%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP085^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 : Wed Feb 25 08:55:25 AM UTC 2026
% Result : Theorem 6.21s 2.11s
% Output : Refutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 15 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 102 ( 5 ~; 0 |; 0 &; 97 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 125 ( 122 usr; 10 con; 0-3 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_li185139947ession: $tType ).
thf(type_def_6,type,
secrecy_Expression: $tType ).
thf(type_def_8,type,
set_list_Secrecy_KS: $tType ).
thf(type_def_9,type,
secrecy_KS: $tType ).
thf(type_def_10,type,
set_li849033543y_Keys: $tType ).
thf(type_def_11,type,
secrecy_Keys: $tType ).
thf(type_def_12,type,
set_li2007071804ecrets: $tType ).
thf(type_def_13,type,
secrecy_Secrets: $tType ).
thf(type_def_14,type,
list_S529945141ession: $tType ).
thf(type_def_15,type,
set_Se1942955227ession: $tType ).
thf(type_def_16,type,
list_Secrecy_KS: $tType ).
thf(type_def_17,type,
set_Secrecy_KS: $tType ).
thf(type_def_18,type,
list_Secrecy_Keys: $tType ).
thf(type_def_19,type,
set_Secrecy_Keys: $tType ).
thf(type_def_20,type,
list_Secrecy_Secrets: $tType ).
thf(type_def_21,type,
set_Secrecy_Secrets: $tType ).
thf(type_def_22,type,
secrecy_specID: $tType ).
thf(type_def_23,type,
list_l425507653ession: $tType ).
thf(type_def_24,type,
list_list_Secrecy_KS: $tType ).
thf(func_def_0,type,
list_l425507653ession: $tType ).
thf(func_def_1,type,
set_li185139947ession: $tType ).
thf(func_def_2,type,
set_li2007071804ecrets: $tType ).
thf(func_def_3,type,
set_li849033543y_Keys: $tType ).
thf(func_def_4,type,
list_list_Secrecy_KS: $tType ).
thf(func_def_5,type,
set_list_Secrecy_KS: $tType ).
thf(func_def_6,type,
list_S529945141ession: $tType ).
thf(func_def_7,type,
set_Se1942955227ession: $tType ).
thf(func_def_8,type,
list_Secrecy_Secrets: $tType ).
thf(func_def_9,type,
set_Secrecy_Secrets: $tType ).
thf(func_def_10,type,
list_Secrecy_Keys: $tType ).
thf(func_def_11,type,
set_Secrecy_Keys: $tType ).
thf(func_def_12,type,
list_Secrecy_KS: $tType ).
thf(func_def_13,type,
set_Secrecy_KS: $tType ).
thf(func_def_14,type,
secrecy_Expression: $tType ).
thf(func_def_15,type,
secrecy_Secrets: $tType ).
thf(func_def_16,type,
secrecy_specID: $tType ).
thf(func_def_17,type,
secrecy_Keys: $tType ).
thf(func_def_18,type,
secrecy_KS: $tType ).
thf(func_def_19,type,
bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession ).
thf(func_def_20,type,
bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS ).
thf(func_def_21,type,
bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys ).
thf(func_def_22,type,
bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets ).
thf(func_def_23,type,
bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession ).
thf(func_def_24,type,
bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_25,type,
bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_26,type,
bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_27,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_28,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(func_def_29,type,
knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_30,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(func_def_31,type,
knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_32,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_33,type,
mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).
thf(func_def_34,type,
append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession ).
thf(func_def_35,type,
append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_36,type,
append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_37,type,
append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_38,type,
append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
thf(func_def_39,type,
append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
thf(func_def_40,type,
bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).
thf(func_def_41,type,
bind_S1823644515ecy_KS: list_S529945141ession > ( secrecy_Expression > list_Secrecy_KS ) > list_Secrecy_KS ).
thf(func_def_42,type,
bind_S711229283ession: list_Secrecy_KS > ( secrecy_KS > list_S529945141ession ) > list_S529945141ession ).
thf(func_def_43,type,
bind_S645462771ecy_KS: list_Secrecy_KS > ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS ).
thf(func_def_44,type,
butlas171474643ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_45,type,
butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_46,type,
concat388015140ession: list_l425507653ession > list_S529945141ession ).
thf(func_def_47,type,
concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_48,type,
distin1076152135ession: list_S529945141ession > $o ).
thf(func_def_49,type,
distin1495927511ecy_KS: list_Secrecy_KS > $o ).
thf(func_def_50,type,
foldr_1531709715ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_l425507653ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_51,type,
foldr_1711005747ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_52,type,
insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
thf(func_def_53,type,
insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_54,type,
last_S1532390982ession: list_S529945141ession > secrecy_Expression ).
thf(func_def_55,type,
last_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
thf(func_def_56,type,
cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession ).
thf(func_def_57,type,
cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_58,type,
cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
thf(func_def_59,type,
cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_60,type,
cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
thf(func_def_61,type,
cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
thf(func_def_62,type,
nil_li311616943ession: list_l425507653ession ).
thf(func_def_63,type,
nil_list_Secrecy_KS: list_list_Secrecy_KS ).
thf(func_def_64,type,
nil_Se901661471ession: list_S529945141ession ).
thf(func_def_65,type,
nil_Secrecy_KS: list_Secrecy_KS ).
thf(func_def_66,type,
nil_Secrecy_Keys: list_Secrecy_Keys ).
thf(func_def_67,type,
nil_Secrecy_Secrets: list_Secrecy_Secrets ).
thf(func_def_68,type,
hd_lis1623417098ession: list_l425507653ession > list_S529945141ession ).
thf(func_def_69,type,
hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_70,type,
hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).
thf(func_def_71,type,
hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
thf(func_def_72,type,
tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_73,type,
tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_74,type,
list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).
thf(func_def_75,type,
list_ex1_Secrecy_KS: ( secrecy_KS > $o ) > list_Secrecy_KS > $o ).
thf(func_def_76,type,
listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
thf(func_def_77,type,
listre565996059ecy_KS: ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession > list_Secrecy_KS > $o ).
thf(func_def_78,type,
listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).
thf(func_def_79,type,
listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
thf(func_def_80,type,
map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_81,type,
map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).
thf(func_def_82,type,
maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
thf(func_def_83,type,
maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).
thf(func_def_84,type,
maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).
thf(func_def_85,type,
maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_86,type,
member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
thf(func_def_87,type,
member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).
thf(func_def_88,type,
lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
thf(func_def_89,type,
lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
thf(func_def_90,type,
produc1450295286ession: list_l425507653ession > list_l425507653ession ).
thf(func_def_91,type,
produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_92,type,
remdup484344169ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_93,type,
remdup351570169ecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_94,type,
rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_95,type,
rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_96,type,
rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_97,type,
rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_98,type,
shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).
thf(func_def_99,type,
shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).
thf(func_def_100,type,
splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_101,type,
splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_102,type,
subseq348280080ession: list_S529945141ession > list_l425507653ession ).
thf(func_def_103,type,
subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_104,type,
succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
thf(func_def_105,type,
succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).
thf(func_def_106,type,
decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_107,type,
enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_108,type,
encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
thf(func_def_109,type,
ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_110,type,
sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_111,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_112,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_113,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_114,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_115,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_116,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_117,type,
secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).
thf(func_def_118,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_119,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_120,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_121,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_122,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_123,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_124,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_125,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_126,type,
member249235532ession: list_S529945141ession > set_li185139947ession > $o ).
thf(func_def_127,type,
member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).
thf(func_def_128,type,
member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).
thf(func_def_129,type,
member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).
thf(func_def_130,type,
member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).
thf(func_def_131,type,
member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
thf(func_def_132,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(func_def_133,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(func_def_134,type,
a: secrecy_specID ).
thf(func_def_135,type,
m: secrecy_Secrets ).
thf(func_def_154,type,
sK0: secrecy_KS > secrecy_Secrets ).
thf(func_def_155,type,
sK1: secrecy_KS > secrecy_Keys ).
thf(func_def_156,type,
sK2: ( secrecy_KS > $o ) > secrecy_Keys ).
thf(func_def_157,type,
sK3: ( secrecy_KS > $o ) > secrecy_Secrets ).
thf(func_def_159,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f1096,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1094,f1061]) ).
thf(f1061,plain,
( ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1047]) ).
thf(f1047,plain,
( ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) )
!= $true ),
inference(flattening,[status(thm)],[f760]) ).
thf(f760,plain,
( ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f759]) ).
thf(f759,plain,
~ ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,negated_conjecture,
~ ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f353,conjecture,
knowle945212990e_know @ a @ ( secrecy_sKS @ m ),
file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',conj_0) ).
thf(f1094,plain,
( ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) )
= $true ),
inference(superposition,[status(thm)],[f1074,f1064]) ).
thf(f1064,plain,
( ( knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f559]) ).
thf(f559,plain,
( ( knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ) )
= $true ),
inference(fool_elimination,[status(thm)],[f558]) ).
thf(f558,plain,
knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',fact_0_assms) ).
thf(f1074,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) )
= ( knowle731562421_knows @ X1 @ ( cons_S112077679ession @ ( secrecy_sE @ X0 ) @ nil_Se901661471ession ) ) ),
inference(forward_demodulation,[status(thm)],[f1063,f1071]) ).
thf(f1071,plain,
! [X0: secrecy_Secrets] :
( ( secrecy_sE @ X0 )
= ( secrec1016742679ession @ ( secrecy_sKS @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f1017]) ).
thf(f1017,plain,
! [X0: secrecy_Secrets] :
( ( secrecy_sE @ X0 )
= ( secrec1016742679ession @ ( secrecy_sKS @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f1016]) ).
thf(f1016,plain,
! [X0: secrecy_Secrets] :
( ( secrecy_sE @ X0 )
= ( secrec1016742679ession @ ( secrecy_sKS @ X0 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X3: secrecy_Secrets] :
( ( secrecy_sE @ X3 )
= ( secrec1016742679ession @ ( secrecy_sKS @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',fact_7_KS2Expression_Osimps_I2_J) ).
thf(f1063,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) )
= ( knowle731562421_knows @ X1 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ X0 ) ) @ nil_Se901661471ession ) ) ),
inference(cnf_transformation,[status(thm)],[f1019]) ).
thf(f1019,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) )
= ( knowle731562421_knows @ X1 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ X0 ) ) @ nil_Se901661471ession ) ) ),
inference(fool_elimination,[status(thm)],[f1018]) ).
thf(f1018,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) )
= ( knowle731562421_knows @ X1 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ X0 ) ) @ nil_Se901661471ession ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: secrecy_Secrets,X4: secrecy_specID] :
( ( knowle731562421_knows @ X4 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ X5 ) ) @ nil_Se901661471ession ) )
= ( knowle945212990e_know @ X4 @ ( secrecy_sKS @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',fact_3_know1s) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP085^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:41 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : ITP085^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.46 % Domain : Interactive Theorem Proving
% 0.28/0.46 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_155__3292644_1
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Des21]
% 0.28/0.46 % Names : KnowledgeKeysSecrets/prob_155__3292644_1 [Des21]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.28/0.46 % Syntax : Number of formulae : 489 ( 193 unt; 136 typ; 0 def)
% 0.28/0.46 % Number of atoms : 953 ( 694 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.28/0.46 % Number of connectives : 3297 ( 212 ~; 62 |; 128 &;2470 @)
% 0.28/0.46 % ( 0 <=>; 425 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 21 ( 6 avg)
% 0.28/0.46 % Number of types : 20 ( 19 usr)
% 0.28/0.46 % Number of type conns : 445 ( 445 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 118 ( 117 usr; 8 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 1081 ( 27 ^; 973 !; 81 ?;1081 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:57.162
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % Could-be-implicit typings (19)
% 0.28/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 0.28/0.46 list_l425507653ession: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 0.28/0.46 set_li185139947ession: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OSecrets_J_J,type,
% 0.28/0.46 set_li2007071804ecrets: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKeys_J_J,type,
% 0.28/0.46 set_li849033543y_Keys: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 0.28/0.46 list_list_Secrecy_KS: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 0.28/0.46 set_list_Secrecy_KS: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 list_S529945141ession: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 set_Se1942955227ession: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 0.28/0.46 list_Secrecy_Secrets: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.28/0.46 set_Secrecy_Secrets: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 0.28/0.46 list_Secrecy_Keys: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.28/0.46 set_Secrecy_Keys: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 list_Secrecy_KS: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 set_Secrecy_KS: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.28/0.46 secrecy_Expression: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.28/0.46 secrecy_Secrets: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.28/0.46 secrecy_specID: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.28/0.46 secrecy_Keys: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.28/0.46 secrecy_KS: $tType ).
% 0.28/0.46
% 0.28/0.46 % Explicit typings (117)
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKS,type,
% 0.28/0.46 bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKeys,type,
% 0.28/0.46 bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OSecrets,type,
% 0.28/0.46 bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKS,type,
% 0.28/0.46 bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKeys,type,
% 0.28/0.46 bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OSecrets,type,
% 0.28/0.46 bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.28/0.46 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.28/0.46 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowsECorrect,type,
% 0.28/0.46 knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.28/0.46 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknows,type,
% 0.28/0.46 knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OKS,type,
% 0.28/0.46 mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oappend_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oappend_001t__Secrecy____types__OKS,type,
% 0.28/0.46 append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oappend_001t__Secrecy____types__OKeys,type,
% 0.28/0.46 append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oappend_001t__Secrecy____types__OSecrets,type,
% 0.28/0.46 append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 0.28/0.46 bind_S1823644515ecy_KS: list_S529945141ession > ( secrecy_Expression > list_Secrecy_KS ) > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 bind_S711229283ession: list_Secrecy_KS > ( secrecy_KS > list_S529945141ession ) > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.28/0.46 bind_S645462771ecy_KS: list_Secrecy_KS > ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obutlast_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 butlas171474643ession: list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obutlast_001t__Secrecy____types__OKS,type,
% 0.28/0.46 butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oconcat_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 concat388015140ession: list_l425507653ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oconcat_001t__Secrecy____types__OKS,type,
% 0.28/0.46 concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 distin1076152135ession: list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OKS,type,
% 0.28/0.46 distin1495927511ecy_KS: list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OExpression_J_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 foldr_1531709715ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_l425507653ession > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OKS_J_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 foldr_1711005747ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oinsert_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oinsert_001t__Secrecy____types__OKS,type,
% 0.28/0.46 insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olast_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 last_S1532390982ession: list_S529945141ession > secrecy_Expression ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olast_001t__Secrecy____types__OKS,type,
% 0.28/0.46 last_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKS,type,
% 0.28/0.46 cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKeys,type,
% 0.28/0.46 cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OSecrets,type,
% 0.28/0.46 cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 nil_li311616943ession: list_l425507653ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 nil_list_Secrecy_KS: list_list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 nil_Se901661471ession: list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKS,type,
% 0.28/0.46 nil_Secrecy_KS: list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKeys,type,
% 0.28/0.46 nil_Secrecy_Keys: list_Secrecy_Keys ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OSecrets,type,
% 0.28/0.46 nil_Secrecy_Secrets: list_Secrecy_Secrets ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 hd_lis1623417098ession: list_l425507653ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OKS,type,
% 0.28/0.46 hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OKS,type,
% 0.28/0.46 tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OKS,type,
% 0.28/0.46 list_ex1_Secrecy_KS: ( secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 0.28/0.46 listre565996059ecy_KS: ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession > list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.28/0.46 listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 0.28/0.46 maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.28/0.46 maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omember_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omember_001t__Secrecy____types__OKS,type,
% 0.28/0.46 member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OKS,type,
% 0.28/0.46 lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 produc1450295286ession: list_l425507653ession > list_l425507653ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OKS,type,
% 0.28/0.46 produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oremdups__adj_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 remdup484344169ession: list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oremdups__adj_001t__Secrecy____types__OKS,type,
% 0.28/0.46 remdup351570169ecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Orev_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Orev_001t__Secrecy____types__OKS,type,
% 0.28/0.46 rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Orotate1_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Orotate1_001t__Secrecy____types__OKS,type,
% 0.28/0.46 rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OKS,type,
% 0.28/0.46 shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Osplice_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Osplice_001t__Secrecy____types__OKS,type,
% 0.28/0.46 splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 subseq348280080ession: list_S529945141ession > list_l425507653ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OKS,type,
% 0.28/0.46 subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OKS,type,
% 0.28/0.46 succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_ODecr,type,
% 0.28/0.46 decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OEnc,type,
% 0.28/0.46 enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 0.28/0.46 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OExt,type,
% 0.28/0.46 ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OSign,type,
% 0.28/0.46 sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_Oeout,type,
% 0.28/0.46 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.28/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.28/0.46 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.28/0.46 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.28/0.46 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.28/0.46 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 0.28/0.46 secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.28/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.28/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.28/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.28/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.28/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.28/0.46 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.28/0.46 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.28/0.46 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.46 member249235532ession: list_S529945141ession > set_li185139947ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.28/0.46 member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 0.28/0.46 member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 0.28/0.46 member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__Secrecy____types__OExpression,type,
% 0.28/0.46 member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.28/0.46 member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.28/0.46 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.28/0.46 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_A,type,
% 0.28/0.46 a: secrecy_specID ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_m,type,
% 0.28/0.46 m: secrecy_Secrets ).
% 0.28/0.46
% 0.28/0.46 % Relevant facts (352)
% 0.28/0.46 thf(fact_0_assms,axiom,
% 0.28/0.46 knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % assms
% 0.28/0.46 thf(fact_1_KS_Oinject_I2_J,axiom,
% 0.28/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.28/0.46 ( ( ( secrecy_sKS @ X2 )
% 0.28/0.46 = ( secrecy_sKS @ Y2 ) )
% 0.28/0.46 = ( X2 = Y2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % KS.inject(2)
% 0.28/0.46 thf(fact_2_know2knows__s,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_sE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know2knows_s
% 0.28/0.46 thf(fact_3_know1s,axiom,
% 0.28/0.46 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 0.28/0.46 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ nil_Se901661471ession ) )
% 0.28/0.46 = ( knowle945212990e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know1s
% 0.28/0.46 thf(fact_4_eoutKnowCorrect__L1s,axiom,
% 0.28/0.46 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.46 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 0.28/0.46 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.28/0.46 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 0.28/0.46 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eoutKnowCorrect_L1s
% 0.28/0.46 thf(fact_5_eout__know__s,axiom,
% 0.28/0.46 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.46 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 0.28/0.46 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.28/0.46 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 0.28/0.46 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eout_know_s
% 0.28/0.46 thf(fact_6_know_Osimps_I2_J,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.46 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.28/0.46 | ( member_Secrecy_KS2 @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know.simps(2)
% 0.28/0.46 thf(fact_7_KS2Expression_Osimps_I2_J,axiom,
% 0.28/0.46 ! [M: secrecy_Secrets] :
% 0.28/0.46 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.28/0.46 = ( secrecy_sE @ M ) ) ).
% 0.28/0.46
% 0.28/0.46 % KS2Expression.simps(2)
% 0.28/0.46 thf(fact_8_knows4,axiom,
% 0.28/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.28/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.28/0.46 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K2 ) )
% 0.28/0.46 & ( knowle731562421_knows @ A @ ( enc @ K1 @ E ) ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows4
% 0.28/0.46 thf(fact_9_knows5,axiom,
% 0.28/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.28/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.28/0.46 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K1 ) )
% 0.28/0.46 & ( knowle731562421_knows @ A @ ( sign @ K2 @ E ) ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows5
% 0.28/0.46 thf(fact_10_knows6,axiom,
% 0.28/0.46 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.28/0.46 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.28/0.46 & ( knowle731562421_knows @ A @ E1 ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ ( enc @ K @ E1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows6
% 0.28/0.46 thf(fact_11_KS_Oinject_I1_J,axiom,
% 0.28/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.28/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.28/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.28/0.46 = ( X1 = Y1 ) ) ).
% 0.28/0.46
% 0.28/0.46 % KS.inject(1)
% 0.28/0.46 thf(fact_12_Expression_Oinject_I2_J,axiom,
% 0.28/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.28/0.46 ( ( ( secrecy_sE @ X2 )
% 0.28/0.46 = ( secrecy_sE @ Y2 ) )
% 0.28/0.46 = ( X2 = Y2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % Expression.inject(2)
% 0.28/0.46 thf(fact_13_know1k,axiom,
% 0.28/0.46 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 0.28/0.46 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ nil_Se901661471ession ) )
% 0.28/0.46 = ( knowle945212990e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know1k
% 0.28/0.46 thf(fact_14_knows__emptyexpression,axiom,
% 0.28/0.46 ! [C: secrecy_specID] : ( knowle731562421_knows @ C @ nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % knows_emptyexpression
% 0.28/0.46 thf(fact_15_KS_Oexhaust,axiom,
% 0.28/0.46 ! [Y: secrecy_KS] :
% 0.28/0.46 ( ! [X12: secrecy_Keys] :
% 0.28/0.46 ( Y
% 0.28/0.46 != ( secrecy_kKS @ X12 ) )
% 0.28/0.46 => ~ ! [X22: secrecy_Secrets] :
% 0.28/0.46 ( Y
% 0.28/0.46 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % KS.exhaust
% 0.28/0.46 thf(fact_16_KS_Oinduct,axiom,
% 0.28/0.46 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.28/0.46 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 0.28/0.46 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 0.28/0.46 => ( P @ KS ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % KS.induct
% 0.28/0.46 thf(fact_17_KS_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.28/0.46 ( ( secrecy_kKS @ X1 )
% 0.28/0.46 != ( secrecy_sKS @ X2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % KS.distinct(1)
% 0.28/0.46 thf(fact_18_knows7,axiom,
% 0.28/0.46 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.28/0.46 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.28/0.46 & ( knowle731562421_knows @ A @ E1 ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ ( sign @ K @ E1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows7
% 0.28/0.46 thf(fact_19_list_Oinject,axiom,
% 0.28/0.46 ! [X21: secrecy_Expression,X222: list_S529945141ession,Y21: secrecy_Expression,Y22: list_S529945141ession] :
% 0.28/0.46 ( ( ( cons_S112077679ession @ X21 @ X222 )
% 0.28/0.46 = ( cons_S112077679ession @ Y21 @ Y22 ) )
% 0.28/0.46 = ( ( X21 = Y21 )
% 0.28/0.46 & ( X222 = Y22 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.inject
% 0.28/0.46 thf(fact_20_list_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [X21: secrecy_KS,X222: list_Secrecy_KS] :
% 0.28/0.46 ( nil_Secrecy_KS
% 0.28/0.46 != ( cons_Secrecy_KS @ X21 @ X222 ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.distinct(1)
% 0.28/0.46 thf(fact_21_list_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.28/0.46 ( nil_Se901661471ession
% 0.28/0.46 != ( cons_S112077679ession @ X21 @ X222 ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.distinct(1)
% 0.28/0.46 thf(fact_22_list_OdiscI,axiom,
% 0.28/0.46 ! [List: list_Secrecy_KS,X21: secrecy_KS,X222: list_Secrecy_KS] :
% 0.28/0.46 ( ( List
% 0.28/0.46 = ( cons_Secrecy_KS @ X21 @ X222 ) )
% 0.28/0.46 => ( List != nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.discI
% 0.28/0.46 thf(fact_23_list_OdiscI,axiom,
% 0.28/0.46 ! [List: list_S529945141ession,X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.28/0.46 ( ( List
% 0.28/0.46 = ( cons_S112077679ession @ X21 @ X222 ) )
% 0.28/0.46 => ( List != nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.discI
% 0.28/0.46 thf(fact_24_list_Oexhaust,axiom,
% 0.28/0.46 ! [Y: list_Secrecy_KS] :
% 0.28/0.46 ( ( Y != nil_Secrecy_KS )
% 0.28/0.46 => ~ ! [X212: secrecy_KS,X223: list_Secrecy_KS] :
% 0.28/0.46 ( Y
% 0.28/0.46 != ( cons_Secrecy_KS @ X212 @ X223 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.exhaust
% 0.28/0.46 thf(fact_25_list_Oexhaust,axiom,
% 0.28/0.46 ! [Y: list_S529945141ession] :
% 0.28/0.46 ( ( Y != nil_Se901661471ession )
% 0.28/0.46 => ~ ! [X212: secrecy_Expression,X223: list_S529945141ession] :
% 0.28/0.46 ( Y
% 0.28/0.46 != ( cons_S112077679ession @ X212 @ X223 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.exhaust
% 0.28/0.46 thf(fact_26_list_Oinducts,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > $o,List: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X12: secrecy_KS,X22: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ X22 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X12 @ X22 ) ) )
% 0.28/0.46 => ( P @ List ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.inducts
% 0.28/0.46 thf(fact_27_list_Oinducts,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > $o,List: list_S529945141ession] :
% 0.28/0.46 ( ( P @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X12: secrecy_Expression,X22: list_S529945141ession] :
% 0.28/0.46 ( ( P @ X22 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X12 @ X22 ) ) )
% 0.28/0.46 => ( P @ List ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.inducts
% 0.28/0.46 thf(fact_28_neq__Nil__conv,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.46 = ( ? [Y3: secrecy_KS,Ys: list_Secrecy_KS] :
% 0.28/0.46 ( Xs
% 0.28/0.46 = ( cons_Secrecy_KS @ Y3 @ Ys ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % neq_Nil_conv
% 0.28/0.46 thf(fact_29_neq__Nil__conv,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession] :
% 0.28/0.46 ( ( Xs != nil_Se901661471ession )
% 0.28/0.46 = ( ? [Y3: secrecy_Expression,Ys: list_S529945141ession] :
% 0.28/0.46 ( Xs
% 0.28/0.46 = ( cons_S112077679ession @ Y3 @ Ys ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % neq_Nil_conv
% 0.28/0.46 thf(fact_30_list__induct2_H,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [Y4: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 0.28/0.46 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_induct2'
% 0.28/0.46 thf(fact_31_list__induct2_H,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > list_S529945141ession > $o,Xs: list_Secrecy_KS,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [Y4: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Secrecy_KS @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 0.28/0.46 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_induct2'
% 0.28/0.46 thf(fact_32_list__induct2_H,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > list_Secrecy_KS > $o,Xs: list_S529945141ession,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [Y4: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Se901661471ession @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 0.28/0.46 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_induct2'
% 0.28/0.46 thf(fact_33_list__induct2_H,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > list_S529945141ession > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [Y4: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Se901661471ession @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 0.28/0.46 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_induct2'
% 0.28/0.46 thf(fact_34_splice_Oinduct,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 0.28/0.46 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ Ys3 @ Xs2 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % splice.induct
% 0.28/0.46 thf(fact_35_splice_Oinduct,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 0.28/0.46 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( P @ Ys3 @ Xs2 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % splice.induct
% 0.28/0.46 thf(fact_36_induct__list012,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.46 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Zs: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ Zs )
% 0.28/0.46 => ( ( P @ ( cons_Secrecy_KS @ Y4 @ Zs ) )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Zs ) ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % induct_list012
% 0.28/0.46 thf(fact_37_induct__list012,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( P @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Zs: list_S529945141ession] :
% 0.28/0.46 ( ( P @ Zs )
% 0.28/0.46 => ( ( P @ ( cons_S112077679ession @ Y4 @ Zs ) )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Zs ) ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % induct_list012
% 0.28/0.46 thf(fact_38_not__Cons__self2,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( cons_S112077679ession @ X3 @ Xs )
% 0.28/0.46 != Xs ) ).
% 0.28/0.46
% 0.28/0.46 % not_Cons_self2
% 0.28/0.46 thf(fact_39_map__tailrec__rev_Oinduct,axiom,
% 0.28/0.46 ! [P: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,A0: secrecy_KS > secrecy_Expression,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 0.28/0.46 ( ! [F: secrecy_KS > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Secrecy_KS @ X_1 )
% 0.28/0.46 => ( ! [F: secrecy_KS > secrecy_Expression,A3: secrecy_KS,As: list_Secrecy_KS,Bs: list_S529945141ession] :
% 0.28/0.46 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 0.28/0.46 => ( P @ F @ ( cons_Secrecy_KS @ A3 @ As ) @ Bs ) )
% 0.28/0.46 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % map_tailrec_rev.induct
% 0.28/0.46 thf(fact_40_map__tailrec__rev_Oinduct,axiom,
% 0.28/0.46 ! [P: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.28/0.46 ( ! [F: secrecy_Expression > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Se901661471ession @ X_1 )
% 0.28/0.46 => ( ! [F: secrecy_Expression > secrecy_Expression,A3: secrecy_Expression,As: list_S529945141ession,Bs: list_S529945141ession] :
% 0.28/0.46 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 0.28/0.46 => ( P @ F @ ( cons_S112077679ession @ A3 @ As ) @ Bs ) )
% 0.28/0.46 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % map_tailrec_rev.induct
% 0.28/0.46 thf(fact_41_list__nonempty__induct,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 0.28/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs2 != nil_Secrecy_KS )
% 0.28/0.46 => ( ( P @ Xs2 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_nonempty_induct
% 0.28/0.46 thf(fact_42_list__nonempty__induct,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 0.28/0.46 ( ( Xs != nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( Xs2 != nil_Se901661471ession )
% 0.28/0.46 => ( ( P @ Xs2 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_nonempty_induct
% 0.28/0.46 thf(fact_43_successively_Oinduct,axiom,
% 0.28/0.46 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 0.28/0.46 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS] : ( P @ P2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.46 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ P2 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) )
% 0.28/0.46 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % successively.induct
% 0.28/0.46 thf(fact_44_successively_Oinduct,axiom,
% 0.28/0.46 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 0.28/0.46 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression] : ( P @ P2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.46 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( P @ P2 @ ( cons_S112077679ession @ Y4 @ Xs2 ) )
% 0.28/0.46 => ( P @ P2 @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % successively.induct
% 0.28/0.46 thf(fact_45_remdups__adj_Oinduct,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > $o,A0: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.46 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( X = Y4 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) )
% 0.28/0.46 => ( ( ( X != Y4 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) )
% 0.28/0.46 => ( P @ A0 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % remdups_adj.induct
% 0.28/0.46 thf(fact_46_remdups__adj_Oinduct,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > $o,A0: list_S529945141ession] :
% 0.28/0.46 ( ( P @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( ( X = Y4 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) )
% 0.28/0.46 => ( ( ( X != Y4 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) )
% 0.28/0.46 => ( P @ A0 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % remdups_adj.induct
% 0.28/0.46 thf(fact_47_sorted__wrt_Oinduct,axiom,
% 0.28/0.46 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 0.28/0.46 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ P2 @ Ys3 )
% 0.28/0.46 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ Ys3 ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sorted_wrt.induct
% 0.28/0.46 thf(fact_48_sorted__wrt_Oinduct,axiom,
% 0.28/0.46 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 0.28/0.46 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( P @ P2 @ Ys3 )
% 0.28/0.46 => ( P @ P2 @ ( cons_S112077679ession @ X @ Ys3 ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sorted_wrt.induct
% 0.28/0.46 thf(fact_49_remdups__adj_Ocases,axiom,
% 0.28/0.46 ! [X3: list_Secrecy_KS] :
% 0.28/0.46 ( ( X3 != nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.46 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % remdups_adj.cases
% 0.28/0.46 thf(fact_50_remdups__adj_Ocases,axiom,
% 0.28/0.46 ! [X3: list_S529945141ession] :
% 0.28/0.46 ( ( X3 != nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.46 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % remdups_adj.cases
% 0.28/0.46 thf(fact_51_mem__Collect__eq,axiom,
% 0.28/0.46 ! [A4: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.28/0.46 ( ( member2138796287ecrets @ A4 @ ( collec836099393ecrets @ P ) )
% 0.28/0.46 = ( P @ A4 ) ) ).
% 0.28/0.46
% 0.28/0.46 % mem_Collect_eq
% 0.28/0.46 thf(fact_52_mem__Collect__eq,axiom,
% 0.28/0.46 ! [A4: secrecy_KS,P: secrecy_KS > $o] :
% 0.28/0.46 ( ( member_Secrecy_KS2 @ A4 @ ( collect_Secrecy_KS @ P ) )
% 0.28/0.46 = ( P @ A4 ) ) ).
% 0.28/0.46
% 0.28/0.46 % mem_Collect_eq
% 0.28/0.46 thf(fact_53_mem__Collect__eq,axiom,
% 0.28/0.46 ! [A4: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.28/0.46 ( ( member_Secrecy_Keys @ A4 @ ( collect_Secrecy_Keys @ P ) )
% 0.28/0.46 = ( P @ A4 ) ) ).
% 0.28/0.46
% 0.28/0.46 % mem_Collect_eq
% 0.28/0.46 thf(fact_54_Collect__mem__eq,axiom,
% 0.28/0.46 ! [A: set_Secrecy_Secrets] :
% 0.28/0.46 ( ( collec836099393ecrets
% 0.28/0.46 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 0.28/0.46 = A ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_mem_eq
% 0.28/0.46 thf(fact_55_Collect__mem__eq,axiom,
% 0.28/0.46 ! [A: set_Secrecy_KS] :
% 0.28/0.46 ( ( collect_Secrecy_KS
% 0.28/0.46 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS2 @ X4 @ A ) )
% 0.28/0.46 = A ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_mem_eq
% 0.28/0.46 thf(fact_56_Collect__mem__eq,axiom,
% 0.28/0.46 ! [A: set_Secrecy_Keys] :
% 0.28/0.46 ( ( collect_Secrecy_Keys
% 0.28/0.46 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 0.28/0.46 = A ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_mem_eq
% 0.28/0.46 thf(fact_57_transpose_Ocases,axiom,
% 0.28/0.46 ! [X3: list_list_Secrecy_KS] :
% 0.28/0.46 ( ( X3 != nil_list_Secrecy_KS )
% 0.28/0.46 => ( ! [Xss: list_list_Secrecy_KS] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ Xss ) )
% 0.28/0.46 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Xss: list_list_Secrecy_KS] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_list_Secrecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % transpose.cases
% 0.28/0.46 thf(fact_58_transpose_Ocases,axiom,
% 0.28/0.46 ! [X3: list_l425507653ession] :
% 0.28/0.46 ( ( X3 != nil_li311616943ession )
% 0.28/0.46 => ( ! [Xss: list_l425507653ession] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_l533358079ession @ nil_Se901661471ession @ Xss ) )
% 0.28/0.46 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession,Xss: list_l425507653ession] :
% 0.28/0.46 ( X3
% 0.28/0.46 != ( cons_l533358079ession @ ( cons_S112077679ession @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % transpose.cases
% 0.28/0.46 thf(fact_59_shuffles_Oinduct,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 0.28/0.46 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.28/0.46 => ( ! [Xs2: list_Secrecy_KS] : ( P @ Xs2 @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ Xs2 @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % shuffles.induct
% 0.28/0.46 thf(fact_60_shuffles_Oinduct,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 0.28/0.46 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.28/0.46 => ( ! [Xs2: list_S529945141ession] : ( P @ Xs2 @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( P @ Xs2 @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % shuffles.induct
% 0.28/0.46 thf(fact_61_knows1k,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.46 = ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows1k
% 0.28/0.46 thf(fact_62_know2knows__k,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know2knows_k
% 0.28/0.46 thf(fact_63_knows2know__k,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.28/0.46 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows2know_k
% 0.28/0.46 thf(fact_64_know2knowsPQ__k,axiom,
% 0.28/0.46 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 0.28/0.46 ( ( ( knowle945212990e_know @ P @ ( secrecy_kKS @ M ) )
% 0.28/0.46 | ( knowle945212990e_know @ Q @ ( secrecy_kKS @ M ) ) )
% 0.28/0.46 => ( ( knowle731562421_knows @ P @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.28/0.46 | ( knowle731562421_knows @ Q @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know2knowsPQ_k
% 0.28/0.46 thf(fact_65_knows2knowPQ__k,axiom,
% 0.28/0.46 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 0.28/0.46 ( ( ( knowle731562421_knows @ P @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.28/0.46 | ( knowle731562421_knows @ Q @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) )
% 0.28/0.46 => ( ( knowle945212990e_know @ P @ ( secrecy_kKS @ M ) )
% 0.28/0.46 | ( knowle945212990e_know @ Q @ ( secrecy_kKS @ M ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows2knowPQ_k
% 0.28/0.46 thf(fact_66_know2knows__neg__k,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.46 => ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know2knows_neg_k
% 0.28/0.46 thf(fact_67_knows2know__neg__k,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.28/0.46 => ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows2know_neg_k
% 0.28/0.46 thf(fact_68_know_Osimps_I1_J,axiom,
% 0.28/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.46 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.28/0.46 | ( member_Secrecy_KS2 @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % know.simps(1)
% 0.28/0.46 thf(fact_69_insert__Nil,axiom,
% 0.28/0.46 ! [X3: secrecy_KS] :
% 0.28/0.46 ( ( insert_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 0.28/0.46 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_Nil
% 0.28/0.46 thf(fact_70_insert__Nil,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression] :
% 0.28/0.46 ( ( insert1173886601ession @ X3 @ nil_Se901661471ession )
% 0.28/0.46 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_Nil
% 0.28/0.46 thf(fact_71_Expression_Oinject_I1_J,axiom,
% 0.28/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.28/0.46 ( ( ( secrecy_kE @ X1 )
% 0.28/0.46 = ( secrecy_kE @ Y1 ) )
% 0.28/0.46 = ( X1 = Y1 ) ) ).
