%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP084^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 6.06s 2.32s
% Output : Refutation 6.06s
% 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 : 127 ( 124 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,
monoid929671412ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_S529945141ession > $o ).
thf(func_def_29,type,
monoid1528146052ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > $o ).
thf(func_def_30,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(func_def_31,type,
knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_32,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(func_def_33,type,
knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_34,type,
disjoi1945222607ession: list_S529945141ession > list_S529945141ession > $o ).
thf(func_def_35,type,
memS_S2026082737ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_36,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_37,type,
mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).
thf(func_def_38,type,
append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession ).
thf(func_def_39,type,
append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_40,type,
append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_41,type,
append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_42,type,
append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
thf(func_def_43,type,
append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
thf(func_def_44,type,
bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).
thf(func_def_45,type,
bind_S1823644515ecy_KS: list_S529945141ession > ( secrecy_Expression > list_Secrecy_KS ) > list_Secrecy_KS ).
thf(func_def_46,type,
bind_S711229283ession: list_Secrecy_KS > ( secrecy_KS > list_S529945141ession ) > list_S529945141ession ).
thf(func_def_47,type,
bind_S645462771ecy_KS: list_Secrecy_KS > ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS ).
thf(func_def_48,type,
butlas171474643ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_49,type,
butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_50,type,
concat388015140ession: list_l425507653ession > list_S529945141ession ).
thf(func_def_51,type,
concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_52,type,
distin1076152135ession: list_S529945141ession > $o ).
thf(func_def_53,type,
distin1495927511ecy_KS: list_Secrecy_KS > $o ).
thf(func_def_54,type,
foldr_1531709715ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_l425507653ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_55,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_56,type,
insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
thf(func_def_57,type,
insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_58,type,
last_S1532390982ession: list_S529945141ession > secrecy_Expression ).
thf(func_def_59,type,
last_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
thf(func_def_60,type,
cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession ).
thf(func_def_61,type,
cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_62,type,
cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
thf(func_def_63,type,
cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_64,type,
cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
thf(func_def_65,type,
cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
thf(func_def_66,type,
nil_li311616943ession: list_l425507653ession ).
thf(func_def_67,type,
nil_list_Secrecy_KS: list_list_Secrecy_KS ).
thf(func_def_68,type,
nil_Se901661471ession: list_S529945141ession ).
thf(func_def_69,type,
nil_Secrecy_KS: list_Secrecy_KS ).
thf(func_def_70,type,
nil_Secrecy_Keys: list_Secrecy_Keys ).
thf(func_def_71,type,
nil_Secrecy_Secrets: list_Secrecy_Secrets ).
thf(func_def_72,type,
hd_lis1623417098ession: list_l425507653ession > list_S529945141ession ).
thf(func_def_73,type,
hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_74,type,
hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).
thf(func_def_75,type,
hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
thf(func_def_76,type,
tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_77,type,
tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_78,type,
list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).
thf(func_def_79,type,
list_ex1_Secrecy_KS: ( secrecy_KS > $o ) > list_Secrecy_KS > $o ).
thf(func_def_80,type,
listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
thf(func_def_81,type,
listre565996059ecy_KS: ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession > list_Secrecy_KS > $o ).
thf(func_def_82,type,
listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).
thf(func_def_83,type,
listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
thf(func_def_84,type,
map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_85,type,
map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).
thf(func_def_86,type,
maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
thf(func_def_87,type,
maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).
thf(func_def_88,type,
maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).
thf(func_def_89,type,
maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_90,type,
member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
thf(func_def_91,type,
member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).
thf(func_def_92,type,
lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
thf(func_def_93,type,
lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
thf(func_def_94,type,
produc1450295286ession: list_l425507653ession > list_l425507653ession ).
thf(func_def_95,type,
produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_96,type,
rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_97,type,
rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_98,type,
rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
thf(func_def_99,type,
rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_100,type,
shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).
thf(func_def_101,type,
shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).
thf(func_def_102,type,
splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(func_def_103,type,
splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
thf(func_def_104,type,
subseq348280080ession: list_S529945141ession > list_l425507653ession ).
