TSTP Solution File: ALG361-1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG361-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:14:59 EDT 2024
% Result : Unsatisfiable 8.35s 3.57s
% Output : Refutation 8.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 156
% Syntax : Number of formulae : 273 ( 89 unt; 40 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 : 65 ( 65 >; 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_____type,type,
v_thesis____: $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_Series_Osuminf_type,type,
c_Series_Osuminf: $i > $i > $i ).
thf(c_Series_Osums_type,type,
c_Series_Osums: $i > $i > $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_SEQ_Omonoseq_type,type,
c_SEQ_Omonoseq: $i > $o ).
thf(c_Series_Osummable_type,type,
c_Series_Osummable: $i > $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(c_Complex_Ocomplex_OComplex_type,type,
c_Complex_Ocomplex_OComplex: $i > $i > $i ).
thf(c_SEQ_Osubseq_type,type,
c_SEQ_Osubseq: $i > $o ).
thf(class_RealVector_Ometric__space_type,type,
class_RealVector_Ometric__space: $i > $o ).
thf(c_SEQ_OLIMSEQ_type,type,
c_SEQ_OLIMSEQ: $i > $i > $i > $o ).
thf(c_Limits_OZfun_type,type,
c_Limits_OZfun: $i > $i > $i > $i > $o ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_Lim_OisCont_type,type,
c_Lim_OisCont: $i > $i > $i > $i > $o ).
thf(c_Complex_OIm_type,type,
c_Complex_OIm: $i ).
thf(c_SEQ_OCauchy_type,type,
c_SEQ_OCauchy: $i > $i > $o ).
thf(c_Complex_ORe_type,type,
c_Complex_ORe: $i ).
thf(c_Complex_Ocnj_type,type,
c_Complex_Ocnj: $i ).
thf(v_z_type,type,
v_z: $i ).
thf(c_Lim_OisUCont_type,type,
c_Lim_OisUCont: $i > $i > $i > $o ).
thf(c_SEQ_Odecseq_type,type,
c_SEQ_Odecseq: $i > $o ).
thf(c_SEQ_Oincseq_type,type,
c_SEQ_Oincseq: $i > $o ).
thf(c_SEQ_OZseq_type,type,
c_SEQ_OZseq: $i > $i > $o ).
thf(c_Limits_Otendsto_type,type,
c_Limits_Otendsto: $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(v_sko__CHAINED__1_type,type,
v_sko__CHAINED__1: $i > $i ).
thf(v_s_type,type,
v_s: $i ).
thf(class_Ring__and__Field_Olordered__ring_type,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add__abs_type,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
thf(class_Ring__and__Field_Oabs__if_type,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(c_SEQ_Osko__SEQ__Xseq__monosub__1__1_type,type,
c_SEQ_Osko__SEQ__Xseq__monosub__1__1: $i > $i ).
thf(class_Ring__and__Field_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osummable @ B @ A )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__summable_0) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osummable @ B @ A )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A )
| ~ ( c_Series_Osummable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__sums_0) ).
thf(125,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A )
| ~ ( c_Series_Osummable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(129,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_SEQ_Oincseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__def_0) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_SEQ_Oincseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(113,axiom,
! [A: $i] :
( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ A @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osuminf_0) ).
thf(333,plain,
! [A: $i] :
( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ A @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ C ) @ B @ C @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osetsum_0) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ C ) @ B @ C @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_SEQ_Odecseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__def_0) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_SEQ_Odecseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ ( hAPP @ c_Complex_ORe @ C ) @ D @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ A @ C @ D @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Otendsto_0) ).
thf(308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ ( hAPP @ c_Complex_ORe @ C ) @ D @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ A @ C @ D @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(64,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(247,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(74,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ D ) @ E @ C @ A )
| ~ ( c_Limits_Otendsto @ B @ D @ E @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tendsto__minus_0) ).
thf(269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ D ) @ E @ C @ A )
| ~ ( c_Limits_Otendsto @ B @ D @ E @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(84,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(288,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(93,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(301,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ ( hAPP @ c_Complex_OIm @ C ) @ D @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ A @ C @ D @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Otendsto_0) ).
