @ ( A @ ( C @ c_Lim_OisUCont ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(499,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(232,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( B @ ( E @ ( G @ ( F @ ( D @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( E @ ( G @ ( F @ ( C @ hAPP ) @ ( E @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_Otendsto_0) ).
thf(1089,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( B @ ( E @ ( G @ ( F @ ( D @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( E @ ( G @ ( F @ ( C @ hAPP ) @ ( E @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ ( D @ ( C @ ( B @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( c_Complex_OIm @ hAPP ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OLIM_0) ).
thf(1234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ ( D @ ( C @ ( B @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( c_Complex_OIm @ hAPP ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(264,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1143,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(387,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(1375,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(253,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
thf(1121,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( A @ ( B @ ( C @ c_COMBK ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__const_0) ).
thf(783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( A @ ( B @ ( C @ c_COMBK ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(250,axiom,
tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( c_Complex_ORe @ c_Lim_OisUCont ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OisUCont_0) ).
thf(1118,plain,
tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( c_Complex_ORe @ c_Lim_OisUCont ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(453,axiom,
v_ga____ @ c_SEQ_Osubseq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_g_I1_J_0) ).
thf(1493,plain,
v_ga____ @ c_SEQ_Osubseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(363,axiom,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_SEQ_OCauchy ) )
| ( tc_RealDef_Oreal @ ( A @ c_SEQ_Oconvergent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__Cauchy__convergent_0) ).
thf(1329,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ c_SEQ_OCauchy ) )
| ( tc_RealDef_Oreal @ ( A @ c_SEQ_Oconvergent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OZseq_0) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( c_Complex_ORe @ hAPP ) )
= ( tc_RealDef_Oreal @ ( C @ ( B @ ( C @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osetsum_0) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( c_Complex_ORe @ hAPP ) )
= ( tc_RealDef_Oreal @ ( C @ ( B @ ( C @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(436,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(1461,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(669,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( ( A @ ( B @ c_SEQ_Olim ) )
= C )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_limI_0) ).
thf(1424,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( ( A @ ( B @ c_SEQ_Olim ) )
= C )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(204,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1039,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Series_Osums ) ) )
| ( A @ ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Osums_0) ).
thf(1419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Series_Osums ) ) )
| ( A @ ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( D @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( D @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_OZfun_0) ).
thf(1028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( D @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( D @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(228,axiom,
tc_Complex_Ocomplex @ class_RealVector_Otopological__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Otopological__space) ).
thf(1082,plain,
tc_Complex_Ocomplex @ class_RealVector_Otopological__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(151,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ ( B @ ( D @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( C = D )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__unique_0) ).
thf(901,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ ( B @ ( D @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( C = D )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_convergent__minus__iff_1) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(476,plain,
! [A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(299,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
thf(1207,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Lim_OisCont ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OisCont_0) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Lim_OisCont ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(270,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( E @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ( B @ ( E @ ( C @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OLIMSEQ_0) ).
thf(1155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( E @ ( D @ c_SEQ_OLIMSEQ ) ) )
| ( B @ ( E @ ( C @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(27,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(547,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(248,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OCauchy ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OCauchy_0) ).
thf(1114,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OCauchy ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(236,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1099,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( c_Complex_OIm @ hAPP ) )
= ( tc_RealDef_Oreal @ ( C @ ( B @ ( C @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osetsum_0) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( c_Complex_OIm @ hAPP ) )
= ( tc_RealDef_Oreal @ ( C @ ( B @ ( C @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zfun__mult__right_0) ).
thf(1131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(291,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
thf(1192,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__offset_0) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(181,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(984,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(419,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( ( tc_Complex_Ocomplex @ ( A @ c_Series_Osuminf ) @ ( c_Complex_ORe @ hAPP ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osuminf_0) ).
thf(1429,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( ( tc_Complex_Ocomplex @ ( A @ c_Series_Osuminf ) @ ( c_Complex_ORe @ hAPP ) )
= ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__zero_0) ).
thf(1246,plain,
! [A: $i] :
( ( A @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(472,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(1525,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(647,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OZfun_0) ).
thf(1150,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ c_Limits_OZfun ) ) ) )
| ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__imp__Cauchy_0) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(329,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
thf(1266,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(311,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1231,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(365,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(1333,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(1434,plain,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(296,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OLIM__left__zero_0) ).
thf(1202,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(230,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(1086,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(317,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( E @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( D @ ( B @ ( A @ ( A @ ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__inverse_0) ).