thf(func_def_105,type,
subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).
thf(func_def_106,type,
succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
thf(func_def_107,type,
succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).
thf(func_def_108,type,
decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_109,type,
enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_110,type,
encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
thf(func_def_111,type,
ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_112,type,
sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_113,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_114,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_115,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_116,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_117,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_118,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_119,type,
secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).
thf(func_def_120,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_121,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_122,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_123,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_124,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_125,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_126,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_127,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_128,type,
member249235532ession: list_S529945141ession > set_li185139947ession > $o ).
thf(func_def_129,type,
member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).
thf(func_def_130,type,
member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).
thf(func_def_131,type,
member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).
thf(func_def_132,type,
member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).
thf(func_def_133,type,
member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
thf(func_def_134,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(func_def_135,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(func_def_136,type,
a: secrecy_specID ).
thf(func_def_137,type,
m: secrecy_Keys ).
thf(func_def_156,type,
sK0: secrecy_KS > secrecy_Secrets ).
thf(func_def_157,type,
sK1: secrecy_KS > secrecy_Keys ).
thf(func_def_158,type,
sK2: ( secrecy_KS > $o ) > secrecy_Secrets ).
thf(func_def_159,type,
sK3: ( secrecy_KS > $o ) > secrecy_Keys ).
thf(func_def_161,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f1114,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1112,f1072]) ).
thf(f1072,plain,
( ( knowle945212990e_know @ a @ ( secrecy_kKS @ m ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1043]) ).
thf(f1043,plain,
( ( knowle945212990e_know @ a @ ( secrecy_kKS @ m ) )
!= $true ),
inference(flattening,[status(thm)],[f770]) ).
thf(f770,plain,
( ( knowle945212990e_know @ a @ ( secrecy_kKS @ m ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f769]) ).
thf(f769,plain,
~ ( knowle945212990e_know @ a @ ( secrecy_kKS @ m ) ),
inference(rectify,[status(thm)],[f353]) ).
thf(f353,negated_conjecture,
~ ( knowle945212990e_know @ a @ ( secrecy_kKS @ m ) ),
inference(negated_conjecture,[status(cth)],[f352]) ).
thf(f352,conjecture,
knowle945212990e_know @ a @ ( secrecy_kKS @ m ),
file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',conj_0) ).
thf(f1112,plain,
( ( knowle945212990e_know @ a @ ( secrecy_kKS @ m ) )
= $true ),
inference(superposition,[status(thm)],[f1089,f1070]) ).
thf(f1070,plain,
( ( knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_kE @ m ) @ nil_Se901661471ession ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f993]) ).
thf(f993,plain,
( ( knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_kE @ m ) @ nil_Se901661471ession ) )
= $true ),
inference(fool_elimination,[status(thm)],[f992]) ).
thf(f992,plain,
knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_kE @ m ) @ nil_Se901661471ession ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_kE @ m ) @ nil_Se901661471ession ),
file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',fact_0_assms) ).
thf(f1089,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( knowle731562421_knows @ X0 @ ( cons_S112077679ession @ ( secrecy_kE @ X1 ) @ nil_Se901661471ession ) )
= ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f1077,f1071]) ).
thf(f1071,plain,
! [X0: secrecy_Keys] :
( ( secrecy_kE @ X0 )
= ( secrec1016742679ession @ ( secrecy_kKS @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f665]) ).
thf(f665,plain,
! [X0: secrecy_Keys] :
( ( secrecy_kE @ X0 )
= ( secrec1016742679ession @ ( secrecy_kKS @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f664]) ).
thf(f664,plain,
! [X0: secrecy_Keys] :
( ( secrecy_kE @ X0 )
= ( secrec1016742679ession @ ( secrecy_kKS @ X0 ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X9: secrecy_Keys] :
( ( secrecy_kE @ X9 )
= ( secrec1016742679ession @ ( secrecy_kKS @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',fact_13_KS2Expression_Osimps_I1_J) ).
thf(f1077,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) )
= ( knowle731562421_knows @ X0 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ X1 ) ) @ nil_Se901661471ession ) ) ),
inference(cnf_transformation,[status(thm)],[f399]) ).
