%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG361-1 : 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 : n016.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 06:46:43 AM UTC 2026
% Result : Unsatisfiable 13.37s 5.03s
% Output : Refutation 14.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 116
% Syntax : Number of formulae : 233 ( 89 unt; 0 typ; 0 def)
% Number of atoms : 485 ( 76 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2612 ( 240 ~; 252 |; 0 &;2120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 10 con; 0-5 aty)
% Number of variables : 470 ( 0 ^; 470 !; 0 ?; 470 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_Series_Osuminf_decl,type,
c_Series_Osuminf: $i > $i > $i ).
thf(c_Series_Osums_decl,type,
c_Series_Osums: $i > $i > $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_SEQ_Omonoseq_decl,type,
c_SEQ_Omonoseq: $i > $o ).
thf(c_Series_Osummable_decl,type,
c_Series_Osummable: $i > $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(c_Complex_Ocomplex_OComplex_decl,type,
c_Complex_Ocomplex_OComplex: $i > $i > $i ).
thf(c_SEQ_Osubseq_decl,type,
c_SEQ_Osubseq: $i > $o ).
thf(class_RealVector_Ometric__space_decl,type,
class_RealVector_Ometric__space: $i > $o ).
thf(c_SEQ_OLIMSEQ_decl,type,
c_SEQ_OLIMSEQ: $i > $i > $i > $o ).
thf(c_Limits_OZfun_decl,type,
c_Limits_OZfun: $i > $i > $i > $i > $o ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_Lim_OisCont_decl,type,
c_Lim_OisCont: $i > $i > $i > $i > $o ).
thf(c_Complex_OIm_decl,type,
c_Complex_OIm: $i ).
thf(c_SEQ_OCauchy_decl,type,
c_SEQ_OCauchy: $i > $i > $o ).
thf(c_Complex_ORe_decl,type,
c_Complex_ORe: $i ).
thf(c_Complex_Ocnj_decl,type,
c_Complex_Ocnj: $i ).
thf(v_z_decl,type,
v_z: $i ).
thf(c_Lim_OisUCont_decl,type,
c_Lim_OisUCont: $i > $i > $i > $o ).
thf(c_SEQ_Odecseq_decl,type,
c_SEQ_Odecseq: $i > $o ).
thf(c_SEQ_Oincseq_decl,type,
c_SEQ_Oincseq: $i > $o ).
thf(c_SEQ_OZseq_decl,type,
c_SEQ_OZseq: $i > $i > $o ).
thf(c_Limits_Otendsto_decl,type,
c_Limits_Otendsto: $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Osetsum_decl,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(v_sko__CHAINED__1_decl,type,
v_sko__CHAINED__1: $i > $i ).
thf(v_s_decl,type,
v_s: $i ).
thf(class_Ring__and__Field_Olordered__ring_decl,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
thf(class_Ring__and__Field_Oabs__if_decl,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(c_SEQ_Osko__SEQ__Xseq__monosub__1__1_decl,type,
c_SEQ_Osko__SEQ__Xseq__monosub__1__1: $i > $i ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(19,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(153,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)],[19]) ).
thf(5,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(125,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)],[5]) ).
thf(7,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(129,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,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(203,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)],[42]) ).
thf(112,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(333,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)],[112]) ).
thf(64,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(249,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)],[64]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( c_Complex_ORe @ hAPP ) )
= ( A @ ( c_Complex_ORe @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__cnj_0) ).
thf(217,plain,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( c_Complex_ORe @ hAPP ) )
= ( A @ ( c_Complex_ORe @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_0) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( A @ ( D @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( A @ c_Limits_Otendsto ) ) ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( c_Complex_Ocnj @ hAPP ) @ ( B @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Otendsto_0) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( A @ c_Limits_Otendsto ) ) ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( D @ ( C @ ( c_Complex_Ocnj @ hAPP ) @ ( B @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Limits_Otendsto ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OZseq ) )
| ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OZseq_0) ).
thf(301,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OZseq ) )
| ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_SEQ_OZseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( C @ ( A @ c_Limits_OZfun ) ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( C @ ( B @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OZfun_0) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( C @ ( A @ c_Limits_OZfun ) ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( C @ ( B @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Limits_OZfun ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(83,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(289,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(70,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(261,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)],[70]) ).
thf(25,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(164,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)],[25]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
thf(179,plain,
! [B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(104,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(321,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)],[104]) ).
thf(66,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(253,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)],[66]) ).
thf(16,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(147,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)],[16]) ).
thf(50,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(221,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)],[50]) ).
thf(87,axiom,
! [A: $i] :
( ~ ( A @ c_SEQ_Oincseq )
| ( A @ c_SEQ_Omonoseq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__imp__monoseq_0) ).