thf(1241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( E @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( D @ ( B @ ( A @ ( A @ ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( B @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_convergent__Cauchy_0) ).
thf(633,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( B @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( B @ ( C @ ( A @ ( B @ c_COMBK ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Otopological__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tendsto__const_0) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( B @ ( C @ ( A @ ( B @ c_COMBK ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Otopological__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Series_Osums ) ) )
| ( B
= ( A @ ( C @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__unique_0) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Series_Osums ) ) )
| ( B
= ( A @ ( C @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(765,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( A @ ( B @ c_SEQ_Olim ) @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_convergent__LIMSEQ__iff_0) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( A @ ( B @ c_SEQ_Olim ) @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OZseq_0) ).
thf(1187,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(467,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
thf(1515,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(196,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( F @ ( E @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( F @ ( D @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Otendsto_0) ).
thf(1026,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( F @ ( E @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( F @ ( D @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__right_0) ).
thf(530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(287,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__mult__right__zero_0) ).
thf(1185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zfun__zero_0) ).
thf(888,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(337,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
thf(1278,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(465,axiom,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__0_0) ).
thf(1510,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_Oof__real @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(618,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(239,axiom,
tc_RealDef_Oreal @ class_SEQ_Ocomplete__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Ocomplete__space) ).
thf(1103,plain,
tc_RealDef_Oreal @ class_SEQ_Ocomplete__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Series_Osuminf ) @ ( B @ c_Series_Osums ) ) )
| ~ ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__iff_2) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Series_Osuminf ) @ ( B @ c_Series_Osums ) ) )
| ~ ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(447,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
thf(1483,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(333,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(1273,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(349,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(1301,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).
thf(573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(386,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ hAPP ) @ ( A @ ( c_Complex_OIm @ c_Lim_OLIM ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Ocont_0) ).
thf(1374,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ hAPP ) @ ( A @ ( c_Complex_OIm @ c_Lim_OLIM ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(93,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( ( A @ ( B @ c_Series_Osuminf ) )
= C )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__iff_1) ).
thf(601,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( ( A @ ( B @ c_Series_Osuminf ) )
= C )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(396,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_ORe @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OLIMSEQ_0) ).
thf(1389,plain,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_ORe @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( A @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_OLIM__zero_0) ).
thf(1125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( A @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
thf(958,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(584,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(269,axiom,
tc_Complex_Ocomplex @ class_HOL_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
thf(1154,plain,
tc_Complex_Ocomplex @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(152,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(904,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(975,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(384,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(1371,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(242,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(1107,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(672,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(418,axiom,
tc_Complex_Ocomplex @ class_SEQ_Ocomplete__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Ocomplete__space) ).
thf(1428,plain,
tc_Complex_Ocomplex @ class_SEQ_Ocomplete__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(704,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Deriv_Odifferentiable ) ) )
| ( ( C @ ( B @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_differentiable__inverse_0) ).
thf(1464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Deriv_Odifferentiable ) ) )
| ( ( C @ ( B @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_COMBB ) ) ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__iff_0) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( B @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Obounded__linear__right_0) ).
thf(831,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(406,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
thf(1408,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_ORe @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_0) ).
thf(990,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_ORe @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Complex_ORe @ hAPP ) )
!= ( B @ ( c_Complex_ORe @ hAPP ) ) )
| ( ( A @ ( c_Complex_OIm @ hAPP ) )
!= ( B @ ( c_Complex_OIm @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__equality_0) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Complex_ORe @ hAPP ) )
!= ( B @ ( c_Complex_ORe @ hAPP ) ) )
| ( ( A @ ( c_Complex_OIm @ hAPP ) )
!= ( B @ ( c_Complex_OIm @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(209,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(1048,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Oadd__right_0) ).
thf(736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( B @ ( D @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__offset__zero_0) ).
thf(1043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( B @ ( D @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( A @ ( B @ c_Series_Osuminf ) @ ( B @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__sums_0) ).
thf(616,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( A @ ( B @ c_Series_Osuminf ) @ ( B @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_1) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(281,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OLIMSEQ_0) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(1471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( ( E @ ( D @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OscaleR_0) ).
thf(535,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ( ( E @ ( D @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(121,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1325,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Lim_OisUCont ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isUCont__isCont_0) ).
thf(964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Lim_OisUCont ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(371,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(1344,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(246,axiom,
tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_f____ @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_f_I2_J_0) ).