% 0.28/0.46
% 0.28/0.46 % Expression.inject(1)
% 0.28/0.46 thf(fact_72_Expression_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.28/0.46 ( ( secrecy_kE @ X1 )
% 0.28/0.46 != ( secrecy_sE @ X2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % Expression.distinct(1)
% 0.28/0.46 thf(fact_73_KS2Expression_Osimps_I1_J,axiom,
% 0.28/0.46 ! [M: secrecy_Keys] :
% 0.28/0.46 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.28/0.46 = ( secrecy_kE @ M ) ) ).
% 0.28/0.46
% 0.28/0.46 % KS2Expression.simps(1)
% 0.28/0.46 thf(fact_74_eoutKnowCorrect__L1k,axiom,
% 0.28/0.46 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 0.28/0.46 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.28/0.46 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.28/0.46 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eoutKnowCorrect_L1k
% 0.28/0.46 thf(fact_75_eout__know__k,axiom,
% 0.28/0.46 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.46 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 0.28/0.46 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.28/0.46 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.28/0.46 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eout_know_k
% 0.28/0.46 thf(fact_76_eoutKnowsECorrect__L1,axiom,
% 0.28/0.46 ! [C: secrecy_specID,E: secrecy_Expression] :
% 0.28/0.46 ( ( knowle1268625169orrect @ C @ E )
% 0.28/0.46 => ( ( eout @ C @ E )
% 0.28/0.46 => ( ? [K3: secrecy_Keys] :
% 0.28/0.46 ( ( E
% 0.28/0.46 = ( secrecy_kE @ K3 ) )
% 0.28/0.46 & ( member_Secrecy_Keys @ K3 @ ( specKeys @ C ) ) )
% 0.28/0.46 | ? [S: secrecy_Secrets] :
% 0.28/0.46 ( ( E
% 0.28/0.46 = ( secrecy_sE @ S ) )
% 0.28/0.46 & ( member2138796287ecrets @ S @ ( specSecrets @ C ) ) )
% 0.28/0.46 | ( knowle731562421_knows @ C @ ( cons_S112077679ession @ E @ nil_Se901661471ession ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eoutKnowsECorrect_L1
% 0.28/0.46 thf(fact_77_eoutKnowsECorrect__def,axiom,
% 0.28/0.46 ( knowle1268625169orrect
% 0.28/0.46 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 0.28/0.46 ( ( eout @ C2 @ E2 )
% 0.28/0.46 = ( ? [K4: secrecy_Keys] :
% 0.28/0.46 ( ( E2
% 0.28/0.46 = ( secrecy_kE @ K4 ) )
% 0.28/0.46 & ( member_Secrecy_Keys @ K4 @ ( specKeys @ C2 ) ) )
% 0.28/0.46 | ? [S2: secrecy_Secrets] :
% 0.28/0.46 ( ( E2
% 0.28/0.46 = ( secrecy_sE @ S2 ) )
% 0.28/0.46 & ( member2138796287ecrets @ S2 @ ( specSecrets @ C2 ) ) )
% 0.28/0.46 | ( knowle731562421_knows @ C2 @ ( cons_S112077679ession @ E2 @ nil_Se901661471ession ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eoutKnowsECorrect_def
% 0.28/0.46 thf(fact_78_product__lists_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( produc1450295286ession @ nil_li311616943ession )
% 0.28/0.46 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % product_lists.simps(1)
% 0.28/0.46 thf(fact_79_product__lists_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( produc713695622ecy_KS @ nil_list_Secrecy_KS )
% 0.28/0.46 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % product_lists.simps(1)
% 0.28/0.46 thf(fact_80_subseqs_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( subseq348280080ession @ nil_Se901661471ession )
% 0.28/0.46 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % subseqs.simps(1)
% 0.28/0.46 thf(fact_81_subseqs_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( subseqs_Secrecy_KS @ nil_Secrecy_KS )
% 0.28/0.46 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % subseqs.simps(1)
% 0.28/0.46 thf(fact_82_Expression2KSL_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( secrec1371625429on2KSL @ nil_Se901661471ession )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % Expression2KSL.simps(1)
% 0.28/0.46 thf(fact_83_list__ex1__simps_I1_J,axiom,
% 0.28/0.46 ! [P: secrecy_Expression > $o] :
% 0.28/0.46 ~ ( list_e1486860828ession @ P @ nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % list_ex1_simps(1)
% 0.28/0.46 thf(fact_84_list__ex1__simps_I1_J,axiom,
% 0.28/0.46 ! [P: secrecy_KS > $o] :
% 0.28/0.46 ~ ( list_ex1_Secrecy_KS @ P @ nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % list_ex1_simps(1)
% 0.28/0.46 thf(fact_85_map__tailrec__rev_Oelims,axiom,
% 0.28/0.46 ! [X3: secrecy_KS > secrecy_Expression,Xa: list_Secrecy_KS,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 0.28/0.46 ( ( ( map_ta623472337ession @ X3 @ Xa @ Xb )
% 0.28/0.46 = Y )
% 0.28/0.46 => ( ( ( Xa = nil_Secrecy_KS )
% 0.28/0.46 => ( Y != Xb ) )
% 0.28/0.46 => ~ ! [A3: secrecy_KS,As: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xa
% 0.28/0.46 = ( cons_Secrecy_KS @ A3 @ As ) )
% 0.28/0.46 => ( Y
% 0.28/0.46 != ( map_ta623472337ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % map_tailrec_rev.elims
% 0.28/0.46 thf(fact_86_map__tailrec__rev_Oelims,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression > secrecy_Expression,Xa: list_S529945141ession,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 0.28/0.46 ( ( ( map_ta1624757057ession @ X3 @ Xa @ Xb )
% 0.28/0.46 = Y )
% 0.28/0.46 => ( ( ( Xa = nil_Se901661471ession )
% 0.28/0.46 => ( Y != Xb ) )
% 0.28/0.46 => ~ ! [A3: secrecy_Expression,As: list_S529945141ession] :
% 0.28/0.46 ( ( Xa
% 0.28/0.46 = ( cons_S112077679ession @ A3 @ As ) )
% 0.28/0.46 => ( Y
% 0.28/0.46 != ( map_ta1624757057ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % map_tailrec_rev.elims
% 0.28/0.46 thf(fact_87_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.28/0.46 ! [Less: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.46 ~ ( lexord948960489ecy_KS @ Less @ ( cons_Secrecy_KS @ X3 @ Xs ) @ nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_simps(3)
% 0.28/0.46 thf(fact_88_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.46 ~ ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_simps(3)
% 0.28/0.46 thf(fact_89_bind__simps_I1_J,axiom,
% 0.28/0.46 ! [F2: secrecy_Expression > list_S529945141ession] :
% 0.28/0.46 ( ( bind_S815874003ession @ nil_Se901661471ession @ F2 )
% 0.28/0.46 = nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % bind_simps(1)
% 0.28/0.46 thf(fact_90_bind__simps_I1_J,axiom,
% 0.28/0.46 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 0.28/0.46 ( ( bind_S1823644515ecy_KS @ nil_Se901661471ession @ F2 )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % bind_simps(1)
% 0.28/0.46 thf(fact_91_bind__simps_I1_J,axiom,
% 0.28/0.46 ! [F2: secrecy_KS > list_S529945141ession] :
% 0.28/0.46 ( ( bind_S711229283ession @ nil_Secrecy_KS @ F2 )
% 0.28/0.46 = nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % bind_simps(1)
% 0.28/0.46 thf(fact_92_bind__simps_I1_J,axiom,
% 0.28/0.46 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 0.28/0.46 ( ( bind_S645462771ecy_KS @ nil_Secrecy_KS @ F2 )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % bind_simps(1)
% 0.28/0.46 thf(fact_93_listrelp_Oinducts,axiom,
% 0.28/0.46 ! [R: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 0.28/0.46 ( ( listre788412843ecy_KS @ R @ X1 @ X2 )
% 0.28/0.46 => ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( R @ X @ Y4 )
% 0.28/0.46 => ( ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 )
% 0.28/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) )
% 0.28/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.inducts
% 0.28/0.46 thf(fact_94_listrelp_Oinducts,axiom,
% 0.28/0.46 ! [R: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,P: list_Secrecy_KS > list_S529945141ession > $o] :
% 0.28/0.46 ( ( listre1601064475ession @ R @ X1 @ X2 )
% 0.28/0.46 => ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_KS,Y4: secrecy_Expression,Xs2: list_Secrecy_KS,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( R @ X @ Y4 )
% 0.28/0.46 => ( ( listre1601064475ession @ R @ Xs2 @ Ys3 )
% 0.28/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) )
% 0.28/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.inducts
% 0.28/0.46 thf(fact_95_listrelp_Oinducts,axiom,
% 0.28/0.46 ! [R: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,P: list_S529945141ession > list_Secrecy_KS > $o] :
% 0.28/0.46 ( ( listre565996059ecy_KS @ R @ X1 @ X2 )
% 0.28/0.46 => ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Y4: secrecy_KS,Xs2: list_S529945141ession,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( R @ X @ Y4 )
% 0.28/0.46 => ( ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 )
% 0.28/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) )
% 0.28/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.inducts
% 0.28/0.46 thf(fact_96_listrelp_Oinducts,axiom,
% 0.28/0.46 ! [R: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 0.28/0.46 ( ( listre84909707ession @ R @ X1 @ X2 )
% 0.28/0.46 => ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( R @ X @ Y4 )
% 0.28/0.46 => ( ( listre84909707ession @ R @ Xs2 @ Ys3 )
% 0.28/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) )
% 0.28/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.inducts
% 0.28/0.46 thf(fact_97_listrelp_Osimps,axiom,
% 0.28/0.46 ( listre788412843ecy_KS
% 0.28/0.46 = ( ^ [R2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( A12 = nil_Secrecy_KS )
% 0.28/0.46 & ( A22 = nil_Secrecy_KS ) )
% 0.28/0.46 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.28/0.46 & ( R2 @ X4 @ Y3 )
% 0.28/0.46 & ( listre788412843ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.simps
% 0.28/0.46 thf(fact_98_listrelp_Osimps,axiom,
% 0.28/0.46 ( listre1601064475ession
% 0.28/0.46 = ( ^ [R2: secrecy_KS > secrecy_Expression > $o,A12: list_Secrecy_KS,A22: list_S529945141ession] :
% 0.28/0.46 ( ( ( A12 = nil_Secrecy_KS )
% 0.28/0.46 & ( A22 = nil_Se901661471ession ) )
% 0.28/0.46 | ? [X4: secrecy_KS,Y3: secrecy_Expression,Xs3: list_Secrecy_KS,Ys: list_S529945141ession] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.28/0.46 & ( R2 @ X4 @ Y3 )
% 0.28/0.46 & ( listre1601064475ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.simps
% 0.28/0.46 thf(fact_99_listrelp_Osimps,axiom,
% 0.28/0.46 ( listre565996059ecy_KS
% 0.28/0.46 = ( ^ [R2: secrecy_Expression > secrecy_KS > $o,A12: list_S529945141ession,A22: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( A12 = nil_Se901661471ession )
% 0.28/0.46 & ( A22 = nil_Secrecy_KS ) )
% 0.28/0.46 | ? [X4: secrecy_Expression,Y3: secrecy_KS,Xs3: list_S529945141ession,Ys: list_Secrecy_KS] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.28/0.46 & ( R2 @ X4 @ Y3 )
% 0.28/0.46 & ( listre565996059ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.simps
% 0.28/0.46 thf(fact_100_listrelp_Osimps,axiom,
% 0.28/0.46 ( listre84909707ession
% 0.28/0.46 = ( ^ [R2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 0.28/0.46 ( ( ( A12 = nil_Se901661471ession )
% 0.28/0.46 & ( A22 = nil_Se901661471ession ) )
% 0.28/0.46 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.28/0.46 & ( R2 @ X4 @ Y3 )
% 0.28/0.46 & ( listre84909707ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.simps
% 0.28/0.46 thf(fact_101_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) )
% 0.28/0.46 = ( ( Less @ X3 @ Y )
% 0.28/0.46 | ( ~ ( Less @ Y @ X3 )
% 0.28/0.46 & ( lexord1123423577ession @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_simps(4)
% 0.28/0.46 thf(fact_102_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( lexord1123423577ession @ Less @ Xs @ nil_Se901661471ession )
% 0.28/0.46 = ( Xs = nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_simps(2)
% 0.28/0.46 thf(fact_103_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.28/0.46 ! [Less: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( lexord948960489ecy_KS @ Less @ Xs @ nil_Secrecy_KS )
% 0.28/0.46 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_simps(2)
% 0.28/0.46 thf(fact_104_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_simps(1)
% 0.28/0.46 thf(fact_105_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.28/0.46 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_simps(1)
% 0.28/0.46 thf(fact_106_ord_Olexordp__eq_OCons,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( Less @ X3 @ Y )
% 0.28/0.46 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.Cons
% 0.28/0.46 thf(fact_107_ord_Olexordp__eq_OCons__eq,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ~ ( Less @ X3 @ Y )
% 0.28/0.46 => ( ~ ( Less @ Y @ X3 )
% 0.28/0.46 => ( ( lexord1123423577ession @ Less @ Xs @ Ys2 )
% 0.28/0.46 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.Cons_eq
% 0.28/0.46 thf(fact_108_ord_Olexordp__eq_ONil,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.Nil
% 0.28/0.46 thf(fact_109_ord_Olexordp__eq_ONil,axiom,
% 0.28/0.46 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.Nil
% 0.28/0.46 thf(fact_110_listrelp_OCons,axiom,
% 0.28/0.46 ! [R: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( R @ X3 @ Y )
% 0.28/0.46 => ( ( listre84909707ession @ R @ Xs @ Ys2 )
% 0.28/0.46 => ( listre84909707ession @ R @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.Cons
% 0.28/0.46 thf(fact_111_listrelp_ONil,axiom,
% 0.28/0.46 ! [R: secrecy_Expression > secrecy_Expression > $o] : ( listre84909707ession @ R @ nil_Se901661471ession @ nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.Nil
% 0.28/0.46 thf(fact_112_listrelp_ONil,axiom,
% 0.28/0.46 ! [R: secrecy_Expression > secrecy_KS > $o] : ( listre565996059ecy_KS @ R @ nil_Se901661471ession @ nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.Nil
% 0.28/0.46 thf(fact_113_listrelp_ONil,axiom,
% 0.28/0.46 ! [R: secrecy_KS > secrecy_Expression > $o] : ( listre1601064475ession @ R @ nil_Secrecy_KS @ nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.Nil
% 0.28/0.46 thf(fact_114_listrelp_ONil,axiom,
% 0.28/0.46 ! [R: secrecy_KS > secrecy_KS > $o] : ( listre788412843ecy_KS @ R @ nil_Secrecy_KS @ nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.Nil
% 0.28/0.46 thf(fact_115_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.28/0.46 ! [F2: secrecy_Expression > secrecy_Expression,A4: secrecy_Expression,As2: list_S529945141ession,Bs2: list_S529945141ession] :
% 0.28/0.46 ( ( map_ta1624757057ession @ F2 @ ( cons_S112077679ession @ A4 @ As2 ) @ Bs2 )
% 0.28/0.46 = ( map_ta1624757057ession @ F2 @ As2 @ ( cons_S112077679ession @ ( F2 @ A4 ) @ Bs2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % map_tailrec_rev.simps(2)
% 0.28/0.46 thf(fact_116_ord_Olexordp__eq_Ocases,axiom,
% 0.28/0.46 ! [Less: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 0.28/0.46 ( ( lexord948960489ecy_KS @ Less @ A1 @ A2 )
% 0.28/0.46 => ( ( A1 != nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS] :
% 0.28/0.46 ( ? [Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( A1
% 0.28/0.46 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.28/0.46 => ! [Y4: secrecy_KS] :
% 0.28/0.46 ( ? [Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( A2
% 0.28/0.46 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.28/0.46 => ~ ( Less @ X @ Y4 ) ) )
% 0.28/0.46 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( A1
% 0.28/0.46 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.28/0.46 => ! [Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ~ ( Less @ X @ Y4 )
% 0.28/0.46 => ( ~ ( Less @ Y4 @ X )
% 0.28/0.46 => ~ ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.cases
% 0.28/0.46 thf(fact_117_ord_Olexordp__eq_Ocases,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.28/0.46 ( ( lexord1123423577ession @ Less @ A1 @ A2 )
% 0.28/0.46 => ( ( A1 != nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression] :
% 0.28/0.46 ( ? [Xs2: list_S529945141ession] :
% 0.28/0.46 ( A1
% 0.28/0.46 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.28/0.46 => ! [Y4: secrecy_Expression] :
% 0.28/0.46 ( ? [Ys3: list_S529945141ession] :
% 0.28/0.46 ( A2
% 0.28/0.46 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.28/0.46 => ~ ( Less @ X @ Y4 ) ) )
% 0.28/0.46 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( A1
% 0.28/0.46 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.28/0.46 => ! [Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ~ ( Less @ X @ Y4 )
% 0.28/0.46 => ( ~ ( Less @ Y4 @ X )
% 0.28/0.46 => ~ ( lexord1123423577ession @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.cases
% 0.28/0.46 thf(fact_118_ord_Olexordp__eq_Osimps,axiom,
% 0.28/0.46 ( lexord948960489ecy_KS
% 0.28/0.46 = ( ^ [Less2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 0.28/0.46 ( ? [Ys: list_Secrecy_KS] :
% 0.28/0.46 ( ( A12 = nil_Secrecy_KS )
% 0.28/0.46 & ( A22 = Ys ) )
% 0.28/0.46 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.28/0.46 & ( Less2 @ X4 @ Y3 ) )
% 0.28/0.46 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.28/0.46 & ~ ( Less2 @ X4 @ Y3 )
% 0.28/0.46 & ~ ( Less2 @ Y3 @ X4 )
% 0.28/0.46 & ( lexord948960489ecy_KS @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.simps
% 0.28/0.46 thf(fact_119_ord_Olexordp__eq_Osimps,axiom,
% 0.28/0.46 ( lexord1123423577ession
% 0.28/0.46 = ( ^ [Less2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 0.28/0.46 ( ? [Ys: list_S529945141ession] :
% 0.28/0.46 ( ( A12 = nil_Se901661471ession )
% 0.28/0.46 & ( A22 = Ys ) )
% 0.28/0.46 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.28/0.46 & ( Less2 @ X4 @ Y3 ) )
% 0.28/0.46 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.28/0.46 ( ( A12
% 0.28/0.46 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.28/0.46 & ( A22
% 0.28/0.46 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.28/0.46 & ~ ( Less2 @ X4 @ Y3 )
% 0.28/0.46 & ~ ( Less2 @ Y3 @ X4 )
% 0.28/0.46 & ( lexord1123423577ession @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.simps
% 0.28/0.46 thf(fact_120_ord_Olexordp__eq_Oinducts,axiom,
% 0.28/0.46 ! [Less: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 0.28/0.46 ( ( lexord948960489ecy_KS @ Less @ X1 @ X2 )
% 0.28/0.46 => ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.28/0.46 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( Less @ X @ Y4 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 0.28/0.46 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ~ ( Less @ X @ Y4 )
% 0.28/0.46 => ( ~ ( Less @ Y4 @ X )
% 0.28/0.46 => ( ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 )
% 0.28/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) ) )
% 0.28/0.46 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.inducts
% 0.28/0.46 thf(fact_121_ord_Olexordp__eq_Oinducts,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 0.28/0.46 ( ( lexord1123423577ession @ Less @ X1 @ X2 )
% 0.28/0.46 => ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( Less @ X @ Y4 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.28/0.46 ( ~ ( Less @ X @ Y4 )
% 0.28/0.46 => ( ~ ( Less @ Y4 @ X )
% 0.28/0.46 => ( ( lexord1123423577ession @ Less @ Xs2 @ Ys3 )
% 0.28/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.28/0.46 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) ) )
% 0.28/0.46 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq.inducts
% 0.28/0.46 thf(fact_122_listrelp_Ocases,axiom,
% 0.28/0.46 ! [R: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 0.28/0.46 ( ( listre788412843ecy_KS @ R @ A1 @ A2 )
% 0.28/0.46 => ( ( ( A1 = nil_Secrecy_KS )
% 0.28/0.46 => ( A2 != nil_Secrecy_KS ) )
% 0.28/0.46 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( A1
% 0.28/0.46 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.28/0.46 => ! [Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ( R @ X @ Y4 )
% 0.28/0.46 => ~ ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.cases
% 0.28/0.46 thf(fact_123_listrelp_Ocases,axiom,
% 0.28/0.46 ! [R: secrecy_KS > secrecy_Expression > $o,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 0.28/0.46 ( ( listre1601064475ession @ R @ A1 @ A2 )
% 0.28/0.46 => ( ( ( A1 = nil_Secrecy_KS )
% 0.28/0.46 => ( A2 != nil_Se901661471ession ) )
% 0.28/0.46 => ~ ! [X: secrecy_KS,Y4: secrecy_Expression,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( A1
% 0.28/0.46 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.28/0.46 => ! [Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ( R @ X @ Y4 )
% 0.28/0.46 => ~ ( listre1601064475ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.cases
% 0.28/0.46 thf(fact_124_listrelp_Ocases,axiom,
% 0.28/0.46 ! [R: secrecy_Expression > secrecy_KS > $o,A1: list_S529945141ession,A2: list_Secrecy_KS] :
% 0.28/0.46 ( ( listre565996059ecy_KS @ R @ A1 @ A2 )
% 0.28/0.46 => ( ( ( A1 = nil_Se901661471ession )
% 0.28/0.46 => ( A2 != nil_Secrecy_KS ) )
% 0.28/0.46 => ~ ! [X: secrecy_Expression,Y4: secrecy_KS,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( A1
% 0.28/0.46 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.28/0.46 => ! [Ys3: list_Secrecy_KS] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ( R @ X @ Y4 )
% 0.28/0.46 => ~ ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.cases
% 0.28/0.46 thf(fact_125_listrelp_Ocases,axiom,
% 0.28/0.46 ! [R: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.28/0.46 ( ( listre84909707ession @ R @ A1 @ A2 )
% 0.28/0.46 => ( ( ( A1 = nil_Se901661471ession )
% 0.28/0.46 => ( A2 != nil_Se901661471ession ) )
% 0.28/0.46 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( A1
% 0.28/0.46 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.28/0.46 => ! [Ys3: list_S529945141ession] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.28/0.46 => ( ( R @ X @ Y4 )
% 0.28/0.46 => ~ ( listre84909707ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % listrelp.cases
% 0.28/0.46 thf(fact_126_notSpecKeysSecretsExpr__L1,axiom,
% 0.28/0.46 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 0.28/0.46 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 0.28/0.46 => ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % notSpecKeysSecretsExpr_L1
% 0.28/0.46 thf(fact_127_member__rec_I2_J,axiom,
% 0.28/0.46 ! [Y: secrecy_Expression] :
% 0.28/0.46 ~ ( member2020590922ession @ nil_Se901661471ession @ Y ) ).
% 0.28/0.46
% 0.28/0.46 % member_rec(2)
% 0.28/0.46 thf(fact_128_member__rec_I2_J,axiom,
% 0.28/0.46 ! [Y: secrecy_KS] :
% 0.28/0.46 ~ ( member_Secrecy_KS @ nil_Secrecy_KS @ Y ) ).
% 0.28/0.46
% 0.28/0.46 % member_rec(2)
% 0.28/0.46 thf(fact_129_member__rec_I1_J,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression] :
% 0.28/0.46 ( ( member2020590922ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Y )
% 0.28/0.46 = ( ( X3 = Y )
% 0.28/0.46 | ( member2020590922ession @ Xs @ Y ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % member_rec(1)
% 0.28/0.46 thf(fact_130_splice_Oelims,axiom,
% 0.28/0.46 ! [X3: list_Secrecy_KS,Xa: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( splice_Secrecy_KS @ X3 @ Xa )
% 0.28/0.46 = Y )
% 0.28/0.46 => ( ( ( X3 = nil_Secrecy_KS )
% 0.28/0.46 => ( Y != Xa ) )
% 0.28/0.46 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( X3
% 0.28/0.46 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.28/0.46 => ( Y
% 0.28/0.46 != ( cons_Secrecy_KS @ X @ ( splice_Secrecy_KS @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % splice.elims
% 0.28/0.46 thf(fact_131_splice_Oelims,axiom,
% 0.28/0.46 ! [X3: list_S529945141ession,Xa: list_S529945141ession,Y: list_S529945141ession] :
% 0.28/0.46 ( ( ( splice1390717708ession @ X3 @ Xa )
% 0.28/0.46 = Y )
% 0.28/0.46 => ( ( ( X3 = nil_Se901661471ession )
% 0.28/0.46 => ( Y != Xa ) )
% 0.28/0.46 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( X3
% 0.28/0.46 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.28/0.46 => ( Y
% 0.28/0.46 != ( cons_S112077679ession @ X @ ( splice1390717708ession @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % splice.elims
% 0.28/0.46 thf(fact_132_bind__simps_I2_J,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession,F2: secrecy_Expression > list_S529945141ession] :
% 0.28/0.46 ( ( bind_S815874003ession @ ( cons_S112077679ession @ X3 @ Xs ) @ F2 )
% 0.28/0.46 = ( append2089414218ession @ ( F2 @ X3 ) @ ( bind_S815874003ession @ Xs @ F2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bind_simps(2)
% 0.28/0.46 thf(fact_133_append_Oassoc,axiom,
% 0.28/0.46 ! [A4: list_S529945141ession,B: list_S529945141ession,C3: list_S529945141ession] :
% 0.28/0.46 ( ( append2089414218ession @ ( append2089414218ession @ A4 @ B ) @ C3 )
% 0.28/0.46 = ( append2089414218ession @ A4 @ ( append2089414218ession @ B @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append.assoc
% 0.28/0.46 thf(fact_134_append__assoc,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.28/0.46 ( ( append2089414218ession @ ( append2089414218ession @ Xs @ Ys2 ) @ Zs2 )
% 0.28/0.46 = ( append2089414218ession @ Xs @ ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_assoc
% 0.28/0.46 thf(fact_135_append__same__eq,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Ys2 @ Xs )
% 0.28/0.46 = ( append2089414218ession @ Zs2 @ Xs ) )
% 0.28/0.46 = ( Ys2 = Zs2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_same_eq
% 0.28/0.46 thf(fact_136_same__append__eq,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.28/0.46 = ( append2089414218ession @ Xs @ Zs2 ) )
% 0.28/0.46 = ( Ys2 = Zs2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % same_append_eq
% 0.28/0.46 thf(fact_137_append_Oright__neutral,axiom,
% 0.28/0.46 ! [A4: list_S529945141ession] :
% 0.28/0.46 ( ( append2089414218ession @ A4 @ nil_Se901661471ession )
% 0.28/0.46 = A4 ) ).
% 0.28/0.46
% 0.28/0.46 % append.right_neutral
% 0.28/0.46 thf(fact_138_append_Oright__neutral,axiom,
% 0.28/0.46 ! [A4: list_Secrecy_KS] :
% 0.28/0.46 ( ( append_Secrecy_KS @ A4 @ nil_Secrecy_KS )
% 0.28/0.46 = A4 ) ).
% 0.28/0.46
% 0.28/0.46 % append.right_neutral
% 0.28/0.46 thf(fact_139_append__is__Nil__conv,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.28/0.46 = nil_Se901661471ession )
% 0.28/0.46 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.46 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_is_Nil_conv
% 0.28/0.46 thf(fact_140_append__is__Nil__conv,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.28/0.46 = nil_Secrecy_KS )
% 0.28/0.46 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.46 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_is_Nil_conv
% 0.28/0.46 thf(fact_141_Nil__is__append__conv,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( nil_Se901661471ession
% 0.28/0.46 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.46 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Nil_is_append_conv
% 0.28/0.46 thf(fact_142_Nil__is__append__conv,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( nil_Secrecy_KS
% 0.28/0.46 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.46 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.46 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Nil_is_append_conv
% 0.28/0.46 thf(fact_143_self__append__conv2,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( Ys2
% 0.28/0.46 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( Xs = nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % self_append_conv2
% 0.28/0.46 thf(fact_144_self__append__conv2,axiom,
% 0.28/0.46 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( Ys2
% 0.28/0.46 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.46 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % self_append_conv2
% 0.28/0.46 thf(fact_145_append__self__conv2,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.28/0.46 = Ys2 )
% 0.28/0.46 = ( Xs = nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_self_conv2
% 0.28/0.46 thf(fact_146_append__self__conv2,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.28/0.46 = Ys2 )
% 0.28/0.46 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_self_conv2
% 0.28/0.46 thf(fact_147_self__append__conv,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( Ys2 = nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % self_append_conv
% 0.28/0.46 thf(fact_148_self__append__conv,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.46 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % self_append_conv
% 0.28/0.46 thf(fact_149_append__self__conv,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.28/0.46 = Xs )
% 0.28/0.46 = ( Ys2 = nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_self_conv
% 0.28/0.46 thf(fact_150_append__self__conv,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.28/0.46 = Xs )
% 0.28/0.46 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_self_conv
% 0.28/0.46 thf(fact_151_append__Nil2,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession] :
% 0.28/0.46 ( ( append2089414218ession @ Xs @ nil_Se901661471ession )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % append_Nil2
% 0.28/0.46 thf(fact_152_append__Nil2,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( append_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % append_Nil2
% 0.28/0.46 thf(fact_153_split__Nil__iff,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( ( splice1390717708ession @ Xs @ Ys2 )
% 0.28/0.46 = nil_Se901661471ession )
% 0.28/0.46 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.46 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % split_Nil_iff
% 0.28/0.46 thf(fact_154_split__Nil__iff,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( splice_Secrecy_KS @ Xs @ Ys2 )
% 0.28/0.46 = nil_Secrecy_KS )
% 0.28/0.46 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.46 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % split_Nil_iff
% 0.28/0.46 thf(fact_155_splice__Nil2,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession] :
% 0.28/0.46 ( ( splice1390717708ession @ Xs @ nil_Se901661471ession )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % splice_Nil2
% 0.28/0.46 thf(fact_156_splice__Nil2,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( splice_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % splice_Nil2
% 0.28/0.46 thf(fact_157_append1__eq__conv,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS,Y: secrecy_KS] :
% 0.28/0.46 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.28/0.46 = ( append_Secrecy_KS @ Ys2 @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) )
% 0.28/0.46 = ( ( Xs = Ys2 )
% 0.28/0.46 & ( X3 = Y ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append1_eq_conv
% 0.28/0.46 thf(fact_158_append1__eq__conv,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession,Y: secrecy_Expression] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.28/0.46 = ( append2089414218ession @ Ys2 @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) )
% 0.28/0.46 = ( ( Xs = Ys2 )
% 0.28/0.46 & ( X3 = Y ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append1_eq_conv
% 0.28/0.46 thf(fact_159_append__eq__appendI,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Xs1: list_S529945141ession,Zs2: list_S529945141ession,Ys2: list_S529945141ession,Us: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ Xs1 )
% 0.28/0.46 = Zs2 )
% 0.28/0.46 => ( ( Ys2
% 0.28/0.46 = ( append2089414218ession @ Xs1 @ Us ) )
% 0.28/0.46 => ( ( append2089414218ession @ Xs @ Ys2 )
% 0.28/0.46 = ( append2089414218ession @ Zs2 @ Us ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_eq_appendI
% 0.28/0.46 thf(fact_160_append__eq__append__conv2,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession,Ts: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.28/0.46 = ( append2089414218ession @ Zs2 @ Ts ) )
% 0.28/0.46 = ( ? [Us2: list_S529945141ession] :
% 0.28/0.46 ( ( ( Xs
% 0.28/0.46 = ( append2089414218ession @ Zs2 @ Us2 ) )
% 0.28/0.46 & ( ( append2089414218ession @ Us2 @ Ys2 )
% 0.28/0.46 = Ts ) )
% 0.28/0.46 | ( ( ( append2089414218ession @ Xs @ Us2 )
% 0.28/0.46 = Zs2 )
% 0.28/0.46 & ( Ys2
% 0.28/0.46 = ( append2089414218ession @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_eq_append_conv2
% 0.28/0.46 thf(fact_161_append__Cons,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( append2089414218ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 0.28/0.46 = ( cons_S112077679ession @ X3 @ ( append2089414218ession @ Xs @ Ys2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_Cons
% 0.28/0.46 thf(fact_162_Cons__eq__appendI,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs1: list_S529945141ession,Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.28/0.46 ( ( ( cons_S112077679ession @ X3 @ Xs1 )
% 0.28/0.46 = Ys2 )
% 0.28/0.46 => ( ( Xs
% 0.28/0.46 = ( append2089414218ession @ Xs1 @ Zs2 ) )
% 0.28/0.46 => ( ( cons_S112077679ession @ X3 @ Xs )
% 0.28/0.46 = ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Cons_eq_appendI
% 0.28/0.46 thf(fact_163_append_Oleft__neutral,axiom,
% 0.28/0.46 ! [A4: list_S529945141ession] :
% 0.28/0.46 ( ( append2089414218ession @ nil_Se901661471ession @ A4 )
% 0.28/0.46 = A4 ) ).
% 0.28/0.46
% 0.28/0.46 % append.left_neutral
% 0.28/0.46 thf(fact_164_append_Oleft__neutral,axiom,
% 0.28/0.46 ! [A4: list_Secrecy_KS] :
% 0.28/0.46 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ A4 )
% 0.28/0.46 = A4 ) ).
% 0.28/0.46
% 0.28/0.46 % append.left_neutral
% 0.28/0.46 thf(fact_165_append__Nil,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( append2089414218ession @ nil_Se901661471ession @ Ys2 )
% 0.28/0.46 = Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % append_Nil
% 0.28/0.46 thf(fact_166_append__Nil,axiom,
% 0.28/0.46 ! [Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 0.28/0.46 = Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % append_Nil
% 0.28/0.46 thf(fact_167_eq__Nil__appendI,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( Xs = Ys2 )
% 0.28/0.46 => ( Xs
% 0.28/0.46 = ( append2089414218ession @ nil_Se901661471ession @ Ys2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_Nil_appendI
% 0.28/0.46 thf(fact_168_eq__Nil__appendI,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs = Ys2 )
% 0.28/0.46 => ( Xs
% 0.28/0.46 = ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_Nil_appendI
% 0.28/0.46 thf(fact_169_knows2b,axiom,
% 0.28/0.46 ! [A: secrecy_specID,E: list_S529945141ession,E1: list_S529945141ession] :
% 0.28/0.46 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E @ E1 ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows2b
% 0.28/0.46 thf(fact_170_knows2a,axiom,
% 0.28/0.46 ! [A: secrecy_specID,E1: list_S529945141ession,E: list_S529945141ession] :
% 0.28/0.46 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows2a
% 0.28/0.46 thf(fact_171_knows3,axiom,
% 0.28/0.46 ! [A: secrecy_specID,E1: list_S529945141ession,E22: list_S529945141ession] :
% 0.28/0.46 ( ( ( knowle731562421_knows @ A @ E1 )
% 0.28/0.46 & ( knowle731562421_knows @ A @ E22 ) )
% 0.28/0.46 => ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E22 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % knows3
% 0.28/0.46 thf(fact_172_ord_Olexordp__eq__pref,axiom,
% 0.28/0.46 ! [Less: secrecy_Expression > secrecy_Expression > $o,U: list_S529945141ession,V: list_S529945141ession] : ( lexord1123423577ession @ Less @ U @ ( append2089414218ession @ U @ V ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord.lexordp_eq_pref
% 0.28/0.46 thf(fact_173_notSpecKeysSecretsExpr__L2,axiom,
% 0.28/0.46 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 0.28/0.46 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 0.28/0.46 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 0.28/0.46
% 0.28/0.46 % notSpecKeysSecretsExpr_L2
% 0.28/0.46 thf(fact_174_splice_Osimps_I2_J,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( splice1390717708ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 0.28/0.46 = ( cons_S112077679ession @ X3 @ ( splice1390717708ession @ Ys2 @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % splice.simps(2)
% 0.28/0.46 thf(fact_175_splice_Osimps_I1_J,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( splice1390717708ession @ nil_Se901661471ession @ Ys2 )
% 0.28/0.46 = Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % splice.simps(1)
% 0.28/0.46 thf(fact_176_splice_Osimps_I1_J,axiom,
% 0.28/0.46 ! [Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( splice_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 0.28/0.46 = Ys2 ) ).