thf(293,plain,
! [A: $i] :
( ~ ( A @ c_SEQ_Oincseq )
| ( A @ c_SEQ_Omonoseq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ c_SEQ_Osubseq )
| ( tc_nat @ ( A @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__suble_0) ).
thf(132,plain,
! [B: $i,A: $i] :
( ~ ( B @ c_SEQ_Osubseq )
| ( tc_nat @ ( A @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(61,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(243,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)],[61]) ).
thf(98,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oabs__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
thf(312,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oabs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( c_Complex_ORe @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj__def_0) ).
thf(206,plain,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( c_Complex_ORe @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( A @ c_SEQ_Odecseq )
| ( A @ c_SEQ_Omonoseq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__imp__monoseq_0) ).
thf(307,plain,
! [A: $i] :
( ~ ( A @ c_SEQ_Odecseq )
| ( A @ c_SEQ_Omonoseq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(86,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Olordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
thf(292,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Olordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Oincseq )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__def_0) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Oincseq )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(117,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(41,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(201,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)],[41]) ).
thf(23,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(160,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)],[23]) ).
thf(89,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(297,plain,
tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( c_Complex_ORe @ c_Lim_OisUCont ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(36,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(192,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( c_Complex_OIm @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Ominus_0) ).
thf(275,plain,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( c_Complex_OIm @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(11,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(137,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)],[11]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ominus_0) ).
thf(197,plain,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(109,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(329,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_ORe @ c_Lim_OisCont ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__minus_0) ).
thf(324,plain,
! [A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(81,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(285,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)],[81]) ).
thf(102,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(317,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)],[102]) ).
thf(21,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(156,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)],[21]) ).
thf(34,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(188,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)],[34]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(169,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,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(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_OIm @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(108,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
thf(328,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(115,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(339,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)],[115]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oincseq )
| ( A @ c_SEQ_Odecseq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__eq__incseq_1) ).
thf(193,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oincseq )
| ( A @ c_SEQ_Odecseq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
thf(124,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( F @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ~ ( tc_nat @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_3) ).
thf(225,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( F @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ~ ( tc_nat @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(10,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(134,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)],[10]) ).
thf(58,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(237,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)],[58]) ).
thf(90,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(298,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(26,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(166,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(71,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( ( tc_Complex_Ocomplex @ ( A @ c_Series_Osuminf ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osuminf_0) ).
thf(264,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( ( tc_Complex_Ocomplex @ ( A @ c_Series_Osuminf ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Series_Osuminf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(78,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( E @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( D @ ( A @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_1) ).
thf(279,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( E @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( D @ ( A @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(17,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(149,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)],[17]) ).
thf(85,axiom,
v_s @ v_sko__CHAINED__1 @ c_SEQ_Osubseq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(291,plain,
v_s @ v_sko__CHAINED__1 @ c_SEQ_Osubseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(79,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(281,plain,
! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_OIm @ c_Lim_OisCont ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(69,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(259,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)],[69]) ).
thf(99,axiom,
! [A: $i] : ( A @ c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ c_SEQ_Osubseq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__monosub_0) ).
thf(313,plain,
! [A: $i] : ( A @ c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ c_SEQ_Osubseq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(113,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(335,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)],[113]) ).
thf(29,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(172,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)],[29]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Odecseq )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__def_0) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Odecseq )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( B @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Complex_Ocomplex_OComplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj_0) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( B @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Complex_Ocomplex_OComplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( A @ c_SEQ_Odecseq )
| ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oincseq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__eq__incseq_0) ).
thf(245,plain,
! [A: $i] :
( ~ ( A @ c_SEQ_Odecseq )
| ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_SEQ_Oincseq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(93,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(303,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)],[93]) ).
thf(74,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(271,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)],[74]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( c_Complex_OIm @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Im__cnj_0) ).
thf(208,plain,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( c_Complex_OIm @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(105,axiom,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(323,plain,
tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( c_Complex_Ocnj @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
thf(213,plain,
! [A: $i] :
( ( A @ ( c_Complex_Ocnj @ hAPP ) @ ( c_Complex_Ocnj @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( C @ ( B @ ( C @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osetsum_0) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Complex_Ocomplex @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( c_Complex_Ocnj @ hAPP ) )
= ( tc_Complex_Ocomplex @ ( C @ ( B @ ( C @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20,axiom,
tc_RealDef_Oreal @ class_RealVector_Ometric__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
thf(155,plain,
tc_RealDef_Oreal @ class_RealVector_Ometric__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(110,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(330,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(8,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(130,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)],[8]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_Ocnj @ hAPP ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OLIMSEQ_0) ).
thf(223,plain,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_Ocnj @ hAPP ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_SEQ_OLIMSEQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(91,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(299,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)],[91]) ).
thf(72,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(267,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)],[72]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( tc_nat @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_2) ).