thf(257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ ( hAPP @ c_Complex_OIm @ C ) @ D @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ A @ C @ D @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= ( c_Complex_Ocomplex_OComplex @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj_0) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= ( c_Complex_Ocomplex_OComplex @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(85,axiom,
c_SEQ_Osubseq @ ( v_sko__CHAINED__1 @ v_s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(289,plain,
c_SEQ_Osubseq @ ( v_sko__CHAINED__1 @ v_s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(25,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Ometric__space @ B )
| ~ ( class_RealVector_Ometric__space @ C )
| ( c_Lim_OisCont @ ( c_COMBB @ D @ E @ C @ B @ A ) @ F @ A @ B )
| ~ ( c_Lim_OisCont @ D @ ( hAPP @ E @ F ) @ C @ B )
| ~ ( c_Lim_OisCont @ E @ F @ A @ C ) ),
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] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Ometric__space @ B )
| ~ ( class_RealVector_Ometric__space @ C )
| ( c_Lim_OisCont @ ( c_COMBB @ D @ E @ C @ B @ A ) @ F @ A @ B )
| ~ ( c_Lim_OisCont @ D @ ( hAPP @ E @ F ) @ C @ B )
| ~ ( c_Lim_OisCont @ E @ F @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(105,axiom,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(321,plain,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(46,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( hAPP @ c_Complex_Ocnj @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
thf(211,plain,
! [A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( hAPP @ c_Complex_Ocnj @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(67,axiom,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__minus__def_0) ).
thf(253,plain,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osummable @ B @ A )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__iff_0) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osummable @ B @ A )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) )
| ~ ( c_Series_Osummable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_suminf__minus_0) ).
thf(280,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) )
| ~ ( c_Series_Osummable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ c_Complex_Ocnj @ B ) @ tc_Complex_Ocomplex )
| ~ ( c_SEQ_OLIMSEQ @ A @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OLIMSEQ_0) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ c_Complex_Ocnj @ B ) @ tc_Complex_Ocomplex )
| ~ ( c_SEQ_OLIMSEQ @ A @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(88,axiom,
! [A: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OCauchy_0) ).
thf(293,plain,
! [A: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ A ) @ tc_nat )
| ~ ( c_SEQ_Osubseq @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__suble_0) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ A ) @ tc_nat )
| ~ ( c_SEQ_Osubseq @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(62,axiom,
! [A: $i] :
( ( c_SEQ_Oincseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal @ tc_RealDef_Oreal @ tc_nat ) )
| ~ ( c_SEQ_Odecseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__eq__incseq_0) ).
thf(243,plain,
! [A: $i] :
( ( c_SEQ_Oincseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal @ tc_RealDef_Oreal @ tc_nat ) )
| ~ ( c_SEQ_Odecseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ B ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ A @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osums_0) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ B ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ A @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(100,axiom,
c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ ( v_sko__CHAINED__1 @ v_s ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
thf(312,plain,
c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ ( v_sko__CHAINED__1 @ v_s ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(44,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ c_Complex_Ocnj @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Im__cnj_0) ).
thf(206,plain,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ c_Complex_Ocnj @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(96,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
thf(307,plain,
class_OrderedGroup_Olordered__ab__group__add__abs @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__minus_0) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
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(42,axiom,
! [A: $i] :
( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ A @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osuminf_0) ).
thf(201,plain,
! [A: $i] :
( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ A @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_Series_Osuminf @ B @ A )
= C )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__iff_1) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( c_Series_Osuminf @ B @ A )
= C )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ C ) @ B @ C @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osetsum_0) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ C ) @ B @ C @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Odecseq @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__le_0) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Odecseq @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
| ~ ( c_Limits_OZfun @ B @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zfun__minus_0) ).
thf(137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
| ~ ( c_Limits_OZfun @ B @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ A )
| ~ ( c_SEQ_OZseq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__minus_0) ).