% 0.28/0.46
% 0.28/0.46 % splice.simps(1)
% 0.28/0.46 thf(fact_177_rev__nonempty__induct,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 0.28/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs2 != nil_Secrecy_KS )
% 0.28/0.46 => ( ( P @ Xs2 )
% 0.28/0.46 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rev_nonempty_induct
% 0.28/0.46 thf(fact_178_rev__nonempty__induct,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 0.28/0.46 ( ( Xs != nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( Xs2 != nil_Se901661471ession )
% 0.28/0.46 => ( ( P @ Xs2 )
% 0.28/0.46 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rev_nonempty_induct
% 0.28/0.46 thf(fact_179_append__eq__Cons__conv,axiom,
% 0.28/0.46 ! [Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( append_Secrecy_KS @ Ys2 @ Zs2 )
% 0.28/0.46 = ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.46 = ( ( ( Ys2 = nil_Secrecy_KS )
% 0.28/0.46 & ( Zs2
% 0.28/0.46 = ( cons_Secrecy_KS @ X3 @ Xs ) ) )
% 0.28/0.46 | ? [Ys4: list_Secrecy_KS] :
% 0.28/0.46 ( ( Ys2
% 0.28/0.46 = ( cons_Secrecy_KS @ X3 @ Ys4 ) )
% 0.28/0.46 & ( ( append_Secrecy_KS @ Ys4 @ Zs2 )
% 0.28/0.46 = Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_eq_Cons_conv
% 0.28/0.46 thf(fact_180_append__eq__Cons__conv,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession,Zs2: list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Ys2 @ Zs2 )
% 0.28/0.46 = ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.46 = ( ( ( Ys2 = nil_Se901661471ession )
% 0.28/0.46 & ( Zs2
% 0.28/0.46 = ( cons_S112077679ession @ X3 @ Xs ) ) )
% 0.28/0.46 | ? [Ys4: list_S529945141ession] :
% 0.28/0.46 ( ( Ys2
% 0.28/0.46 = ( cons_S112077679ession @ X3 @ Ys4 ) )
% 0.28/0.46 & ( ( append2089414218ession @ Ys4 @ Zs2 )
% 0.28/0.46 = Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_eq_Cons_conv
% 0.28/0.46 thf(fact_181_Cons__eq__append__conv,axiom,
% 0.28/0.46 ! [X3: secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( cons_Secrecy_KS @ X3 @ Xs )
% 0.28/0.46 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 0.28/0.46 = ( ( ( Ys2 = nil_Secrecy_KS )
% 0.28/0.46 & ( ( cons_Secrecy_KS @ X3 @ Xs )
% 0.28/0.46 = Zs2 ) )
% 0.28/0.46 | ? [Ys4: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( cons_Secrecy_KS @ X3 @ Ys4 )
% 0.28/0.46 = Ys2 )
% 0.28/0.46 & ( Xs
% 0.28/0.46 = ( append_Secrecy_KS @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Cons_eq_append_conv
% 0.28/0.46 thf(fact_182_Cons__eq__append__conv,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.28/0.46 ( ( ( cons_S112077679ession @ X3 @ Xs )
% 0.28/0.46 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.28/0.46 = ( ( ( Ys2 = nil_Se901661471ession )
% 0.28/0.46 & ( ( cons_S112077679ession @ X3 @ Xs )
% 0.28/0.46 = Zs2 ) )
% 0.28/0.46 | ? [Ys4: list_S529945141ession] :
% 0.28/0.46 ( ( ( cons_S112077679ession @ X3 @ Ys4 )
% 0.28/0.46 = Ys2 )
% 0.28/0.46 & ( Xs
% 0.28/0.46 = ( append2089414218ession @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Cons_eq_append_conv
% 0.28/0.46 thf(fact_183_rev__exhaust,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.46 => ~ ! [Ys3: list_Secrecy_KS,Y4: secrecy_KS] :
% 0.28/0.46 ( Xs
% 0.28/0.46 != ( append_Secrecy_KS @ Ys3 @ ( cons_Secrecy_KS @ Y4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rev_exhaust
% 0.28/0.46 thf(fact_184_rev__exhaust,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession] :
% 0.28/0.46 ( ( Xs != nil_Se901661471ession )
% 0.28/0.46 => ~ ! [Ys3: list_S529945141ession,Y4: secrecy_Expression] :
% 0.28/0.46 ( Xs
% 0.28/0.46 != ( append2089414218ession @ Ys3 @ ( cons_S112077679ession @ Y4 @ nil_Se901661471ession ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rev_exhaust
% 0.28/0.46 thf(fact_185_rev__induct,axiom,
% 0.28/0.46 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ nil_Secrecy_KS )
% 0.28/0.46 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( P @ Xs2 )
% 0.28/0.46 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rev_induct
% 0.28/0.46 thf(fact_186_rev__induct,axiom,
% 0.28/0.46 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( P @ nil_Se901661471ession )
% 0.28/0.46 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.46 ( ( P @ Xs2 )
% 0.28/0.46 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rev_induct
% 0.28/0.46 thf(fact_187_maps__simps_I1_J,axiom,
% 0.28/0.46 ! [F2: secrecy_Expression > list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( maps_S599402637ession @ F2 @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.46 = ( append2089414218ession @ ( F2 @ X3 ) @ ( maps_S599402637ession @ F2 @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % maps_simps(1)
% 0.28/0.46 thf(fact_188_ExtSign,axiom,
% 0.28/0.46 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 0.28/0.46 ( ( encrDecrKeys @ K12 @ K22 )
% 0.28/0.46 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 0.28/0.46 = E3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % ExtSign
% 0.28/0.46 thf(fact_189_DecrEnc,axiom,
% 0.28/0.46 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 0.28/0.46 ( ( encrDecrKeys @ K12 @ K22 )
% 0.28/0.46 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 0.28/0.46 = E3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % DecrEnc
% 0.28/0.46 thf(fact_190_concat__eq__append__conv,axiom,
% 0.28/0.46 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.28/0.46 ( ( ( concat388015140ession @ Xss2 )
% 0.28/0.46 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.28/0.46 = ( ( ( Xss2 = nil_li311616943ession )
% 0.28/0.46 => ( ( Ys2 = nil_Se901661471ession )
% 0.28/0.46 & ( Zs2 = nil_Se901661471ession ) ) )
% 0.28/0.46 & ( ( Xss2 != nil_li311616943ession )
% 0.28/0.46 => ? [Xss1: list_l425507653ession,Xs3: list_S529945141ession,Xs4: list_S529945141ession,Xss22: list_l425507653ession] :
% 0.28/0.46 ( ( Xss2
% 0.28/0.46 = ( append1105297242ession @ Xss1 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.28/0.46 & ( Ys2
% 0.28/0.46 = ( append2089414218ession @ ( concat388015140ession @ Xss1 ) @ Xs3 ) )
% 0.28/0.46 & ( Zs2
% 0.28/0.46 = ( append2089414218ession @ Xs4 @ ( concat388015140ession @ Xss22 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % concat_eq_append_conv
% 0.28/0.46 thf(fact_191_concat__eq__append__conv,axiom,
% 0.28/0.46 ! [Xss2: list_list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( concat_Secrecy_KS @ Xss2 )
% 0.28/0.46 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 0.28/0.46 = ( ( ( Xss2 = nil_list_Secrecy_KS )
% 0.28/0.46 => ( ( Ys2 = nil_Secrecy_KS )
% 0.28/0.46 & ( Zs2 = nil_Secrecy_KS ) ) )
% 0.28/0.46 & ( ( Xss2 != nil_list_Secrecy_KS )
% 0.28/0.46 => ? [Xss1: list_list_Secrecy_KS,Xs3: list_Secrecy_KS,Xs4: list_Secrecy_KS,Xss22: list_list_Secrecy_KS] :
% 0.28/0.46 ( ( Xss2
% 0.28/0.46 = ( append1376766698ecy_KS @ Xss1 @ ( cons_list_Secrecy_KS @ ( append_Secrecy_KS @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.28/0.46 & ( Ys2
% 0.28/0.46 = ( append_Secrecy_KS @ ( concat_Secrecy_KS @ Xss1 ) @ Xs3 ) )
% 0.28/0.46 & ( Zs2
% 0.28/0.46 = ( append_Secrecy_KS @ Xs4 @ ( concat_Secrecy_KS @ Xss22 ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % concat_eq_append_conv
% 0.28/0.46 thf(fact_192_rotate1_Osimps_I2_J,axiom,
% 0.28/0.46 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( rotate1_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.46 = ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rotate1.simps(2)
% 0.28/0.46 thf(fact_193_rotate1_Osimps_I2_J,axiom,
% 0.28/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( rotate1237234450ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.46 = ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % rotate1.simps(2)
% 0.28/0.46 thf(fact_194_rotate1__is__Nil__conv,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession] :
% 0.28/0.46 ( ( ( rotate1237234450ession @ Xs )
% 0.28/0.46 = nil_Se901661471ession )
% 0.28/0.46 = ( Xs = nil_Se901661471ession ) ) ).
% 0.28/0.46
% 0.28/0.46 % rotate1_is_Nil_conv
% 0.28/0.46 thf(fact_195_rotate1__is__Nil__conv,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( rotate1_Secrecy_KS @ Xs )
% 0.28/0.46 = nil_Secrecy_KS )
% 0.28/0.46 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.28/0.46
% 0.28/0.46 % rotate1_is_Nil_conv
% 0.28/0.46 thf(fact_196_concat__append,axiom,
% 0.28/0.46 ! [Xs: list_l425507653ession,Ys2: list_l425507653ession] :
% 0.28/0.46 ( ( concat388015140ession @ ( append1105297242ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( append2089414218ession @ ( concat388015140ession @ Xs ) @ ( concat388015140ession @ Ys2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % concat_append
% 0.28/0.46 thf(fact_197_rotate1_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( rotate1237234450ession @ nil_Se901661471ession )
% 0.28/0.46 = nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % rotate1.simps(1)
% 0.28/0.46 thf(fact_198_rotate1_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( rotate1_Secrecy_KS @ nil_Secrecy_KS )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % rotate1.simps(1)
% 0.28/0.46 thf(fact_199_concat_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( concat388015140ession @ nil_li311616943ession )
% 0.28/0.46 = nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % concat.simps(1)
% 0.28/0.46 thf(fact_200_concat_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( concat_Secrecy_KS @ nil_list_Secrecy_KS )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % concat.simps(1)
% 0.28/0.46 thf(fact_201_concat_Osimps_I2_J,axiom,
% 0.28/0.46 ! [X3: list_S529945141ession,Xs: list_l425507653ession] :
% 0.28/0.46 ( ( concat388015140ession @ ( cons_l533358079ession @ X3 @ Xs ) )
% 0.28/0.46 = ( append2089414218ession @ X3 @ ( concat388015140ession @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % concat.simps(2)
% 0.28/0.46 thf(fact_202_maps__simps_I2_J,axiom,
% 0.28/0.46 ! [F2: secrecy_Expression > list_S529945141ession] :
% 0.28/0.46 ( ( maps_S599402637ession @ F2 @ nil_Se901661471ession )
% 0.28/0.46 = nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % maps_simps(2)
% 0.28/0.46 thf(fact_203_maps__simps_I2_J,axiom,
% 0.28/0.46 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 0.28/0.46 ( ( maps_S399472669ecy_KS @ F2 @ nil_Se901661471ession )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % maps_simps(2)
% 0.28/0.46 thf(fact_204_maps__simps_I2_J,axiom,
% 0.28/0.46 ! [F2: secrecy_KS > list_S529945141ession] :
% 0.28/0.46 ( ( maps_S1434541085ession @ F2 @ nil_Secrecy_KS )
% 0.28/0.46 = nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % maps_simps(2)
% 0.28/0.46 thf(fact_205_maps__simps_I2_J,axiom,
% 0.28/0.46 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 0.28/0.46 ( ( maps_S377605037ecy_KS @ F2 @ nil_Secrecy_KS )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % maps_simps(2)
% 0.28/0.46 thf(fact_206_concat__eq__appendD,axiom,
% 0.28/0.46 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.28/0.46 ( ( ( concat388015140ession @ Xss2 )
% 0.28/0.46 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.28/0.46 => ( ( Xss2 != nil_li311616943ession )
% 0.28/0.46 => ? [Xss12: list_l425507653ession,Xs2: list_S529945141ession,Xs5: list_S529945141ession,Xss23: list_l425507653ession] :
% 0.28/0.46 ( ( Xss2
% 0.28/0.46 = ( append1105297242ession @ Xss12 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.28/0.46 & ( Ys2
% 0.28/0.46 = ( append2089414218ession @ ( concat388015140ession @ Xss12 ) @ Xs2 ) )
% 0.28/0.46 & ( Zs2
% 0.28/0.46 = ( append2089414218ession @ Xs5 @ ( concat388015140ession @ Xss23 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % concat_eq_appendD
% 0.28/0.46 thf(fact_207_butlast__snoc,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.46 ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % butlast_snoc
% 0.28/0.46 thf(fact_208_butlast__snoc,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.28/0.46 ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % butlast_snoc
% 0.28/0.46 thf(fact_209_last__snoc,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.46 ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 0.28/0.46 = X3 ) ).
% 0.28/0.46
% 0.28/0.46 % last_snoc
% 0.28/0.46 thf(fact_210_last__snoc,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.28/0.46 ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 0.28/0.46 = X3 ) ).
% 0.28/0.46
% 0.28/0.46 % last_snoc
% 0.28/0.46 thf(fact_211_notSpecKeysSecretsExpr__def,axiom,
% 0.28/0.46 ( notSpe1586871396tsExpr
% 0.28/0.46 = ( ^ [P3: secrecy_specID,E2: list_S529945141ession] :
% 0.28/0.46 ( ! [X4: secrecy_Keys] :
% 0.28/0.46 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E2 )
% 0.28/0.46 => ~ ( member_Secrecy_KS2 @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 0.28/0.46 & ! [Y3: secrecy_Secrets] :
% 0.28/0.46 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y3 ) @ E2 )
% 0.28/0.46 => ~ ( member_Secrecy_KS2 @ ( secrecy_sKS @ Y3 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % notSpecKeysSecretsExpr_def
% 0.28/0.46 thf(fact_212_last__appendR,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( Ys2 != nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_S1532390982ession @ Ys2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_appendR
% 0.28/0.46 thf(fact_213_last__appendR,axiom,
% 0.28/0.46 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( Ys2 != nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_Secrecy_KS @ Ys2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_appendR
% 0.28/0.46 thf(fact_214_last__appendL,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( Ys2 = nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_appendL
% 0.28/0.46 thf(fact_215_last__appendL,axiom,
% 0.28/0.46 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( Ys2 = nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_appendL
% 0.28/0.46 thf(fact_216_append__butlast__last__id,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.46 => ( ( append_Secrecy_KS @ ( butlast_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( last_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) )
% 0.28/0.46 = Xs ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_butlast_last_id
% 0.28/0.46 thf(fact_217_append__butlast__last__id,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession] :
% 0.28/0.46 ( ( Xs != nil_Se901661471ession )
% 0.28/0.46 => ( ( append2089414218ession @ ( butlas171474643ession @ Xs ) @ ( cons_S112077679ession @ ( last_S1532390982ession @ Xs ) @ nil_Se901661471ession ) )
% 0.28/0.46 = Xs ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_butlast_last_id
% 0.28/0.46 thf(fact_218_butlast_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( butlas171474643ession @ nil_Se901661471ession )
% 0.28/0.46 = nil_Se901661471ession ) ).
% 0.28/0.46
% 0.28/0.46 % butlast.simps(1)
% 0.28/0.46 thf(fact_219_butlast_Osimps_I1_J,axiom,
% 0.28/0.46 ( ( butlast_Secrecy_KS @ nil_Secrecy_KS )
% 0.28/0.46 = nil_Secrecy_KS ) ).
% 0.28/0.46
% 0.28/0.46 % butlast.simps(1)
% 0.28/0.46 thf(fact_220_snoc__eq__iff__butlast,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.28/0.46 = Ys2 )
% 0.28/0.46 = ( ( Ys2 != nil_Secrecy_KS )
% 0.28/0.46 & ( ( butlast_Secrecy_KS @ Ys2 )
% 0.28/0.46 = Xs )
% 0.28/0.46 & ( ( last_Secrecy_KS @ Ys2 )
% 0.28/0.46 = X3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % snoc_eq_iff_butlast
% 0.28/0.46 thf(fact_221_snoc__eq__iff__butlast,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.28/0.46 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.28/0.46 = Ys2 )
% 0.28/0.46 = ( ( Ys2 != nil_Se901661471ession )
% 0.28/0.46 & ( ( butlas171474643ession @ Ys2 )
% 0.28/0.46 = Xs )
% 0.28/0.46 & ( ( last_S1532390982ession @ Ys2 )
% 0.28/0.46 = X3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % snoc_eq_iff_butlast
% 0.28/0.46 thf(fact_222_last__ConsR,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.46 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_ConsR
% 0.28/0.46 thf(fact_223_last__ConsR,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.28/0.46 ( ( Xs != nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.46 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_ConsR
% 0.28/0.46 thf(fact_224_last__ConsL,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.46 ( ( Xs = nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.46 = X3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_ConsL
% 0.28/0.46 thf(fact_225_last__ConsL,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.28/0.46 ( ( Xs = nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.46 = X3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_ConsL
% 0.28/0.46 thf(fact_226_last_Osimps,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.46 ( ( ( Xs = nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.46 = X3 ) )
% 0.28/0.46 & ( ( Xs != nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.46 = ( last_Secrecy_KS @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last.simps
% 0.28/0.46 thf(fact_227_last_Osimps,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.28/0.46 ( ( ( Xs = nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.46 = X3 ) )
% 0.28/0.46 & ( ( Xs != nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.46 = ( last_S1532390982ession @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last.simps
% 0.28/0.46 thf(fact_228_longest__common__suffix,axiom,
% 0.28/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.46 ? [Ss: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 = ( append2089414218ession @ Xs5 @ Ss ) )
% 0.28/0.46 & ( Ys2
% 0.28/0.46 = ( append2089414218ession @ Ys5 @ Ss ) )
% 0.28/0.46 & ( ( Xs5 = nil_Se901661471ession )
% 0.28/0.46 | ( Ys5 = nil_Se901661471ession )
% 0.28/0.46 | ( ( last_S1532390982ession @ Xs5 )
% 0.28/0.46 != ( last_S1532390982ession @ Ys5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % longest_common_suffix
% 0.28/0.46 thf(fact_229_longest__common__suffix,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.46 ? [Ss: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 = ( append_Secrecy_KS @ Xs5 @ Ss ) )
% 0.28/0.46 & ( Ys2
% 0.28/0.46 = ( append_Secrecy_KS @ Ys5 @ Ss ) )
% 0.28/0.46 & ( ( Xs5 = nil_Secrecy_KS )
% 0.28/0.46 | ( Ys5 = nil_Secrecy_KS )
% 0.28/0.46 | ( ( last_Secrecy_KS @ Xs5 )
% 0.28/0.46 != ( last_Secrecy_KS @ Ys5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % longest_common_suffix
% 0.28/0.46 thf(fact_230_last__append,axiom,
% 0.28/0.46 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.28/0.46 ( ( ( Ys2 = nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_S1532390982ession @ Xs ) ) )
% 0.28/0.46 & ( ( Ys2 != nil_Se901661471ession )
% 0.28/0.46 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_S1532390982ession @ Ys2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_append
% 0.28/0.46 thf(fact_231_last__append,axiom,
% 0.28/0.46 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.46 ( ( ( Ys2 = nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_Secrecy_KS @ Xs ) ) )
% 0.28/0.46 & ( ( Ys2 != nil_Secrecy_KS )
% 0.28/0.46 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.46 = ( last_Secrecy_KS @ Ys2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % last_append
% 0.28/0.46 thf(fact_232_butlast_Osimps_I2_J,axiom,
% 0.28/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.46 ( ( ( Xs = nil_Secrecy_KS )
% 0.28/0.46 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.47 = nil_Secrecy_KS ) )
% 0.28/0.47 & ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.47 = ( cons_Secrecy_KS @ X3 @ ( butlast_Secrecy_KS @ Xs ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % butlast.simps(2)
% 0.28/0.47 thf(fact_233_butlast_Osimps_I2_J,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.28/0.47 ( ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.47 = nil_Se901661471ession ) )
% 0.28/0.47 & ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.47 = ( cons_S112077679ession @ X3 @ ( butlas171474643ession @ Xs ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % butlast.simps(2)
% 0.28/0.47 thf(fact_234_butlast__append,axiom,
% 0.28/0.47 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( ( Ys2 = nil_Se901661471ession )
% 0.28/0.47 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( butlas171474643ession @ Xs ) ) )
% 0.28/0.47 & ( ( Ys2 != nil_Se901661471ession )
% 0.28/0.47 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( append2089414218ession @ Xs @ ( butlas171474643ession @ Ys2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % butlast_append
% 0.28/0.47 thf(fact_235_butlast__append,axiom,
% 0.28/0.47 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( Ys2 = nil_Secrecy_KS )
% 0.28/0.47 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( butlast_Secrecy_KS @ Xs ) ) )
% 0.28/0.47 & ( ( Ys2 != nil_Secrecy_KS )
% 0.28/0.47 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( append_Secrecy_KS @ Xs @ ( butlast_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % butlast_append
% 0.28/0.47 thf(fact_236_mem_Osimps_I1_J,axiom,
% 0.28/0.47 ! [X3: secrecy_KS] :
% 0.28/0.47 ~ ( mem_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ).
% 0.28/0.47
% 0.28/0.47 % mem.simps(1)
% 0.28/0.47 thf(fact_237_mem_Osimps_I1_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression] :
% 0.28/0.47 ~ ( mem_Se1967555118ession @ X3 @ nil_Se901661471ession ) ).
% 0.28/0.47
% 0.28/0.47 % mem.simps(1)
% 0.28/0.47 thf(fact_238_mem_Osimps_I2_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Y: secrecy_Expression,L: list_S529945141ession] :
% 0.28/0.47 ( ( mem_Se1967555118ession @ X3 @ ( cons_S112077679ession @ Y @ L ) )
% 0.28/0.47 = ( ( X3 = Y )
% 0.28/0.47 | ( mem_Se1967555118ession @ X3 @ L ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem.simps(2)
% 0.28/0.47 thf(fact_239_concat__conv__foldr,axiom,
% 0.28/0.47 ( concat388015140ession
% 0.28/0.47 = ( ^ [Xss3: list_l425507653ession] : ( foldr_1531709715ession @ append2089414218ession @ Xss3 @ nil_Se901661471ession ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat_conv_foldr
% 0.28/0.47 thf(fact_240_concat__conv__foldr,axiom,
% 0.28/0.47 ( concat_Secrecy_KS
% 0.28/0.47 = ( ^ [Xss3: list_list_Secrecy_KS] : ( foldr_1711005747ecy_KS @ append_Secrecy_KS @ Xss3 @ nil_Secrecy_KS ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat_conv_foldr
% 0.28/0.47 thf(fact_241_SuccI,axiom,
% 0.28/0.47 ! [Kl: list_Secrecy_Secrets,K: secrecy_Secrets,Kl2: set_li2007071804ecrets] :
% 0.28/0.47 ( ( member1138497285ecrets @ ( append186372209ecrets @ Kl @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl2 )
% 0.28/0.47 => ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ Kl ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccI
% 0.28/0.47 thf(fact_242_SuccI,axiom,
% 0.28/0.47 ! [Kl: list_Secrecy_Keys,K: secrecy_Keys,Kl2: set_li849033543y_Keys] :
% 0.28/0.47 ( ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl2 )
% 0.28/0.47 => ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ Kl ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccI
% 0.28/0.47 thf(fact_243_SuccI,axiom,
% 0.28/0.47 ! [Kl: list_Secrecy_KS,K: secrecy_KS,Kl2: set_list_Secrecy_KS] :
% 0.28/0.47 ( ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl2 )
% 0.28/0.47 => ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ Kl ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccI
% 0.28/0.47 thf(fact_244_SuccI,axiom,
% 0.28/0.47 ! [Kl: list_S529945141ession,K: secrecy_Expression,Kl2: set_li185139947ession] :
% 0.28/0.47 ( ( member249235532ession @ ( append2089414218ession @ Kl @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl2 )
% 0.28/0.47 => ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ Kl ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccI
% 0.28/0.47 thf(fact_245_SuccD,axiom,
% 0.28/0.47 ! [K: secrecy_Secrets,Kl2: set_li2007071804ecrets,Kl: list_Secrecy_Secrets] :
% 0.28/0.47 ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ Kl ) )
% 0.28/0.47 => ( member1138497285ecrets @ ( append186372209ecrets @ Kl @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccD
% 0.28/0.47 thf(fact_246_SuccD,axiom,
% 0.28/0.47 ! [K: secrecy_Keys,Kl2: set_li849033543y_Keys,Kl: list_Secrecy_Keys] :
% 0.28/0.47 ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ Kl ) )
% 0.28/0.47 => ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccD
% 0.28/0.47 thf(fact_247_SuccD,axiom,
% 0.28/0.47 ! [K: secrecy_KS,Kl2: set_list_Secrecy_KS,Kl: list_Secrecy_KS] :
% 0.28/0.47 ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ Kl ) )
% 0.28/0.47 => ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccD
% 0.28/0.47 thf(fact_248_SuccD,axiom,
% 0.28/0.47 ! [K: secrecy_Expression,Kl2: set_li185139947ession,Kl: list_S529945141ession] :
% 0.28/0.47 ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ Kl ) )
% 0.28/0.47 => ( member249235532ession @ ( append2089414218ession @ Kl @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % SuccD
% 0.28/0.47 thf(fact_249_rev__eq__Cons__iff,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Y: secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( rev_Secrecy_KS @ Xs )
% 0.28/0.47 = ( cons_Secrecy_KS @ Y @ Ys2 ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Ys2 ) @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_eq_Cons_iff
% 0.28/0.47 thf(fact_250_rev__eq__Cons__iff,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( ( rev_Se1073238207ession @ Xs )
% 0.28/0.47 = ( cons_S112077679ession @ Y @ Ys2 ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_eq_Cons_iff
% 0.28/0.47 thf(fact_251_Nil__is__rev__conv,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( nil_Se901661471ession
% 0.28/0.47 = ( rev_Se1073238207ession @ Xs ) )
% 0.28/0.47 = ( Xs = nil_Se901661471ession ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_is_rev_conv
% 0.28/0.47 thf(fact_252_Nil__is__rev__conv,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( nil_Secrecy_KS
% 0.28/0.47 = ( rev_Secrecy_KS @ Xs ) )
% 0.28/0.47 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_is_rev_conv
% 0.28/0.47 thf(fact_253_rev__is__Nil__conv,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( ( rev_Se1073238207ession @ Xs )
% 0.28/0.47 = nil_Se901661471ession )
% 0.28/0.47 = ( Xs = nil_Se901661471ession ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_is_Nil_conv
% 0.28/0.47 thf(fact_254_rev__is__Nil__conv,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( rev_Secrecy_KS @ Xs )
% 0.28/0.47 = nil_Secrecy_KS )
% 0.28/0.47 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_is_Nil_conv
% 0.28/0.47 thf(fact_255_rev__append,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( rev_Se1073238207ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( rev_Se1073238207ession @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_append
% 0.28/0.47 thf(fact_256_singleton__rev__conv,axiom,
% 0.28/0.47 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 0.28/0.47 = ( rev_Secrecy_KS @ Xs ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % singleton_rev_conv
% 0.28/0.47 thf(fact_257_singleton__rev__conv,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( ( cons_S112077679ession @ X3 @ nil_Se901661471ession )
% 0.28/0.47 = ( rev_Se1073238207ession @ Xs ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % singleton_rev_conv
% 0.28/0.47 thf(fact_258_rev__singleton__conv,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.47 ( ( ( rev_Secrecy_KS @ Xs )
% 0.28/0.47 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_singleton_conv
% 0.28/0.47 thf(fact_259_rev__singleton__conv,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.28/0.47 ( ( ( rev_Se1073238207ession @ Xs )
% 0.28/0.47 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_singleton_conv
% 0.28/0.47 thf(fact_260_rev_Osimps_I1_J,axiom,
% 0.28/0.47 ( ( rev_Se1073238207ession @ nil_Se901661471ession )
% 0.28/0.47 = nil_Se901661471ession ) ).
% 0.28/0.47
% 0.28/0.47 % rev.simps(1)
% 0.28/0.47 thf(fact_261_rev_Osimps_I1_J,axiom,
% 0.28/0.47 ( ( rev_Secrecy_KS @ nil_Secrecy_KS )
% 0.28/0.47 = nil_Secrecy_KS ) ).
% 0.28/0.47
% 0.28/0.47 % rev.simps(1)
% 0.28/0.47 thf(fact_262_rev_Osimps_I2_J,axiom,
% 0.28/0.47 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( rev_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.47 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev.simps(2)
% 0.28/0.47 thf(fact_263_rev_Osimps_I2_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( rev_Se1073238207ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.47 = ( append2089414218ession @ ( rev_Se1073238207ession @ Xs ) @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev.simps(2)
% 0.28/0.47 thf(fact_264_empty__Shift,axiom,
% 0.28/0.47 ! [Kl2: set_li2007071804ecrets,K: secrecy_Secrets] :
% 0.28/0.47 ( ( member1138497285ecrets @ nil_Secrecy_Secrets @ Kl2 )
% 0.28/0.47 => ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ nil_Secrecy_Secrets ) )
% 0.28/0.47 => ( member1138497285ecrets @ nil_Secrecy_Secrets @ ( bNF_Gr28627573ecrets @ Kl2 @ K ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % empty_Shift
% 0.28/0.47 thf(fact_265_empty__Shift,axiom,
% 0.28/0.47 ! [Kl2: set_li849033543y_Keys,K: secrecy_Keys] :
% 0.28/0.47 ( ( member341114536y_Keys @ nil_Secrecy_Keys @ Kl2 )
% 0.28/0.47 => ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ nil_Secrecy_Keys ) )
% 0.28/0.47 => ( member341114536y_Keys @ nil_Secrecy_Keys @ ( bNF_Gr414702370y_Keys @ Kl2 @ K ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % empty_Shift
% 0.28/0.47 thf(fact_266_empty__Shift,axiom,
% 0.28/0.47 ! [Kl2: set_li185139947ession,K: secrecy_Expression] :
% 0.28/0.47 ( ( member249235532ession @ nil_Se901661471ession @ Kl2 )
% 0.28/0.47 => ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ nil_Se901661471ession ) )
% 0.28/0.47 => ( member249235532ession @ nil_Se901661471ession @ ( bNF_Gr275623750ession @ Kl2 @ K ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % empty_Shift
% 0.28/0.47 thf(fact_267_empty__Shift,axiom,
% 0.28/0.47 ! [Kl2: set_list_Secrecy_KS,K: secrecy_KS] :
% 0.28/0.47 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ Kl2 )
% 0.28/0.47 => ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ nil_Secrecy_KS ) )
% 0.28/0.47 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( bNF_Gr660123862ecy_KS @ Kl2 @ K ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % empty_Shift
% 0.28/0.47 thf(fact_268_ShiftD,axiom,
% 0.28/0.47 ! [Kl: list_S529945141ession,Kl2: set_li185139947ession,K: secrecy_Expression] :
% 0.28/0.47 ( ( member249235532ession @ Kl @ ( bNF_Gr275623750ession @ Kl2 @ K ) )
% 0.28/0.47 => ( member249235532ession @ ( cons_S112077679ession @ K @ Kl ) @ Kl2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % ShiftD
% 0.28/0.47 thf(fact_269_Succ__Shift,axiom,
% 0.28/0.47 ! [Kl2: set_li185139947ession,K: secrecy_Expression,Kl: list_S529945141ession] :
% 0.28/0.47 ( ( bNF_Gr979629770ession @ ( bNF_Gr275623750ession @ Kl2 @ K ) @ Kl )
% 0.28/0.47 = ( bNF_Gr979629770ession @ Kl2 @ ( cons_S112077679ession @ K @ Kl ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Succ_Shift
% 0.28/0.47 thf(fact_270_last__rev,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( last_S1532390982ession @ ( rev_Se1073238207ession @ Xs ) )
% 0.28/0.47 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_rev
% 0.28/0.47 thf(fact_271_last__rev,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( last_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 0.28/0.47 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_rev
% 0.28/0.47 thf(fact_272_hd__rev,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( hd_Sec357328890ession @ ( rev_Se1073238207ession @ Xs ) )
% 0.28/0.47 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_rev
% 0.28/0.47 thf(fact_273_hd__rev,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( hd_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 0.28/0.47 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_rev
% 0.28/0.47 thf(fact_274_hd__append2,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_append2
% 0.28/0.47 thf(fact_275_hd__append2,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_append2
% 0.28/0.47 thf(fact_276_hd__append,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( hd_Sec357328890ession @ Ys2 ) ) )
% 0.28/0.47 & ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( hd_Sec357328890ession @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_append
% 0.28/0.47 thf(fact_277_hd__append,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( hd_Secrecy_KS @ Ys2 ) ) )
% 0.28/0.47 & ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( hd_Secrecy_KS @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_append
% 0.28/0.47 thf(fact_278_longest__common__prefix,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ? [Ps: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append2089414218ession @ Ps @ Xs5 ) )
% 0.28/0.47 & ( Ys2
% 0.28/0.47 = ( append2089414218ession @ Ps @ Ys5 ) )
% 0.28/0.47 & ( ( Xs5 = nil_Se901661471ession )
% 0.28/0.47 | ( Ys5 = nil_Se901661471ession )
% 0.28/0.47 | ( ( hd_Sec357328890ession @ Xs5 )
% 0.28/0.47 != ( hd_Sec357328890ession @ Ys5 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % longest_common_prefix
% 0.28/0.47 thf(fact_279_longest__common__prefix,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ? [Ps: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append_Secrecy_KS @ Ps @ Xs5 ) )
% 0.28/0.47 & ( Ys2
% 0.28/0.47 = ( append_Secrecy_KS @ Ps @ Ys5 ) )
% 0.28/0.47 & ( ( Xs5 = nil_Secrecy_KS )
% 0.28/0.47 | ( Ys5 = nil_Secrecy_KS )
% 0.28/0.47 | ( ( hd_Secrecy_KS @ Xs5 )
% 0.28/0.47 != ( hd_Secrecy_KS @ Ys5 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % longest_common_prefix
% 0.28/0.47 thf(fact_280_hd__concat,axiom,
% 0.28/0.47 ! [Xs: list_l425507653ession] :
% 0.28/0.47 ( ( Xs != nil_li311616943ession )
% 0.28/0.47 => ( ( ( hd_lis1623417098ession @ Xs )
% 0.28/0.47 != nil_Se901661471ession )
% 0.28/0.47 => ( ( hd_Sec357328890ession @ ( concat388015140ession @ Xs ) )
% 0.28/0.47 = ( hd_Sec357328890ession @ ( hd_lis1623417098ession @ Xs ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_concat
% 0.28/0.47 thf(fact_281_hd__concat,axiom,
% 0.28/0.47 ! [Xs: list_list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs != nil_list_Secrecy_KS )
% 0.28/0.47 => ( ( ( hd_list_Secrecy_KS @ Xs )
% 0.28/0.47 != nil_Secrecy_KS )
% 0.28/0.47 => ( ( hd_Secrecy_KS @ ( concat_Secrecy_KS @ Xs ) )
% 0.28/0.47 = ( hd_Secrecy_KS @ ( hd_list_Secrecy_KS @ Xs ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_concat
% 0.28/0.47 thf(fact_282_list_Osel_I1_J,axiom,
% 0.28/0.47 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.28/0.47 ( ( hd_Sec357328890ession @ ( cons_S112077679ession @ X21 @ X222 ) )
% 0.28/0.47 = X21 ) ).