thf(f399,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) )
= ( knowle731562421_knows @ X0 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ X1 ) ) @ nil_Se901661471ession ) ) ),
inference(fool_elimination,[status(thm)],[f398]) ).
thf(f398,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) )
= ( knowle731562421_knows @ X0 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ X1 ) ) @ nil_Se901661471ession ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X10: secrecy_specID,X11: secrecy_Keys] :
( ( knowle731562421_knows @ X10 @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ X11 ) ) @ nil_Se901661471ession ) )
= ( knowle945212990e_know @ X10 @ ( secrecy_kKS @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',fact_7_know1k) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP084^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:25:40 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : ITP084^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.45 % Domain : Interactive Theorem Proving
% 0.18/0.45 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_119__3292052_1
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Des21]
% 0.18/0.45 % Names : KnowledgeKeysSecrets/prob_119__3292052_1 [Des21]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % 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
% 0.18/0.45 % Syntax : Number of formulae : 490 ( 194 unt; 138 typ; 0 def)
% 0.18/0.45 % Number of atoms : 899 ( 677 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 13 ( 2 avg)
% 0.18/0.45 % Number of connectives : 3113 ( 202 ~; 52 |; 122 &;2319 @)
% 0.18/0.45 % ( 0 <=>; 418 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 21 ( 6 avg)
% 0.18/0.45 % Number of types : 20 ( 19 usr)
% 0.18/0.45 % Number of type conns : 445 ( 445 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 120 ( 119 usr; 8 con; 0-3 aty)
% 0.18/0.45 % Number of variables : 1113 ( 27 ^; 999 !; 87 ?;1113 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:46.381
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % Could-be-implicit typings (19)
% 0.18/0.45 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 0.18/0.45 list_l425507653ession: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 0.18/0.45 set_li185139947ession: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OSecrets_J_J,type,
% 0.18/0.45 set_li2007071804ecrets: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKeys_J_J,type,
% 0.18/0.45 set_li849033543y_Keys: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 0.18/0.45 list_list_Secrecy_KS: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 0.18/0.45 set_list_Secrecy_KS: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 list_S529945141ession: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 set_Se1942955227ession: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 0.18/0.45 list_Secrecy_Secrets: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.18/0.45 set_Secrecy_Secrets: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 0.18/0.45 list_Secrecy_Keys: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.18/0.45 set_Secrecy_Keys: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 list_Secrecy_KS: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 set_Secrecy_KS: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.18/0.45 secrecy_Expression: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.18/0.45 secrecy_Secrets: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.18/0.45 secrecy_specID: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.18/0.45 secrecy_Keys: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.18/0.45 secrecy_KS: $tType ).
% 0.18/0.45
% 0.18/0.45 % Explicit typings (119)
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKS,type,
% 0.18/0.45 bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKeys,type,
% 0.18/0.45 bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OSecrets,type,
% 0.18/0.45 bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKS,type,
% 0.18/0.45 bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKeys,type,
% 0.18/0.45 bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OSecrets,type,
% 0.18/0.45 bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.18/0.45 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Omonoid_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 monoid929671412ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Omonoid_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 monoid1528146052ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.18/0.45 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowsECorrect,type,
% 0.18/0.45 knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.18/0.45 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknows,type,
% 0.18/0.45 knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_ListExtras_Odisjoint_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 disjoi1945222607ession: list_S529945141ession > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_ListExtras_OmemS_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 memS_S2026082737ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OKS,type,
% 0.18/0.45 mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__Secrecy____types__OKS,type,
% 0.18/0.45 append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__Secrecy____types__OKeys,type,
% 0.18/0.45 append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__Secrecy____types__OSecrets,type,
% 0.18/0.45 append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 0.18/0.45 bind_S1823644515ecy_KS: list_S529945141ession > ( secrecy_Expression > list_Secrecy_KS ) > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 bind_S711229283ession: list_Secrecy_KS > ( secrecy_KS > list_S529945141ession ) > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.18/0.45 bind_S645462771ecy_KS: list_Secrecy_KS > ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Obutlast_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 butlas171474643ession: list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Obutlast_001t__Secrecy____types__OKS,type,
% 0.18/0.45 butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oconcat_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 concat388015140ession: list_l425507653ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oconcat_001t__Secrecy____types__OKS,type,