thf(197,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ A )
| ~ ( c_SEQ_OZseq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ A @ C @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OZfun_0) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ A @ C @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(107,axiom,
! [A: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osummable_0) ).
thf(324,plain,
! [A: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ C @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Oincseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__le_0) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ C @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Oincseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ B ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ A @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osums_0) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ B ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ A @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(21,axiom,
! [A: $i] :
( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ A ) @ ( hAPP @ c_Complex_OIm @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__surj_0) ).
thf(156,plain,
! [A: $i] :
( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ A ) @ ( hAPP @ c_Complex_OIm @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_0) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_0) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(328,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(116,axiom,
! [A: $i] :
( v_thesis____
| ~ ( c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ A @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) )
| ~ ( c_SEQ_Osubseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(339,plain,
! [A: $i] :
( v_thesis____
| ~ ( c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ A @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) )
| ~ ( c_SEQ_Osubseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ c_Complex_Ocnj @ B ) @ tc_Complex_Ocomplex )
| ~ ( c_Series_Osums @ A @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osums_0) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ c_Complex_Ocnj @ B ) @ tc_Complex_Ocomplex )
| ~ ( c_Series_Osums @ A @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
thf(124,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Complex_Ocnj @ A )
!= ( hAPP @ c_Complex_Ocnj @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Complex_Ocnj @ A )
!= ( hAPP @ c_Complex_Ocnj @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ( B = C )
| ~ ( c_SEQ_OLIMSEQ @ D @ C @ A )
| ~ ( c_SEQ_OLIMSEQ @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__unique_0) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ( B = C )
| ~ ( c_SEQ_OLIMSEQ @ D @ C @ A )
| ~ ( c_SEQ_OLIMSEQ @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Ometric__space @ B )
| ( c_SEQ_OCauchy @ ( c_COMBB @ C @ D @ A @ B @ tc_nat ) @ B )
| ~ ( c_SEQ_OCauchy @ D @ A )
| ~ ( c_Lim_OisUCont @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isUCont__Cauchy_0) ).
thf(237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Ometric__space @ B )
| ( c_SEQ_OCauchy @ ( c_COMBB @ C @ D @ A @ B @ tc_nat ) @ B )
| ~ ( c_SEQ_OCauchy @ D @ A )
| ~ ( c_Lim_OisUCont @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(99,axiom,
! [A: $i] : ( c_SEQ_Osubseq @ ( c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__monosub_0) ).
thf(311,plain,
! [A: $i] : ( c_SEQ_Osubseq @ ( c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(26,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(166,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(79,axiom,
! [A: $i] : ( c_Lim_OisCont @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OisCont_0) ).
thf(279,plain,
! [A: $i] : ( c_Lim_OisCont @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(90,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(296,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ A )
| ~ ( c_Series_Osummable @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__minus_0) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ A )
| ~ ( c_Series_Osummable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ( c_lessequals @ B @ A @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ( c_lessequals @ B @ A @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(37,axiom,
! [A: $i] :
( ( c_SEQ_Odecseq @ A )
| ~ ( c_SEQ_Oincseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal @ tc_RealDef_Oreal @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__eq__incseq_1) ).
thf(191,plain,
! [A: $i] :
( ( c_SEQ_Odecseq @ A )
| ~ ( c_SEQ_Oincseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal @ tc_RealDef_Oreal @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(87,axiom,
! [A: $i] :
( ( c_SEQ_Omonoseq @ A )
| ~ ( c_SEQ_Oincseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__imp__monoseq_0) ).
thf(291,plain,
! [A: $i] :
( ( c_SEQ_Omonoseq @ A )
| ~ ( c_SEQ_Oincseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(43,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_Ocnj @ A )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj__def_0) ).
thf(204,plain,
! [A: $i] :
( ( hAPP @ c_Complex_Ocnj @ A )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ B ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OLIMSEQ_0) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ B ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(32,axiom,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(181,plain,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ A @ B )
!= ( c_Complex_Ocomplex_OComplex @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex_Oinject_0) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ A @ B )
!= ( c_Complex_Ocomplex_OComplex @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(50,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Limits_Otendsto @ B @ C @ D @ E @ A )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ E ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ D @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tendsto__minus__cancel_0) ).