% 0.28/0.47
% 0.28/0.47 % list.sel(1)
% 0.28/0.47 thf(fact_283_rotate1__hd__tl,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( rotate1_Secrecy_KS @ Xs )
% 0.28/0.47 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rotate1_hd_tl
% 0.28/0.47 thf(fact_284_rotate1__hd__tl,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( rotate1237234450ession @ Xs )
% 0.28/0.47 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ nil_Se901661471ession ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rotate1_hd_tl
% 0.28/0.47 thf(fact_285_distinct__adj__append__iff,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( distin1076152135ession @ Xs )
% 0.28/0.47 & ( distin1076152135ession @ Ys2 )
% 0.28/0.47 & ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ( Ys2 = nil_Se901661471ession )
% 0.28/0.47 | ( ( last_S1532390982ession @ Xs )
% 0.28/0.47 != ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_append_iff
% 0.28/0.47 thf(fact_286_distinct__adj__append__iff,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( distin1495927511ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( distin1495927511ecy_KS @ Xs )
% 0.28/0.47 & ( distin1495927511ecy_KS @ Ys2 )
% 0.28/0.47 & ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ( Ys2 = nil_Secrecy_KS )
% 0.28/0.47 | ( ( last_Secrecy_KS @ Xs )
% 0.28/0.47 != ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_append_iff
% 0.28/0.47 thf(fact_287_distinct__adj__Cons__Cons,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.28/0.47 = ( ( X3 != Y )
% 0.28/0.47 & ( distin1076152135ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_Cons_Cons
% 0.28/0.47 thf(fact_288_tl__append2,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( tl_Sec1905266422ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % tl_append2
% 0.28/0.47 thf(fact_289_tl__append2,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( tl_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % tl_append2
% 0.28/0.47 thf(fact_290_list_Ocollapse,axiom,
% 0.28/0.47 ! [List: list_Secrecy_KS] :
% 0.28/0.47 ( ( List != nil_Secrecy_KS )
% 0.28/0.47 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) )
% 0.28/0.47 = List ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.collapse
% 0.28/0.47 thf(fact_291_list_Ocollapse,axiom,
% 0.28/0.47 ! [List: list_S529945141ession] :
% 0.28/0.47 ( ( List != nil_Se901661471ession )
% 0.28/0.47 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) )
% 0.28/0.47 = List ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.collapse
% 0.28/0.47 thf(fact_292_hd__Cons__tl,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ ( tl_Secrecy_KS @ Xs ) )
% 0.28/0.47 = Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_Cons_tl
% 0.28/0.47 thf(fact_293_hd__Cons__tl,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ ( tl_Sec1905266422ession @ Xs ) )
% 0.28/0.47 = Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % hd_Cons_tl
% 0.28/0.47 thf(fact_294_list_Oexpand,axiom,
% 0.28/0.47 ! [List: list_S529945141ession,List2: list_S529945141ession] :
% 0.28/0.47 ( ( ( List = nil_Se901661471ession )
% 0.28/0.47 = ( List2 = nil_Se901661471ession ) )
% 0.28/0.47 => ( ( ( List != nil_Se901661471ession )
% 0.28/0.47 => ( ( List2 != nil_Se901661471ession )
% 0.28/0.47 => ( ( ( hd_Sec357328890ession @ List )
% 0.28/0.47 = ( hd_Sec357328890ession @ List2 ) )
% 0.28/0.47 & ( ( tl_Sec1905266422ession @ List )
% 0.28/0.47 = ( tl_Sec1905266422ession @ List2 ) ) ) ) )
% 0.28/0.47 => ( List = List2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.expand
% 0.28/0.47 thf(fact_295_list_Oexpand,axiom,
% 0.28/0.47 ! [List: list_Secrecy_KS,List2: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( List = nil_Secrecy_KS )
% 0.28/0.47 = ( List2 = nil_Secrecy_KS ) )
% 0.28/0.47 => ( ( ( List != nil_Secrecy_KS )
% 0.28/0.47 => ( ( List2 != nil_Secrecy_KS )
% 0.28/0.47 => ( ( ( hd_Secrecy_KS @ List )
% 0.28/0.47 = ( hd_Secrecy_KS @ List2 ) )
% 0.28/0.47 & ( ( tl_Secrecy_KS @ List )
% 0.28/0.47 = ( tl_Secrecy_KS @ List2 ) ) ) ) )
% 0.28/0.47 => ( List = List2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.expand
% 0.28/0.47 thf(fact_296_distinct__adj__appendD1,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 => ( distin1076152135ession @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_appendD1
% 0.28/0.47 thf(fact_297_distinct__adj__appendD2,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 => ( distin1076152135ession @ Ys2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_appendD2
% 0.28/0.47 thf(fact_298_distinct__adj__Nil,axiom,
% 0.28/0.47 distin1076152135ession @ nil_Se901661471ession ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_Nil
% 0.28/0.47 thf(fact_299_distinct__adj__Nil,axiom,
% 0.28/0.47 distin1495927511ecy_KS @ nil_Secrecy_KS ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_Nil
% 0.28/0.47 thf(fact_300_distinct__adj__ConsD,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.47 => ( distin1076152135ession @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_ConsD
% 0.28/0.47 thf(fact_301_list_Osel_I2_J,axiom,
% 0.28/0.47 ( ( tl_Sec1905266422ession @ nil_Se901661471ession )
% 0.28/0.47 = nil_Se901661471ession ) ).
% 0.28/0.47
% 0.28/0.47 % list.sel(2)
% 0.28/0.47 thf(fact_302_list_Osel_I2_J,axiom,
% 0.28/0.47 ( ( tl_Secrecy_KS @ nil_Secrecy_KS )
% 0.28/0.47 = nil_Secrecy_KS ) ).
% 0.28/0.47
% 0.28/0.47 % list.sel(2)
% 0.28/0.47 thf(fact_303_list_Osel_I3_J,axiom,
% 0.28/0.47 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.28/0.47 ( ( tl_Sec1905266422ession @ ( cons_S112077679ession @ X21 @ X222 ) )
% 0.28/0.47 = X222 ) ).
% 0.28/0.47
% 0.28/0.47 % list.sel(3)
% 0.28/0.47 thf(fact_304_tl__Nil,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( tl_Secrecy_KS @ Xs )
% 0.28/0.47 = nil_Secrecy_KS )
% 0.28/0.47 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ? [X4: secrecy_KS] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % tl_Nil
% 0.28/0.47 thf(fact_305_tl__Nil,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( ( tl_Sec1905266422ession @ Xs )
% 0.28/0.47 = nil_Se901661471ession )
% 0.28/0.47 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ? [X4: secrecy_Expression] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % tl_Nil
% 0.28/0.47 thf(fact_306_Nil__tl,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( nil_Secrecy_KS
% 0.28/0.47 = ( tl_Secrecy_KS @ Xs ) )
% 0.28/0.47 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ? [X4: secrecy_KS] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_tl
% 0.28/0.47 thf(fact_307_Nil__tl,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( nil_Se901661471ession
% 0.28/0.47 = ( tl_Sec1905266422ession @ Xs ) )
% 0.28/0.47 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ? [X4: secrecy_Expression] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_tl
% 0.28/0.47 thf(fact_308_last__tl,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ( ( tl_Sec1905266422ession @ Xs )
% 0.28/0.47 != nil_Se901661471ession ) )
% 0.28/0.47 => ( ( last_S1532390982ession @ ( tl_Sec1905266422ession @ Xs ) )
% 0.28/0.47 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_tl
% 0.28/0.47 thf(fact_309_last__tl,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ( ( tl_Secrecy_KS @ Xs )
% 0.28/0.47 != nil_Secrecy_KS ) )
% 0.28/0.47 => ( ( last_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) )
% 0.28/0.47 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_tl
% 0.28/0.47 thf(fact_310_distinct__adj__singleton,axiom,
% 0.28/0.47 ! [X3: secrecy_KS] : ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_singleton
% 0.28/0.47 thf(fact_311_distinct__adj__singleton,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression] : ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_singleton
% 0.28/0.47 thf(fact_312_list_Oexhaust__sel,axiom,
% 0.28/0.47 ! [List: list_Secrecy_KS] :
% 0.28/0.47 ( ( List != nil_Secrecy_KS )
% 0.28/0.47 => ( List
% 0.28/0.47 = ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.exhaust_sel
% 0.28/0.47 thf(fact_313_list_Oexhaust__sel,axiom,
% 0.28/0.47 ! [List: list_S529945141ession] :
% 0.28/0.47 ( ( List != nil_Se901661471ession )
% 0.28/0.47 => ( List
% 0.28/0.47 = ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.exhaust_sel
% 0.28/0.47 thf(fact_314_distinct__adj__Cons,axiom,
% 0.28/0.47 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.47 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ( ( X3
% 0.28/0.47 != ( hd_Secrecy_KS @ Xs ) )
% 0.28/0.47 & ( distin1495927511ecy_KS @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_Cons
% 0.28/0.47 thf(fact_315_distinct__adj__Cons,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.47 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ( ( X3
% 0.28/0.47 != ( hd_Sec357328890ession @ Xs ) )
% 0.28/0.47 & ( distin1076152135ession @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % distinct_adj_Cons
% 0.28/0.47 thf(fact_316_successively__append__iff,axiom,
% 0.28/0.47 ! [P: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( succes1388047762ession @ P @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( succes1388047762ession @ P @ Xs )
% 0.28/0.47 & ( succes1388047762ession @ P @ Ys2 )
% 0.28/0.47 & ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ( Ys2 = nil_Se901661471ession )
% 0.28/0.47 | ( P @ ( last_S1532390982ession @ Xs ) @ ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively_append_iff
% 0.28/0.47 thf(fact_317_successively__append__iff,axiom,
% 0.28/0.47 ! [P: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( succes590251810ecy_KS @ P @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( succes590251810ecy_KS @ P @ Xs )
% 0.28/0.47 & ( succes590251810ecy_KS @ P @ Ys2 )
% 0.28/0.47 & ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ( Ys2 = nil_Secrecy_KS )
% 0.28/0.47 | ( P @ ( last_Secrecy_KS @ Xs ) @ ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively_append_iff
% 0.28/0.47 thf(fact_318_Cons__in__shuffles__iff,axiom,
% 0.28/0.47 ! [Z: secrecy_KS,Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( member193705948ecy_KS @ ( cons_Secrecy_KS @ Z @ Zs2 ) @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( ( Xs != nil_Secrecy_KS )
% 0.28/0.47 & ( ( hd_Secrecy_KS @ Xs )
% 0.28/0.47 = Z )
% 0.28/0.47 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) )
% 0.28/0.47 | ( ( Ys2 != nil_Secrecy_KS )
% 0.28/0.47 & ( ( hd_Secrecy_KS @ Ys2 )
% 0.28/0.47 = Z )
% 0.28/0.47 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ ( tl_Secrecy_KS @ Ys2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_in_shuffles_iff
% 0.28/0.47 thf(fact_319_Cons__in__shuffles__iff,axiom,
% 0.28/0.47 ! [Z: secrecy_Expression,Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( ( Xs != nil_Se901661471ession )
% 0.28/0.47 & ( ( hd_Sec357328890ession @ Xs )
% 0.28/0.47 = Z )
% 0.28/0.47 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) )
% 0.28/0.47 | ( ( Ys2 != nil_Se901661471ession )
% 0.28/0.47 & ( ( hd_Sec357328890ession @ Ys2 )
% 0.28/0.47 = Z )
% 0.28/0.47 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ ( tl_Sec1905266422ession @ Ys2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_in_shuffles_iff
% 0.28/0.47 thf(fact_320_Nil__in__shuffles,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_in_shuffles
% 0.28/0.47 thf(fact_321_Nil__in__shuffles,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_in_shuffles
% 0.28/0.47 thf(fact_322_shufflesE,axiom,
% 0.28/0.47 ! [Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 => ( ( ( Zs2 = Xs )
% 0.28/0.47 => ( Ys2 != nil_Secrecy_KS ) )
% 0.28/0.47 => ( ( ( Zs2 = Ys2 )
% 0.28/0.47 => ( Xs != nil_Secrecy_KS ) )
% 0.28/0.47 => ( ! [X: secrecy_KS,Xs5: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( cons_Secrecy_KS @ X @ Xs5 ) )
% 0.28/0.47 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 0.28/0.47 ( ( Zs2
% 0.28/0.47 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 0.28/0.47 => ( ( X = Z2 )
% 0.28/0.47 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs5 @ Ys2 ) ) ) ) )
% 0.28/0.47 => ~ ! [Y4: secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.28/0.47 ( ( Ys2
% 0.28/0.47 = ( cons_Secrecy_KS @ Y4 @ Ys5 ) )
% 0.28/0.47 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 0.28/0.47 ( ( Zs2
% 0.28/0.47 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 0.28/0.47 => ( ( Y4 = Z2 )
% 0.28/0.47 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % shufflesE
% 0.28/0.47 thf(fact_323_shufflesE,axiom,
% 0.28/0.47 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.28/0.47 => ( ( ( Zs2 = Xs )
% 0.28/0.47 => ( Ys2 != nil_Se901661471ession ) )
% 0.28/0.47 => ( ( ( Zs2 = Ys2 )
% 0.28/0.47 => ( Xs != nil_Se901661471ession ) )
% 0.28/0.47 => ( ! [X: secrecy_Expression,Xs5: list_S529945141ession] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( cons_S112077679ession @ X @ Xs5 ) )
% 0.28/0.47 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 0.28/0.47 ( ( Zs2
% 0.28/0.47 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 0.28/0.47 => ( ( X = Z2 )
% 0.28/0.47 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs5 @ Ys2 ) ) ) ) )
% 0.28/0.47 => ~ ! [Y4: secrecy_Expression,Ys5: list_S529945141ession] :
% 0.28/0.47 ( ( Ys2
% 0.28/0.47 = ( cons_S112077679ession @ Y4 @ Ys5 ) )
% 0.28/0.47 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 0.28/0.47 ( ( Zs2
% 0.28/0.47 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 0.28/0.47 => ( ( Y4 = Z2 )
% 0.28/0.47 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % shufflesE
% 0.28/0.47 thf(fact_324_successively_Osimps_I2_J,axiom,
% 0.28/0.47 ! [P: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS] : ( succes590251810ecy_KS @ P @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.simps(2)
% 0.28/0.47 thf(fact_325_successively_Osimps_I2_J,axiom,
% 0.28/0.47 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression] : ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.simps(2)
% 0.28/0.47 thf(fact_326_successively_Oelims_I1_J,axiom,
% 0.28/0.47 ! [X3: secrecy_KS > secrecy_KS > $o,Xa: list_Secrecy_KS,Y: $o] :
% 0.28/0.47 ( ( ( succes590251810ecy_KS @ X3 @ Xa )
% 0.28/0.47 = Y )
% 0.28/0.47 => ( ( ( Xa = nil_Secrecy_KS )
% 0.28/0.47 => ~ Y )
% 0.28/0.47 => ( ( ? [X: secrecy_KS] :
% 0.28/0.47 ( Xa
% 0.28/0.47 = ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.47 => ~ Y )
% 0.28/0.47 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xa
% 0.28/0.47 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.28/0.47 => ( Y
% 0.28/0.47 = ( ~ ( ( X3 @ X @ Y4 )
% 0.28/0.47 & ( succes590251810ecy_KS @ X3 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.elims(1)
% 0.28/0.47 thf(fact_327_successively_Oelims_I1_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession,Y: $o] :
% 0.28/0.47 ( ( ( succes1388047762ession @ X3 @ Xa )
% 0.28/0.47 = Y )
% 0.28/0.47 => ( ( ( Xa = nil_Se901661471ession )
% 0.28/0.47 => ~ Y )
% 0.28/0.47 => ( ( ? [X: secrecy_Expression] :
% 0.28/0.47 ( Xa
% 0.28/0.47 = ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.47 => ~ Y )
% 0.28/0.47 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.47 ( ( Xa
% 0.28/0.47 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.28/0.47 => ( Y
% 0.28/0.47 = ( ~ ( ( X3 @ X @ Y4 )
% 0.28/0.47 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.elims(1)
% 0.28/0.47 thf(fact_328_successively_Oelims_I2_J,axiom,
% 0.28/0.47 ! [X3: secrecy_KS > secrecy_KS > $o,Xa: list_Secrecy_KS] :
% 0.28/0.47 ( ( succes590251810ecy_KS @ X3 @ Xa )
% 0.28/0.47 => ( ( Xa != nil_Secrecy_KS )
% 0.28/0.47 => ( ! [X: secrecy_KS] :
% 0.28/0.47 ( Xa
% 0.28/0.47 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.47 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xa
% 0.28/0.47 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.28/0.47 => ~ ( ( X3 @ X @ Y4 )
% 0.28/0.47 & ( succes590251810ecy_KS @ X3 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.elims(2)
% 0.28/0.47 thf(fact_329_successively_Oelims_I2_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession] :
% 0.28/0.47 ( ( succes1388047762ession @ X3 @ Xa )
% 0.28/0.47 => ( ( Xa != nil_Se901661471ession )
% 0.28/0.47 => ( ! [X: secrecy_Expression] :
% 0.28/0.47 ( Xa
% 0.28/0.47 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.47 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.47 ( ( Xa
% 0.28/0.47 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.28/0.47 => ~ ( ( X3 @ X @ Y4 )
% 0.28/0.47 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.elims(2)
% 0.28/0.47 thf(fact_330_successively_Osimps_I1_J,axiom,
% 0.28/0.47 ! [P: secrecy_Expression > secrecy_Expression > $o] : ( succes1388047762ession @ P @ nil_Se901661471ession ) ).
% 0.28/0.47
% 0.28/0.47 % successively.simps(1)
% 0.28/0.47 thf(fact_331_successively_Osimps_I1_J,axiom,
% 0.28/0.47 ! [P: secrecy_KS > secrecy_KS > $o] : ( succes590251810ecy_KS @ P @ nil_Secrecy_KS ) ).
% 0.28/0.47
% 0.28/0.47 % successively.simps(1)
% 0.28/0.47 thf(fact_332_successively_Osimps_I3_J,axiom,
% 0.28/0.47 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.28/0.47 = ( ( P @ X3 @ Y )
% 0.28/0.47 & ( succes1388047762ession @ P @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.simps(3)
% 0.28/0.47 thf(fact_333_successively_Oelims_I3_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession] :
% 0.28/0.47 ( ~ ( succes1388047762ession @ X3 @ Xa )
% 0.28/0.47 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.47 ( ( Xa
% 0.28/0.47 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.28/0.47 => ( ( X3 @ X @ Y4 )
% 0.28/0.47 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.elims(3)
% 0.28/0.47 thf(fact_334_Nil__in__shufflesI,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 => ( ( Ys2 = nil_Se901661471ession )
% 0.28/0.47 => ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_in_shufflesI
% 0.28/0.47 thf(fact_335_Nil__in__shufflesI,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 => ( ( Ys2 = nil_Secrecy_KS )
% 0.28/0.47 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_in_shufflesI
% 0.28/0.47 thf(fact_336_Cons__in__shuffles__rightI,axiom,
% 0.28/0.47 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession,Z: secrecy_Expression] :
% 0.28/0.47 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.28/0.47 => ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ ( cons_S112077679ession @ Z @ Ys2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_in_shuffles_rightI
% 0.28/0.47 thf(fact_337_Cons__in__shuffles__leftI,axiom,
% 0.28/0.47 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession,Z: secrecy_Expression] :
% 0.28/0.47 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.28/0.47 => ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ ( cons_S112077679ession @ Z @ Xs ) @ Ys2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_in_shuffles_leftI
% 0.28/0.47 thf(fact_338_successively__Cons,axiom,
% 0.28/0.47 ! [P: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( succes590251810ecy_KS @ P @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.28/0.47 = ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ( ( P @ X3 @ ( hd_Secrecy_KS @ Xs ) )
% 0.28/0.47 & ( succes590251810ecy_KS @ P @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively_Cons
% 0.28/0.47 thf(fact_339_successively__Cons,axiom,
% 0.28/0.47 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.28/0.47 = ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ( ( P @ X3 @ ( hd_Sec357328890ession @ Xs ) )
% 0.28/0.47 & ( succes1388047762ession @ P @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively_Cons
% 0.28/0.47 thf(fact_340_remdups__adj__append_H,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.28/0.47 ( ( ( Xs = nil_Se901661471ession )
% 0.28/0.47 | ( Ys2 = nil_Se901661471ession )
% 0.28/0.47 | ( ( last_S1532390982ession @ Xs )
% 0.28/0.47 != ( hd_Sec357328890ession @ Ys2 ) ) )
% 0.28/0.47 => ( ( remdup484344169ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.28/0.47 = ( append2089414218ession @ ( remdup484344169ession @ Xs ) @ ( remdup484344169ession @ Ys2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj_append'
% 0.28/0.47 thf(fact_341_remdups__adj__append_H,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( Xs = nil_Secrecy_KS )
% 0.28/0.47 | ( Ys2 = nil_Secrecy_KS )
% 0.28/0.47 | ( ( last_Secrecy_KS @ Xs )
% 0.28/0.47 != ( hd_Secrecy_KS @ Ys2 ) ) )
% 0.28/0.47 => ( ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.28/0.47 = ( append_Secrecy_KS @ ( remdup351570169ecy_KS @ Xs ) @ ( remdup351570169ecy_KS @ Ys2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj_append'
% 0.28/0.47 thf(fact_342_remdups__adj__append,axiom,
% 0.28/0.47 ! [Xs_1: list_Secrecy_KS,X3: secrecy_KS,Xs_2: list_Secrecy_KS] :
% 0.28/0.47 ( ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs_1 @ ( cons_Secrecy_KS @ X3 @ Xs_2 ) ) )
% 0.28/0.47 = ( append_Secrecy_KS @ ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs_1 @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) @ ( tl_Secrecy_KS @ ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs_2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj_append
% 0.28/0.47 thf(fact_343_remdups__adj__append,axiom,
% 0.28/0.47 ! [Xs_1: list_S529945141ession,X3: secrecy_Expression,Xs_2: list_S529945141ession] :
% 0.28/0.47 ( ( remdup484344169ession @ ( append2089414218ession @ Xs_1 @ ( cons_S112077679ession @ X3 @ Xs_2 ) ) )
% 0.28/0.47 = ( append2089414218ession @ ( remdup484344169ession @ ( append2089414218ession @ Xs_1 @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs_2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj_append
% 0.28/0.47 thf(fact_344_remdups__adj__Nil__iff,axiom,
% 0.28/0.47 ! [Xs: list_S529945141ession] :
% 0.28/0.47 ( ( ( remdup484344169ession @ Xs )
% 0.28/0.47 = nil_Se901661471ession )
% 0.28/0.47 = ( Xs = nil_Se901661471ession ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj_Nil_iff
% 0.28/0.47 thf(fact_345_remdups__adj__Nil__iff,axiom,
% 0.28/0.47 ! [Xs: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( remdup351570169ecy_KS @ Xs )
% 0.28/0.47 = nil_Secrecy_KS )
% 0.28/0.47 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj_Nil_iff
% 0.28/0.47 thf(fact_346_remdups__adj__Cons__alt,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( cons_S112077679ession @ X3 @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) )
% 0.28/0.47 = ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj_Cons_alt
% 0.28/0.47 thf(fact_347_remdups__adj_Osimps_I2_J,axiom,
% 0.28/0.47 ! [X3: secrecy_KS] :
% 0.28/0.47 ( ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.28/0.47 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj.simps(2)
% 0.28/0.47 thf(fact_348_remdups__adj_Osimps_I2_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression] :
% 0.28/0.47 ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.28/0.47 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj.simps(2)
% 0.28/0.47 thf(fact_349_remdups__adj_Oelims,axiom,
% 0.28/0.47 ! [X3: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 0.28/0.47 ( ( ( remdup351570169ecy_KS @ X3 )
% 0.28/0.47 = Y )
% 0.28/0.47 => ( ( ( X3 = nil_Secrecy_KS )
% 0.28/0.47 => ( Y != nil_Secrecy_KS ) )
% 0.28/0.47 => ( ! [X: secrecy_KS] :
% 0.28/0.47 ( ( X3
% 0.28/0.47 = ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.28/0.47 => ( Y
% 0.28/0.47 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) )
% 0.28/0.47 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.28/0.47 ( ( X3
% 0.28/0.47 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.28/0.47 => ~ ( ( ( X = Y4 )
% 0.28/0.47 => ( Y
% 0.28/0.47 = ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 0.28/0.47 & ( ( X != Y4 )
% 0.28/0.47 => ( Y
% 0.28/0.47 = ( cons_Secrecy_KS @ X @ ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj.elims
% 0.28/0.47 thf(fact_350_remdups__adj_Oelims,axiom,
% 0.28/0.47 ! [X3: list_S529945141ession,Y: list_S529945141ession] :
% 0.28/0.47 ( ( ( remdup484344169ession @ X3 )
% 0.28/0.47 = Y )
% 0.28/0.47 => ( ( ( X3 = nil_Se901661471ession )
% 0.28/0.47 => ( Y != nil_Se901661471ession ) )
% 0.28/0.47 => ( ! [X: secrecy_Expression] :
% 0.28/0.47 ( ( X3
% 0.28/0.47 = ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.28/0.47 => ( Y
% 0.28/0.47 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) )
% 0.28/0.47 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.28/0.47 ( ( X3
% 0.28/0.47 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.28/0.47 => ~ ( ( ( X = Y4 )
% 0.28/0.47 => ( Y
% 0.28/0.47 = ( remdup484344169ession @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 0.28/0.47 & ( ( X != Y4 )
% 0.28/0.47 => ( Y
% 0.28/0.47 = ( cons_S112077679ession @ X @ ( remdup484344169ession @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj.elims
% 0.28/0.47 thf(fact_351_remdups__adj_Osimps_I3_J,axiom,
% 0.28/0.47 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 0.28/0.47 ( ( ( X3 = Y )
% 0.28/0.47 => ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.28/0.47 = ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) )
% 0.28/0.47 & ( ( X3 != Y )
% 0.28/0.47 => ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.28/0.47 = ( cons_S112077679ession @ X3 @ ( remdup484344169ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % remdups_adj.simps(3)
% 0.28/0.47
% 0.28/0.47 % Conjectures (1)
% 0.28/0.47 thf(conj_0,conjecture,
% 0.28/0.47 knowle945212990e_know @ a @ ( secrecy_sKS @ m ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.82/1.54 ---- Embedded in THF ---
% 2.82/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.82/1.54 %%% Generated on Tue Feb 24 08:25:42 EST 2026
% 2.82/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.82/1.54 %%% Logic specification used:
% 2.82/1.54 %%% thf(spec, logic, $$dhol).
% 2.82/1.54
% 2.82/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2DTF18072.p
% See solution above
% 2.82/1.54 ------------------------
% 2.82/1.58 ---- Cleaned THF ---
% 2.82/1.58 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 2.82/1.58 list_l425507653ession: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 2.82/1.58 set_li185139947ession: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OSecrets_J_J,type,
% 2.82/1.58 set_li2007071804ecrets: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKeys_J_J,type,
% 2.82/1.58 set_li849033543y_Keys: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 2.82/1.58 list_list_Secrecy_KS: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 2.82/1.58 set_list_Secrecy_KS: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 list_S529945141ession: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 set_Se1942955227ession: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 2.82/1.58 list_Secrecy_Secrets: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.82/1.58 set_Secrecy_Secrets: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 2.82/1.58 list_Secrecy_Keys: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.82/1.58 set_Secrecy_Keys: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 list_Secrecy_KS: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 set_Secrecy_KS: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Secrecy____types__OExpression,type,
% 2.82/1.58 secrecy_Expression: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 2.82/1.58 secrecy_Secrets: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Secrecy____types__OspecID,type,
% 2.82/1.58 secrecy_specID: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Secrecy____types__OKeys,type,
% 2.82/1.58 secrecy_Keys: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(ty_n_t__Secrecy____types__OKS,type,
% 2.82/1.58 secrecy_KS: $tType ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKS,type,
% 2.82/1.58 bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKeys,type,
% 2.82/1.58 bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OSecrets,type,
% 2.82/1.58 bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKS,type,
% 2.82/1.58 bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKeys,type,
% 2.82/1.58 bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OSecrets,type,
% 2.82/1.58 bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.82/1.58 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 2.82/1.58 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowsECorrect,type,
% 2.82/1.58 knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 2.82/1.58 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknows,type,
% 2.82/1.58 knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OKS,type,
% 2.82/1.58 mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oappend_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oappend_001t__Secrecy____types__OKS,type,
% 2.82/1.58 append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oappend_001t__Secrecy____types__OKeys,type,
% 2.82/1.58 append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oappend_001t__Secrecy____types__OSecrets,type,
% 2.82/1.58 append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 2.82/1.58 bind_S1823644515ecy_KS: list_S529945141ession > ( secrecy_Expression > list_Secrecy_KS ) > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 bind_S711229283ession: list_Secrecy_KS > ( secrecy_KS > list_S529945141ession ) > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 2.82/1.58 bind_S645462771ecy_KS: list_Secrecy_KS > ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Obutlast_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 butlas171474643ession: list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Obutlast_001t__Secrecy____types__OKS,type,
% 2.82/1.58 butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oconcat_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 concat388015140ession: list_l425507653ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oconcat_001t__Secrecy____types__OKS,type,
% 2.82/1.58 concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 distin1076152135ession: list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OKS,type,
% 2.82/1.58 distin1495927511ecy_KS: list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OExpression_J_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 foldr_1531709715ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_l425507653ession > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OKS_J_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 foldr_1711005747ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oinsert_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oinsert_001t__Secrecy____types__OKS,type,
% 2.82/1.58 insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olast_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 last_S1532390982ession: list_S529945141ession > secrecy_Expression ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olast_001t__Secrecy____types__OKS,type,
% 2.82/1.58 last_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKS,type,
% 2.82/1.58 cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKeys,type,
% 2.82/1.58 cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OSecrets,type,
% 2.82/1.58 cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 nil_li311616943ession: list_l425507653ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 nil_list_Secrecy_KS: list_list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 nil_Se901661471ession: list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKS,type,
% 2.82/1.58 nil_Secrecy_KS: list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKeys,type,
% 2.82/1.58 nil_Secrecy_Keys: list_Secrecy_Keys ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OSecrets,type,
% 2.82/1.58 nil_Secrecy_Secrets: list_Secrecy_Secrets ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 hd_lis1623417098ession: list_l425507653ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OKS,type,
% 2.82/1.58 hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OKS,type,
% 2.82/1.58 tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OKS,type,
% 2.82/1.58 list_ex1_Secrecy_KS: ( secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 2.82/1.58 listre565996059ecy_KS: ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession > list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 2.82/1.58 listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 2.82/1.58 maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 2.82/1.58 maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omember_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Omember_001t__Secrecy____types__OKS,type,
% 2.82/1.58 member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OKS,type,
% 2.82/1.58 lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 produc1450295286ession: list_l425507653ession > list_l425507653ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OKS,type,
% 2.82/1.58 produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oremdups__adj_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 remdup484344169ession: list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oremdups__adj_001t__Secrecy____types__OKS,type,
% 2.82/1.58 remdup351570169ecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Orev_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Orev_001t__Secrecy____types__OKS,type,
% 2.82/1.58 rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Orotate1_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Orotate1_001t__Secrecy____types__OKS,type,
% 2.82/1.58 rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OKS,type,
% 2.82/1.58 shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Osplice_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Osplice_001t__Secrecy____types__OKS,type,
% 2.82/1.58 splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 subseq348280080ession: list_S529945141ession > list_l425507653ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OKS,type,
% 2.82/1.58 subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OKS,type,
% 2.82/1.58 succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_ODecr,type,
% 2.82/1.58 decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OEnc,type,
% 2.82/1.58 enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 2.82/1.58 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OExt,type,
% 2.82/1.58 ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OSign,type,
% 2.82/1.58 sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_Oeout,type,
% 2.82/1.58 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_Oine,type,
% 2.82/1.58 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 2.82/1.58 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OspecKeys,type,
% 2.82/1.58 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 2.82/1.58 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy_OspecSecrets,type,
% 2.82/1.58 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 2.82/1.58 secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 2.82/1.58 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 2.82/1.58 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 2.82/1.58 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 2.82/1.58 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 2.82/1.58 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 2.82/1.58 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 2.82/1.58 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 2.82/1.58 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.82/1.58 member249235532ession: list_S529945141ession > set_li185139947ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.82/1.58 member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 2.82/1.58 member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 2.82/1.58 member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__Secrecy____types__OExpression,type,
% 2.82/1.58 member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 2.82/1.58 member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 2.82/1.58 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 2.82/1.58 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 2.82/1.58
% 2.82/1.58 thf(sy_v_A,type,
% 2.82/1.58 a: secrecy_specID ).
% 2.82/1.58
% 2.82/1.58 thf(sy_v_m,type,
% 2.82/1.58 m: secrecy_Secrets ).