thf(1112,plain,
tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_f____ @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(848,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_Lim_OisUCont ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OisUCont_0) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_Lim_OisUCont ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(282,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(1177,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(392,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Osetsum_0) ).
thf(1381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__minus_0) ).
thf(1474,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(883,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) )
= ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
thf(1015,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) )
= ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(247,axiom,
tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_g_I2_J_0) ).
thf(1113,plain,
tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(505,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(653,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(912,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(76,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(685,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Series_Osums ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Osums_0) ).
thf(1198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Series_Osums ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1396,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Osetsum_0) ).
thf(1213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
thf(768,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(219,axiom,
tc_RealDef_Oreal @ class_RealVector_Ometric__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
thf(1066,plain,
tc_RealDef_Oreal @ class_RealVector_Ometric__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_SEQ_OCauchy ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OCauchy_0) ).
thf(1445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_SEQ_OCauchy ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(474,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
thf(1528,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( B @ ( A @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__minus_0) ).
thf(1364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( B @ ( A @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( E @ ( D @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Otendsto_0) ).
thf(1250,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( E @ ( D @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(238,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(1102,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OLIMSEQ_0) ).
thf(1413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(201,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(1034,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(1304,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__mult__left__zero_0) ).
thf(1166,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(1208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(439,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(1467,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ocont_0) ).
thf(680,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(336,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
thf(1277,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1018,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(553,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(836,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_OLIMSEQ_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(675,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( B @ c_SEQ_OCauchy ) )
| ~ ( A @ class_SEQ_Ocomplete__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cauchy__convergent__iff_1) ).
thf(939,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( A @ ( B @ c_SEQ_OCauchy ) )
| ~ ( A @ class_SEQ_Ocomplete__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(369,axiom,
tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conv2_0) ).
thf(1340,plain,
tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_Oconvergent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(322,axiom,
tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( c_Complex_OIm @ c_Lim_OisUCont ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OisUCont_0) ).
thf(1252,plain,
tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( c_Complex_OIm @ c_Lim_OisUCont ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( E @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ( C = D )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__const__eq_0) ).
thf(739,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( E @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ( C = D )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_RealVector_Oof__real @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
thf(1267,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_RealVector_Oof__real @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zfun__mult__left_0) ).
thf(1484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_Lim_OisCont ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OisCont_0) ).
thf(690,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_Lim_OisCont ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(468,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
thf(1516,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( E @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(308,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( E @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( E @ ( D @ ( C @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tendsto__minus__cancel_0) ).
thf(1225,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( E @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( E @ ( D @ ( C @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(402,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(1400,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(420,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( B @ ( E @ ( F @ ( D @ c_Limits_OZfun ) ) ) )
| ( A @ ( E @ ( F @ ( E @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OZfun_0) ).
thf(1432,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( B @ ( E @ ( F @ ( D @ c_Limits_OZfun ) ) ) )
| ( A @ ( E @ ( F @ ( E @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(431,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(1452,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(203,axiom,
tc_RealDef_Oreal @ class_SEQ_Obanach,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
thf(1038,plain,
tc_RealDef_Oreal @ class_SEQ_Obanach,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OCauchy ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OCauchy_0) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OCauchy ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(37,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(576,plain,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__mult_0) ).
thf(1218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__minus_0) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Osummable_0) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(212,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( F @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( F @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OLIM_0) ).
thf(1053,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( F @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( F @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( C @ ( B @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__norm_0) ).
thf(1499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( C @ ( B @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(404,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_OZfun_0) ).
thf(1404,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(263,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( G @ ( D @ c_Lim_OisCont ) ) ) )
| ~ ( A @ ( C @ ( G @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( C @ ( G @ ( D @ hAPP ) @ ( F @ ( C @ ( B @ ( A @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__LIM__compose_0) ).
thf(1141,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( G @ ( D @ c_Lim_OisCont ) ) ) )
| ~ ( A @ ( C @ ( G @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( C @ ( G @ ( D @ hAPP ) @ ( F @ ( C @ ( B @ ( A @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(656,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( B = C )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__const__iff_0) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_nat @ ( A @ ( B @ c_COMBK ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( B = C )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(463,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(1506,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(417,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(1427,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(332,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1272,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(316,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
thf(1240,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(461,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(1504,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ ( c_Complex_OIm @ hAPP ) @ ( A @ ( c_Complex_ORe @ hAPP ) @ c_Complex_Ocomplex_OComplex ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__surj_0) ).