thf(219,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Limits_Otendsto @ B @ C @ D @ E @ A )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ E ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(55,axiom,
c_Lim_OisUCont @ c_Complex_OIm @ tc_Complex_Ocomplex @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OisUCont_0) ).
thf(230,plain,
c_Lim_OisUCont @ c_Complex_OIm @ tc_Complex_Ocomplex @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ tc_RealDef_Oreal )
| ( c_lessequals @ ( hAPP @ B @ D ) @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_0) ).
thf(245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ tc_RealDef_Oreal )
| ( c_lessequals @ ( hAPP @ B @ D ) @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(94,axiom,
! [A: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex )
| ~ ( c_SEQ_OCauchy @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OCauchy_0) ).
thf(303,plain,
! [A: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex )
| ~ ( c_SEQ_OCauchy @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(75,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ominus_0) ).
thf(271,plain,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Complex_OIm @ A )
!= ( hAPP @ c_Complex_OIm @ B ) )
| ( ( hAPP @ c_Complex_ORe @ A )
!= ( hAPP @ c_Complex_ORe @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__equality_0) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Complex_OIm @ A )
!= ( hAPP @ c_Complex_OIm @ B ) )
| ( ( hAPP @ c_Complex_ORe @ A )
!= ( hAPP @ c_Complex_ORe @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,axiom,
! [A: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osummable_0) ).
thf(213,plain,
! [A: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ A @ C @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OZfun_0) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ B ) @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ A @ C @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(20,axiom,
class_RealVector_Ometric__space @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
thf(155,plain,
class_RealVector_Ometric__space @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ~ ( c_Series_Osummable @ B @ A )
| ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__iff_2) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ~ ( c_Series_Osummable @ B @ A )
| ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(52,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ( c_lessequals @ ( hAPP @ A @ D ) @ ( hAPP @ A @ E ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ D @ E @ tc_nat )
| ~ ( c_SEQ_OLIMSEQ @ A @ F @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_3) ).
thf(223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ( c_lessequals @ ( hAPP @ A @ D ) @ ( hAPP @ A @ E ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ D @ E @ tc_nat )
| ~ ( c_SEQ_OLIMSEQ @ A @ F @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(92,axiom,
! [A: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex )
| ~ ( c_SEQ_OZseq @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OZseq_0) ).
thf(299,plain,
! [A: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex )
| ~ ( c_SEQ_OZseq @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ B ) @ ( hAPP @ c_Complex_Ocnj @ C ) @ D @ B @ tc_Complex_Ocomplex )
| ~ ( c_Limits_Otendsto @ A @ C @ D @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Otendsto_0) ).
thf(267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ B ) @ ( hAPP @ c_Complex_Ocnj @ C ) @ D @ B @ tc_Complex_Ocomplex )
| ~ ( c_Limits_Otendsto @ A @ C @ D @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__minus_0) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_Series_Osums @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ B ) @ C @ B @ tc_Complex_Ocomplex )
| ~ ( c_Limits_OZfun @ A @ C @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OZfun_0) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ B ) @ C @ B @ tc_Complex_Ocomplex )
| ~ ( c_Limits_OZfun @ A @ C @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(89,axiom,
c_Lim_OisUCont @ c_Complex_ORe @ tc_Complex_Ocomplex @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OisUCont_0) ).
thf(295,plain,
c_Lim_OisUCont @ c_Complex_ORe @ tc_Complex_Ocomplex @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(109,axiom,
! [A: $i] : ( c_Lim_OisCont @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OisCont_0) ).