% 2.82/1.58
% 2.82/1.58 thf(fact_0_assms,axiom,
% 2.82/1.58 knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_1_KS_Oinject_I2_J,axiom,
% 2.82/1.58 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.82/1.58 ( ( ( secrecy_sKS @ X2 )
% 2.82/1.58 = ( secrecy_sKS @ Y2 ) )
% 2.82/1.58 = ( X2 = Y2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_2_know2knows__s,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.82/1.58 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_sE @ M ) @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_3_know1s,axiom,
% 2.82/1.58 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 2.82/1.58 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ nil_Se901661471ession ) )
% 2.82/1.58 = ( knowle945212990e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_4_eoutKnowCorrect__L1s,axiom,
% 2.82/1.58 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 2.82/1.58 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 2.82/1.58 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 2.82/1.58 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 2.82/1.58 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_5_eout__know__s,axiom,
% 2.82/1.58 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 2.82/1.58 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 2.82/1.58 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 2.82/1.58 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 2.82/1.58 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_6_know_Osimps_I2_J,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.82/1.58 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.82/1.58 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 2.82/1.58 | ( member_Secrecy_KS2 @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_7_KS2Expression_Osimps_I2_J,axiom,
% 2.82/1.58 ! [M: secrecy_Secrets] :
% 2.82/1.58 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 2.82/1.58 = ( secrecy_sE @ M ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_8_knows4,axiom,
% 2.82/1.58 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 2.82/1.58 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.82/1.58 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K2 ) )
% 2.82/1.58 & ( knowle731562421_knows @ A @ ( enc @ K1 @ E ) ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_9_knows5,axiom,
% 2.82/1.58 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 2.82/1.58 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.82/1.58 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K1 ) )
% 2.82/1.58 & ( knowle731562421_knows @ A @ ( sign @ K2 @ E ) ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_10_knows6,axiom,
% 2.82/1.58 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 2.82/1.58 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 2.82/1.58 & ( knowle731562421_knows @ A @ E1 ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ ( enc @ K @ E1 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_11_KS_Oinject_I1_J,axiom,
% 2.82/1.58 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.82/1.58 ( ( ( secrecy_kKS @ X1 )
% 2.82/1.58 = ( secrecy_kKS @ Y1 ) )
% 2.82/1.58 = ( X1 = Y1 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_12_Expression_Oinject_I2_J,axiom,
% 2.82/1.58 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.82/1.58 ( ( ( secrecy_sE @ X2 )
% 2.82/1.58 = ( secrecy_sE @ Y2 ) )
% 2.82/1.58 = ( X2 = Y2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_13_know1k,axiom,
% 2.82/1.58 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 2.82/1.58 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ nil_Se901661471ession ) )
% 2.82/1.58 = ( knowle945212990e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_14_knows__emptyexpression,axiom,
% 2.82/1.58 ! [C: secrecy_specID] : ( knowle731562421_knows @ C @ nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_15_KS_Oexhaust,axiom,
% 2.82/1.58 ! [Y: secrecy_KS] :
% 2.82/1.58 ( ! [X12: secrecy_Keys] :
% 2.82/1.58 ( Y
% 2.82/1.58 != ( secrecy_kKS @ X12 ) )
% 2.82/1.58 => ~ ! [X22: secrecy_Secrets] :
% 2.82/1.58 ( Y
% 2.82/1.58 != ( secrecy_sKS @ X22 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_16_KS_Oinduct,axiom,
% 2.82/1.58 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 2.82/1.58 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 2.82/1.58 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 2.82/1.58 => ( P @ KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_17_KS_Odistinct_I1_J,axiom,
% 2.82/1.58 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.82/1.58 ( ( secrecy_kKS @ X1 )
% 2.82/1.58 != ( secrecy_sKS @ X2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_18_knows7,axiom,
% 2.82/1.58 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 2.82/1.58 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 2.82/1.58 & ( knowle731562421_knows @ A @ E1 ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ ( sign @ K @ E1 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_19_list_Oinject,axiom,
% 2.82/1.58 ! [X21: secrecy_Expression,X222: list_S529945141ession,Y21: secrecy_Expression,Y22: list_S529945141ession] :
% 2.82/1.58 ( ( ( cons_S112077679ession @ X21 @ X222 )
% 2.82/1.58 = ( cons_S112077679ession @ Y21 @ Y22 ) )
% 2.82/1.58 = ( ( X21 = Y21 )
% 2.82/1.58 & ( X222 = Y22 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_20_list_Odistinct_I1_J,axiom,
% 2.82/1.58 ! [X21: secrecy_KS,X222: list_Secrecy_KS] :
% 2.82/1.58 ( nil_Secrecy_KS
% 2.82/1.58 != ( cons_Secrecy_KS @ X21 @ X222 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_21_list_Odistinct_I1_J,axiom,
% 2.82/1.58 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 2.82/1.58 ( nil_Se901661471ession
% 2.82/1.58 != ( cons_S112077679ession @ X21 @ X222 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_22_list_OdiscI,axiom,
% 2.82/1.58 ! [List: list_Secrecy_KS,X21: secrecy_KS,X222: list_Secrecy_KS] :
% 2.82/1.58 ( ( List
% 2.82/1.58 = ( cons_Secrecy_KS @ X21 @ X222 ) )
% 2.82/1.58 => ( List != nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_23_list_OdiscI,axiom,
% 2.82/1.58 ! [List: list_S529945141ession,X21: secrecy_Expression,X222: list_S529945141ession] :
% 2.82/1.58 ( ( List
% 2.82/1.58 = ( cons_S112077679ession @ X21 @ X222 ) )
% 2.82/1.58 => ( List != nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_24_list_Oexhaust,axiom,
% 2.82/1.58 ! [Y: list_Secrecy_KS] :
% 2.82/1.58 ( ( Y != nil_Secrecy_KS )
% 2.82/1.58 => ~ ! [X212: secrecy_KS,X223: list_Secrecy_KS] :
% 2.82/1.58 ( Y
% 2.82/1.58 != ( cons_Secrecy_KS @ X212 @ X223 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_25_list_Oexhaust,axiom,
% 2.82/1.58 ! [Y: list_S529945141ession] :
% 2.82/1.58 ( ( Y != nil_Se901661471ession )
% 2.82/1.58 => ~ ! [X212: secrecy_Expression,X223: list_S529945141ession] :
% 2.82/1.58 ( Y
% 2.82/1.58 != ( cons_S112077679ession @ X212 @ X223 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_26_list_Oinducts,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > $o,List: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X12: secrecy_KS,X22: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ X22 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X12 @ X22 ) ) )
% 2.82/1.58 => ( P @ List ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_27_list_Oinducts,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > $o,List: list_S529945141ession] :
% 2.82/1.58 ( ( P @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X12: secrecy_Expression,X22: list_S529945141ession] :
% 2.82/1.58 ( ( P @ X22 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X12 @ X22 ) ) )
% 2.82/1.58 => ( P @ List ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_28_neq__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 = ( ? [Y3: secrecy_KS,Ys: list_Secrecy_KS] :
% 2.82/1.58 ( Xs
% 2.82/1.58 = ( cons_Secrecy_KS @ Y3 @ Ys ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_29_neq__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 = ( ? [Y3: secrecy_Expression,Ys: list_S529945141ession] :
% 2.82/1.58 ( Xs
% 2.82/1.58 = ( cons_S112077679ession @ Y3 @ Ys ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_30_list__induct2_H,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [Y4: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 2.82/1.58 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_31_list__induct2_H,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > list_S529945141ession > $o,Xs: list_Secrecy_KS,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [Y4: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Secrecy_KS @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 2.82/1.58 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_32_list__induct2_H,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > list_Secrecy_KS > $o,Xs: list_S529945141ession,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [Y4: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Se901661471ession @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 2.82/1.58 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_33_list__induct2_H,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > list_S529945141ession > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [Y4: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Se901661471ession @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 2.82/1.58 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_34_splice_Oinduct,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 2.82/1.58 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ Ys3 @ Xs2 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_35_splice_Oinduct,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 2.82/1.58 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( P @ Ys3 @ Xs2 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_36_induct__list012,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.58 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Zs: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ Zs )
% 2.82/1.58 => ( ( P @ ( cons_Secrecy_KS @ Y4 @ Zs ) )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Zs ) ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_37_induct__list012,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( P @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Zs: list_S529945141ession] :
% 2.82/1.58 ( ( P @ Zs )
% 2.82/1.58 => ( ( P @ ( cons_S112077679ession @ Y4 @ Zs ) )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Zs ) ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_38_not__Cons__self2,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( cons_S112077679ession @ X3 @ Xs )
% 2.82/1.58 != Xs ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_39_map__tailrec__rev_Oinduct,axiom,
% 2.82/1.58 ! [P: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,A0: secrecy_KS > secrecy_Expression,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 2.82/1.58 ( ! [F: secrecy_KS > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Secrecy_KS @ X_1 )
% 2.82/1.58 => ( ! [F: secrecy_KS > secrecy_Expression,A3: secrecy_KS,As: list_Secrecy_KS,Bs: list_S529945141ession] :
% 2.82/1.58 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 2.82/1.58 => ( P @ F @ ( cons_Secrecy_KS @ A3 @ As ) @ Bs ) )
% 2.82/1.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_40_map__tailrec__rev_Oinduct,axiom,
% 2.82/1.58 ! [P: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression,A1: list_S529945141ession,A2: list_S529945141ession] :
% 2.82/1.58 ( ! [F: secrecy_Expression > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Se901661471ession @ X_1 )
% 2.82/1.58 => ( ! [F: secrecy_Expression > secrecy_Expression,A3: secrecy_Expression,As: list_S529945141ession,Bs: list_S529945141ession] :
% 2.82/1.58 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 2.82/1.58 => ( P @ F @ ( cons_S112077679ession @ A3 @ As ) @ Bs ) )
% 2.82/1.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_41_list__nonempty__induct,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs2 != nil_Secrecy_KS )
% 2.82/1.58 => ( ( P @ Xs2 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_42_list__nonempty__induct,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( Xs2 != nil_Se901661471ession )
% 2.82/1.58 => ( ( P @ Xs2 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_43_successively_Oinduct,axiom,
% 2.82/1.58 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 2.82/1.58 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS] : ( P @ P2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.58 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ P2 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) )
% 2.82/1.58 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_44_successively_Oinduct,axiom,
% 2.82/1.58 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 2.82/1.58 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression] : ( P @ P2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.58 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( P @ P2 @ ( cons_S112077679ession @ Y4 @ Xs2 ) )
% 2.82/1.58 => ( P @ P2 @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_45_remdups__adj_Oinduct,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > $o,A0: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.58 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( X = Y4 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) )
% 2.82/1.58 => ( ( ( X != Y4 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) )
% 2.82/1.58 => ( P @ A0 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_46_remdups__adj_Oinduct,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > $o,A0: list_S529945141ession] :
% 2.82/1.58 ( ( P @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( ( X = Y4 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) )
% 2.82/1.58 => ( ( ( X != Y4 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) )
% 2.82/1.58 => ( P @ A0 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_47_sorted__wrt_Oinduct,axiom,
% 2.82/1.58 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 2.82/1.58 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ P2 @ Ys3 )
% 2.82/1.58 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ Ys3 ) ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_48_sorted__wrt_Oinduct,axiom,
% 2.82/1.58 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 2.82/1.58 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( P @ P2 @ Ys3 )
% 2.82/1.58 => ( P @ P2 @ ( cons_S112077679ession @ X @ Ys3 ) ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_49_remdups__adj_Ocases,axiom,
% 2.82/1.58 ! [X3: list_Secrecy_KS] :
% 2.82/1.58 ( ( X3 != nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.58 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_50_remdups__adj_Ocases,axiom,
% 2.82/1.58 ! [X3: list_S529945141ession] :
% 2.82/1.58 ( ( X3 != nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.58 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_51_mem__Collect__eq,axiom,
% 2.82/1.58 ! [A4: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 2.82/1.58 ( ( member2138796287ecrets @ A4 @ ( collec836099393ecrets @ P ) )
% 2.82/1.58 = ( P @ A4 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_52_mem__Collect__eq,axiom,
% 2.82/1.58 ! [A4: secrecy_KS,P: secrecy_KS > $o] :
% 2.82/1.58 ( ( member_Secrecy_KS2 @ A4 @ ( collect_Secrecy_KS @ P ) )
% 2.82/1.58 = ( P @ A4 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_53_mem__Collect__eq,axiom,
% 2.82/1.58 ! [A4: secrecy_Keys,P: secrecy_Keys > $o] :
% 2.82/1.58 ( ( member_Secrecy_Keys @ A4 @ ( collect_Secrecy_Keys @ P ) )
% 2.82/1.58 = ( P @ A4 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_54_Collect__mem__eq,axiom,
% 2.82/1.58 ! [A: set_Secrecy_Secrets] :
% 2.82/1.58 ( ( collec836099393ecrets
% 2.82/1.58 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 2.82/1.58 = A ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_55_Collect__mem__eq,axiom,
% 2.82/1.58 ! [A: set_Secrecy_KS] :
% 2.82/1.58 ( ( collect_Secrecy_KS
% 2.82/1.58 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS2 @ X4 @ A ) )
% 2.82/1.58 = A ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_56_Collect__mem__eq,axiom,
% 2.82/1.58 ! [A: set_Secrecy_Keys] :
% 2.82/1.58 ( ( collect_Secrecy_Keys
% 2.82/1.58 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 2.82/1.58 = A ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_57_transpose_Ocases,axiom,
% 2.82/1.58 ! [X3: list_list_Secrecy_KS] :
% 2.82/1.58 ( ( X3 != nil_list_Secrecy_KS )
% 2.82/1.58 => ( ! [Xss: list_list_Secrecy_KS] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ Xss ) )
% 2.82/1.58 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Xss: list_list_Secrecy_KS] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_list_Secrecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_58_transpose_Ocases,axiom,
% 2.82/1.58 ! [X3: list_l425507653ession] :
% 2.82/1.58 ( ( X3 != nil_li311616943ession )
% 2.82/1.58 => ( ! [Xss: list_l425507653ession] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_l533358079ession @ nil_Se901661471ession @ Xss ) )
% 2.82/1.58 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession,Xss: list_l425507653ession] :
% 2.82/1.58 ( X3
% 2.82/1.58 != ( cons_l533358079ession @ ( cons_S112077679ession @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_59_shuffles_Oinduct,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 2.82/1.58 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 2.82/1.58 => ( ! [Xs2: list_Secrecy_KS] : ( P @ Xs2 @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ Xs2 @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_60_shuffles_Oinduct,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 2.82/1.58 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 2.82/1.58 => ( ! [Xs2: list_S529945141ession] : ( P @ Xs2 @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( P @ Xs2 @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) )
% 2.82/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_61_knows1k,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.82/1.58 = ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_62_know2knows__k,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_63_knows2know__k,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 2.82/1.58 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_64_know2knowsPQ__k,axiom,
% 2.82/1.58 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 2.82/1.58 ( ( ( knowle945212990e_know @ P @ ( secrecy_kKS @ M ) )
% 2.82/1.58 | ( knowle945212990e_know @ Q @ ( secrecy_kKS @ M ) ) )
% 2.82/1.58 => ( ( knowle731562421_knows @ P @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 2.82/1.58 | ( knowle731562421_knows @ Q @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_65_knows2knowPQ__k,axiom,
% 2.82/1.58 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 2.82/1.58 ( ( ( knowle731562421_knows @ P @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 2.82/1.58 | ( knowle731562421_knows @ Q @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) )
% 2.82/1.58 => ( ( knowle945212990e_know @ P @ ( secrecy_kKS @ M ) )
% 2.82/1.58 | ( knowle945212990e_know @ Q @ ( secrecy_kKS @ M ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_66_know2knows__neg__k,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.82/1.58 => ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_67_knows2know__neg__k,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 2.82/1.58 => ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_68_know_Osimps_I1_J,axiom,
% 2.82/1.58 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.82/1.58 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 2.82/1.58 | ( member_Secrecy_KS2 @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_69_insert__Nil,axiom,
% 2.82/1.58 ! [X3: secrecy_KS] :
% 2.82/1.58 ( ( insert_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_70_insert__Nil,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression] :
% 2.82/1.58 ( ( insert1173886601ession @ X3 @ nil_Se901661471ession )
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_71_Expression_Oinject_I1_J,axiom,
% 2.82/1.58 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.82/1.58 ( ( ( secrecy_kE @ X1 )
% 2.82/1.58 = ( secrecy_kE @ Y1 ) )
% 2.82/1.58 = ( X1 = Y1 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_72_Expression_Odistinct_I1_J,axiom,
% 2.82/1.58 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.82/1.58 ( ( secrecy_kE @ X1 )
% 2.82/1.58 != ( secrecy_sE @ X2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_73_KS2Expression_Osimps_I1_J,axiom,
% 2.82/1.58 ! [M: secrecy_Keys] :
% 2.82/1.58 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 2.82/1.58 = ( secrecy_kE @ M ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_74_eoutKnowCorrect__L1k,axiom,
% 2.82/1.58 ! [C: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 2.82/1.58 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 2.82/1.58 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 2.82/1.58 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_75_eout__know__k,axiom,
% 2.82/1.58 ! [C: secrecy_specID,M: secrecy_Keys] :
% 2.82/1.58 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 2.82/1.58 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 2.82/1.58 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 2.82/1.58 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_76_eoutKnowsECorrect__L1,axiom,
% 2.82/1.58 ! [C: secrecy_specID,E: secrecy_Expression] :
% 2.82/1.58 ( ( knowle1268625169orrect @ C @ E )
% 2.82/1.58 => ( ( eout @ C @ E )
% 2.82/1.58 => ( ? [K3: secrecy_Keys] :
% 2.82/1.58 ( ( E
% 2.82/1.58 = ( secrecy_kE @ K3 ) )
% 2.82/1.58 & ( member_Secrecy_Keys @ K3 @ ( specKeys @ C ) ) )
% 2.82/1.58 | ? [S: secrecy_Secrets] :
% 2.82/1.58 ( ( E
% 2.82/1.58 = ( secrecy_sE @ S ) )
% 2.82/1.58 & ( member2138796287ecrets @ S @ ( specSecrets @ C ) ) )
% 2.82/1.58 | ( knowle731562421_knows @ C @ ( cons_S112077679ession @ E @ nil_Se901661471ession ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_77_eoutKnowsECorrect__def,axiom,
% 2.82/1.58 ( knowle1268625169orrect
% 2.82/1.58 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 2.82/1.58 ( ( eout @ C2 @ E2 )
% 2.82/1.58 = ( ? [K4: secrecy_Keys] :
% 2.82/1.58 ( ( E2
% 2.82/1.58 = ( secrecy_kE @ K4 ) )
% 2.82/1.58 & ( member_Secrecy_Keys @ K4 @ ( specKeys @ C2 ) ) )
% 2.82/1.58 | ? [S2: secrecy_Secrets] :
% 2.82/1.58 ( ( E2
% 2.82/1.58 = ( secrecy_sE @ S2 ) )
% 2.82/1.58 & ( member2138796287ecrets @ S2 @ ( specSecrets @ C2 ) ) )
% 2.82/1.58 | ( knowle731562421_knows @ C2 @ ( cons_S112077679ession @ E2 @ nil_Se901661471ession ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_78_product__lists_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( produc1450295286ession @ nil_li311616943ession )
% 2.82/1.58 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_79_product__lists_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( produc713695622ecy_KS @ nil_list_Secrecy_KS )
% 2.82/1.58 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_80_subseqs_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( subseq348280080ession @ nil_Se901661471ession )
% 2.82/1.58 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_81_subseqs_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( subseqs_Secrecy_KS @ nil_Secrecy_KS )
% 2.82/1.58 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_82_Expression2KSL_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( secrec1371625429on2KSL @ nil_Se901661471ession )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_83_list__ex1__simps_I1_J,axiom,
% 2.82/1.58 ! [P: secrecy_Expression > $o] :
% 2.82/1.58 ~ ( list_e1486860828ession @ P @ nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_84_list__ex1__simps_I1_J,axiom,
% 2.82/1.58 ! [P: secrecy_KS > $o] :
% 2.82/1.58 ~ ( list_ex1_Secrecy_KS @ P @ nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_85_map__tailrec__rev_Oelims,axiom,
% 2.82/1.58 ! [X3: secrecy_KS > secrecy_Expression,Xa: list_Secrecy_KS,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 2.82/1.58 ( ( ( map_ta623472337ession @ X3 @ Xa @ Xb )
% 2.82/1.58 = Y )
% 2.82/1.58 => ( ( ( Xa = nil_Secrecy_KS )
% 2.82/1.58 => ( Y != Xb ) )
% 2.82/1.58 => ~ ! [A3: secrecy_KS,As: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xa
% 2.82/1.58 = ( cons_Secrecy_KS @ A3 @ As ) )
% 2.82/1.58 => ( Y
% 2.82/1.58 != ( map_ta623472337ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_86_map__tailrec__rev_Oelims,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression > secrecy_Expression,Xa: list_S529945141ession,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 2.82/1.58 ( ( ( map_ta1624757057ession @ X3 @ Xa @ Xb )
% 2.82/1.58 = Y )
% 2.82/1.58 => ( ( ( Xa = nil_Se901661471ession )
% 2.82/1.58 => ( Y != Xb ) )
% 2.82/1.58 => ~ ! [A3: secrecy_Expression,As: list_S529945141ession] :
% 2.82/1.58 ( ( Xa
% 2.82/1.58 = ( cons_S112077679ession @ A3 @ As ) )
% 2.82/1.58 => ( Y
% 2.82/1.58 != ( map_ta1624757057ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_87_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.82/1.58 ! [Less: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ~ ( lexord948960489ecy_KS @ Less @ ( cons_Secrecy_KS @ X3 @ Xs ) @ nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_88_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ~ ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_89_bind__simps_I1_J,axiom,
% 2.82/1.58 ! [F2: secrecy_Expression > list_S529945141ession] :
% 2.82/1.58 ( ( bind_S815874003ession @ nil_Se901661471ession @ F2 )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_90_bind__simps_I1_J,axiom,
% 2.82/1.58 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 2.82/1.58 ( ( bind_S1823644515ecy_KS @ nil_Se901661471ession @ F2 )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_91_bind__simps_I1_J,axiom,
% 2.82/1.58 ! [F2: secrecy_KS > list_S529945141ession] :
% 2.82/1.58 ( ( bind_S711229283ession @ nil_Secrecy_KS @ F2 )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_92_bind__simps_I1_J,axiom,
% 2.82/1.58 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 2.82/1.58 ( ( bind_S645462771ecy_KS @ nil_Secrecy_KS @ F2 )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_93_listrelp_Oinducts,axiom,
% 2.82/1.58 ! [R: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 2.82/1.58 ( ( listre788412843ecy_KS @ R @ X1 @ X2 )
% 2.82/1.58 => ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( R @ X @ Y4 )
% 2.82/1.58 => ( ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 )
% 2.82/1.58 => ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) )
% 2.82/1.58 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_94_listrelp_Oinducts,axiom,
% 2.82/1.58 ! [R: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,P: list_Secrecy_KS > list_S529945141ession > $o] :
% 2.82/1.58 ( ( listre1601064475ession @ R @ X1 @ X2 )
% 2.82/1.58 => ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_KS,Y4: secrecy_Expression,Xs2: list_Secrecy_KS,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( R @ X @ Y4 )
% 2.82/1.58 => ( ( listre1601064475ession @ R @ Xs2 @ Ys3 )
% 2.82/1.58 => ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) )
% 2.82/1.58 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_95_listrelp_Oinducts,axiom,
% 2.82/1.58 ! [R: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,P: list_S529945141ession > list_Secrecy_KS > $o] :
% 2.82/1.58 ( ( listre565996059ecy_KS @ R @ X1 @ X2 )
% 2.82/1.58 => ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Y4: secrecy_KS,Xs2: list_S529945141ession,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( R @ X @ Y4 )
% 2.82/1.58 => ( ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 )
% 2.82/1.58 => ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) )
% 2.82/1.58 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_96_listrelp_Oinducts,axiom,
% 2.82/1.58 ! [R: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 2.82/1.58 ( ( listre84909707ession @ R @ X1 @ X2 )
% 2.82/1.58 => ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( R @ X @ Y4 )
% 2.82/1.58 => ( ( listre84909707ession @ R @ Xs2 @ Ys3 )
% 2.82/1.58 => ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) )
% 2.82/1.58 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_97_listrelp_Osimps,axiom,
% 2.82/1.58 ( listre788412843ecy_KS
% 2.82/1.58 = ( ^ [R2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( A12 = nil_Secrecy_KS )
% 2.82/1.58 & ( A22 = nil_Secrecy_KS ) )
% 2.82/1.58 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 2.82/1.58 & ( R2 @ X4 @ Y3 )
% 2.82/1.58 & ( listre788412843ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_98_listrelp_Osimps,axiom,
% 2.82/1.58 ( listre1601064475ession
% 2.82/1.58 = ( ^ [R2: secrecy_KS > secrecy_Expression > $o,A12: list_Secrecy_KS,A22: list_S529945141ession] :
% 2.82/1.58 ( ( ( A12 = nil_Secrecy_KS )
% 2.82/1.58 & ( A22 = nil_Se901661471ession ) )
% 2.82/1.58 | ? [X4: secrecy_KS,Y3: secrecy_Expression,Xs3: list_Secrecy_KS,Ys: list_S529945141ession] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 2.82/1.58 & ( R2 @ X4 @ Y3 )
% 2.82/1.58 & ( listre1601064475ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_99_listrelp_Osimps,axiom,
% 2.82/1.58 ( listre565996059ecy_KS
% 2.82/1.58 = ( ^ [R2: secrecy_Expression > secrecy_KS > $o,A12: list_S529945141ession,A22: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( A12 = nil_Se901661471ession )
% 2.82/1.58 & ( A22 = nil_Secrecy_KS ) )
% 2.82/1.58 | ? [X4: secrecy_Expression,Y3: secrecy_KS,Xs3: list_S529945141ession,Ys: list_Secrecy_KS] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 2.82/1.58 & ( R2 @ X4 @ Y3 )
% 2.82/1.58 & ( listre565996059ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_100_listrelp_Osimps,axiom,
% 2.82/1.58 ( listre84909707ession
% 2.82/1.58 = ( ^ [R2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 2.82/1.58 ( ( ( A12 = nil_Se901661471ession )
% 2.82/1.58 & ( A22 = nil_Se901661471ession ) )
% 2.82/1.58 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 2.82/1.58 & ( R2 @ X4 @ Y3 )
% 2.82/1.58 & ( listre84909707ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_101_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) )
% 2.82/1.58 = ( ( Less @ X3 @ Y )
% 2.82/1.58 | ( ~ ( Less @ Y @ X3 )
% 2.82/1.58 & ( lexord1123423577ession @ Less @ Xs @ Ys2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_102_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( lexord1123423577ession @ Less @ Xs @ nil_Se901661471ession )
% 2.82/1.58 = ( Xs = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_103_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.82/1.58 ! [Less: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( lexord948960489ecy_KS @ Less @ Xs @ nil_Secrecy_KS )
% 2.82/1.58 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_104_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_105_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.82/1.58 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_106_ord_Olexordp__eq_OCons,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( Less @ X3 @ Y )
% 2.82/1.58 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_107_ord_Olexordp__eq_OCons__eq,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ~ ( Less @ X3 @ Y )
% 2.82/1.58 => ( ~ ( Less @ Y @ X3 )
% 2.82/1.58 => ( ( lexord1123423577ession @ Less @ Xs @ Ys2 )
% 2.82/1.58 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_108_ord_Olexordp__eq_ONil,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_109_ord_Olexordp__eq_ONil,axiom,
% 2.82/1.58 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_110_listrelp_OCons,axiom,
% 2.82/1.58 ! [R: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( R @ X3 @ Y )
% 2.82/1.58 => ( ( listre84909707ession @ R @ Xs @ Ys2 )
% 2.82/1.58 => ( listre84909707ession @ R @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_111_listrelp_ONil,axiom,
% 2.82/1.58 ! [R: secrecy_Expression > secrecy_Expression > $o] : ( listre84909707ession @ R @ nil_Se901661471ession @ nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_112_listrelp_ONil,axiom,
% 2.82/1.58 ! [R: secrecy_Expression > secrecy_KS > $o] : ( listre565996059ecy_KS @ R @ nil_Se901661471ession @ nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_113_listrelp_ONil,axiom,
% 2.82/1.58 ! [R: secrecy_KS > secrecy_Expression > $o] : ( listre1601064475ession @ R @ nil_Secrecy_KS @ nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_114_listrelp_ONil,axiom,
% 2.82/1.58 ! [R: secrecy_KS > secrecy_KS > $o] : ( listre788412843ecy_KS @ R @ nil_Secrecy_KS @ nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_115_map__tailrec__rev_Osimps_I2_J,axiom,
% 2.82/1.58 ! [F2: secrecy_Expression > secrecy_Expression,A4: secrecy_Expression,As2: list_S529945141ession,Bs2: list_S529945141ession] :
% 2.82/1.58 ( ( map_ta1624757057ession @ F2 @ ( cons_S112077679ession @ A4 @ As2 ) @ Bs2 )
% 2.82/1.58 = ( map_ta1624757057ession @ F2 @ As2 @ ( cons_S112077679ession @ ( F2 @ A4 ) @ Bs2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_116_ord_Olexordp__eq_Ocases,axiom,
% 2.82/1.58 ! [Less: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 2.82/1.58 ( ( lexord948960489ecy_KS @ Less @ A1 @ A2 )
% 2.82/1.58 => ( ( A1 != nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS] :
% 2.82/1.58 ( ? [Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( A1
% 2.82/1.58 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.82/1.58 => ! [Y4: secrecy_KS] :
% 2.82/1.58 ( ? [Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( A2
% 2.82/1.58 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 2.82/1.58 => ~ ( Less @ X @ Y4 ) ) )
% 2.82/1.58 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( A1
% 2.82/1.58 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.82/1.58 => ! [Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( A2
% 2.82/1.58 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ~ ( Less @ X @ Y4 )
% 2.82/1.58 => ( ~ ( Less @ Y4 @ X )
% 2.82/1.58 => ~ ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_117_ord_Olexordp__eq_Ocases,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 2.82/1.58 ( ( lexord1123423577ession @ Less @ A1 @ A2 )
% 2.82/1.58 => ( ( A1 != nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression] :
% 2.82/1.58 ( ? [Xs2: list_S529945141ession] :
% 2.82/1.58 ( A1
% 2.82/1.58 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.82/1.58 => ! [Y4: secrecy_Expression] :
% 2.82/1.58 ( ? [Ys3: list_S529945141ession] :
% 2.82/1.58 ( A2
% 2.82/1.58 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 2.82/1.58 => ~ ( Less @ X @ Y4 ) ) )
% 2.82/1.58 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( A1
% 2.82/1.58 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.82/1.58 => ! [Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( A2
% 2.82/1.58 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ~ ( Less @ X @ Y4 )
% 2.82/1.58 => ( ~ ( Less @ Y4 @ X )
% 2.82/1.58 => ~ ( lexord1123423577ession @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_118_ord_Olexordp__eq_Osimps,axiom,
% 2.82/1.58 ( lexord948960489ecy_KS
% 2.82/1.58 = ( ^ [Less2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 2.82/1.58 ( ? [Ys: list_Secrecy_KS] :
% 2.82/1.58 ( ( A12 = nil_Secrecy_KS )
% 2.82/1.58 & ( A22 = Ys ) )
% 2.82/1.58 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 2.82/1.58 & ( Less2 @ X4 @ Y3 ) )
% 2.82/1.58 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 2.82/1.58 & ~ ( Less2 @ X4 @ Y3 )
% 2.82/1.58 & ~ ( Less2 @ Y3 @ X4 )
% 2.82/1.58 & ( lexord948960489ecy_KS @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_119_ord_Olexordp__eq_Osimps,axiom,
% 2.82/1.58 ( lexord1123423577ession
% 2.82/1.58 = ( ^ [Less2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 2.82/1.58 ( ? [Ys: list_S529945141ession] :
% 2.82/1.58 ( ( A12 = nil_Se901661471ession )
% 2.82/1.58 & ( A22 = Ys ) )
% 2.82/1.58 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 2.82/1.58 & ( Less2 @ X4 @ Y3 ) )
% 2.82/1.58 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 2.82/1.58 ( ( A12
% 2.82/1.58 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.82/1.58 & ( A22
% 2.82/1.58 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 2.82/1.58 & ~ ( Less2 @ X4 @ Y3 )
% 2.82/1.58 & ~ ( Less2 @ Y3 @ X4 )
% 2.82/1.58 & ( lexord1123423577ession @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_120_ord_Olexordp__eq_Oinducts,axiom,
% 2.82/1.58 ! [Less: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 2.82/1.58 ( ( lexord948960489ecy_KS @ Less @ X1 @ X2 )
% 2.82/1.58 => ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 2.82/1.58 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( Less @ X @ Y4 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 2.82/1.58 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ~ ( Less @ X @ Y4 )
% 2.82/1.58 => ( ~ ( Less @ Y4 @ X )
% 2.82/1.58 => ( ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 )
% 2.82/1.58 => ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) ) )
% 2.82/1.58 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_121_ord_Olexordp__eq_Oinducts,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 2.82/1.58 ( ( lexord1123423577ession @ Less @ X1 @ X2 )
% 2.82/1.58 => ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( Less @ X @ Y4 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.82/1.58 ( ~ ( Less @ X @ Y4 )
% 2.82/1.58 => ( ~ ( Less @ Y4 @ X )
% 2.82/1.58 => ( ( lexord1123423577ession @ Less @ Xs2 @ Ys3 )
% 2.82/1.58 => ( ( P @ Xs2 @ Ys3 )
% 2.82/1.58 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) ) )
% 2.82/1.58 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_122_listrelp_Ocases,axiom,
% 2.82/1.58 ! [R: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 2.82/1.58 ( ( listre788412843ecy_KS @ R @ A1 @ A2 )
% 2.82/1.58 => ( ( ( A1 = nil_Secrecy_KS )
% 2.82/1.58 => ( A2 != nil_Secrecy_KS ) )
% 2.82/1.58 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( A1
% 2.82/1.58 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.82/1.58 => ! [Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( A2
% 2.82/1.58 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ( R @ X @ Y4 )
% 2.82/1.58 => ~ ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_123_listrelp_Ocases,axiom,
% 2.82/1.58 ! [R: secrecy_KS > secrecy_Expression > $o,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 2.82/1.58 ( ( listre1601064475ession @ R @ A1 @ A2 )
% 2.82/1.58 => ( ( ( A1 = nil_Secrecy_KS )
% 2.82/1.58 => ( A2 != nil_Se901661471ession ) )
% 2.82/1.58 => ~ ! [X: secrecy_KS,Y4: secrecy_Expression,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( A1
% 2.82/1.58 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.82/1.58 => ! [Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( A2
% 2.82/1.58 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ( R @ X @ Y4 )
% 2.82/1.58 => ~ ( listre1601064475ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_124_listrelp_Ocases,axiom,
% 2.82/1.58 ! [R: secrecy_Expression > secrecy_KS > $o,A1: list_S529945141ession,A2: list_Secrecy_KS] :
% 2.82/1.58 ( ( listre565996059ecy_KS @ R @ A1 @ A2 )
% 2.82/1.58 => ( ( ( A1 = nil_Se901661471ession )
% 2.82/1.58 => ( A2 != nil_Secrecy_KS ) )
% 2.82/1.58 => ~ ! [X: secrecy_Expression,Y4: secrecy_KS,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( A1
% 2.82/1.58 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.82/1.58 => ! [Ys3: list_Secrecy_KS] :
% 2.82/1.58 ( ( A2
% 2.82/1.58 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ( R @ X @ Y4 )
% 2.82/1.58 => ~ ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_125_listrelp_Ocases,axiom,
% 2.82/1.58 ! [R: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 2.82/1.58 ( ( listre84909707ession @ R @ A1 @ A2 )
% 2.82/1.58 => ( ( ( A1 = nil_Se901661471ession )
% 2.82/1.58 => ( A2 != nil_Se901661471ession ) )
% 2.82/1.58 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( A1
% 2.82/1.58 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.82/1.58 => ! [Ys3: list_S529945141ession] :
% 2.82/1.58 ( ( A2
% 2.82/1.58 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 2.82/1.58 => ( ( R @ X @ Y4 )
% 2.82/1.58 => ~ ( listre84909707ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_126_notSpecKeysSecretsExpr__L1,axiom,
% 2.82/1.58 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 2.82/1.58 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 2.82/1.58 => ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_127_member__rec_I2_J,axiom,
% 2.82/1.58 ! [Y: secrecy_Expression] :
% 2.82/1.58 ~ ( member2020590922ession @ nil_Se901661471ession @ Y ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_128_member__rec_I2_J,axiom,
% 2.82/1.58 ! [Y: secrecy_KS] :
% 2.82/1.58 ~ ( member_Secrecy_KS @ nil_Secrecy_KS @ Y ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_129_member__rec_I1_J,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression] :
% 2.82/1.58 ( ( member2020590922ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Y )
% 2.82/1.58 = ( ( X3 = Y )
% 2.82/1.58 | ( member2020590922ession @ Xs @ Y ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_130_splice_Oelims,axiom,
% 2.82/1.58 ! [X3: list_Secrecy_KS,Xa: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( splice_Secrecy_KS @ X3 @ Xa )
% 2.82/1.58 = Y )
% 2.82/1.58 => ( ( ( X3 = nil_Secrecy_KS )
% 2.82/1.58 => ( Y != Xa ) )
% 2.82/1.58 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( X3
% 2.82/1.58 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.82/1.58 => ( Y
% 2.82/1.58 != ( cons_Secrecy_KS @ X @ ( splice_Secrecy_KS @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_131_splice_Oelims,axiom,
% 2.82/1.58 ! [X3: list_S529945141ession,Xa: list_S529945141ession,Y: list_S529945141ession] :
% 2.82/1.58 ( ( ( splice1390717708ession @ X3 @ Xa )
% 2.82/1.58 = Y )
% 2.82/1.58 => ( ( ( X3 = nil_Se901661471ession )
% 2.82/1.58 => ( Y != Xa ) )
% 2.82/1.58 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( X3
% 2.82/1.58 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.82/1.58 => ( Y
% 2.82/1.58 != ( cons_S112077679ession @ X @ ( splice1390717708ession @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_132_bind__simps_I2_J,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession,F2: secrecy_Expression > list_S529945141ession] :
% 2.82/1.58 ( ( bind_S815874003ession @ ( cons_S112077679ession @ X3 @ Xs ) @ F2 )
% 2.82/1.58 = ( append2089414218ession @ ( F2 @ X3 ) @ ( bind_S815874003ession @ Xs @ F2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_133_append_Oassoc,axiom,
% 2.82/1.58 ! [A4: list_S529945141ession,B: list_S529945141ession,C3: list_S529945141ession] :
% 2.82/1.58 ( ( append2089414218ession @ ( append2089414218ession @ A4 @ B ) @ C3 )
% 2.82/1.58 = ( append2089414218ession @ A4 @ ( append2089414218ession @ B @ C3 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_134_append__assoc,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.82/1.58 ( ( append2089414218ession @ ( append2089414218ession @ Xs @ Ys2 ) @ Zs2 )
% 2.82/1.58 = ( append2089414218ession @ Xs @ ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_135_append__same__eq,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Ys2 @ Xs )
% 2.82/1.58 = ( append2089414218ession @ Zs2 @ Xs ) )
% 2.82/1.58 = ( Ys2 = Zs2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_136_same__append__eq,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.82/1.58 = ( append2089414218ession @ Xs @ Zs2 ) )
% 2.82/1.58 = ( Ys2 = Zs2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_137_append_Oright__neutral,axiom,
% 2.82/1.58 ! [A4: list_S529945141ession] :
% 2.82/1.58 ( ( append2089414218ession @ A4 @ nil_Se901661471ession )
% 2.82/1.58 = A4 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_138_append_Oright__neutral,axiom,
% 2.82/1.58 ! [A4: list_Secrecy_KS] :
% 2.82/1.58 ( ( append_Secrecy_KS @ A4 @ nil_Secrecy_KS )
% 2.82/1.58 = A4 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_139_append__is__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.82/1.58 = nil_Se901661471ession )
% 2.82/1.58 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_140_append__is__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 2.82/1.58 = nil_Secrecy_KS )
% 2.82/1.58 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_141_Nil__is__append__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( nil_Se901661471ession
% 2.82/1.58 = ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_142_Nil__is__append__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( nil_Secrecy_KS
% 2.82/1.58 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_143_self__append__conv2,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Ys2
% 2.82/1.58 = ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( Xs = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_144_self__append__conv2,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Ys2
% 2.82/1.58 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_145_append__self__conv2,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.82/1.58 = Ys2 )
% 2.82/1.58 = ( Xs = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_146_append__self__conv2,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 2.82/1.58 = Ys2 )
% 2.82/1.58 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_147_self__append__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( Xs
% 2.82/1.58 = ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( Ys2 = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_148_self__append__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs
% 2.82/1.58 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_149_append__self__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.82/1.58 = Xs )
% 2.82/1.58 = ( Ys2 = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_150_append__self__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 2.82/1.58 = Xs )
% 2.82/1.58 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_151_append__Nil2,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( append2089414218ession @ Xs @ nil_Se901661471ession )
% 2.82/1.58 = Xs ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_152_append__Nil2,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( append_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 2.82/1.58 = Xs ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_153_split__Nil__iff,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( ( splice1390717708ession @ Xs @ Ys2 )
% 2.82/1.58 = nil_Se901661471ession )
% 2.82/1.58 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_154_split__Nil__iff,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( splice_Secrecy_KS @ Xs @ Ys2 )
% 2.82/1.58 = nil_Secrecy_KS )
% 2.82/1.58 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_155_splice__Nil2,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( splice1390717708ession @ Xs @ nil_Se901661471ession )
% 2.82/1.58 = Xs ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_156_splice__Nil2,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( splice_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 2.82/1.58 = Xs ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_157_append1__eq__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS,Y: secrecy_KS] :
% 2.82/1.58 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 2.82/1.58 = ( append_Secrecy_KS @ Ys2 @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) )
% 2.82/1.58 = ( ( Xs = Ys2 )
% 2.82/1.58 & ( X3 = Y ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_158_append1__eq__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession,Y: secrecy_Expression] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 2.82/1.58 = ( append2089414218ession @ Ys2 @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) )
% 2.82/1.58 = ( ( Xs = Ys2 )
% 2.82/1.58 & ( X3 = Y ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_159_append__eq__appendI,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Xs1: list_S529945141ession,Zs2: list_S529945141ession,Ys2: list_S529945141ession,Us: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ Xs1 )
% 2.82/1.58 = Zs2 )
% 2.82/1.58 => ( ( Ys2
% 2.82/1.58 = ( append2089414218ession @ Xs1 @ Us ) )
% 2.82/1.58 => ( ( append2089414218ession @ Xs @ Ys2 )
% 2.82/1.58 = ( append2089414218ession @ Zs2 @ Us ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_160_append__eq__append__conv2,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession,Ts: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.82/1.58 = ( append2089414218ession @ Zs2 @ Ts ) )
% 2.82/1.58 = ( ? [Us2: list_S529945141ession] :
% 2.82/1.58 ( ( ( Xs
% 2.82/1.58 = ( append2089414218ession @ Zs2 @ Us2 ) )
% 2.82/1.58 & ( ( append2089414218ession @ Us2 @ Ys2 )
% 2.82/1.58 = Ts ) )
% 2.82/1.58 | ( ( ( append2089414218ession @ Xs @ Us2 )
% 2.82/1.58 = Zs2 )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append2089414218ession @ Us2 @ Ts ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_161_append__Cons,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( append2089414218ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ ( append2089414218ession @ Xs @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_162_Cons__eq__appendI,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs1: list_S529945141ession,Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.82/1.58 ( ( ( cons_S112077679ession @ X3 @ Xs1 )
% 2.82/1.58 = Ys2 )
% 2.82/1.58 => ( ( Xs
% 2.82/1.58 = ( append2089414218ession @ Xs1 @ Zs2 ) )
% 2.82/1.58 => ( ( cons_S112077679ession @ X3 @ Xs )
% 2.82/1.58 = ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_163_append_Oleft__neutral,axiom,
% 2.82/1.58 ! [A4: list_S529945141ession] :
% 2.82/1.58 ( ( append2089414218ession @ nil_Se901661471ession @ A4 )
% 2.82/1.58 = A4 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_164_append_Oleft__neutral,axiom,
% 2.82/1.58 ! [A4: list_Secrecy_KS] :
% 2.82/1.58 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ A4 )
% 2.82/1.58 = A4 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_165_append__Nil,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( append2089414218ession @ nil_Se901661471ession @ Ys2 )
% 2.82/1.58 = Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_166_append__Nil,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 2.82/1.58 = Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_167_eq__Nil__appendI,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( Xs = Ys2 )
% 2.82/1.58 => ( Xs
% 2.82/1.58 = ( append2089414218ession @ nil_Se901661471ession @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_168_eq__Nil__appendI,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs = Ys2 )
% 2.82/1.58 => ( Xs
% 2.82/1.58 = ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_169_knows2b,axiom,
% 2.82/1.58 ! [A: secrecy_specID,E: list_S529945141ession,E1: list_S529945141ession] :
% 2.82/1.58 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E @ E1 ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_170_knows2a,axiom,
% 2.82/1.58 ! [A: secrecy_specID,E1: list_S529945141ession,E: list_S529945141ession] :
% 2.82/1.58 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_171_knows3,axiom,
% 2.82/1.58 ! [A: secrecy_specID,E1: list_S529945141ession,E22: list_S529945141ession] :
% 2.82/1.58 ( ( ( knowle731562421_knows @ A @ E1 )
% 2.82/1.58 & ( knowle731562421_knows @ A @ E22 ) )
% 2.82/1.58 => ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E22 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_172_ord_Olexordp__eq__pref,axiom,
% 2.82/1.58 ! [Less: secrecy_Expression > secrecy_Expression > $o,U: list_S529945141ession,V: list_S529945141ession] : ( lexord1123423577ession @ Less @ U @ ( append2089414218ession @ U @ V ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_173_notSpecKeysSecretsExpr__L2,axiom,
% 2.82/1.58 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 2.82/1.58 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 2.82/1.58 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_174_splice_Osimps_I2_J,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( splice1390717708ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ ( splice1390717708ession @ Ys2 @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_175_splice_Osimps_I1_J,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( splice1390717708ession @ nil_Se901661471ession @ Ys2 )
% 2.82/1.58 = Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_176_splice_Osimps_I1_J,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( splice_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 2.82/1.58 = Ys2 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_177_rev__nonempty__induct,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs2 != nil_Secrecy_KS )
% 2.82/1.58 => ( ( P @ Xs2 )
% 2.82/1.58 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_178_rev__nonempty__induct,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( Xs2 != nil_Se901661471ession )
% 2.82/1.58 => ( ( P @ Xs2 )
% 2.82/1.58 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_179_append__eq__Cons__conv,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( append_Secrecy_KS @ Ys2 @ Zs2 )
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = ( ( ( Ys2 = nil_Secrecy_KS )
% 2.82/1.58 & ( Zs2
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ Xs ) ) )
% 2.82/1.58 | ? [Ys4: list_Secrecy_KS] :
% 2.82/1.58 ( ( Ys2
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ Ys4 ) )
% 2.82/1.58 & ( ( append_Secrecy_KS @ Ys4 @ Zs2 )
% 2.82/1.58 = Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_180_append__eq__Cons__conv,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession,Zs2: list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Ys2 @ Zs2 )
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( ( ( Ys2 = nil_Se901661471ession )
% 2.82/1.58 & ( Zs2
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ Xs ) ) )
% 2.82/1.58 | ? [Ys4: list_S529945141ession] :
% 2.82/1.58 ( ( Ys2
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ Ys4 ) )
% 2.82/1.58 & ( ( append2089414218ession @ Ys4 @ Zs2 )
% 2.82/1.58 = Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_181_Cons__eq__append__conv,axiom,
% 2.82/1.58 ! [X3: secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( cons_Secrecy_KS @ X3 @ Xs )
% 2.82/1.58 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 2.82/1.58 = ( ( ( Ys2 = nil_Secrecy_KS )
% 2.82/1.58 & ( ( cons_Secrecy_KS @ X3 @ Xs )
% 2.82/1.58 = Zs2 ) )
% 2.82/1.58 | ? [Ys4: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( cons_Secrecy_KS @ X3 @ Ys4 )
% 2.82/1.58 = Ys2 )
% 2.82/1.58 & ( Xs
% 2.82/1.58 = ( append_Secrecy_KS @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_182_Cons__eq__append__conv,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.82/1.58 ( ( ( cons_S112077679ession @ X3 @ Xs )
% 2.82/1.58 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 2.82/1.58 = ( ( ( Ys2 = nil_Se901661471ession )
% 2.82/1.58 & ( ( cons_S112077679ession @ X3 @ Xs )
% 2.82/1.58 = Zs2 ) )
% 2.82/1.58 | ? [Ys4: list_S529945141ession] :
% 2.82/1.58 ( ( ( cons_S112077679ession @ X3 @ Ys4 )
% 2.82/1.58 = Ys2 )
% 2.82/1.58 & ( Xs
% 2.82/1.58 = ( append2089414218ession @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_183_rev__exhaust,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ~ ! [Ys3: list_Secrecy_KS,Y4: secrecy_KS] :
% 2.82/1.58 ( Xs
% 2.82/1.58 != ( append_Secrecy_KS @ Ys3 @ ( cons_Secrecy_KS @ Y4 @ nil_Secrecy_KS ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_184_rev__exhaust,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ~ ! [Ys3: list_S529945141ession,Y4: secrecy_Expression] :
% 2.82/1.58 ( Xs
% 2.82/1.58 != ( append2089414218ession @ Ys3 @ ( cons_S112077679ession @ Y4 @ nil_Se901661471ession ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_185_rev__induct,axiom,
% 2.82/1.58 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ nil_Secrecy_KS )
% 2.82/1.58 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( P @ Xs2 )
% 2.82/1.58 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_186_rev__induct,axiom,
% 2.82/1.58 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( P @ nil_Se901661471ession )
% 2.82/1.58 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.58 ( ( P @ Xs2 )
% 2.82/1.58 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) )
% 2.82/1.58 => ( P @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_187_maps__simps_I1_J,axiom,
% 2.82/1.58 ! [F2: secrecy_Expression > list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( maps_S599402637ession @ F2 @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( append2089414218ession @ ( F2 @ X3 ) @ ( maps_S599402637ession @ F2 @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_188_ExtSign,axiom,
% 2.82/1.58 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 2.82/1.58 ( ( encrDecrKeys @ K12 @ K22 )
% 2.82/1.58 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 2.82/1.58 = E3 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_189_DecrEnc,axiom,
% 2.82/1.58 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 2.82/1.58 ( ( encrDecrKeys @ K12 @ K22 )
% 2.82/1.58 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 2.82/1.58 = E3 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_190_concat__eq__append__conv,axiom,
% 2.82/1.58 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.82/1.58 ( ( ( concat388015140ession @ Xss2 )
% 2.82/1.58 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 2.82/1.58 = ( ( ( Xss2 = nil_li311616943ession )
% 2.82/1.58 => ( ( Ys2 = nil_Se901661471ession )
% 2.82/1.58 & ( Zs2 = nil_Se901661471ession ) ) )
% 2.82/1.58 & ( ( Xss2 != nil_li311616943ession )
% 2.82/1.58 => ? [Xss1: list_l425507653ession,Xs3: list_S529945141ession,Xs4: list_S529945141ession,Xss22: list_l425507653ession] :
% 2.82/1.58 ( ( Xss2
% 2.82/1.58 = ( append1105297242ession @ Xss1 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append2089414218ession @ ( concat388015140ession @ Xss1 ) @ Xs3 ) )
% 2.82/1.58 & ( Zs2
% 2.82/1.58 = ( append2089414218ession @ Xs4 @ ( concat388015140ession @ Xss22 ) ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_191_concat__eq__append__conv,axiom,
% 2.82/1.58 ! [Xss2: list_list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( concat_Secrecy_KS @ Xss2 )
% 2.82/1.58 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 2.82/1.58 = ( ( ( Xss2 = nil_list_Secrecy_KS )
% 2.82/1.58 => ( ( Ys2 = nil_Secrecy_KS )
% 2.82/1.58 & ( Zs2 = nil_Secrecy_KS ) ) )
% 2.82/1.58 & ( ( Xss2 != nil_list_Secrecy_KS )
% 2.82/1.58 => ? [Xss1: list_list_Secrecy_KS,Xs3: list_Secrecy_KS,Xs4: list_Secrecy_KS,Xss22: list_list_Secrecy_KS] :
% 2.82/1.58 ( ( Xss2
% 2.82/1.58 = ( append1376766698ecy_KS @ Xss1 @ ( cons_list_Secrecy_KS @ ( append_Secrecy_KS @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append_Secrecy_KS @ ( concat_Secrecy_KS @ Xss1 ) @ Xs3 ) )
% 2.82/1.58 & ( Zs2
% 2.82/1.58 = ( append_Secrecy_KS @ Xs4 @ ( concat_Secrecy_KS @ Xss22 ) ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_192_rotate1_Osimps_I2_J,axiom,
% 2.82/1.58 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( rotate1_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_193_rotate1_Osimps_I2_J,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( rotate1237234450ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_194_rotate1__is__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( rotate1237234450ession @ Xs )
% 2.82/1.58 = nil_Se901661471ession )
% 2.82/1.58 = ( Xs = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_195_rotate1__is__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( rotate1_Secrecy_KS @ Xs )
% 2.82/1.58 = nil_Secrecy_KS )
% 2.82/1.58 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_196_concat__append,axiom,
% 2.82/1.58 ! [Xs: list_l425507653ession,Ys2: list_l425507653ession] :
% 2.82/1.58 ( ( concat388015140ession @ ( append1105297242ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( append2089414218ession @ ( concat388015140ession @ Xs ) @ ( concat388015140ession @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_197_rotate1_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( rotate1237234450ession @ nil_Se901661471ession )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_198_rotate1_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( rotate1_Secrecy_KS @ nil_Secrecy_KS )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_199_concat_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( concat388015140ession @ nil_li311616943ession )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_200_concat_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( concat_Secrecy_KS @ nil_list_Secrecy_KS )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_201_concat_Osimps_I2_J,axiom,
% 2.82/1.58 ! [X3: list_S529945141ession,Xs: list_l425507653ession] :
% 2.82/1.58 ( ( concat388015140ession @ ( cons_l533358079ession @ X3 @ Xs ) )
% 2.82/1.58 = ( append2089414218ession @ X3 @ ( concat388015140ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_202_maps__simps_I2_J,axiom,
% 2.82/1.58 ! [F2: secrecy_Expression > list_S529945141ession] :
% 2.82/1.58 ( ( maps_S599402637ession @ F2 @ nil_Se901661471ession )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_203_maps__simps_I2_J,axiom,
% 2.82/1.58 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 2.82/1.58 ( ( maps_S399472669ecy_KS @ F2 @ nil_Se901661471ession )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_204_maps__simps_I2_J,axiom,
% 2.82/1.58 ! [F2: secrecy_KS > list_S529945141ession] :
% 2.82/1.58 ( ( maps_S1434541085ession @ F2 @ nil_Secrecy_KS )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_205_maps__simps_I2_J,axiom,
% 2.82/1.58 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 2.82/1.58 ( ( maps_S377605037ecy_KS @ F2 @ nil_Secrecy_KS )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_206_concat__eq__appendD,axiom,
% 2.82/1.58 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.82/1.58 ( ( ( concat388015140ession @ Xss2 )
% 2.82/1.58 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 2.82/1.58 => ( ( Xss2 != nil_li311616943ession )
% 2.82/1.58 => ? [Xss12: list_l425507653ession,Xs2: list_S529945141ession,Xs5: list_S529945141ession,Xss23: list_l425507653ession] :
% 2.82/1.58 ( ( Xss2
% 2.82/1.58 = ( append1105297242ession @ Xss12 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append2089414218ession @ ( concat388015140ession @ Xss12 ) @ Xs2 ) )
% 2.82/1.58 & ( Zs2
% 2.82/1.58 = ( append2089414218ession @ Xs5 @ ( concat388015140ession @ Xss23 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_207_butlast__snoc,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.82/1.58 ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 2.82/1.58 = Xs ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_208_butlast__snoc,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.82/1.58 ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 2.82/1.58 = Xs ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_209_last__snoc,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.82/1.58 ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 2.82/1.58 = X3 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_210_last__snoc,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.82/1.58 ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 2.82/1.58 = X3 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_211_notSpecKeysSecretsExpr__def,axiom,
% 2.82/1.58 ( notSpe1586871396tsExpr
% 2.82/1.58 = ( ^ [P3: secrecy_specID,E2: list_S529945141ession] :
% 2.82/1.58 ( ! [X4: secrecy_Keys] :
% 2.82/1.58 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E2 )
% 2.82/1.58 => ~ ( member_Secrecy_KS2 @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 2.82/1.58 & ! [Y3: secrecy_Secrets] :
% 2.82/1.58 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y3 ) @ E2 )
% 2.82/1.58 => ~ ( member_Secrecy_KS2 @ ( secrecy_sKS @ Y3 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_212_last__appendR,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Ys2 != nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_S1532390982ession @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_213_last__appendR,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Ys2 != nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_214_last__appendL,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Ys2 = nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_215_last__appendL,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Ys2 = nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_216_append__butlast__last__id,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( append_Secrecy_KS @ ( butlast_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( last_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) )
% 2.82/1.58 = Xs ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_217_append__butlast__last__id,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( append2089414218ession @ ( butlas171474643ession @ Xs ) @ ( cons_S112077679ession @ ( last_S1532390982ession @ Xs ) @ nil_Se901661471ession ) )
% 2.82/1.58 = Xs ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_218_butlast_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( butlas171474643ession @ nil_Se901661471ession )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_219_butlast_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( butlast_Secrecy_KS @ nil_Secrecy_KS )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_220_snoc__eq__iff__butlast,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 2.82/1.58 = Ys2 )
% 2.82/1.58 = ( ( Ys2 != nil_Secrecy_KS )
% 2.82/1.58 & ( ( butlast_Secrecy_KS @ Ys2 )
% 2.82/1.58 = Xs )
% 2.82/1.58 & ( ( last_Secrecy_KS @ Ys2 )
% 2.82/1.58 = X3 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_221_snoc__eq__iff__butlast,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 2.82/1.58 = Ys2 )
% 2.82/1.58 = ( ( Ys2 != nil_Se901661471ession )
% 2.82/1.58 & ( ( butlas171474643ession @ Ys2 )
% 2.82/1.58 = Xs )
% 2.82/1.58 & ( ( last_S1532390982ession @ Ys2 )
% 2.82/1.58 = X3 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_222_last__ConsR,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_223_last__ConsR,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_224_last__ConsL,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.82/1.58 ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = X3 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_225_last__ConsL,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.82/1.58 ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = X3 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_226_last_Osimps,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.82/1.58 ( ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = X3 ) )
% 2.82/1.58 & ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_227_last_Osimps,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.82/1.58 ( ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = X3 ) )
% 2.82/1.58 & ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( last_S1532390982ession @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_228_longest__common__suffix,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ? [Ss: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 2.82/1.58 ( ( Xs
% 2.82/1.58 = ( append2089414218ession @ Xs5 @ Ss ) )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append2089414218ession @ Ys5 @ Ss ) )
% 2.82/1.58 & ( ( Xs5 = nil_Se901661471ession )
% 2.82/1.58 | ( Ys5 = nil_Se901661471ession )
% 2.82/1.58 | ( ( last_S1532390982ession @ Xs5 )
% 2.82/1.58 != ( last_S1532390982ession @ Ys5 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_229_longest__common__suffix,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ? [Ss: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs
% 2.82/1.58 = ( append_Secrecy_KS @ Xs5 @ Ss ) )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append_Secrecy_KS @ Ys5 @ Ss ) )
% 2.82/1.58 & ( ( Xs5 = nil_Secrecy_KS )
% 2.82/1.58 | ( Ys5 = nil_Secrecy_KS )
% 2.82/1.58 | ( ( last_Secrecy_KS @ Xs5 )
% 2.82/1.58 != ( last_Secrecy_KS @ Ys5 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_230_last__append,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( Ys2 = nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_S1532390982ession @ Xs ) ) )
% 2.82/1.58 & ( ( Ys2 != nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_S1532390982ession @ Ys2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_231_last__append,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( Ys2 = nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Xs ) ) )
% 2.82/1.58 & ( ( Ys2 != nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Ys2 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_232_butlast_Osimps_I2_J,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.82/1.58 ( ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = nil_Secrecy_KS ) )
% 2.82/1.58 & ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ ( butlast_Secrecy_KS @ Xs ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_233_butlast_Osimps_I2_J,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.82/1.58 ( ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = nil_Se901661471ession ) )
% 2.82/1.58 & ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ ( butlas171474643ession @ Xs ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_234_butlast__append,axiom,
% 2.82/1.58 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( Ys2 = nil_Se901661471ession )
% 2.82/1.58 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( butlas171474643ession @ Xs ) ) )
% 2.82/1.58 & ( ( Ys2 != nil_Se901661471ession )
% 2.82/1.58 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( append2089414218ession @ Xs @ ( butlas171474643ession @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_235_butlast__append,axiom,
% 2.82/1.58 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( Ys2 = nil_Secrecy_KS )
% 2.82/1.58 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( butlast_Secrecy_KS @ Xs ) ) )
% 2.82/1.58 & ( ( Ys2 != nil_Secrecy_KS )
% 2.82/1.58 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( append_Secrecy_KS @ Xs @ ( butlast_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_236_mem_Osimps_I1_J,axiom,
% 2.82/1.58 ! [X3: secrecy_KS] :
% 2.82/1.58 ~ ( mem_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_237_mem_Osimps_I1_J,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression] :
% 2.82/1.58 ~ ( mem_Se1967555118ession @ X3 @ nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_238_mem_Osimps_I2_J,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Y: secrecy_Expression,L: list_S529945141ession] :
% 2.82/1.58 ( ( mem_Se1967555118ession @ X3 @ ( cons_S112077679ession @ Y @ L ) )
% 2.82/1.58 = ( ( X3 = Y )
% 2.82/1.58 | ( mem_Se1967555118ession @ X3 @ L ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_239_concat__conv__foldr,axiom,
% 2.82/1.58 ( concat388015140ession
% 2.82/1.58 = ( ^ [Xss3: list_l425507653ession] : ( foldr_1531709715ession @ append2089414218ession @ Xss3 @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_240_concat__conv__foldr,axiom,
% 2.82/1.58 ( concat_Secrecy_KS
% 2.82/1.58 = ( ^ [Xss3: list_list_Secrecy_KS] : ( foldr_1711005747ecy_KS @ append_Secrecy_KS @ Xss3 @ nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_241_SuccI,axiom,
% 2.82/1.58 ! [Kl: list_Secrecy_Secrets,K: secrecy_Secrets,Kl2: set_li2007071804ecrets] :
% 2.82/1.58 ( ( member1138497285ecrets @ ( append186372209ecrets @ Kl @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl2 )
% 2.82/1.58 => ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ Kl ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_242_SuccI,axiom,
% 2.82/1.58 ! [Kl: list_Secrecy_Keys,K: secrecy_Keys,Kl2: set_li849033543y_Keys] :
% 2.82/1.58 ( ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl2 )
% 2.82/1.58 => ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ Kl ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_243_SuccI,axiom,
% 2.82/1.58 ! [Kl: list_Secrecy_KS,K: secrecy_KS,Kl2: set_list_Secrecy_KS] :
% 2.82/1.58 ( ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl2 )
% 2.82/1.58 => ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ Kl ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_244_SuccI,axiom,
% 2.82/1.58 ! [Kl: list_S529945141ession,K: secrecy_Expression,Kl2: set_li185139947ession] :
% 2.82/1.58 ( ( member249235532ession @ ( append2089414218ession @ Kl @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl2 )
% 2.82/1.58 => ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ Kl ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_245_SuccD,axiom,
% 2.82/1.58 ! [K: secrecy_Secrets,Kl2: set_li2007071804ecrets,Kl: list_Secrecy_Secrets] :
% 2.82/1.58 ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ Kl ) )
% 2.82/1.58 => ( member1138497285ecrets @ ( append186372209ecrets @ Kl @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_246_SuccD,axiom,
% 2.82/1.58 ! [K: secrecy_Keys,Kl2: set_li849033543y_Keys,Kl: list_Secrecy_Keys] :
% 2.82/1.58 ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ Kl ) )
% 2.82/1.58 => ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_247_SuccD,axiom,
% 2.82/1.58 ! [K: secrecy_KS,Kl2: set_list_Secrecy_KS,Kl: list_Secrecy_KS] :
% 2.82/1.58 ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ Kl ) )
% 2.82/1.58 => ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_248_SuccD,axiom,
% 2.82/1.58 ! [K: secrecy_Expression,Kl2: set_li185139947ession,Kl: list_S529945141ession] :
% 2.82/1.58 ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ Kl ) )
% 2.82/1.58 => ( member249235532ession @ ( append2089414218ession @ Kl @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_249_rev__eq__Cons__iff,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Y: secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( rev_Secrecy_KS @ Xs )
% 2.82/1.58 = ( cons_Secrecy_KS @ Y @ Ys2 ) )
% 2.82/1.58 = ( Xs
% 2.82/1.58 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Ys2 ) @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_250_rev__eq__Cons__iff,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( ( rev_Se1073238207ession @ Xs )
% 2.82/1.58 = ( cons_S112077679ession @ Y @ Ys2 ) )
% 2.82/1.58 = ( Xs
% 2.82/1.58 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_251_Nil__is__rev__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( nil_Se901661471ession
% 2.82/1.58 = ( rev_Se1073238207ession @ Xs ) )
% 2.82/1.58 = ( Xs = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_252_Nil__is__rev__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( nil_Secrecy_KS
% 2.82/1.58 = ( rev_Secrecy_KS @ Xs ) )
% 2.82/1.58 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_253_rev__is__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( rev_Se1073238207ession @ Xs )
% 2.82/1.58 = nil_Se901661471ession )
% 2.82/1.58 = ( Xs = nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_254_rev__is__Nil__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( rev_Secrecy_KS @ Xs )
% 2.82/1.58 = nil_Secrecy_KS )
% 2.82/1.58 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_255_rev__append,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( rev_Se1073238207ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( rev_Se1073238207ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_256_singleton__rev__conv,axiom,
% 2.82/1.58 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 2.82/1.58 = ( rev_Secrecy_KS @ Xs ) )
% 2.82/1.58 = ( Xs
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_257_singleton__rev__conv,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( cons_S112077679ession @ X3 @ nil_Se901661471ession )
% 2.82/1.58 = ( rev_Se1073238207ession @ Xs ) )
% 2.82/1.58 = ( Xs
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_258_rev__singleton__conv,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.82/1.58 ( ( ( rev_Secrecy_KS @ Xs )
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 2.82/1.58 = ( Xs
% 2.82/1.58 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_259_rev__singleton__conv,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.82/1.58 ( ( ( rev_Se1073238207ession @ Xs )
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 2.82/1.58 = ( Xs
% 2.82/1.58 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_260_rev_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( rev_Se1073238207ession @ nil_Se901661471ession )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_261_rev_Osimps_I1_J,axiom,
% 2.82/1.58 ( ( rev_Secrecy_KS @ nil_Secrecy_KS )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_262_rev_Osimps_I2_J,axiom,
% 2.82/1.58 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( rev_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_263_rev_Osimps_I2_J,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( rev_Se1073238207ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( append2089414218ession @ ( rev_Se1073238207ession @ Xs ) @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_264_empty__Shift,axiom,
% 2.82/1.58 ! [Kl2: set_li2007071804ecrets,K: secrecy_Secrets] :
% 2.82/1.58 ( ( member1138497285ecrets @ nil_Secrecy_Secrets @ Kl2 )
% 2.82/1.58 => ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ nil_Secrecy_Secrets ) )
% 2.82/1.58 => ( member1138497285ecrets @ nil_Secrecy_Secrets @ ( bNF_Gr28627573ecrets @ Kl2 @ K ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_265_empty__Shift,axiom,
% 2.82/1.58 ! [Kl2: set_li849033543y_Keys,K: secrecy_Keys] :
% 2.82/1.58 ( ( member341114536y_Keys @ nil_Secrecy_Keys @ Kl2 )
% 2.82/1.58 => ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ nil_Secrecy_Keys ) )
% 2.82/1.58 => ( member341114536y_Keys @ nil_Secrecy_Keys @ ( bNF_Gr414702370y_Keys @ Kl2 @ K ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_266_empty__Shift,axiom,
% 2.82/1.58 ! [Kl2: set_li185139947ession,K: secrecy_Expression] :
% 2.82/1.58 ( ( member249235532ession @ nil_Se901661471ession @ Kl2 )
% 2.82/1.58 => ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ nil_Se901661471ession ) )
% 2.82/1.58 => ( member249235532ession @ nil_Se901661471ession @ ( bNF_Gr275623750ession @ Kl2 @ K ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_267_empty__Shift,axiom,
% 2.82/1.58 ! [Kl2: set_list_Secrecy_KS,K: secrecy_KS] :
% 2.82/1.58 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ Kl2 )
% 2.82/1.58 => ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ nil_Secrecy_KS ) )
% 2.82/1.58 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( bNF_Gr660123862ecy_KS @ Kl2 @ K ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_268_ShiftD,axiom,
% 2.82/1.58 ! [Kl: list_S529945141ession,Kl2: set_li185139947ession,K: secrecy_Expression] :
% 2.82/1.58 ( ( member249235532ession @ Kl @ ( bNF_Gr275623750ession @ Kl2 @ K ) )
% 2.82/1.58 => ( member249235532ession @ ( cons_S112077679ession @ K @ Kl ) @ Kl2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_269_Succ__Shift,axiom,
% 2.82/1.58 ! [Kl2: set_li185139947ession,K: secrecy_Expression,Kl: list_S529945141ession] :
% 2.82/1.58 ( ( bNF_Gr979629770ession @ ( bNF_Gr275623750ession @ Kl2 @ K ) @ Kl )
% 2.82/1.58 = ( bNF_Gr979629770ession @ Kl2 @ ( cons_S112077679ession @ K @ Kl ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_270_last__rev,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( rev_Se1073238207ession @ Xs ) )
% 2.82/1.58 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_271_last__rev,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 2.82/1.58 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_272_hd__rev,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( hd_Sec357328890ession @ ( rev_Se1073238207ession @ Xs ) )
% 2.82/1.58 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_273_hd__rev,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( hd_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_274_hd__append2,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_275_hd__append2,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_276_hd__append,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( hd_Sec357328890ession @ Ys2 ) ) )
% 2.82/1.58 & ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( hd_Sec357328890ession @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_277_hd__append,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( hd_Secrecy_KS @ Ys2 ) ) )
% 2.82/1.58 & ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( hd_Secrecy_KS @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_278_longest__common__prefix,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ? [Ps: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 2.82/1.58 ( ( Xs
% 2.82/1.58 = ( append2089414218ession @ Ps @ Xs5 ) )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append2089414218ession @ Ps @ Ys5 ) )
% 2.82/1.58 & ( ( Xs5 = nil_Se901661471ession )
% 2.82/1.58 | ( Ys5 = nil_Se901661471ession )
% 2.82/1.58 | ( ( hd_Sec357328890ession @ Xs5 )
% 2.82/1.58 != ( hd_Sec357328890ession @ Ys5 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_279_longest__common__prefix,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ? [Ps: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs
% 2.82/1.58 = ( append_Secrecy_KS @ Ps @ Xs5 ) )
% 2.82/1.58 & ( Ys2
% 2.82/1.58 = ( append_Secrecy_KS @ Ps @ Ys5 ) )
% 2.82/1.58 & ( ( Xs5 = nil_Secrecy_KS )
% 2.82/1.58 | ( Ys5 = nil_Secrecy_KS )
% 2.82/1.58 | ( ( hd_Secrecy_KS @ Xs5 )
% 2.82/1.58 != ( hd_Secrecy_KS @ Ys5 ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_280_hd__concat,axiom,
% 2.82/1.58 ! [Xs: list_l425507653ession] :
% 2.82/1.58 ( ( Xs != nil_li311616943ession )
% 2.82/1.58 => ( ( ( hd_lis1623417098ession @ Xs )
% 2.82/1.58 != nil_Se901661471ession )
% 2.82/1.58 => ( ( hd_Sec357328890ession @ ( concat388015140ession @ Xs ) )
% 2.82/1.58 = ( hd_Sec357328890ession @ ( hd_lis1623417098ession @ Xs ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_281_hd__concat,axiom,
% 2.82/1.58 ! [Xs: list_list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_list_Secrecy_KS )
% 2.82/1.58 => ( ( ( hd_list_Secrecy_KS @ Xs )
% 2.82/1.58 != nil_Secrecy_KS )
% 2.82/1.58 => ( ( hd_Secrecy_KS @ ( concat_Secrecy_KS @ Xs ) )
% 2.82/1.58 = ( hd_Secrecy_KS @ ( hd_list_Secrecy_KS @ Xs ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_282_list_Osel_I1_J,axiom,
% 2.82/1.58 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 2.82/1.58 ( ( hd_Sec357328890ession @ ( cons_S112077679ession @ X21 @ X222 ) )
% 2.82/1.58 = X21 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_283_rotate1__hd__tl,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( rotate1_Secrecy_KS @ Xs )
% 2.82/1.58 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_284_rotate1__hd__tl,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( rotate1237234450ession @ Xs )
% 2.82/1.58 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ nil_Se901661471ession ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_285_distinct__adj__append__iff,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( ( distin1076152135ession @ Xs )
% 2.82/1.58 & ( distin1076152135ession @ Ys2 )
% 2.82/1.58 & ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 | ( Ys2 = nil_Se901661471ession )
% 2.82/1.58 | ( ( last_S1532390982ession @ Xs )
% 2.82/1.58 != ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_286_distinct__adj__append__iff,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( distin1495927511ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( ( distin1495927511ecy_KS @ Xs )
% 2.82/1.58 & ( distin1495927511ecy_KS @ Ys2 )
% 2.82/1.58 & ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 | ( Ys2 = nil_Secrecy_KS )
% 2.82/1.58 | ( ( last_Secrecy_KS @ Xs )
% 2.82/1.58 != ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_287_distinct__adj__Cons__Cons,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 2.82/1.58 = ( ( X3 != Y )
% 2.82/1.58 & ( distin1076152135ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_288_tl__append2,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( tl_Sec1905266422ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_289_tl__append2,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( tl_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.58 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_290_list_Ocollapse,axiom,
% 2.82/1.58 ! [List: list_Secrecy_KS] :
% 2.82/1.58 ( ( List != nil_Secrecy_KS )
% 2.82/1.58 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) )
% 2.82/1.58 = List ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_291_list_Ocollapse,axiom,
% 2.82/1.58 ! [List: list_S529945141ession] :
% 2.82/1.58 ( ( List != nil_Se901661471ession )
% 2.82/1.58 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) )
% 2.82/1.58 = List ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_292_hd__Cons__tl,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( Xs != nil_Secrecy_KS )
% 2.82/1.58 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ ( tl_Secrecy_KS @ Xs ) )
% 2.82/1.58 = Xs ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_293_hd__Cons__tl,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( Xs != nil_Se901661471ession )
% 2.82/1.58 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ ( tl_Sec1905266422ession @ Xs ) )
% 2.82/1.58 = Xs ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_294_list_Oexpand,axiom,
% 2.82/1.58 ! [List: list_S529945141ession,List2: list_S529945141ession] :
% 2.82/1.58 ( ( ( List = nil_Se901661471ession )
% 2.82/1.58 = ( List2 = nil_Se901661471ession ) )
% 2.82/1.58 => ( ( ( List != nil_Se901661471ession )
% 2.82/1.58 => ( ( List2 != nil_Se901661471ession )
% 2.82/1.58 => ( ( ( hd_Sec357328890ession @ List )
% 2.82/1.58 = ( hd_Sec357328890ession @ List2 ) )
% 2.82/1.58 & ( ( tl_Sec1905266422ession @ List )
% 2.82/1.58 = ( tl_Sec1905266422ession @ List2 ) ) ) ) )
% 2.82/1.58 => ( List = List2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_295_list_Oexpand,axiom,
% 2.82/1.58 ! [List: list_Secrecy_KS,List2: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( List = nil_Secrecy_KS )
% 2.82/1.58 = ( List2 = nil_Secrecy_KS ) )
% 2.82/1.58 => ( ( ( List != nil_Secrecy_KS )
% 2.82/1.58 => ( ( List2 != nil_Secrecy_KS )
% 2.82/1.58 => ( ( ( hd_Secrecy_KS @ List )
% 2.82/1.58 = ( hd_Secrecy_KS @ List2 ) )
% 2.82/1.58 & ( ( tl_Secrecy_KS @ List )
% 2.82/1.58 = ( tl_Secrecy_KS @ List2 ) ) ) ) )
% 2.82/1.58 => ( List = List2 ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_296_distinct__adj__appendD1,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 => ( distin1076152135ession @ Xs ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_297_distinct__adj__appendD2,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 => ( distin1076152135ession @ Ys2 ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_298_distinct__adj__Nil,axiom,
% 2.82/1.58 distin1076152135ession @ nil_Se901661471ession ).
% 2.82/1.58
% 2.82/1.58 thf(fact_299_distinct__adj__Nil,axiom,
% 2.82/1.58 distin1495927511ecy_KS @ nil_Secrecy_KS ).
% 2.82/1.58
% 2.82/1.58 thf(fact_300_distinct__adj__ConsD,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 => ( distin1076152135ession @ Xs ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_301_list_Osel_I2_J,axiom,
% 2.82/1.58 ( ( tl_Sec1905266422ession @ nil_Se901661471ession )
% 2.82/1.58 = nil_Se901661471ession ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_302_list_Osel_I2_J,axiom,
% 2.82/1.58 ( ( tl_Secrecy_KS @ nil_Secrecy_KS )
% 2.82/1.58 = nil_Secrecy_KS ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_303_list_Osel_I3_J,axiom,
% 2.82/1.58 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 2.82/1.58 ( ( tl_Sec1905266422ession @ ( cons_S112077679ession @ X21 @ X222 ) )
% 2.82/1.58 = X222 ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_304_tl__Nil,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( tl_Secrecy_KS @ Xs )
% 2.82/1.58 = nil_Secrecy_KS )
% 2.82/1.58 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 | ? [X4: secrecy_KS] :
% 2.82/1.58 ( Xs
% 2.82/1.58 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_305_tl__Nil,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( tl_Sec1905266422ession @ Xs )
% 2.82/1.58 = nil_Se901661471ession )
% 2.82/1.58 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 | ? [X4: secrecy_Expression] :
% 2.82/1.58 ( Xs
% 2.82/1.58 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_306_Nil__tl,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( nil_Secrecy_KS
% 2.82/1.58 = ( tl_Secrecy_KS @ Xs ) )
% 2.82/1.58 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 | ? [X4: secrecy_KS] :
% 2.82/1.58 ( Xs
% 2.82/1.58 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_307_Nil__tl,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( nil_Se901661471ession
% 2.82/1.58 = ( tl_Sec1905266422ession @ Xs ) )
% 2.82/1.58 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 | ? [X4: secrecy_Expression] :
% 2.82/1.58 ( Xs
% 2.82/1.58 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_308_last__tl,axiom,
% 2.82/1.58 ! [Xs: list_S529945141ession] :
% 2.82/1.58 ( ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 | ( ( tl_Sec1905266422ession @ Xs )
% 2.82/1.58 != nil_Se901661471ession ) )
% 2.82/1.58 => ( ( last_S1532390982ession @ ( tl_Sec1905266422ession @ Xs ) )
% 2.82/1.58 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_309_last__tl,axiom,
% 2.82/1.58 ! [Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 | ( ( tl_Secrecy_KS @ Xs )
% 2.82/1.58 != nil_Secrecy_KS ) )
% 2.82/1.58 => ( ( last_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) )
% 2.82/1.58 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_310_distinct__adj__singleton,axiom,
% 2.82/1.58 ! [X3: secrecy_KS] : ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_311_distinct__adj__singleton,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression] : ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_312_list_Oexhaust__sel,axiom,
% 2.82/1.58 ! [List: list_Secrecy_KS] :
% 2.82/1.58 ( ( List != nil_Secrecy_KS )
% 2.82/1.58 => ( List
% 2.82/1.58 = ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_313_list_Oexhaust__sel,axiom,
% 2.82/1.58 ! [List: list_S529945141ession] :
% 2.82/1.58 ( ( List != nil_Se901661471ession )
% 2.82/1.58 => ( List
% 2.82/1.58 = ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_314_distinct__adj__Cons,axiom,
% 2.82/1.58 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.58 ( ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.58 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.58 | ( ( X3
% 2.82/1.58 != ( hd_Secrecy_KS @ Xs ) )
% 2.82/1.58 & ( distin1495927511ecy_KS @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_315_distinct__adj__Cons,axiom,
% 2.82/1.58 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.58 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.58 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.58 | ( ( X3
% 2.82/1.58 != ( hd_Sec357328890ession @ Xs ) )
% 2.82/1.58 & ( distin1076152135ession @ Xs ) ) ) ) ).