thf(1094,plain,
! [A: $i] :
( ( A @ ( c_Complex_OIm @ hAPP ) @ ( A @ ( c_Complex_ORe @ hAPP ) @ c_Complex_Ocomplex_OComplex ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__mult__right_0) ).
thf(1372,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(595,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(845,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__iff_0) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( C @ ( A @ c_Limits_OZfun ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( C @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OZfun_0) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( C @ ( A @ c_Limits_OZfun ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( C @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(284,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( F @ ( E @ ( C @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( D @ ( F @ ( E @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Otendsto_0) ).
thf(1180,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( F @ ( E @ ( C @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( D @ ( F @ ( E @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OscaleR_0) ).
thf(556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= C )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= C )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(271,axiom,
tc_Complex_Ocomplex @ class_RealVector_Ometric__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
thf(1157,plain,
tc_Complex_Ocomplex @ class_RealVector_Ometric__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_HOL_Ozero )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__not__zero_0) ).
thf(759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_HOL_Ozero )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Deriv_Odifferentiable ) ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_differentiable__minus_0) ).
thf(1216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Deriv_Odifferentiable ) ) )
| ( A @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_SEQ_OZseq ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OZseq_0) ).
thf(1189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_SEQ_OZseq ) )
| ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(771,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(243,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
thf(1108,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(343,axiom,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
thf(1289,plain,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( C @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Osums_0) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_Series_Osums ) ) )
| ( A @ ( C @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(335,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(1276,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(323,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
thf(1253,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_RealVector_Oof__real @ hAPP ) )
!= ( C @ ( A @ c_RealVector_Oof__real @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_RealVector_Oof__real @ hAPP ) )
!= ( C @ ( A @ c_RealVector_Oof__real @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(444,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Series_Osums ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_OIm @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osums_0) ).
thf(1476,plain,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Series_Osums ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_OIm @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(217,axiom,
tc_Complex_Ocomplex @ class_SEQ_Obanach,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
thf(1062,plain,
tc_Complex_Ocomplex @ class_SEQ_Obanach,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( C @ ( A @ c_Limits_OZfun ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( C @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OZfun_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( C @ ( A @ c_Limits_OZfun ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( C @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(185,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(995,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( ( A @ ( C @ c_Series_Osuminf ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Osuminf_0) ).
thf(1341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( ( A @ ( C @ c_Series_Osuminf ) @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) )
!= ( D @ ( C @ c_Complex_Ocomplex_OComplex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex_Oinject_1) ).
thf(896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) )
!= ( D @ ( C @ c_Complex_Ocomplex_OComplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__inverse__fun_0) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(424,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(1440,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(353,axiom,
tc_RealDef_Oreal @ class_HOL_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
thf(1308,plain,
tc_RealDef_Oreal @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Olim ) )
= ( A @ ( B @ c_SEQ_Olim ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lim__uminus_0) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_Oconvergent ) )
| ( ( A @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Olim ) )
= ( A @ ( B @ c_SEQ_Olim ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_OIm @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OLIMSEQ_0) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( c_Complex_OIm @ hAPP ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(466,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OLIM__zero_0) ).
thf(1513,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( B @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__minus__cancel_0) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_nat @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(207,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( E @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) @ ( D @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__norm_0) ).
thf(1045,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( E @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) @ ( D @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(198,axiom,
tc_nat @ class_HOL_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
thf(1030,plain,
tc_nat @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(452,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( E @ ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tendsto__minus_0) ).
thf(1491,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( A @ ( C @ ( E @ ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__def_0) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_Series_Osummable ) )
| ( ( A @ ( D @ c_Series_Osuminf ) @ ( C @ hAPP ) )
= ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_Osuminf_0) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( D @ c_Series_Osummable ) )
| ( ( A @ ( D @ c_Series_Osuminf ) @ ( C @ hAPP ) )
= ( B @ ( tc_nat @ ( B @ ( A @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( D @ ( B @ ( A @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__of__real_0) ).
thf(1161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( E @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( E @ ( A @ c_RealVector_Oof__real @ hAPP ) @ ( D @ ( B @ ( A @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_COMBK ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_differentiable__const_0) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_COMBK ) ) @ c_Deriv_Odifferentiable ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_SEQ_Olim ) @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_convergent__LIMSEQ__iff_1) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_SEQ_Olim ) @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(374,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( F @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( D @ ( F @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OLIM_0) ).