thf(241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ c_SEQ_Omonoseq )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ~ ( tc_nat @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( c_Complex_ORe @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__minus__def_0) ).
thf(255,plain,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( c_Complex_ORe @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,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(295,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)],[88]) ).
thf(80,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(282,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)],[80]) ).
thf(97,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(310,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)],[97]) ).
thf(40,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(199,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)],[40]) ).
thf(111,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(331,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)],[111]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__minus_0) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(114,axiom,
! [A: $i] : ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_nat @ ( A @ c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ ( A @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__monosub_1) ).
thf(338,plain,
! [A: $i] : ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_nat @ ( A @ c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ ( A @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(182,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(100,axiom,
tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_s @ v_sko__CHAINED__1 @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
thf(314,plain,
tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( v_s @ v_sko__CHAINED__1 @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_RealDef_Oreal @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(103,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(319,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)],[103]) ).
thf(22,axiom,
( ( v_z @ ( c_Complex_Ocnj @ hAPP ) )
= ( v_z @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( v_z @ ( c_Complex_ORe @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj__def__raw_0) ).
thf(158,plain,
( ( v_z @ ( c_Complex_Ocnj @ hAPP ) )
= ( v_z @ ( c_Complex_OIm @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( v_z @ ( c_Complex_ORe @ hAPP ) @ c_Complex_Ocomplex_OComplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,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(139,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)],[12]) ).
thf(57,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(235,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)],[57]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Oincseq )
| ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__le_0) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Oincseq )
| ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(84,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(290,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(2,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(119,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)],[2]) ).
thf(18,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(151,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)],[18]) ).
thf(101,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(315,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)],[101]) ).
thf(35,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(190,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Complex_Ocomplex_OComplex ) @ ( c_Complex_ORe @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(33,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(183,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)],[33]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( c_Complex_ORe @ hAPP ) )
= ( A @ ( c_Complex_ORe @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ominus_0) ).
thf(273,plain,
! [A: $i] :
( ( A @ ( tc_Complex_Ocomplex @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( c_Complex_ORe @ hAPP ) )
= ( A @ ( c_Complex_ORe @ hAPP ) @ ( tc_RealDef_Oreal @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(94,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OCauchy ) )
| ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OCauchy_0) ).
thf(305,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_SEQ_OCauchy ) )
| ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_SEQ_OCauchy ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(45,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(210,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)],[45]) ).
thf(107,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(326,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)],[107]) ).
thf(59,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(239,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)],[59]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( A @ c_SEQ_Osubseq )
| ~ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( A @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(341,plain,
! [A: $i] :
( ~ ( A @ c_SEQ_Osubseq )
| ~ ( tc_nat @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( A @ ( v_s @ c_COMBB ) ) ) ) @ ( c_Complex_ORe @ c_COMBB ) ) ) ) @ c_SEQ_Omonoseq )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Series_Osums ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_Ocnj @ hAPP ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osums_0) ).
thf(195,plain,
! [B: $i,A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Series_Osums ) ) )
| ( tc_Complex_Ocomplex @ ( B @ ( c_Complex_Ocnj @ hAPP ) @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Series_Osums ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24,axiom,
tc_Complex_Ocomplex @ class_RealVector_Ometric__space,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
thf(163,plain,
tc_Complex_Ocomplex @ class_RealVector_Ometric__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_SEQ_Odecseq )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__le_0) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_SEQ_Odecseq )
| ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_SEQ_OLIMSEQ ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Complex_Ocnj @ hAPP ) )
!= ( B @ ( c_Complex_Ocnj @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Complex_Ocnj @ hAPP ) )
!= ( B @ ( c_Complex_Ocnj @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ~ ( tc_nat @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__def_0) ).
thf(122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_SEQ_Omonoseq )
| ~ ( tc_nat @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( E @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_RealDef_Oreal @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(96,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
thf(309,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(47,axiom,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Series_Osummable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osummable_0) ).
thf(215,plain,
! [A: $i] :
( ~ ( tc_Complex_Ocomplex @ ( A @ c_Series_Osummable ) )
| ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( c_Complex_Ocnj @ c_COMBB ) ) ) ) @ c_Series_Osummable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(55,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(232,plain,
tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( c_Complex_OIm @ c_Lim_OisUCont ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(343,plain,
$false,
inference(e,[status(thm)],[153,125,129,203,333,249,217,247,269,301,257,289,261,164,179,321,253,147,221,293,132,243,312,206,307,292,233,117,201,160,297,192,275,137,197,329,324,285,317,156,188,169,141,328,339,193,124,225,134,237,298,166,264,279,149,291,281,259,313,335,172,219,230,245,303,271,208,323,213,251,155,330,130,223,299,267,241,167,255,145,295,282,310,199,331,127,338,177,182,314,143,319,158,139,235,287,290,119,151,315,190,183,273,305,210,326,239,341,195,163,277,227,122,309,215,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG361-1 : 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
% 0.13/0.40 % Computer : n016.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 21:59:46 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 1.29/1.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.07/1.86 % [INFO] Parsing done (609ms).