% 2.82/1.58
% 2.82/1.58 thf(fact_316_successively__append__iff,axiom,
% 2.82/1.58 ! [P: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.58 ( ( succes1388047762ession @ P @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.58 = ( ( succes1388047762ession @ P @ Xs )
% 2.82/1.59 & ( succes1388047762ession @ P @ Ys2 )
% 2.82/1.59 & ( ( Xs = nil_Se901661471ession )
% 2.82/1.59 | ( Ys2 = nil_Se901661471ession )
% 2.82/1.59 | ( P @ ( last_S1532390982ession @ Xs ) @ ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_317_successively__append__iff,axiom,
% 2.82/1.59 ! [P: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.59 ( ( succes590251810ecy_KS @ P @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.59 = ( ( succes590251810ecy_KS @ P @ Xs )
% 2.82/1.59 & ( succes590251810ecy_KS @ P @ Ys2 )
% 2.82/1.59 & ( ( Xs = nil_Secrecy_KS )
% 2.82/1.59 | ( Ys2 = nil_Secrecy_KS )
% 2.82/1.59 | ( P @ ( last_Secrecy_KS @ Xs ) @ ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_318_Cons__in__shuffles__iff,axiom,
% 2.82/1.59 ! [Z: secrecy_KS,Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.59 ( ( member193705948ecy_KS @ ( cons_Secrecy_KS @ Z @ Zs2 ) @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.59 = ( ( ( Xs != nil_Secrecy_KS )
% 2.82/1.59 & ( ( hd_Secrecy_KS @ Xs )
% 2.82/1.59 = Z )
% 2.82/1.59 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) )
% 2.82/1.59 | ( ( Ys2 != nil_Secrecy_KS )
% 2.82/1.59 & ( ( hd_Secrecy_KS @ Ys2 )
% 2.82/1.59 = Z )
% 2.82/1.59 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ ( tl_Secrecy_KS @ Ys2 ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_319_Cons__in__shuffles__iff,axiom,
% 2.82/1.59 ! [Z: secrecy_Expression,Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.59 ( ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.82/1.59 = ( ( ( Xs != nil_Se901661471ession )
% 2.82/1.59 & ( ( hd_Sec357328890ession @ Xs )
% 2.82/1.59 = Z )
% 2.82/1.59 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) )
% 2.82/1.59 | ( ( Ys2 != nil_Se901661471ession )
% 2.82/1.59 & ( ( hd_Sec357328890ession @ Ys2 )
% 2.82/1.59 = Z )
% 2.82/1.59 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ ( tl_Sec1905266422ession @ Ys2 ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_320_Nil__in__shuffles,axiom,
% 2.82/1.59 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.59 ( ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.82/1.59 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.59 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_321_Nil__in__shuffles,axiom,
% 2.82/1.59 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.59 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.59 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.59 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_322_shufflesE,axiom,
% 2.82/1.59 ! [Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.59 ( ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.59 => ( ( ( Zs2 = Xs )
% 2.82/1.59 => ( Ys2 != nil_Secrecy_KS ) )
% 2.82/1.59 => ( ( ( Zs2 = Ys2 )
% 2.82/1.59 => ( Xs != nil_Secrecy_KS ) )
% 2.82/1.59 => ( ! [X: secrecy_KS,Xs5: list_Secrecy_KS] :
% 2.82/1.59 ( ( Xs
% 2.82/1.59 = ( cons_Secrecy_KS @ X @ Xs5 ) )
% 2.82/1.59 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 2.82/1.59 ( ( Zs2
% 2.82/1.59 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 2.82/1.59 => ( ( X = Z2 )
% 2.82/1.59 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs5 @ Ys2 ) ) ) ) )
% 2.82/1.59 => ~ ! [Y4: secrecy_KS,Ys5: list_Secrecy_KS] :
% 2.82/1.59 ( ( Ys2
% 2.82/1.59 = ( cons_Secrecy_KS @ Y4 @ Ys5 ) )
% 2.82/1.59 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 2.82/1.59 ( ( Zs2
% 2.82/1.59 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 2.82/1.59 => ( ( Y4 = Z2 )
% 2.82/1.59 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_323_shufflesE,axiom,
% 2.82/1.59 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.59 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.82/1.59 => ( ( ( Zs2 = Xs )
% 2.82/1.59 => ( Ys2 != nil_Se901661471ession ) )
% 2.82/1.59 => ( ( ( Zs2 = Ys2 )
% 2.82/1.59 => ( Xs != nil_Se901661471ession ) )
% 2.82/1.59 => ( ! [X: secrecy_Expression,Xs5: list_S529945141ession] :
% 2.82/1.59 ( ( Xs
% 2.82/1.59 = ( cons_S112077679ession @ X @ Xs5 ) )
% 2.82/1.59 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 2.82/1.59 ( ( Zs2
% 2.82/1.59 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 2.82/1.59 => ( ( X = Z2 )
% 2.82/1.59 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs5 @ Ys2 ) ) ) ) )
% 2.82/1.59 => ~ ! [Y4: secrecy_Expression,Ys5: list_S529945141ession] :
% 2.82/1.59 ( ( Ys2
% 2.82/1.59 = ( cons_S112077679ession @ Y4 @ Ys5 ) )
% 2.82/1.59 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 2.82/1.59 ( ( Zs2
% 2.82/1.59 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 2.82/1.59 => ( ( Y4 = Z2 )
% 2.82/1.59 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_324_successively_Osimps_I2_J,axiom,
% 2.82/1.59 ! [P: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS] : ( succes590251810ecy_KS @ P @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_325_successively_Osimps_I2_J,axiom,
% 2.82/1.59 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression] : ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_326_successively_Oelims_I1_J,axiom,
% 2.82/1.59 ! [X3: secrecy_KS > secrecy_KS > $o,Xa: list_Secrecy_KS,Y: $o] :
% 2.82/1.59 ( ( ( succes590251810ecy_KS @ X3 @ Xa )
% 2.82/1.59 = Y )
% 2.82/1.59 => ( ( ( Xa = nil_Secrecy_KS )
% 2.82/1.59 => ~ Y )
% 2.82/1.59 => ( ( ? [X: secrecy_KS] :
% 2.82/1.59 ( Xa
% 2.82/1.59 = ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.59 => ~ Y )
% 2.82/1.59 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.59 ( ( Xa
% 2.82/1.59 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 2.82/1.59 => ( Y
% 2.82/1.59 = ( ~ ( ( X3 @ X @ Y4 )
% 2.82/1.59 & ( succes590251810ecy_KS @ X3 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_327_successively_Oelims_I1_J,axiom,
% 2.82/1.59 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession,Y: $o] :
% 2.82/1.59 ( ( ( succes1388047762ession @ X3 @ Xa )
% 2.82/1.59 = Y )
% 2.82/1.59 => ( ( ( Xa = nil_Se901661471ession )
% 2.82/1.59 => ~ Y )
% 2.82/1.59 => ( ( ? [X: secrecy_Expression] :
% 2.82/1.59 ( Xa
% 2.82/1.59 = ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.59 => ~ Y )
% 2.82/1.59 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.59 ( ( Xa
% 2.82/1.59 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 2.82/1.59 => ( Y
% 2.82/1.59 = ( ~ ( ( X3 @ X @ Y4 )
% 2.82/1.59 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_328_successively_Oelims_I2_J,axiom,
% 2.82/1.59 ! [X3: secrecy_KS > secrecy_KS > $o,Xa: list_Secrecy_KS] :
% 2.82/1.59 ( ( succes590251810ecy_KS @ X3 @ Xa )
% 2.82/1.59 => ( ( Xa != nil_Secrecy_KS )
% 2.82/1.59 => ( ! [X: secrecy_KS] :
% 2.82/1.59 ( Xa
% 2.82/1.59 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.59 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.59 ( ( Xa
% 2.82/1.59 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 2.82/1.59 => ~ ( ( X3 @ X @ Y4 )
% 2.82/1.59 & ( succes590251810ecy_KS @ X3 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_329_successively_Oelims_I2_J,axiom,
% 2.82/1.59 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession] :
% 2.82/1.59 ( ( succes1388047762ession @ X3 @ Xa )
% 2.82/1.59 => ( ( Xa != nil_Se901661471ession )
% 2.82/1.59 => ( ! [X: secrecy_Expression] :
% 2.82/1.59 ( Xa
% 2.82/1.59 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.59 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.59 ( ( Xa
% 2.82/1.59 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 2.82/1.59 => ~ ( ( X3 @ X @ Y4 )
% 2.82/1.59 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_330_successively_Osimps_I1_J,axiom,
% 2.82/1.59 ! [P: secrecy_Expression > secrecy_Expression > $o] : ( succes1388047762ession @ P @ nil_Se901661471ession ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_331_successively_Osimps_I1_J,axiom,
% 2.82/1.59 ! [P: secrecy_KS > secrecy_KS > $o] : ( succes590251810ecy_KS @ P @ nil_Secrecy_KS ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_332_successively_Osimps_I3_J,axiom,
% 2.82/1.59 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.59 ( ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 2.82/1.59 = ( ( P @ X3 @ Y )
% 2.82/1.59 & ( succes1388047762ession @ P @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_333_successively_Oelims_I3_J,axiom,
% 2.82/1.59 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession] :
% 2.82/1.59 ( ~ ( succes1388047762ession @ X3 @ Xa )
% 2.82/1.59 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.59 ( ( Xa
% 2.82/1.59 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 2.82/1.59 => ( ( X3 @ X @ Y4 )
% 2.82/1.59 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_334_Nil__in__shufflesI,axiom,
% 2.82/1.59 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.59 ( ( Xs = nil_Se901661471ession )
% 2.82/1.59 => ( ( Ys2 = nil_Se901661471ession )
% 2.82/1.59 => ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_335_Nil__in__shufflesI,axiom,
% 2.82/1.59 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.59 ( ( Xs = nil_Secrecy_KS )
% 2.82/1.59 => ( ( Ys2 = nil_Secrecy_KS )
% 2.82/1.59 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_336_Cons__in__shuffles__rightI,axiom,
% 2.82/1.59 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession,Z: secrecy_Expression] :
% 2.82/1.59 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.82/1.59 => ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ ( cons_S112077679ession @ Z @ Ys2 ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_337_Cons__in__shuffles__leftI,axiom,
% 2.82/1.59 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession,Z: secrecy_Expression] :
% 2.82/1.59 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.82/1.59 => ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ ( cons_S112077679ession @ Z @ Xs ) @ Ys2 ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_338_successively__Cons,axiom,
% 2.82/1.59 ! [P: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.82/1.59 ( ( succes590251810ecy_KS @ P @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.82/1.59 = ( ( Xs = nil_Secrecy_KS )
% 2.82/1.59 | ( ( P @ X3 @ ( hd_Secrecy_KS @ Xs ) )
% 2.82/1.59 & ( succes590251810ecy_KS @ P @ Xs ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_339_successively__Cons,axiom,
% 2.82/1.59 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.59 ( ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.82/1.59 = ( ( Xs = nil_Se901661471ession )
% 2.82/1.59 | ( ( P @ X3 @ ( hd_Sec357328890ession @ Xs ) )
% 2.82/1.59 & ( succes1388047762ession @ P @ Xs ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_340_remdups__adj__append_H,axiom,
% 2.82/1.59 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.82/1.59 ( ( ( Xs = nil_Se901661471ession )
% 2.82/1.59 | ( Ys2 = nil_Se901661471ession )
% 2.82/1.59 | ( ( last_S1532390982ession @ Xs )
% 2.82/1.59 != ( hd_Sec357328890ession @ Ys2 ) ) )
% 2.82/1.59 => ( ( remdup484344169ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.82/1.59 = ( append2089414218ession @ ( remdup484344169ession @ Xs ) @ ( remdup484344169ession @ Ys2 ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_341_remdups__adj__append_H,axiom,
% 2.82/1.59 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.82/1.59 ( ( ( Xs = nil_Secrecy_KS )
% 2.82/1.59 | ( Ys2 = nil_Secrecy_KS )
% 2.82/1.59 | ( ( last_Secrecy_KS @ Xs )
% 2.82/1.59 != ( hd_Secrecy_KS @ Ys2 ) ) )
% 2.82/1.59 => ( ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.82/1.59 = ( append_Secrecy_KS @ ( remdup351570169ecy_KS @ Xs ) @ ( remdup351570169ecy_KS @ Ys2 ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_342_remdups__adj__append,axiom,
% 2.82/1.59 ! [Xs_1: list_Secrecy_KS,X3: secrecy_KS,Xs_2: list_Secrecy_KS] :
% 2.82/1.59 ( ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs_1 @ ( cons_Secrecy_KS @ X3 @ Xs_2 ) ) )
% 2.82/1.59 = ( append_Secrecy_KS @ ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs_1 @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) @ ( tl_Secrecy_KS @ ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs_2 ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_343_remdups__adj__append,axiom,
% 2.82/1.59 ! [Xs_1: list_S529945141ession,X3: secrecy_Expression,Xs_2: list_S529945141ession] :
% 2.82/1.59 ( ( remdup484344169ession @ ( append2089414218ession @ Xs_1 @ ( cons_S112077679ession @ X3 @ Xs_2 ) ) )
% 2.82/1.59 = ( append2089414218ession @ ( remdup484344169ession @ ( append2089414218ession @ Xs_1 @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs_2 ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_344_remdups__adj__Nil__iff,axiom,
% 2.82/1.59 ! [Xs: list_S529945141ession] :
% 2.82/1.59 ( ( ( remdup484344169ession @ Xs )
% 2.82/1.59 = nil_Se901661471ession )
% 2.82/1.59 = ( Xs = nil_Se901661471ession ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_345_remdups__adj__Nil__iff,axiom,
% 2.82/1.59 ! [Xs: list_Secrecy_KS] :
% 2.82/1.59 ( ( ( remdup351570169ecy_KS @ Xs )
% 2.82/1.59 = nil_Secrecy_KS )
% 2.82/1.59 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_346_remdups__adj__Cons__alt,axiom,
% 2.82/1.59 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.59 ( ( cons_S112077679ession @ X3 @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) )
% 2.82/1.59 = ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_347_remdups__adj_Osimps_I2_J,axiom,
% 2.82/1.59 ! [X3: secrecy_KS] :
% 2.82/1.59 ( ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 2.82/1.59 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_348_remdups__adj_Osimps_I2_J,axiom,
% 2.82/1.59 ! [X3: secrecy_Expression] :
% 2.82/1.59 ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 2.82/1.59 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_349_remdups__adj_Oelims,axiom,
% 2.82/1.59 ! [X3: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 2.82/1.59 ( ( ( remdup351570169ecy_KS @ X3 )
% 2.82/1.59 = Y )
% 2.82/1.59 => ( ( ( X3 = nil_Secrecy_KS )
% 2.82/1.59 => ( Y != nil_Secrecy_KS ) )
% 2.82/1.59 => ( ! [X: secrecy_KS] :
% 2.82/1.59 ( ( X3
% 2.82/1.59 = ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.82/1.59 => ( Y
% 2.82/1.59 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) )
% 2.82/1.59 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.82/1.59 ( ( X3
% 2.82/1.59 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 2.82/1.59 => ~ ( ( ( X = Y4 )
% 2.82/1.59 => ( Y
% 2.82/1.59 = ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 2.82/1.59 & ( ( X != Y4 )
% 2.82/1.59 => ( Y
% 2.82/1.59 = ( cons_Secrecy_KS @ X @ ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_350_remdups__adj_Oelims,axiom,
% 2.82/1.59 ! [X3: list_S529945141ession,Y: list_S529945141ession] :
% 2.82/1.59 ( ( ( remdup484344169ession @ X3 )
% 2.82/1.59 = Y )
% 2.82/1.59 => ( ( ( X3 = nil_Se901661471ession )
% 2.82/1.59 => ( Y != nil_Se901661471ession ) )
% 2.82/1.59 => ( ! [X: secrecy_Expression] :
% 2.82/1.59 ( ( X3
% 2.82/1.59 = ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.82/1.59 => ( Y
% 2.82/1.59 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) )
% 2.82/1.59 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.82/1.59 ( ( X3
% 2.82/1.59 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 2.82/1.59 => ~ ( ( ( X = Y4 )
% 2.82/1.59 => ( Y
% 2.82/1.59 = ( remdup484344169ession @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 2.82/1.59 & ( ( X != Y4 )
% 2.82/1.59 => ( Y
% 2.82/1.59 = ( cons_S112077679ession @ X @ ( remdup484344169ession @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(fact_351_remdups__adj_Osimps_I3_J,axiom,
% 2.82/1.59 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 2.82/1.59 ( ( ( X3 = Y )
% 2.82/1.59 => ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 2.82/1.59 = ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) )
% 2.82/1.59 & ( ( X3 != Y )
% 2.82/1.59 => ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 2.82/1.59 = ( cons_S112077679ession @ X3 @ ( remdup484344169ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ) ) ).
% 2.82/1.59
% 2.82/1.59 thf(conj_0,conjecture,
% 2.82/1.59 knowle945212990e_know @ a @ ( secrecy_sKS @ m ) ).
% 2.82/1.59 ------------------------
% 2.92/1.62 % (18286)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/2Mi)
% 2.92/1.62 % (18283)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/183Mi)
% 2.92/1.63 % (18286)Instruction limit reached!
% 2.92/1.63 % (18286)------------------------------
% 2.92/1.63 % (18286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (18286)Termination reason: Unknown
% 2.92/1.63 % (18286)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (18286)Memory used [KB]: 1535
% 2.92/1.63 % (18286)Time elapsed: 0.003 s
% 2.92/1.63 % (18286)Instructions burned: 4 (million)
% 2.92/1.63 % (18286)------------------------------
% 2.92/1.63 % (18286)------------------------------
% 2.92/1.63 % (18284)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/4Mi)
% 2.92/1.63 % (18284)Instruction limit reached!
% 2.92/1.63 % (18284)------------------------------
% 2.92/1.63 % (18284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (18284)Termination reason: Unknown
% 2.92/1.63 % (18284)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (18284)Memory used [KB]: 1535
% 2.92/1.63 % (18284)Time elapsed: 0.003 s
% 2.92/1.63 % (18284)Instructions burned: 4 (million)
% 2.92/1.63 % (18284)------------------------------
% 2.92/1.63 % (18284)------------------------------
% 2.92/1.63 % (18289)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/18Mi)
% 2.92/1.63 % (18285)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/27Mi)
% 2.92/1.63 % (18287)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/2Mi)
% 2.92/1.63 % (18288)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/275Mi)
% 2.92/1.63 % (18287)Instruction limit reached!
% 2.92/1.63 % (18287)------------------------------
% 2.92/1.63 % (18287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (18287)Termination reason: Unknown
% 2.92/1.63 % (18287)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (18287)Memory used [KB]: 1535
% 2.92/1.63 % (18287)Time elapsed: 0.004 s
% 2.92/1.63 % (18287)Instructions burned: 2 (million)
% 2.92/1.63 % (18287)------------------------------
% 2.92/1.63 % (18287)------------------------------
% 2.92/1.63 % (18290)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/3Mi)
% 2.92/1.64 % (18290)Instruction limit reached!
% 2.92/1.64 % (18290)------------------------------
% 2.92/1.64 % (18290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (18290)Termination reason: Unknown
% 2.92/1.64 % (18290)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (18290)Memory used [KB]: 1535
% 2.92/1.64 % (18290)Time elapsed: 0.002 s
% 2.92/1.64 % (18290)Instructions burned: 3 (million)
% 2.92/1.64 % (18290)------------------------------
% 2.92/1.64 % (18290)------------------------------
% 2.92/1.64 % (18291)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/37Mi)
% 2.92/1.64 % (18289)Instruction limit reached!
% 2.92/1.64 % (18289)------------------------------
% 2.92/1.64 % (18289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (18289)Termination reason: Unknown
% 2.92/1.64 % (18289)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (18289)Memory used [KB]: 1918
% 2.92/1.64 % (18289)Time elapsed: 0.013 s
% 2.92/1.64 % (18289)Instructions burned: 19 (million)
% 2.92/1.64 % (18289)------------------------------
% 2.92/1.64 % (18289)------------------------------
% 2.92/1.64 % (18293)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/3Mi)
% 2.92/1.65 % (18293)Instruction limit reached!
% 2.92/1.65 % (18293)------------------------------
% 2.92/1.65 % (18293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (18293)Termination reason: Unknown
% 2.92/1.65 % (18293)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (18293)Memory used [KB]: 1535
% 2.92/1.65 % (18293)Time elapsed: 0.002 s
% 2.92/1.65 % (18293)Instructions burned: 3 (million)
% 2.92/1.65 % (18293)------------------------------
% 2.92/1.65 % (18293)------------------------------
% 2.92/1.65 % (18285)Instruction limit reached!
% 2.92/1.65 % (18285)------------------------------
% 2.92/1.65 % (18285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (18285)Termination reason: Unknown
% 2.92/1.65 % (18285)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (18285)Memory used [KB]: 2046
% 2.92/1.65 % (18285)Time elapsed: 0.018 s
% 2.92/1.65 % (18285)Instructions burned: 27 (million)
% 2.92/1.65 % (18285)------------------------------
% 2.92/1.65 % (18285)------------------------------
% 2.92/1.65 % (18292)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/15Mi)
% 2.92/1.65 % (18291)Instruction limit reached!
% 2.92/1.65 % (18291)------------------------------
% 2.92/1.65 % (18291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (18291)Termination reason: Unknown
% 2.92/1.65 % (18291)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (18291)Memory used [KB]: 2302
% 2.92/1.65 % (18291)Time elapsed: 0.014 s
% 2.92/1.65 % (18291)Instructions burned: 39 (million)
% 2.92/1.65 % (18291)------------------------------
% 2.92/1.65 % (18291)------------------------------
% 2.92/1.66 % (18294)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/1041Mi)
% 2.92/1.66 % (18295)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/7Mi)
% 2.92/1.66 % (18295)Instruction limit reached!
% 2.92/1.66 % (18295)------------------------------
% 2.92/1.66 % (18295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (18295)Termination reason: Unknown
% 2.92/1.66 % (18295)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (18295)Memory used [KB]: 1791
% 2.92/1.66 % (18295)Time elapsed: 0.004 s
% 2.92/1.66 % (18295)Instructions burned: 9 (million)
% 2.92/1.66 % (18295)------------------------------
% 2.92/1.66 % (18295)------------------------------
% 2.92/1.66 % (18292)Instruction limit reached!
% 2.92/1.66 % (18292)------------------------------
% 2.92/1.66 % (18292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (18292)Termination reason: Unknown
% 2.92/1.66 % (18292)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (18292)Memory used [KB]: 1791
% 2.92/1.66 % (18292)Time elapsed: 0.011 s
% 2.92/1.66 % (18292)Instructions burned: 15 (million)
% 2.92/1.66 % (18292)------------------------------
% 2.92/1.66 % (18292)------------------------------
% 2.92/1.66 % (18297)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/3Mi)
% 2.92/1.66 % (18297)Instruction limit reached!
% 2.92/1.66 % (18297)------------------------------
% 2.92/1.66 % (18297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (18297)Termination reason: Unknown
% 2.92/1.66 % (18297)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (18297)Memory used [KB]: 1535
% 2.92/1.66 % (18297)Time elapsed: 0.003 s
% 2.92/1.66 % (18297)Instructions burned: 3 (million)
% 2.92/1.66 % (18297)------------------------------
% 2.92/1.66 % (18297)------------------------------
% 2.92/1.66 % (18296)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/16Mi)
% 2.92/1.67 % (18288)Refutation not found, incomplete strategy
% 2.92/1.67 % (18288)------------------------------
% 2.92/1.67 % (18288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (18288)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.67
% 2.92/1.67
% 2.92/1.67 % (18288)Memory used [KB]: 6652
% 2.92/1.67 % (18288)Time elapsed: 0.036 s
% 2.92/1.67 % (18288)Instructions burned: 59 (million)
% 2.92/1.67 % (18288)------------------------------
% 2.92/1.67 % (18288)------------------------------
% 2.92/1.67 % (18298)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/3Mi)
% 2.92/1.67 % (18298)Instruction limit reached!
% 2.92/1.67 % (18298)------------------------------
% 2.92/1.67 % (18298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (18298)Termination reason: Unknown
% 2.92/1.67 % (18298)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (18298)Memory used [KB]: 1535
% 2.92/1.67 % (18298)Time elapsed: 0.002 s
% 2.92/1.67 % (18298)Instructions burned: 3 (million)
% 2.92/1.67 % (18298)------------------------------
% 2.92/1.67 % (18298)------------------------------
% 2.92/1.67 % (18300)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/3Mi)
% 2.92/1.67 % (18300)Instruction limit reached!
% 2.92/1.67 % (18300)------------------------------
% 2.92/1.67 % (18300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (18300)Termination reason: Unknown
% 2.92/1.67 % (18300)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (18300)Memory used [KB]: 1535
% 2.92/1.67 % (18300)Time elapsed: 0.003 s
% 2.92/1.67 % (18300)Instructions burned: 4 (million)
% 2.92/1.67 % (18300)------------------------------
% 2.92/1.67 % (18300)------------------------------
% 2.92/1.67 % (18296)Instruction limit reached!
% 2.92/1.67 % (18296)------------------------------
% 2.92/1.67 % (18296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (18296)Termination reason: Unknown
% 2.92/1.67 % (18296)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (18296)Memory used [KB]: 1918
% 2.92/1.67 % (18296)Time elapsed: 0.012 s
% 2.92/1.67 % (18296)Instructions burned: 17 (million)
% 2.92/1.67 % (18296)------------------------------
% 2.92/1.67 % (18296)------------------------------
% 2.92/1.68 % (18299)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/7Mi)
% 2.92/1.68 % (18302)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/18Mi)
% 2.92/1.68 % (18301)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/4Mi)
% 2.92/1.68 % (18283)Instruction limit reached!
% 2.92/1.68 % (18283)------------------------------
% 2.92/1.68 % (18283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (18283)Termination reason: Unknown
% 2.92/1.68 % (18283)Termination phase: Saturation
% 2.92/1.68
% 2.92/1.68 % (18283)Memory used [KB]: 7675
% 2.92/1.68 % (18283)Time elapsed: 0.056 s
% 2.92/1.68 % (18283)Instructions burned: 185 (million)
% 2.92/1.68 % (18283)------------------------------
% 2.92/1.68 % (18283)------------------------------
% 2.92/1.68 % (18301)Instruction limit reached!
% 2.92/1.68 % (18301)------------------------------
% 2.92/1.68 % (18301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (18301)Termination reason: Unknown
% 2.92/1.68 % (18301)Termination phase: shuffling
% 2.92/1.68
% 2.92/1.68 % (18301)Memory used [KB]: 1663
% 2.92/1.68 % (18301)Time elapsed: 0.004 s
% 2.92/1.68 % (18301)Instructions burned: 6 (million)
% 2.92/1.68 % (18301)------------------------------
% 2.92/1.68 % (18301)------------------------------
% 2.92/1.68 % (18299)Instruction limit reached!
% 2.92/1.68 % (18299)------------------------------
% 2.92/1.68 % (18299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (18299)Termination reason: Unknown
% 2.92/1.68 % (18299)Termination phase: shuffling
% 2.92/1.68
% 2.92/1.68 % (18299)Memory used [KB]: 1663
% 2.92/1.68 % (18299)Time elapsed: 0.006 s
% 2.92/1.68 % (18299)Instructions burned: 7 (million)
% 2.92/1.68 % (18299)------------------------------
% 2.92/1.68 % (18299)------------------------------
% 2.92/1.68 % (18303)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/710Mi)
% 2.92/1.68 % (18302)Instruction limit reached!
% 2.92/1.68 % (18302)------------------------------
% 2.92/1.68 % (18302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (18302)Termination reason: Unknown
% 2.92/1.68 % (18302)Termination phase: shuffling
% 2.92/1.68
% 2.92/1.68 % (18302)Memory used [KB]: 1918
% 2.92/1.68 % (18302)Time elapsed: 0.007 s
% 2.92/1.68 % (18302)Instructions burned: 19 (million)
% 2.92/1.68 % (18302)------------------------------
% 2.92/1.68 % (18302)------------------------------
% 2.92/1.69 % (18305)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/902Mi)
% 2.92/1.69 % (18306)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/21Mi)
% 2.92/1.69 % (18304)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/6Mi)
% 2.92/1.69 % (18308)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/6Mi)
% 2.92/1.70 % (18308)Instruction limit reached!
% 2.92/1.70 % (18308)------------------------------
% 2.92/1.70 % (18308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.70 % (18308)Termination reason: Unknown
% 2.92/1.70 % (18308)Termination phase: shuffling
% 2.92/1.70
% 2.92/1.70 % (18308)Memory used [KB]: 1663
% 2.92/1.70 % (18308)Time elapsed: 0.003 s
% 2.92/1.70 % (18308)Instructions burned: 6 (million)
% 2.92/1.70 % (18308)------------------------------
% 2.92/1.70 % (18308)------------------------------
% 2.92/1.70 % (18307)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/5Mi)
% 2.92/1.70 % (18304)Instruction limit reached!
% 2.92/1.70 % (18304)------------------------------
% 2.92/1.70 % (18304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.70 % (18304)Termination reason: Unknown
% 2.92/1.70 % (18304)Termination phase: shuffling
% 2.92/1.70
% 2.92/1.70 % (18304)Memory used [KB]: 1663
% 2.92/1.70 % (18304)Time elapsed: 0.006 s
% 2.92/1.70 % (18304)Instructions burned: 7 (million)
% 2.92/1.70 % (18304)------------------------------
% 2.92/1.70 % (18304)------------------------------
% 2.92/1.70 % (18307)Instruction limit reached!
% 2.92/1.70 % (18307)------------------------------
% 2.92/1.70 % (18307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.70 % (18307)Termination reason: Unknown
% 2.92/1.70 % (18307)Termination phase: shuffling
% 2.92/1.70
% 2.92/1.70 % (18307)Memory used [KB]: 1663
% 2.92/1.70 % (18307)Time elapsed: 0.004 s
% 2.92/1.70 % (18307)Instructions burned: 7 (million)
% 2.92/1.70 % (18307)------------------------------
% 2.92/1.70 % (18307)------------------------------
% 2.92/1.70 % (18306)Instruction limit reached!
% 2.92/1.70 % (18306)------------------------------
% 2.92/1.70 % (18306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.70 % (18306)Termination reason: Unknown
% 2.92/1.70 % (18306)Termination phase: shuffling
% 2.92/1.70
% 2.92/1.70 % (18306)Memory used [KB]: 1918
% 2.92/1.70 % (18306)Time elapsed: 0.009 s
% 2.92/1.70 % (18306)Instructions burned: 22 (million)
% 2.92/1.70 % (18306)------------------------------
% 2.92/1.70 % (18306)------------------------------
% 2.92/1.70 % (18309)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18072 for (2999ds/377Mi)
% 2.92/1.71 % (18311)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/19Mi)
% 2.92/1.71 % (18312)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/879Mi)
% 2.92/1.71 % (18311)Instruction limit reached!
% 2.92/1.71 % (18311)------------------------------
% 2.92/1.71 % (18311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.71 % (18311)Termination reason: Unknown
% 2.92/1.71 % (18311)Termination phase: shuffling
% 2.92/1.71
% 2.92/1.71 % (18311)Memory used [KB]: 2046
% 2.92/1.71 % (18311)Time elapsed: 0.007 s
% 2.92/1.71 % (18311)Instructions burned: 22 (million)
% 2.92/1.71 % (18311)------------------------------
% 2.92/1.71 % (18311)------------------------------
% 2.92/1.71 % (18310)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/779Mi)
% 2.92/1.72 % (18313)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/17Mi)
% 2.92/1.73 % (18313)Instruction limit reached!
% 2.92/1.73 % (18313)------------------------------
% 2.92/1.73 % (18313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (18313)Termination reason: Unknown
% 2.92/1.73 % (18313)Termination phase: shuffling
% 2.92/1.73
% 2.92/1.73 % (18313)Memory used [KB]: 1918
% 2.92/1.73 % (18313)Time elapsed: 0.007 s
% 2.92/1.73 % (18313)Instructions burned: 19 (million)
% 2.92/1.73 % (18313)------------------------------
% 2.92/1.73 % (18313)------------------------------
% 2.92/1.74 % (18314)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/3Mi)
% 2.92/1.74 % (18314)Instruction limit reached!
% 2.92/1.74 % (18314)------------------------------
% 2.92/1.74 % (18314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.74 % (18314)Termination reason: Unknown
% 2.92/1.74 % (18314)Termination phase: shuffling
% 2.92/1.74
% 2.92/1.74 % (18314)Memory used [KB]: 1535
% 2.92/1.74 % (18314)Time elapsed: 0.002 s
% 2.92/1.74 % (18314)Instructions burned: 3 (million)
% 2.92/1.74 % (18314)------------------------------
% 2.92/1.74 % (18314)------------------------------
% 2.92/1.75 % (18315)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/30Mi)
% 2.92/1.75 % (18305)Refutation not found, incomplete strategy
% 2.92/1.75 % (18305)------------------------------
% 2.92/1.75 % (18305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.75 % (18305)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.75
% 2.92/1.75
% 2.92/1.75 % (18305)Memory used [KB]: 8571
% 2.92/1.75 % (18305)Time elapsed: 0.064 s
% 2.92/1.75 % (18305)Instructions burned: 199 (million)
% 2.92/1.75 % (18305)------------------------------
% 2.92/1.75 % (18305)------------------------------
% 2.92/1.76 % (18315)Instruction limit reached!
% 2.92/1.76 % (18315)------------------------------
% 2.92/1.76 % (18315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.76 % (18315)Termination reason: Unknown
% 2.92/1.76 % (18315)Termination phase: shuffling
% 2.92/1.76
% 2.92/1.76 % (18315)Memory used [KB]: 2046
% 2.92/1.76 % (18315)Time elapsed: 0.011 s
% 2.92/1.76 % (18315)Instructions burned: 31 (million)
% 2.92/1.76 % (18315)------------------------------
% 2.92/1.76 % (18315)------------------------------
% 2.92/1.76 % (18316)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/127Mi)
% 2.92/1.77 % (18317)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/100Mi)
% 2.92/1.79 % (18317)Instruction limit reached!
% 2.92/1.79 % (18317)------------------------------
% 2.92/1.79 % (18317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.79 % (18317)Termination reason: Unknown
% 2.92/1.79 % (18317)Termination phase: Property scanning
% 2.92/1.79
% 2.92/1.79 % (18317)Memory used [KB]: 2814
% 2.92/1.79 % (18317)Time elapsed: 0.027 s
% 2.92/1.79 % (18317)Instructions burned: 102 (million)
% 2.92/1.79 % (18317)------------------------------
% 2.92/1.79 % (18317)------------------------------
% 2.92/1.80 % (18316)Instruction limit reached!
% 2.92/1.80 % (18316)------------------------------
% 2.92/1.80 % (18316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.80 % (18316)Termination reason: Unknown
% 2.92/1.80 % (18316)Termination phase: Property scanning
% 2.92/1.80
% 2.92/1.80 % (18316)Memory used [KB]: 2942
% 2.92/1.80 % (18316)Time elapsed: 0.041 s
% 2.92/1.80 % (18316)Instructions burned: 130 (million)
% 2.92/1.80 % (18316)------------------------------
% 2.92/1.80 % (18316)------------------------------
% 2.92/1.80 % (18318)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_18072 for (2998ds/3Mi)
% 2.92/1.81 % (18318)Instruction limit reached!
% 2.92/1.81 % (18318)------------------------------
% 2.92/1.81 % (18318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (18318)Termination reason: Unknown
% 2.92/1.81 % (18318)Termination phase: shuffling
% 2.92/1.81
% 2.92/1.81 % (18318)Memory used [KB]: 1663
% 2.92/1.81 % (18318)Time elapsed: 0.003 s
% 2.92/1.81 % (18318)Instructions burned: 5 (million)
% 2.92/1.81 % (18318)------------------------------
% 2.92/1.81 % (18318)------------------------------
% 2.92/1.81 % (18319)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/20Mi)
% 2.92/1.81 % (18320)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/86Mi)
% 2.92/1.82 % (18309)Instruction limit reached!
% 2.92/1.82 % (18309)------------------------------
% 2.92/1.82 % (18309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.82 % (18309)Termination reason: Unknown
% 2.92/1.82 % (18309)Termination phase: Saturation
% 2.92/1.82
% 2.92/1.82 % (18309)Memory used [KB]: 9210
% 2.92/1.82 % (18309)Time elapsed: 0.112 s
% 2.92/1.82 % (18309)Instructions burned: 380 (million)
% 2.92/1.82 % (18309)------------------------------
% 2.92/1.82 % (18309)------------------------------
% 2.92/1.82 % (18319)Instruction limit reached!
% 2.92/1.82 % (18319)------------------------------
% 2.92/1.82 % (18319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.82 % (18319)Termination reason: Unknown
% 2.92/1.82 % (18319)Termination phase: shuffling
% 2.92/1.82
% 2.92/1.82 % (18319)Memory used [KB]: 1918
% 2.92/1.82 % (18319)Time elapsed: 0.009 s
% 2.92/1.82 % (18319)Instructions burned: 21 (million)
% 2.92/1.82 % (18319)------------------------------
% 2.92/1.82 % (18319)------------------------------
% 2.92/1.83 % (18321)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/107Mi)
% 2.92/1.83 % (18322)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/39Mi)
% 2.92/1.84 % (18320)Instruction limit reached!