thf(1348,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( F @ ( E @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( A @ ( B @ ( D @ ( F @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( A @ ( B @ ( D @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(833,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(310,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OZfun_0) ).
thf(1229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( B @ c_Limits_OZfun ) ) ) )
| ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) ) @ c_Limits_OZfun ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(391,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
thf(1380,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__norm__zero_0) ).
thf(1248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ c_Lim_OLIM ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( D @ ( B @ ( tc_RealDef_Oreal @ ( A @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( E @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tendsto__norm_0) ).
thf(1436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Limits_Otendsto ) ) ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( E @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_Lim_OisUCont ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OisUCont_0) ).
thf(918,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_Lim_OisUCont ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_0) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(455,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Series_Osummable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osummable_0) ).
thf(1495,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_Series_Osummable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__add_0) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(68,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(200,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
thf(1033,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(635,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(279,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(1172,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(408,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Series_Osuminf ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_suminf__zero_0) ).
thf(1410,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Series_Osuminf ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Lim_OisUCont ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OisUCont_0) ).
thf(886,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_Lim_OisUCont ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(376,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( C @ ( G @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( C @ ( G @ ( D @ hAPP ) @ ( F @ ( C @ ( B @ ( A @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OLIM_0) ).
thf(1352,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_RealVector_Obounded__linear ) ) )
| ~ ( A @ ( C @ ( G @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( C @ ( G @ ( D @ hAPP ) @ ( F @ ( C @ ( B @ ( A @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__iff_1) ).
thf(1129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ ( C @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(327,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( G @ ( D @ hAPP ) @ ( G @ ( D @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ ( C @ ( G @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( C @ ( G @ ( D @ hAPP ) @ ( F @ ( C @ ( B @ ( A @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__compose_0) ).
thf(1261,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( G @ ( D @ hAPP ) @ ( G @ ( D @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ ( C @ ( G @ ( F @ ( E @ c_Lim_OLIM ) ) ) ) )
| ( B @ ( C @ ( G @ ( D @ hAPP ) @ ( F @ ( C @ ( B @ ( A @ ( E @ ( D @ c_COMBB ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( C @ class_RealVector_Ometric__space )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(268,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Series_Osummable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osummable_0) ).
thf(1152,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Series_Osummable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(860,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B = C )
| ( ( B @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) )
!= ( C @ ( A @ c_HOL_Oinverse__class_Oinverse @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_convergent__def_1) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( B @ c_SEQ_Oconvergent ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(389,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(1378,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIM__const_0) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ c_COMBK ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( B @ class_RealVector_Ometric__space )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_0) ).
thf(644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( A @ c_Limits_Otendsto ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( D @ ( C @ ( c_Complex_ORe @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Otendsto_0) ).
thf(1357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( A @ c_Limits_Otendsto ) ) ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( D @ ( C @ ( c_Complex_ORe @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Ocont_0) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_RealVector_OscaleR__class_OscaleR @ hAPP ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_OZseq ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__norm__iff_1) ).
thf(1299,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_SEQ_OZseq ) )
| ( tc_RealDef_Oreal @ ( tc_nat @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( A @ c_RealVector_Onorm__class_Onorm @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(462,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(1505,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(252,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
thf(1120,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(607,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(624,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(839,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__zero_0) ).
thf(1236,plain,
! [A: $i] :
( ( A @ ( tc_nat @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_OZseq_0) ).
thf(1331,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ c_SEQ_OZseq ) )
| ( A @ ( tc_nat @ ( A @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) )
| ~ ( A @ class_RealVector_Oreal__algebra__1 )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Osummable_0) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Series_Osummable ) )
| ( A @ ( tc_nat @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Series_Osummable ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OisCont_0) ).
thf(923,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(286,axiom,
tc_RealDef_Oreal @ class_RealVector_Otopological__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Otopological__space) ).
thf(1184,plain,
tc_RealDef_Oreal @ class_RealVector_Otopological__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ocont_0) ).
thf(659,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( A @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBC ) ) ) ) @ c_Lim_OLIM ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Suc @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__Suc_0) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( A @ ( C @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Suc @ ( B @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(429,axiom,
tc_RealDef_Oreal @ ( v_s @ ( v_ga____ @ ( v_f____ @ v_sko__CHAINED__1 ) ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1449,plain,
tc_RealDef_Oreal @ ( v_s @ ( v_ga____ @ ( v_f____ @ v_sko__CHAINED__1 ) ) @ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( v_ga____ @ ( v_f____ @ c_COMBB ) ) ) ) @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_OIm @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(43,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(592,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(440,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1468,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( A @ ( B @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__of__real_0) ).