thf(327,plain,
! [A: $i] : ( c_Lim_OisCont @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(98,axiom,
class_Ring__and__Field_Oabs__if @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
thf(310,plain,
class_Ring__and__Field_Oabs__if @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ B ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OLIMSEQ_0) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ B ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ A @ B )
!= ( c_Complex_Ocomplex_OComplex @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex_Oinject_1) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ A @ B )
!= ( c_Complex_Ocomplex_OComplex @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(112,axiom,
! [A: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OCauchy_0) ).
thf(331,plain,
! [A: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__minus_0) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ A @ B ) )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(114,axiom,
! [A: $i] : ( c_SEQ_Omonoseq @ ( c_COMBB @ A @ ( c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ A ) @ tc_nat @ tc_RealDef_Oreal @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__monosub_1) ).
thf(336,plain,
! [A: $i] : ( c_SEQ_Omonoseq @ ( c_COMBB @ A @ ( c_SEQ_Osko__SEQ__Xseq__monosub__1__1 @ A ) @ tc_nat @ tc_RealDef_Oreal @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(104,axiom,
! [A: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OZseq_0) ).
thf(319,plain,
! [A: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(22,axiom,
( ( hAPP @ c_Complex_Ocnj @ v_z )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ v_z ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ v_z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj__def__raw_0) ).
thf(158,plain,
( ( hAPP @ c_Complex_Ocnj @ v_z )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ v_z ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ v_z ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Ometric__space @ B )
| ( c_Lim_OisCont @ C @ D @ A @ B )
| ~ ( c_Lim_OisUCont @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isUCont__isCont_0) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Ometric__space @ B )
| ( c_Lim_OisCont @ C @ D @ A @ B )
| ~ ( c_Lim_OisUCont @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Oreal__normed__vector @ B )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ B ) @ C @ B @ B @ A ) @ D @ A @ B )
| ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isCont__minus_0) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ~ ( class_RealVector_Oreal__normed__vector @ B )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ B ) @ C @ B @ B @ A ) @ D @ A @ B )
| ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ C ) @ B @ C @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osetsum_0) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ C ) @ B @ C @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(83,axiom,
class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(287,plain,
class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(86,axiom,
class_Ring__and__Field_Olordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
thf(290,plain,
class_Ring__and__Field_Olordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( B
= ( c_Series_Osuminf @ C @ A ) )
| ~ ( c_Series_Osums @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__unique_0) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( B
= ( c_Series_Osuminf @ C @ A ) )
| ~ ( c_Series_Osums @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ( c_SEQ_OCauchy @ B @ A )
| ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__imp__Cauchy_0) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Ometric__space @ A )
| ( c_SEQ_OCauchy @ B @ A )
| ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(102,axiom,
! [A: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osummable_0) ).
thf(315,plain,
! [A: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(71,axiom,
! [A: $i] :
( ( ( hAPP @ c_Complex_Ocnj @ ( c_Series_Osuminf @ A @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex ) )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osuminf_0) ).
thf(262,plain,
! [A: $i] :
( ( ( hAPP @ c_Complex_Ocnj @ ( c_Series_Osuminf @ A @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_Ocnj @ A @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex ) )
| ~ ( c_Series_Osummable @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(36,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(190,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(76,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Ominus_0) ).
thf(273,plain,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(95,axiom,
! [A: $i] :
( ( c_SEQ_Omonoseq @ A )
| ~ ( c_SEQ_Odecseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__imp__monoseq_0) ).
thf(305,plain,
! [A: $i] :
( ( c_SEQ_Omonoseq @ A )
| ~ ( c_SEQ_Odecseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
thf(326,plain,
class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ tc_RealDef_Oreal )
| ( c_lessequals @ ( hAPP @ B @ D ) @ ( hAPP @ B @ E ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ D @ E @ tc_nat )
| ~ ( c_SEQ_OLIMSEQ @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_2) ).
thf(239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ tc_RealDef_Oreal )
| ( c_lessequals @ ( hAPP @ B @ D ) @ ( hAPP @ B @ E ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ D @ E @ tc_nat )
| ~ ( c_SEQ_OLIMSEQ @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(39,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ ( hAPP @ c_Complex_Ocnj @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ominus_0) ).