% 2.92/1.84 % (18320)------------------------------
% 2.92/1.84 % (18320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.84 % (18320)Termination reason: Unknown
% 2.92/1.84 % (18320)Termination phase: Property scanning
% 2.92/1.84
% 2.92/1.84 % (18320)Memory used [KB]: 2814
% 2.92/1.84 % (18320)Time elapsed: 0.026 s
% 2.92/1.84 % (18320)Instructions burned: 89 (million)
% 2.92/1.84 % (18320)------------------------------
% 2.92/1.84 % (18320)------------------------------
% 2.92/1.84 % (18322)Instruction limit reached!
% 2.92/1.84 % (18322)------------------------------
% 2.92/1.84 % (18322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.84 % (18322)Termination reason: Unknown
% 2.92/1.84 % (18322)Termination phase: shuffling
% 2.92/1.84
% 2.92/1.84 % (18322)Memory used [KB]: 2302
% 2.92/1.84 % (18322)Time elapsed: 0.014 s
% 2.92/1.84 % (18322)Instructions burned: 42 (million)
% 2.92/1.84 % (18322)------------------------------
% 2.92/1.84 % (18322)------------------------------
% 2.92/1.85 % (18323)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/448Mi)
% 2.92/1.85 % (18324)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/46Mi)
% 2.92/1.86 % (18321)Instruction limit reached!
% 2.92/1.86 % (18321)------------------------------
% 2.92/1.86 % (18321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.86 % (18321)Termination reason: Unknown
% 2.92/1.86 % (18321)Termination phase: Saturation
% 2.92/1.86
% 2.92/1.86 % (18321)Memory used [KB]: 7036
% 2.92/1.86 % (18321)Time elapsed: 0.032 s
% 2.92/1.86 % (18321)Instructions burned: 109 (million)
% 2.92/1.86 % (18321)------------------------------
% 2.92/1.86 % (18321)------------------------------
% 2.92/1.87 % (18325)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/98Mi)
% 2.92/1.87 % (18324)Instruction limit reached!
% 2.92/1.87 % (18324)------------------------------
% 2.92/1.87 % (18324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.87 % (18324)Termination reason: Unknown
% 2.92/1.87 % (18324)Termination phase: Property scanning
% 2.92/1.87
% 2.92/1.87 % (18324)Memory used [KB]: 2046
% 2.92/1.87 % (18324)Time elapsed: 0.016 s
% 2.92/1.87 % (18324)Instructions burned: 46 (million)
% 2.92/1.87 % (18324)------------------------------
% 2.92/1.87 % (18324)------------------------------
% 2.92/1.88 % (18326)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_18072 for (2997ds/507Mi)
% 2.92/1.89 % (18325)Instruction limit reached!
% 2.92/1.89 % (18325)------------------------------
% 2.92/1.89 % (18325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (18325)Termination reason: Unknown
% 2.92/1.89 % (18325)Termination phase: Property scanning
% 2.92/1.89
% 2.92/1.89 % (18325)Memory used [KB]: 2814
% 2.92/1.89 % (18325)Time elapsed: 0.027 s
% 2.92/1.89 % (18325)Instructions burned: 98 (million)
% 2.92/1.89 % (18325)------------------------------
% 2.92/1.89 % (18325)------------------------------
% 2.92/1.90 % (18303)Instruction limit reached!
% 2.92/1.90 % (18303)------------------------------
% 2.92/1.90 % (18303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.90 % (18303)Termination reason: Unknown
% 2.92/1.90 % (18303)Termination phase: Saturation
% 2.92/1.90
% 2.92/1.90 % (18303)Memory used [KB]: 7547
% 2.92/1.90 % (18303)Time elapsed: 0.217 s
% 2.92/1.90 % (18303)Instructions burned: 711 (million)
% 2.92/1.90 % (18303)------------------------------
% 2.92/1.90 % (18303)------------------------------
% 2.92/1.90 % (18327)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/149Mi)
% 2.92/1.91 % (18328)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/39Mi)
% 2.92/1.92 % (18328)Instruction limit reached!
% 2.92/1.92 % (18328)------------------------------
% 2.92/1.92 % (18328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.92 % (18328)Termination reason: Unknown
% 2.92/1.92 % (18328)Termination phase: Property scanning
% 2.92/1.92
% 2.92/1.92 % (18328)Memory used [KB]: 2046
% 2.92/1.92 % (18328)Time elapsed: 0.014 s
% 2.92/1.92 % (18328)Instructions burned: 42 (million)
% 2.92/1.92 % (18328)------------------------------
% 2.92/1.92 % (18328)------------------------------
% 2.92/1.93 % (18329)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/6Mi)
% 2.92/1.93 % (18329)Instruction limit reached!
% 2.92/1.93 % (18329)------------------------------
% 2.92/1.93 % (18329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.93 % (18329)Termination reason: Unknown
% 2.92/1.93 % (18329)Termination phase: shuffling
% 2.92/1.93
% 2.92/1.93 % (18329)Memory used [KB]: 1663
% 2.92/1.93 % (18329)Time elapsed: 0.003 s
% 2.92/1.93 % (18329)Instructions burned: 7 (million)
% 2.92/1.93 % (18329)------------------------------
% 2.92/1.93 % (18329)------------------------------
% 2.92/1.94 % (18327)Instruction limit reached!
% 2.92/1.94 % (18327)------------------------------
% 2.92/1.94 % (18327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (18327)Termination reason: Unknown
% 2.92/1.94 % (18327)Termination phase: Property scanning
% 2.92/1.94
% 2.92/1.94 % (18327)Memory used [KB]: 3070
% 2.92/1.94 % (18327)Time elapsed: 0.042 s
% 2.92/1.94 % (18327)Instructions burned: 150 (million)
% 2.92/1.94 % (18327)------------------------------
% 2.92/1.94 % (18327)------------------------------
% 2.92/1.94 % (18330)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/1087Mi)
% 2.92/1.94 % (18326)Refutation not found, incomplete strategy
% 2.92/1.94 % (18326)------------------------------
% 2.92/1.94 % (18326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (18326)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.94
% 2.92/1.94
% 2.92/1.94 % (18326)Memory used [KB]: 8955
% 2.92/1.94 % (18326)Time elapsed: 0.070 s
% 2.92/1.94 % (18326)Instructions burned: 218 (million)
% 2.92/1.94 % (18326)------------------------------
% 2.92/1.94 % (18326)------------------------------
% 2.92/1.95 % (18331)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/47Mi)
% 2.92/1.96 % (18332)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/44Mi)
% 2.92/1.97 % (18331)Instruction limit reached!
% 2.92/1.97 % (18331)------------------------------
% 2.92/1.97 % (18331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.97 % (18331)Termination reason: Unknown
% 2.92/1.97 % (18331)Termination phase: Preprocessing 1
% 2.92/1.97
% 2.92/1.97 % (18331)Memory used [KB]: 2046
% 2.92/1.97 % (18331)Time elapsed: 0.015 s
% 2.92/1.97 % (18331)Instructions burned: 50 (million)
% 2.92/1.97 % (18331)------------------------------
% 2.92/1.97 % (18331)------------------------------
% 2.92/1.97 % (18332)Instruction limit reached!
% 2.92/1.97 % (18332)------------------------------
% 2.92/1.97 % (18332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.97 % (18332)Termination reason: Unknown
% 2.92/1.97 % (18332)Termination phase: shuffling
% 2.92/1.97
% 2.92/1.97 % (18332)Memory used [KB]: 2302
% 2.92/1.97 % (18332)Time elapsed: 0.015 s
% 2.92/1.97 % (18332)Instructions burned: 45 (million)
% 2.92/1.97 % (18332)------------------------------
% 2.92/1.97 % (18332)------------------------------
% 2.92/1.98 % (18333)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/432Mi)
% 2.92/1.98 % (18334)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/62Mi)
% 2.92/1.98 % (18323)Instruction limit reached!
% 2.92/1.98 % (18323)------------------------------
% 2.92/1.98 % (18323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (18323)Termination reason: Unknown
% 2.92/1.98 % (18323)Termination phase: Saturation
% 2.92/1.98
% 2.92/1.98 % (18323)Memory used [KB]: 8827
% 2.92/1.98 % (18323)Time elapsed: 0.156 s
% 2.92/1.98 % (18323)Instructions burned: 450 (million)
% 2.92/1.98 % (18323)------------------------------
% 2.92/1.98 % (18323)------------------------------
% 2.92/1.99 % (18310)Instruction limit reached!
% 2.92/1.99 % (18310)------------------------------
% 2.92/1.99 % (18310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.99 % (18310)Termination reason: Unknown
% 2.92/1.99 % (18310)Termination phase: Saturation
% 2.92/1.99
% 2.92/1.99 % (18310)Memory used [KB]: 8827
% 2.92/1.99 % (18310)Time elapsed: 0.275 s
% 2.92/1.99 % (18310)Instructions burned: 780 (million)
% 2.92/1.99 % (18310)------------------------------
% 2.92/1.99 % (18310)------------------------------
% 2.92/1.99 % (18335)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_18072 for (2996ds/31Mi)
% 2.92/1.99 % (18294)Instruction limit reached!
% 2.92/1.99 % (18294)------------------------------
% 2.92/1.99 % (18294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.99 % (18294)Termination reason: Unknown
% 2.92/1.99 % (18294)Termination phase: Saturation
% 2.92/1.99
% 2.92/1.99 % (18294)Memory used [KB]: 10490
% 2.92/1.99 % (18294)Time elapsed: 0.339 s
% 2.92/1.99 % (18294)Instructions burned: 1043 (million)
% 2.92/1.99 % (18294)------------------------------
% 2.92/1.99 % (18294)------------------------------
% 2.92/2.00 % (18334)Instruction limit reached!
% 2.92/2.00 % (18334)------------------------------
% 2.92/2.00 % (18334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/2.00 % (18334)Termination reason: Unknown
% 2.92/2.00 % (18334)Termination phase: shuffling
% 2.92/2.00
% 2.92/2.00 % (18334)Memory used [KB]: 2686
% 2.92/2.00 % (18334)Time elapsed: 0.018 s
% 2.92/2.00 % (18334)Instructions burned: 62 (million)
% 2.92/2.00 % (18334)------------------------------
% 2.92/2.00 % (18334)------------------------------
% 2.92/2.00 % (18336)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/96Mi)
% 2.92/2.00 % (18312)Instruction limit reached!
% 2.92/2.00 % (18312)------------------------------
% 2.92/2.00 % (18312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/2.00 % (18312)Termination reason: Unknown
% 2.92/2.00 % (18312)Termination phase: Saturation
% 2.92/2.00
% 2.92/2.00 % (18312)Memory used [KB]: 7291
% 2.92/2.00 % (18312)Time elapsed: 0.294 s
% 2.92/2.00 % (18312)Instructions burned: 880 (million)
% 2.92/2.00 % (18312)------------------------------
% 2.92/2.00 % (18312)------------------------------
% 2.92/2.00 % (18335)Instruction limit reached!
% 2.92/2.00 % (18335)------------------------------
% 2.92/2.00 % (18335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/2.00 % (18335)Termination reason: Unknown
% 2.92/2.00 % (18335)Termination phase: Property scanning
% 2.92/2.00
% 2.92/2.00 % (18335)Memory used [KB]: 2046
% 2.92/2.00 % (18335)Time elapsed: 0.011 s
% 2.92/2.00 % (18335)Instructions burned: 33 (million)
% 2.92/2.00 % (18335)------------------------------
% 2.92/2.00 % (18335)------------------------------
% 2.92/2.00 % (18337)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/453Mi)
% 5.68/2.01 % (18339)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/83Mi)
% 5.68/2.01 % (18340)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/11Mi)
% 5.68/2.01 % (18338)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/71Mi)
% 5.68/2.02 % (18340)Instruction limit reached!
% 5.68/2.02 % (18340)------------------------------
% 5.68/2.02 % (18340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.02 % (18340)Termination reason: Unknown
% 5.68/2.02 % (18340)Termination phase: shuffling
% 5.68/2.02
% 5.68/2.02 % (18340)Memory used [KB]: 1791
% 5.68/2.02 % (18340)Time elapsed: 0.005 s
% 5.68/2.02 % (18340)Instructions burned: 14 (million)
% 5.68/2.02 % (18340)------------------------------
% 5.68/2.02 % (18340)------------------------------
% 5.68/2.03 % (18336)Instruction limit reached!
% 5.68/2.03 % (18336)------------------------------
% 5.68/2.03 % (18336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.03 % (18336)Termination reason: Unknown
% 5.68/2.03 % (18336)Termination phase: Property scanning
% 5.68/2.03
% 5.68/2.03 % (18336)Memory used [KB]: 2814
% 5.68/2.03 % (18336)Time elapsed: 0.031 s
% 5.68/2.03 % (18336)Instructions burned: 96 (million)
% 5.68/2.03 % (18336)------------------------------
% 5.68/2.03 % (18336)------------------------------
% 5.68/2.03 % (18341)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/41Mi)
% 5.68/2.04 % (18342)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/6Mi)
% 5.68/2.04 % (18341)Instruction limit reached!
% 5.68/2.04 % (18341)------------------------------
% 5.68/2.04 % (18341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.04 % (18341)Termination reason: Unknown
% 5.68/2.04 % (18341)Termination phase: shuffling
% 5.68/2.04
% 5.68/2.04 % (18341)Memory used [KB]: 2302
% 5.68/2.04 % (18341)Time elapsed: 0.013 s
% 5.68/2.04 % (18341)Instructions burned: 43 (million)
% 5.68/2.04 % (18341)------------------------------
% 5.68/2.04 % (18341)------------------------------
% 5.68/2.04 % (18339)Instruction limit reached!
% 5.68/2.04 % (18339)------------------------------
% 5.68/2.04 % (18339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.04 % (18339)Termination reason: Unknown
% 5.68/2.04 % (18339)Termination phase: Saturation
% 5.68/2.04
% 5.68/2.04 % (18339)Memory used [KB]: 6908
% 5.68/2.04 % (18339)Time elapsed: 0.029 s
% 5.68/2.04 % (18342)Instruction limit reached!
% 5.68/2.04 % (18342)------------------------------
% 5.68/2.04 % (18342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.04 % (18339)Instructions burned: 84 (million)
% 5.68/2.04 % (18342)Termination reason: Unknown
% 5.68/2.04 % (18339)------------------------------
% 5.68/2.04 % (18339)------------------------------
% 5.68/2.04 % (18342)Termination phase: shuffling
% 5.68/2.04
% 5.68/2.04 % (18342)Memory used [KB]: 1663
% 5.68/2.04 % (18342)Time elapsed: 0.004 s
% 5.68/2.04 % (18342)Instructions burned: 6 (million)
% 5.68/2.04 % (18342)------------------------------
% 5.68/2.04 % (18342)------------------------------
% 5.68/2.05 % (18343)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/150Mi)
% 5.68/2.05 % (18345)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/109Mi)
% 5.68/2.05 % (18344)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/343Mi)
% 5.68/2.05 % (18338)Instruction limit reached!
% 5.68/2.05 % (18338)------------------------------
% 5.68/2.05 % (18338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.05 % (18338)Termination reason: Unknown
% 5.68/2.05 % (18338)Termination phase: Preprocessing 3
% 5.68/2.05
% 5.68/2.05 % (18338)Memory used [KB]: 2686
% 5.68/2.05 % (18338)Time elapsed: 0.042 s
% 5.68/2.05 % (18338)Instructions burned: 72 (million)
% 5.68/2.05 % (18338)------------------------------
% 5.68/2.05 % (18338)------------------------------
% 5.68/2.07 % (18346)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/253Mi)
% 5.68/2.08 % (18345)Instruction limit reached!
% 5.68/2.08 % (18345)------------------------------
% 5.68/2.08 % (18345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.08 % (18345)Termination reason: Unknown
% 5.68/2.08 % (18345)Termination phase: Function definition elimination
% 5.68/2.08
% 5.68/2.08 % (18345)Memory used [KB]: 2814
% 5.68/2.08 % (18345)Time elapsed: 0.032 s
% 5.68/2.08 % (18345)Instructions burned: 112 (million)
% 5.68/2.08 % (18345)------------------------------
% 5.68/2.08 % (18345)------------------------------
% 5.68/2.09 % (18343)Instruction limit reached!
% 5.68/2.09 % (18343)------------------------------
% 5.68/2.09 % (18343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.09 % (18343)Termination reason: Unknown
% 5.68/2.09 % (18343)Termination phase: Property scanning
% 5.68/2.09
% 5.68/2.09 % (18343)Memory used [KB]: 3198
% 5.68/2.09 % (18343)Time elapsed: 0.042 s
% 5.68/2.09 % (18343)Instructions burned: 150 (million)
% 5.68/2.09 % (18343)------------------------------
% 5.68/2.09 % (18343)------------------------------
% 5.68/2.09 % (18347)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/140Mi)
% 5.68/2.10 % (18348)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_18072 for (2995ds/614Mi)
% 5.68/2.10 % (18333)Instruction limit reached!
% 5.68/2.10 % (18333)------------------------------
% 5.68/2.10 % (18333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.10 % (18333)Termination reason: Unknown
% 5.68/2.10 % (18333)Termination phase: Saturation
% 5.68/2.10
% 5.68/2.10 % (18333)Memory used [KB]: 3965
% 5.68/2.10 % (18333)Time elapsed: 0.126 s
% 5.68/2.10 % (18333)Instructions burned: 434 (million)
% 5.68/2.10 % (18333)------------------------------
% 5.68/2.10 % (18333)------------------------------
% 5.68/2.11 % (18349)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_18072 for (2994ds/202Mi)
% 5.68/2.11 % (18347)First to succeed.
% 5.68/2.11 % (18346)Refutation not found, incomplete strategy
% 5.68/2.11 % (18346)------------------------------
% 5.68/2.11 % (18346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.11 % (18346)Termination reason: Refutation not found, incomplete strategy
% 5.68/2.11
% 5.68/2.11
% 5.68/2.11 % (18346)Memory used [KB]: 7164
% 5.68/2.11 % (18346)Time elapsed: 0.041 s
% 5.68/2.11 % (18346)Instructions burned: 88 (million)
% 5.68/2.11 % (18346)------------------------------
% 5.68/2.11 % (18346)------------------------------
% 6.21/2.11 % (18347)Refutation found. Thanks to Tanya!
% 6.21/2.11 % SZS status Theorem for DTF2THF_18072
% 6.21/2.11 % SZS output start Proof for DTF2THF_18072
% 6.21/2.11 thf(type_def_5, type, set_li185139947ession: $tType).
% 6.21/2.11 thf(type_def_6, type, secrecy_Expression: $tType).
% 6.21/2.11 thf(type_def_8, type, set_list_Secrecy_KS: $tType).
% 6.21/2.11 thf(type_def_9, type, secrecy_KS: $tType).
% 6.21/2.11 thf(type_def_10, type, set_li849033543y_Keys: $tType).
% 6.21/2.11 thf(type_def_11, type, secrecy_Keys: $tType).
% 6.21/2.11 thf(type_def_12, type, set_li2007071804ecrets: $tType).
% 6.21/2.11 thf(type_def_13, type, secrecy_Secrets: $tType).
% 6.21/2.11 thf(type_def_14, type, list_S529945141ession: $tType).
% 6.21/2.11 thf(type_def_15, type, set_Se1942955227ession: $tType).
% 6.21/2.11 thf(type_def_16, type, list_Secrecy_KS: $tType).
% 6.21/2.11 thf(type_def_17, type, set_Secrecy_KS: $tType).
% 6.21/2.11 thf(type_def_18, type, list_Secrecy_Keys: $tType).
% 6.21/2.11 thf(type_def_19, type, set_Secrecy_Keys: $tType).
% 6.21/2.11 thf(type_def_20, type, list_Secrecy_Secrets: $tType).
% 6.21/2.11 thf(type_def_21, type, set_Secrecy_Secrets: $tType).
% 6.21/2.11 thf(type_def_22, type, secrecy_specID: $tType).
% 6.21/2.11 thf(type_def_23, type, list_l425507653ession: $tType).
% 6.21/2.11 thf(type_def_24, type, list_list_Secrecy_KS: $tType).
% 6.21/2.11 thf(func_def_0, type, list_l425507653ession: $tType).
% 6.21/2.11 thf(func_def_1, type, set_li185139947ession: $tType).
% 6.21/2.11 thf(func_def_2, type, set_li2007071804ecrets: $tType).
% 6.21/2.11 thf(func_def_3, type, set_li849033543y_Keys: $tType).
% 6.21/2.11 thf(func_def_4, type, list_list_Secrecy_KS: $tType).
% 6.21/2.11 thf(func_def_5, type, set_list_Secrecy_KS: $tType).
% 6.21/2.11 thf(func_def_6, type, list_S529945141ession: $tType).
% 6.21/2.11 thf(func_def_7, type, set_Se1942955227ession: $tType).
% 6.21/2.11 thf(func_def_8, type, list_Secrecy_Secrets: $tType).
% 6.21/2.11 thf(func_def_9, type, set_Secrecy_Secrets: $tType).
% 6.21/2.11 thf(func_def_10, type, list_Secrecy_Keys: $tType).
% 6.21/2.11 thf(func_def_11, type, set_Secrecy_Keys: $tType).
% 6.21/2.11 thf(func_def_12, type, list_Secrecy_KS: $tType).
% 6.21/2.11 thf(func_def_13, type, set_Secrecy_KS: $tType).
% 6.21/2.11 thf(func_def_14, type, secrecy_Expression: $tType).
% 6.21/2.11 thf(func_def_15, type, secrecy_Secrets: $tType).
% 6.21/2.11 thf(func_def_16, type, secrecy_specID: $tType).
% 6.21/2.11 thf(func_def_17, type, secrecy_Keys: $tType).
% 6.21/2.11 thf(func_def_18, type, secrecy_KS: $tType).
% 6.21/2.11 thf(func_def_19, type, bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession).
% 6.21/2.11 thf(func_def_20, type, bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS).
% 6.21/2.11 thf(func_def_21, type, bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys).
% 6.21/2.11 thf(func_def_22, type, bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets).
% 6.21/2.11 thf(func_def_23, type, bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession).
% 6.21/2.11 thf(func_def_24, type, bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS).
% 6.21/2.11 thf(func_def_25, type, bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys).
% 6.21/2.11 thf(func_def_26, type, bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets).
% 6.21/2.11 thf(func_def_27, type, localSecrets: secrecy_specID > set_Secrecy_KS).
% 6.21/2.11 thf(func_def_28, type, knowle233900195orrect: secrecy_specID > secrecy_KS > $o).
% 6.21/2.11 thf(func_def_29, type, knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o).
% 6.21/2.11 thf(func_def_30, type, knowle945212990e_know: secrecy_specID > secrecy_KS > $o).
% 6.21/2.11 thf(func_def_31, type, knowle731562421_knows: secrecy_specID > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_32, type, mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_33, type, mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_34, type, append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession).
% 6.21/2.11 thf(func_def_35, type, append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS).
% 6.21/2.11 thf(func_def_36, type, append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_37, type, append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_38, type, append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys).
% 6.21/2.11 thf(func_def_39, type, append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets).
% 6.21/2.11 thf(func_def_40, type, bind_S815874003ession: list_S529945141ession > (secrecy_Expression > list_S529945141ession) > list_S529945141ession).
% 6.21/2.11 thf(func_def_41, type, bind_S1823644515ecy_KS: list_S529945141ession > (secrecy_Expression > list_Secrecy_KS) > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_42, type, bind_S711229283ession: list_Secrecy_KS > (secrecy_KS > list_S529945141ession) > list_S529945141ession).
% 6.21/2.11 thf(func_def_43, type, bind_S645462771ecy_KS: list_Secrecy_KS > (secrecy_KS > list_Secrecy_KS) > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_44, type, butlas171474643ession: list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_45, type, butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_46, type, concat388015140ession: list_l425507653ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_47, type, concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_48, type, distin1076152135ession: list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_49, type, distin1495927511ecy_KS: list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_50, type, foldr_1531709715ession: (list_S529945141ession > list_S529945141ession > list_S529945141ession) > list_l425507653ession > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_51, type, foldr_1711005747ecy_KS: (list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_52, type, insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_53, type, insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_54, type, last_S1532390982ession: list_S529945141ession > secrecy_Expression).
% 6.21/2.11 thf(func_def_55, type, last_Secrecy_KS: list_Secrecy_KS > secrecy_KS).
% 6.21/2.11 thf(func_def_56, type, cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession).
% 6.21/2.11 thf(func_def_57, type, cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS).
% 6.21/2.11 thf(func_def_58, type, cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_59, type, cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_60, type, cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys).
% 6.21/2.11 thf(func_def_61, type, cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets).
% 6.21/2.11 thf(func_def_62, type, nil_li311616943ession: list_l425507653ession).
% 6.21/2.11 thf(func_def_63, type, nil_list_Secrecy_KS: list_list_Secrecy_KS).
% 6.21/2.11 thf(func_def_64, type, nil_Se901661471ession: list_S529945141ession).
% 6.21/2.11 thf(func_def_65, type, nil_Secrecy_KS: list_Secrecy_KS).
% 6.21/2.11 thf(func_def_66, type, nil_Secrecy_Keys: list_Secrecy_Keys).
% 6.21/2.11 thf(func_def_67, type, nil_Secrecy_Secrets: list_Secrecy_Secrets).
% 6.21/2.11 thf(func_def_68, type, hd_lis1623417098ession: list_l425507653ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_69, type, hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_70, type, hd_Sec357328890ession: list_S529945141ession > secrecy_Expression).
% 6.21/2.11 thf(func_def_71, type, hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS).
% 6.21/2.11 thf(func_def_72, type, tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_73, type, tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_74, type, list_e1486860828ession: (secrecy_Expression > $o) > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_75, type, list_ex1_Secrecy_KS: (secrecy_KS > $o) > list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_76, type, listre84909707ession: (secrecy_Expression > secrecy_Expression > $o) > list_S529945141ession > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_77, type, listre565996059ecy_KS: (secrecy_Expression > secrecy_KS > $o) > list_S529945141ession > list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_78, type, listre1601064475ession: (secrecy_KS > secrecy_Expression > $o) > list_Secrecy_KS > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_79, type, listre788412843ecy_KS: (secrecy_KS > secrecy_KS > $o) > list_Secrecy_KS > list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_80, type, map_ta1624757057ession: (secrecy_Expression > secrecy_Expression) > list_S529945141ession > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_81, type, map_ta623472337ession: (secrecy_KS > secrecy_Expression) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_82, type, maps_S599402637ession: (secrecy_Expression > list_S529945141ession) > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_83, type, maps_S399472669ecy_KS: (secrecy_Expression > list_Secrecy_KS) > list_S529945141ession > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_84, type, maps_S1434541085ession: (secrecy_KS > list_S529945141ession) > list_Secrecy_KS > list_S529945141ession).
% 6.21/2.11 thf(func_def_85, type, maps_S377605037ecy_KS: (secrecy_KS > list_Secrecy_KS) > list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_86, type, member2020590922ession: list_S529945141ession > secrecy_Expression > $o).
% 6.21/2.11 thf(func_def_87, type, member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o).
% 6.21/2.11 thf(func_def_88, type, lexord1123423577ession: (secrecy_Expression > secrecy_Expression > $o) > list_S529945141ession > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_89, type, lexord948960489ecy_KS: (secrecy_KS > secrecy_KS > $o) > list_Secrecy_KS > list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_90, type, produc1450295286ession: list_l425507653ession > list_l425507653ession).
% 6.21/2.11 thf(func_def_91, type, produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS).
% 6.21/2.11 thf(func_def_92, type, remdup484344169ession: list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_93, type, remdup351570169ecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_94, type, rev_Se1073238207ession: list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_95, type, rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_96, type, rotate1237234450ession: list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_97, type, rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_98, type, shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession).
% 6.21/2.11 thf(func_def_99, type, shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS).
% 6.21/2.11 thf(func_def_100, type, splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_101, type, splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_102, type, subseq348280080ession: list_S529945141ession > list_l425507653ession).
% 6.21/2.11 thf(func_def_103, type, subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS).
% 6.21/2.11 thf(func_def_104, type, succes1388047762ession: (secrecy_Expression > secrecy_Expression > $o) > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_105, type, succes590251810ecy_KS: (secrecy_KS > secrecy_KS > $o) > list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_106, type, decr: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_107, type, enc: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_108, type, encrDecrKeys: secrecy_Keys > secrecy_Keys > $o).
% 6.21/2.11 thf(func_def_109, type, ext: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_110, type, sign: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.21/2.11 thf(func_def_111, type, eout: secrecy_specID > secrecy_Expression > $o).
% 6.21/2.11 thf(func_def_112, type, ine: secrecy_specID > secrecy_Expression > $o).
% 6.21/2.11 thf(func_def_113, type, notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o).
% 6.21/2.11 thf(func_def_114, type, specKeys: secrecy_specID > set_Secrecy_Keys).
% 6.21/2.11 thf(func_def_115, type, specKeysSecrets: secrecy_specID > set_Secrecy_KS).
% 6.21/2.11 thf(func_def_116, type, specSecrets: secrecy_specID > set_Secrecy_Secrets).
% 6.21/2.11 thf(func_def_117, type, secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS).
% 6.21/2.11 thf(func_def_118, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 6.21/2.11 thf(func_def_119, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 6.21/2.11 thf(func_def_120, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 6.21/2.11 thf(func_def_121, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 6.21/2.11 thf(func_def_122, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 6.21/2.11 thf(func_def_123, type, collect_Secrecy_KS: (secrecy_KS > $o) > set_Secrecy_KS).
% 6.21/2.11 thf(func_def_124, type, collect_Secrecy_Keys: (secrecy_Keys > $o) > set_Secrecy_Keys).
% 6.21/2.11 thf(func_def_125, type, collec836099393ecrets: (secrecy_Secrets > $o) > set_Secrecy_Secrets).
% 6.21/2.11 thf(func_def_126, type, member249235532ession: list_S529945141ession > set_li185139947ession > $o).
% 6.21/2.11 thf(func_def_127, type, member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_128, type, member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o).
% 6.21/2.11 thf(func_def_129, type, member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o).
% 6.21/2.11 thf(func_def_130, type, member279582780ession: secrecy_Expression > set_Se1942955227ession > $o).
% 6.21/2.11 thf(func_def_131, type, member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o).
% 6.21/2.11 thf(func_def_132, type, member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o).
% 6.21/2.11 thf(func_def_133, type, member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o).
% 6.21/2.11 thf(func_def_134, type, a: secrecy_specID).
% 6.21/2.11 thf(func_def_135, type, m: secrecy_Secrets).
% 6.21/2.11 thf(func_def_154, type, sK0: secrecy_KS > secrecy_Secrets).
% 6.21/2.11 thf(func_def_155, type, sK1: secrecy_KS > secrecy_Keys).
% 6.21/2.11 thf(func_def_156, type, sK2: (secrecy_KS > $o) > secrecy_Keys).
% 6.21/2.11 thf(func_def_157, type, sK3: (secrecy_KS > $o) > secrecy_Secrets).
% 6.21/2.11 thf(func_def_159, type, ph5: !>[X0: $tType]:(X0)).
% 6.21/2.11 thf(f1096,plain,(
% 6.21/2.11 $false),
% 6.21/2.11 inference(subsumption_resolution,[status(thm)],[f1094,f1061])).
% 6.21/2.11 thf(f1061,plain,(
% 6.21/2.11 ((knowle945212990e_know @ a @ (secrecy_sKS @ m)) != $true)),
% 6.21/2.11 inference(cnf_transformation,[status(thm)],[f1047])).
% 6.21/2.11 thf(f1047,plain,(
% 6.21/2.11 ((knowle945212990e_know @ a @ (secrecy_sKS @ m)) != $true)),
% 6.21/2.11 inference(flattening,[status(thm)],[f760])).
% 6.21/2.11 thf(f760,plain,(
% 6.21/2.11 ~((knowle945212990e_know @ a @ (secrecy_sKS @ m)) = $true)),
% 6.21/2.11 inference(fool_elimination,[status(thm)],[f759])).
% 6.21/2.11 thf(f759,plain,(
% 6.21/2.11 ~(knowle945212990e_know @ a @ (secrecy_sKS @ m))),
% 6.21/2.11 inference(rectify,[status(thm)],[f354])).
% 6.21/2.11 thf(f354,negated_conjecture,(
% 6.21/2.11 ~(knowle945212990e_know @ a @ (secrecy_sKS @ m))),
% 6.21/2.11 inference(negated_conjecture,[status(cth)],[f353])).
% 6.21/2.11 thf(f353,conjecture,(
% 6.21/2.11 (knowle945212990e_know @ a @ (secrecy_sKS @ m))),
% 6.21/2.11 file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',conj_0)).
% 6.21/2.11 thf(f1094,plain,(
% 6.21/2.11 ((knowle945212990e_know @ a @ (secrecy_sKS @ m)) = $true)),
% 6.21/2.11 inference(superposition,[status(thm)],[f1074,f1064])).
% 6.21/2.11 thf(f1064,plain,(
% 6.21/2.11 ((knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_sE @ m) @ nil_Se901661471ession)) = $true)),
% 6.21/2.11 inference(cnf_transformation,[status(thm)],[f559])).
% 6.21/2.11 thf(f559,plain,(
% 6.21/2.11 ((knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_sE @ m) @ nil_Se901661471ession)) = $true)),
% 6.21/2.11 inference(fool_elimination,[status(thm)],[f558])).
% 6.21/2.11 thf(f558,plain,(
% 6.21/2.11 (knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_sE @ m) @ nil_Se901661471ession))),
% 6.21/2.11 inference(rectify,[status(thm)],[f1])).
% 6.21/2.11 thf(f1,axiom,(
% 6.21/2.11 (knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_sE @ m) @ nil_Se901661471ession))),
% 6.21/2.11 file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',fact_0_assms)).
% 6.21/2.11 thf(f1074,plain,(
% 6.21/2.11 ( ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : (((knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)) = (knowle731562421_knows @ X1 @ (cons_S112077679ession @ (secrecy_sE @ X0) @ nil_Se901661471ession)))) )),
% 6.21/2.11 inference(forward_demodulation,[status(thm)],[f1063,f1071])).
% 6.21/2.11 thf(f1071,plain,(
% 6.21/2.11 ( ! [X0 : secrecy_Secrets] : (((secrecy_sE @ X0) = (secrec1016742679ession @ (secrecy_sKS @ X0)))) )),
% 6.21/2.11 inference(cnf_transformation,[status(thm)],[f1017])).
% 6.21/2.11 thf(f1017,plain,(
% 6.21/2.11 ! [X0 : secrecy_Secrets] : ((secrecy_sE @ X0) = (secrec1016742679ession @ (secrecy_sKS @ X0)))),
% 6.21/2.11 inference(fool_elimination,[status(thm)],[f1016])).
% 6.21/2.11 thf(f1016,plain,(
% 6.21/2.11 ! [X0 : secrecy_Secrets] : ((secrecy_sE @ X0) = (secrec1016742679ession @ (secrecy_sKS @ X0)))),
% 6.21/2.11 inference(rectify,[status(thm)],[f8])).
% 6.21/2.11 thf(f8,axiom,(
% 6.21/2.11 ! [X3 : secrecy_Secrets] : ((secrecy_sE @ X3) = (secrec1016742679ession @ (secrecy_sKS @ X3)))),
% 6.21/2.11 file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',fact_7_KS2Expression_Osimps_I2_J)).
% 6.21/2.11 thf(f1063,plain,(
% 6.21/2.11 ( ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : (((knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)) = (knowle731562421_knows @ X1 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_sKS @ X0)) @ nil_Se901661471ession)))) )),
% 6.21/2.11 inference(cnf_transformation,[status(thm)],[f1019])).
% 6.21/2.11 thf(f1019,plain,(
% 6.21/2.11 ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : ((knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)) = (knowle731562421_knows @ X1 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_sKS @ X0)) @ nil_Se901661471ession)))),
% 6.21/2.11 inference(fool_elimination,[status(thm)],[f1018])).
% 6.21/2.11 thf(f1018,plain,(
% 6.21/2.11 ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : ((knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)) = (knowle731562421_knows @ X1 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_sKS @ X0)) @ nil_Se901661471ession)))),
% 6.21/2.11 inference(rectify,[status(thm)],[f4])).
% 6.21/2.11 thf(f4,axiom,(
% 6.21/2.11 ! [X5 : secrecy_Secrets,X4 : secrecy_specID] : ((knowle731562421_knows @ X4 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_sKS @ X5)) @ nil_Se901661471ession)) = (knowle945212990e_know @ X4 @ (secrecy_sKS @ X5)))),
% 6.21/2.11 file('/export/starexec/sandbox2/tmp/tmp.SCvJyCGelC/DTF2THF_18072.p',fact_3_know1s)).
% 6.21/2.11 % SZS output end Proof for DTF2THF_18072
% 6.21/2.11 % (18347)------------------------------
% 6.21/2.11 % (18347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.21/2.11 % (18347)Termination reason: Refutation
% 6.21/2.11
% 6.21/2.11 % (18347)Memory used [KB]: 6908
% 6.21/2.11 % (18347)Time elapsed: 0.023 s
% 6.21/2.11 % (18347)Instructions burned: 72 (million)
% 6.21/2.11 % (18347)------------------------------
% 6.21/2.11 % (18347)------------------------------
% 6.21/2.11 % (18282)Success in time 0.515 s
%------------------------------------------------------------------------------