thf(1069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( A @ ( D @ ( C @ c_Lim_OisCont ) ) ) )
| ( B @ ( A @ ( D @ ( A @ ( B @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_RealVector_Oof__real @ c_COMBB ) ) ) ) @ c_Lim_OisCont ) ) ) )
| ~ ( B @ class_RealVector_Oreal__normed__algebra__1 )
| ~ ( A @ class_RealVector_Ometric__space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(411,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(1417,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1531,plain,
$false,
inference(e,[status(thm)],[1322,1036,1501,1369,1168,893,1083,941,777,1110,1024,1469,479,1105,909,1031,1200,1211,1406,1522,1443,1401,1073,511,1158,582,762,730,1290,1173,1486,1497,533,550,715,1327,698,1063,1164,797,538,1354,1507,1222,829,1196,1001,1127,1391,1441,709,1359,1386,1254,565,1366,1287,570,785,587,751,802,1279,1455,949,724,1055,1409,934,1191,1462,1059,559,638,1379,1087,1147,1319,1398,1494,1362,1100,1232,969,1347,475,1450,1418,1334,514,966,1283,1051,1489,1415,1302,756,1040,1109,485,1136,981,1377,1447,866,1394,1526,998,1345,1104,1521,1169,687,877,692,1119,774,1074,1206,920,678,925,1306,810,1338,1311,1067,1438,661,1047,1057,1163,1274,1387,1223,1091,1021,952,1519,1255,598,1502,1487,630,788,1238,1423,1178,1457,522,493,1079,682,1128,1281,1392,842,1012,1350,742,1270,650,1227,1498,1096,1006,1138,869,610,499,857,1089,1234,874,1143,1375,1121,783,1118,1493,1329,1292,1182,1461,669,1424,1039,1419,1028,1082,901,1075,476,1207,590,1155,547,1114,1099,701,1297,1131,1192,1060,984,721,1429,1246,1525,647,1263,1150,1478,1266,1231,1333,1434,1202,1086,1241,633,805,508,541,765,1071,1187,1515,1026,530,1185,794,718,888,906,1278,1510,618,1103,824,1483,1273,745,1301,573,1374,733,601,819,1389,1125,826,579,958,584,1154,562,904,975,936,1371,1107,672,641,1428,1258,704,1464,947,604,831,1408,990,567,1144,1048,736,880,1043,616,1122,863,1175,890,1471,535,816,621,1325,964,915,1344,1112,848,520,1177,1381,1474,695,780,883,1015,1113,505,653,912,685,1198,1396,1213,768,1066,1445,1528,1364,1250,851,1102,1413,1034,1304,1166,1208,944,1467,680,1277,487,1018,553,836,1049,490,675,939,1340,525,1252,739,1267,1484,712,1003,690,1516,1225,1400,707,1432,1452,791,1038,502,1317,576,1218,1336,1220,544,1053,1499,1404,1141,656,613,1284,1506,1427,1272,1240,1504,727,1094,978,1372,595,845,1421,627,1459,1180,556,931,482,1157,759,1216,1189,771,1108,1289,1453,1276,1253,517,1476,1062,1244,995,961,813,1341,896,748,1440,1308,1193,1077,1513,1309,1045,1030,1491,667,1294,1161,800,1116,1133,1348,833,1229,1380,854,1248,1480,1436,918,1314,1495,807,664,1033,635,955,1172,1410,886,928,1352,1129,1261,1152,860,1384,1378,528,644,1357,992,822,1299,871,1505,1120,607,624,839,1236,987,1331,1320,1009,923,1184,659,1204,1449,592,1468,496,1069,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG365-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n020.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 21:56:04 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.87/1.35 % [INFO] Parsing done (358ms).
% 1.87/1.37 % [INFO] Running in sequential loop mode.
% 2.80/1.75 % [INFO] eprover registered as external prover.
% 2.80/1.77 % [INFO] Scanning for conjecture ...
% 3.25/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 475 axioms. Running axiom selection ...
% 3.78/2.15 % [INFO] Axiom selection finished. Selected 472 axioms (removed 3 axioms).
% 5.40/2.48 % [INFO] Problem is propositional (TPTP CNF).