thf(195,plain,
! [A: $i] :
( ( hAPP @ c_Complex_Ocnj @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ A ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ tc_Complex_Ocomplex ) @ ( hAPP @ c_Complex_Ocnj @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_SEQ_OLIMSEQ @ B @ C @ A )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__minus__cancel_0) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_SEQ_OLIMSEQ @ B @ C @ A )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(24,axiom,
class_RealVector_Ometric__space @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
thf(163,plain,
class_RealVector_Ometric__space @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(78,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ( c_lessequals @ ( hAPP @ A @ D ) @ E @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ E @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__le_1) ).
thf(277,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ( c_lessequals @ ( hAPP @ A @ D ) @ E @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ A @ E @ tc_RealDef_Oreal )
| ~ ( c_SEQ_Omonoseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(106,axiom,
! [A: $i] :
( ( c_SEQ_Omonoseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal @ tc_RealDef_Oreal @ tc_nat ) )
| ~ ( c_SEQ_Omonoseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__minus_0) ).
thf(322,plain,
! [A: $i] :
( ( c_SEQ_Omonoseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal @ tc_RealDef_Oreal @ tc_nat ) )
| ~ ( c_SEQ_Omonoseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(48,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ c_Complex_Ocnj @ A ) )
= ( hAPP @ c_Complex_ORe @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__cnj_0) ).
thf(215,plain,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ c_Complex_Ocnj @ A ) )
= ( hAPP @ c_Complex_ORe @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(115,axiom,
! [A: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ A @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OZseq_0) ).
thf(337,plain,
! [A: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ A @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ A @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ( c_lessequals @ ( hAPP @ A @ D ) @ ( hAPP @ A @ E ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ D @ E @ tc_nat )
| ~ ( c_SEQ_Omonoseq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__def_0) ).
thf(122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ( c_lessequals @ ( hAPP @ A @ D ) @ ( hAPP @ A @ E ) @ tc_RealDef_Oreal )
| ~ ( c_lessequals @ D @ E @ tc_nat )
| ~ ( c_SEQ_Omonoseq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(341,plain,
$false,
inference(e,[status(thm)],[153,125,129,231,333,249,217,308,247,269,288,301,257,228,289,164,321,211,253,147,280,221,293,132,243,265,312,206,307,233,117,201,160,297,275,137,197,329,324,285,317,156,188,169,141,328,339,193,124,225,134,237,311,166,279,296,149,176,191,291,204,259,313,181,172,219,230,245,303,271,208,213,251,155,130,223,299,267,241,167,255,145,295,327,310,199,182,331,127,336,143,319,158,186,139,235,287,290,119,151,315,262,190,273,305,326,239,195,283,163,178,277,322,215,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : ALG361-1 : TPTP v8.2.0. Released v4.1.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat May 18 23:40:53 EDT 2024
% 0.11/0.33 % CPUTime :
% 1.10/1.08 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.42 % [INFO] Parsing done (337ms).
% 1.96/1.43 % [INFO] Running in sequential loop mode.
% 3.09/1.85 % [INFO] eprover registered as external prover.
% 3.09/1.85 % [INFO] cvc4 registered as external prover.
% 3.09/1.86 % [INFO] Scanning for conjecture ...
% 3.46/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 594 axioms. Running axiom selection ...
% 4.38/2.23 % [INFO] Axiom selection finished. Selected 115 axioms (removed 479 axioms).
% 4.70/2.34 % [INFO] Problem is propositional (TPTP CNF).
% 4.70/2.36 % [INFO] Type checking passed.
% 4.70/2.36 % [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 ...
% 8.35/3.56 % External prover 'e' found a proof!
% 8.35/3.56 % [INFO] Killing All external provers ...
% 8.35/3.56 % Time passed: 3066ms (effective reasoning time: 2123ms)
% 8.35/3.57 % 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
% 8.35/3.57 % No. of inferences in proof: 233
% 8.35/3.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3066 ms resp. 2123 ms w/o parsing
% 8.79/3.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.79/3.68 % [INFO] Killing All external provers ...
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