% 3.07/1.88 % [INFO] Running in sequential loop mode.
% 4.54/2.49 % [INFO] eprover registered as external prover.
% 4.76/2.50 % [INFO] Scanning for conjecture ...
% 5.26/2.79 % [INFO] Found a conjecture (or negated_conjecture) and 594 axioms. Running axiom selection ...
% 6.67/3.11 % [INFO] Axiom selection finished. Selected 115 axioms (removed 479 axioms).
% 7.87/3.31 % [INFO] Problem is propositional (TPTP CNF).
% 7.87/3.33 % [INFO] Type checking passed.
% 7.87/3.34 % [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 ...
% 13.37/5.02 % External prover 'e' found a proof!
% 13.37/5.02 % [INFO] Killing All external provers ...
% 13.37/5.02 % Time passed: 4428ms (effective reasoning time: 3133ms)
% 13.37/5.03 % Axioms used in derivation (115): cls_incseq__def_0, cls_tendsto__minus_0, cls_sums__iff_1, cls_Im_OisUCont_0, clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if, cls_isCont__minus_0, cls_decseq__eq__incseq_1, cls_Re_OZseq_0, cls_eq__imp__le_0, cls_Re_OisUCont_0, cls_cnj_Osums_0, cls_Re_Otendsto_0, cls_monoseq__minus_0, cls_complex__surj_0, cls_incseq__le_0, cls_tendsto__minus__cancel_0, cls_CHAINED_0, cls_Im_OLIMSEQ_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_monoseq__le_1, cls_seq__suble_0, cls_Re_OisCont_0, cls_Re_OLIMSEQ_0, cls_cnj__def_0, cls_Re_OZfun_0, cls_real__le__trans_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_COMBB__def_0, cls_decseq__eq__incseq_0, cls_Im_Osummable_0, cls_complex__cnj__cancel__iff_0, cls_sums__unique_0, cls_Im_0, cls_le__antisym_0, cls_LIMSEQ__minus__cancel_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1, cls_real__le__linear_0, cls_isCont__o2_0, cls_complex__equality_0, cls_Zfun__minus_0, cls_Im_OisCont_0, cls_LIMSEQ__minus_0, cls_Im_OCauchy_0, cls_cnj_OZfun_0, cls_sums__summable_0, clsarity_Complex__Ocomplex__RealVector_Ometric__space, cls_Re_0, cls_sums__iff_2, cls_CHAINED_1, clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring, cls_Im_OZseq_0, cls_real__le__refl_0, cls_cnj_Otendsto_0, cls_summable__minus_0, cls_Re_Osummable_0, cls_complex_Oinject_1, cls_decseq__def_0, cls_complex__minus_0, cls_Re_OCauchy_0, cls_monoseq__le_2, cls_decseq__imp__monoseq_0, cls_cnj_Osummable_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, cls_Im_OZfun_0, cls_Im_Osetsum_0, cls_Im_Otendsto_0, cls_Re_Osums_0, cls_LIMSEQ__imp__Cauchy_0, cls_seq__monosub_1, clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, cls_Im_Ominus_0, cls_le__trans_0, cls_complex__minus__def_0, cls_monoseq__le_3, cls_complex_Oinject_0, cls_Re_Osuminf_0, cls_Im_Osuminf_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, cls_suminf__minus_0, cls_LIMSEQ__unique_0, cls_cnj__def__raw_0, cls_complex__cnj_0, cls_real__le__antisym_0, cls_Re_Osetsum_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_nat__le__linear_0, cls_decseq__le_0, cls_Im_Osums_0, cls_incseq__imp__monoseq_0, cls_cnj_Ominus_0, cls_Re_Ominus_0, cls_isUCont__isCont_0, cls_cnj_Osuminf_0, cls_complex__cnj__cnj_0, cls_sums__iff_0, cls_sums__minus_0, cls_monoseq__le_0, cls_summable__sums_0, cls_cnj_OCauchy_0, cls_complex__Im__cnj_0, cls_setsum__negf_0, cls_cnj_OLIMSEQ_0, cls_that_0, cls_cnj_Osetsum_0, cls_image__image_0, cls_Zseq__minus_0, clsarity_RealDef__Oreal__RealVector_Ometric__space, cls_cnj_OZseq_0, cls_seq__monosub_0, cls_monoseq__def_0, cls_complex__Re__cnj_0, cls_le__refl_0, cls_isUCont__Cauchy_0
% 13.37/5.03 % No. of inferences in proof: 233
% 13.37/5.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4428 ms resp. 3133 ms w/o parsing
% 14.40/5.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.40/5.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------