% 5.82/2.51 % [INFO] Type checking passed.
% 5.82/2.52 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 14.37/4.67 % External prover 'e' found a proof!
% 14.37/4.67 % [INFO] Killing All external provers ...
% 14.37/4.67 % Time passed: 4125ms (effective reasoning time: 3301ms)
% 14.37/4.68 % Axioms used in derivation (472): cls_scaleR_Obounded__linear__right_0, clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add, cls_add__0__left_0, cls_add__Suc__shift_0, cls_add__cancel__end_1, cls_mult_Obounded__linear__left_0, cls_isCont__minus_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_mult__zero__right_0, cls_of__real_Osums_0, cls_mult__right_Osuminf_0, cls_comm__semiring__class_Odistrib_0, cls_bounded__linear_Otendsto_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_scaleR__cancel__left_0, cls_Zseq__const__iff_0, cls_sums__zero_0, cls_class__ringb_Oadd__r0__iff_1, cls_isCont__norm_0, clsarity_RealDef__Oreal__SEQ_Ocomplete__space, cls_scaleR_OZfun__right_0, cls_mult__right_Ozero_0, cls_Re_OZseq_0, cls_bounded__linear_OLIM_0, cls_Suc__inject_0, cls_COMBC__def_0, cls_scaleR__cancel__right_1, cls_sum__squares__eq__zero__iff_0, cls_Suc__n__not__n_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_square__eq__iff_1, cls_class__semiring_Osemiring__rules_I9_J_0, clsarity_RealDef__Oreal__RealVector_Oreal__vector, cls_scaleR_OLIM__right__zero_0, cls_setsum__0_0, cls_inverse__zero__imp__zero_0, cls_Re_OisUCont_0, cls_left__minus_0, clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1, cls_bounded__linear_Osuminf_0, cls_Re_Otendsto_0, cls_minus__zero_0, cls_scaleR_Oadd__right_0, cls_norm__zero_0, cls_bounded__linear_OLIMSEQ_0, cls_complex__surj_0, cls_inverse__eq__iff__eq_0, cls_LIMSEQ__inverse_0, cls_mult__right_OisUCont_0, cls_Zseq__norm__iff_0, cls_tendsto__minus__cancel_0, cls_Zseq__mult__right_0, cls_CHAINED_0, cls_COMBK__def_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_isCont__iff_1, cls_scaleR__right_OCauchy_0, cls_Im_OLIMSEQ_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_LIM__norm__zero_0, cls_Zseq__norm__iff_1, cls_minus__add__distrib_0, cls_Re_OZfun_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_add__imp__eq_0, cls_Re_OisCont_0, cls_LIM__not__zero_0, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, cls_mult__scaleR__right_0, cls_scaleR_OLIM__left__zero_0, cls_bounded__linear_OCauchy_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_class__semiring_Osemiring__rules_I10_J_0, cls_of__real__0_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, cls_LIM__const__not__eq_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring, cls_compl__eq__compl__iff_0, cls_Re_OLIMSEQ_0, cls_LIMSEQ__const_0, cls_class__ringb_Onoteq__reduce_0, cls_comm__monoid__add_Omult__1__right_0, cls_LIM__isCont__iff_0, cls_minus__minus_0, cls_comm__monoid__add_Omult__assoc_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_add__cancel__21_1, cls_add__left__cancel_0, cls_scaleR__eq__0__iff_0, cls_Zfun__zero_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, clsarity_Complex__Ocomplex__RealVector_Oreal__vector, clsarity_nat__HOL_Ozero, cls_mult__right_OscaleR_0, cls_convergent__def_1, cls_mult__left_Otendsto_0, cls_minus__unique_0, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0, cls_Re_OLIM_0, cls_Im_Osummable_0, cls_mult__eq__0__iff_0, cls_COMBB__def_0, cls_class__ringb_Oadd__mul__solve_1, cls_isCont__of__real_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, cls_tendsto__inverse_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_sums__unique_0, cls_class__semiring_Omul__0_0, cls_neg__equal__iff__equal_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring, cls_Im_0, cls_of__real_Otendsto_0, cls_mult__left_OLIM_0, cls_ab__left__minus_0, cls_isCont__const_0, cls_real__Cauchy__convergent_0, cls_LIM__unique_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_mult_Ozero__left_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_scaleR_Ominus__right_0, cls_summable__LIMSEQ__zero_0, cls_limI_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, cls_mult__left_OisUCont_0, cls_scaleR__right_Osuminf_0, cls_LIMSEQ__minus__cancel_0, cls_mult__right_Ocont_0, cls_double__eq__0__iff_1, clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, cls_mult_Ozero__right_0, cls_mult_OscaleR__right_0, cls_tendsto__const_0, cls_isCont__o2_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, cls_scaleR__cancel__right_0, cls_of__real_OLIM__zero_0, cls_mult_Oadd__left_0, cls_complex__equality_0, cls_inverse__minus__eq_0, cls_mult__left_Osetsum_0, cls_mult_Obounded__linear__right_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, cls_LIMSEQ__SEQ__conv1_0, cls_class__semiring_Omul__c_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_add__cancel__end_0, cls_convergent__minus__iff_0, cls_Zfun__minus_0, cls_Im_OisCont_0, cls_LIMSEQ__minus_0, cls_LIM__mult__right__zero_0, cls_differentiable__compose_0, cls_add__Suc_0, cls_minus__add__cancel_0, cls_inverse__nonzero__iff__nonzero_0, cls_of__real__eq__0__iff_0, cls_Im_OCauchy_0, cls_convergent__Cauchy_0, cls_mult__right_Oadd_0, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_LIMSEQ__const__iff_1, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero, cls_differentiable__inverse_0, cls_sums__summable_0, cls_sums__iff_2, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, clsarity_Complex__Ocomplex__SEQ_Obanach, cls_nat__add__left__commute_0, cls_mult__left_OZfun_0, cls_scaleR__right_Oadd_0, clsarity_Complex__Ocomplex__RealVector_Ometric__space, cls_Re_0, cls_LIM__isCont__iff_1, cls_scaleR__minus__right_0, cls_of__real_Osummable_0, cls_no__zero__divisors_0, cls_mult__right_OisCont_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_ATP__Linkup_OCOMBC__def_0, cls_isCont__inverse_0, cls_combine__common__factor_0, cls_scaleR__right_Osetsum_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_Im_OZseq_0, cls_scaleR__right_OisCont_0, cls_of__real_Ozero_0, cls_Zseq__zero_0, clsarity_Complex__Ocomplex__RealVector_Otopological__space, cls_class__semiring_Osemiring__rules_I15_J_0, cls_g_I2_J_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add, cls_bounded__linear_OZfun_0, cls_class__semiring_Oadd__a_0, cls_minus__mult__commute_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, cls_class__ringb_Onoteq__reduce_1, cls_of__real_Osuminf_0, cls_Re_Osummable_0, cls_complex_Oinject_1, cls_Re_OCauchy_0, cls_class__semiring_Osemiring__rules_I17_J_0, cls_mult__left_OscaleR_0, cls_comm__monoid__add_Omult__commute_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_summable__minus_0, cls_class__semiring_Osemiring__rules_I19_J_0, cls_add__right__cancel_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra, cls_LIM__const__eq_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add, cls_class__semiring_Osemiring__rules_I1_J_0, cls_mult__right_OLIMSEQ_0, cls_isCont__LIM__compose_0, cls_class__semiring_Oadd__0_0, cls_nat__add__assoc_0, clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1, cls_mult_Ominus__right_0, cls_differentiable__minus_0, cls_scaleR__right_OLIM_0, cls_summable__ignore__initial__segment_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, cls_class__ringb_Oadd__mul__solve_0, cls_ATP__Linkup_OCOMBB__def_0, cls_bounded__linear_Ocont_0, cls_Re_Ocont_0, cls_sum__squares__eq__zero__iff_1, cls_LIM__inverse__fun_0, cls_neg__equal__0__iff__equal_0, cls_LIM__offset__zero__cancel_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add, cls_LIM__mult__left__zero_0, cls_LIMSEQ__norm__zero_1, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_mult__right_OZfun_0, cls_class__semiring_Omul__d_0, cls_tendsto__norm_0, cls_conv1_0, cls_Im_Osetsum_0, cls_Im_Otendsto_0, cls_add__cancel__21_0, cls_nonzero__inverse__minus__eq_0, 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clsarity_RealDef__Oreal__RealVector_Oreal__algebra, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, clsarity_Complex__Ocomplex__HOL_Ozero, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_LIM__compose_0
% 14.37/4.68 % No. of inferences in proof: 949
% 14.37/4.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4125 ms resp. 3301 ms w/o parsing
% 15.33/5.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.96/5.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------