% 0.18/0.45 concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 distin1076152135ession: list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OKS,type,
% 0.18/0.45 distin1495927511ecy_KS: list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OExpression_J_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 foldr_1531709715ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_l425507653ession > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OKS_J_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 foldr_1711005747ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oinsert_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oinsert_001t__Secrecy____types__OKS,type,
% 0.18/0.45 insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olast_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 last_S1532390982ession: list_S529945141ession > secrecy_Expression ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olast_001t__Secrecy____types__OKS,type,
% 0.18/0.45 last_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKS,type,
% 0.18/0.45 cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKeys,type,
% 0.18/0.45 cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OSecrets,type,
% 0.18/0.45 cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 nil_li311616943ession: list_l425507653ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 nil_list_Secrecy_KS: list_list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 nil_Se901661471ession: list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKS,type,
% 0.18/0.45 nil_Secrecy_KS: list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKeys,type,
% 0.18/0.45 nil_Secrecy_Keys: list_Secrecy_Keys ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OSecrets,type,
% 0.18/0.45 nil_Secrecy_Secrets: list_Secrecy_Secrets ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 hd_lis1623417098ession: list_l425507653ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OKS,type,
% 0.18/0.45 hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OKS,type,
% 0.18/0.45 tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OKS,type,
% 0.18/0.45 list_ex1_Secrecy_KS: ( secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 0.18/0.45 listre565996059ecy_KS: ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession > list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.18/0.45 listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 0.18/0.45 maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.18/0.45 maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omember_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Omember_001t__Secrecy____types__OKS,type,
% 0.18/0.45 member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OKS,type,
% 0.18/0.45 lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 produc1450295286ession: list_l425507653ession > list_l425507653ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OKS,type,
% 0.18/0.45 produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Orev_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Orev_001t__Secrecy____types__OKS,type,
% 0.18/0.45 rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Orotate1_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Orotate1_001t__Secrecy____types__OKS,type,
% 0.18/0.45 rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OKS,type,
% 0.18/0.45 shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Osplice_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Osplice_001t__Secrecy____types__OKS,type,
% 0.18/0.45 splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 subseq348280080ession: list_S529945141ession > list_l425507653ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OKS,type,
% 0.18/0.45 subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OKS,type,
% 0.18/0.45 succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_ODecr,type,
% 0.18/0.45 decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OEnc,type,
% 0.18/0.45 enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 0.18/0.45 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OExt,type,
% 0.18/0.45 ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OSign,type,
% 0.18/0.45 sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_Oeout,type,
% 0.18/0.45 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_Oine,type,
% 0.18/0.45 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.18/0.45 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OspecKeys,type,
% 0.18/0.45 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.18/0.45 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.18/0.45 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 0.18/0.45 secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.18/0.45 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.18/0.45 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.18/0.45 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.18/0.45 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.18/0.45 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.18/0.45 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.18/0.45 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.18/0.45 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.18/0.45 member249235532ession: list_S529945141ession > set_li185139947ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.18/0.45 member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 0.18/0.45 member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 0.18/0.45 member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__Secrecy____types__OExpression,type,
% 0.18/0.45 member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.18/0.45 member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.18/0.45 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.18/0.45 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_A,type,
% 0.18/0.45 a: secrecy_specID ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_m,type,
% 0.18/0.45 m: secrecy_Keys ).
% 0.18/0.45
% 0.18/0.45 % Relevant facts (351)
% 0.18/0.45 thf(fact_0_assms,axiom,
% 0.18/0.45 knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_kE @ m ) @ nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % assms
% 0.18/0.45 thf(fact_1_KS_Oinject_I1_J,axiom,
% 0.18/0.45 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.18/0.45 ( ( ( secrecy_kKS @ X1 )
% 0.18/0.45 = ( secrecy_kKS @ Y1 ) )
% 0.18/0.45 = ( X1 = Y1 ) ) ).
% 0.18/0.45
% 0.18/0.45 % KS.inject(1)
% 0.18/0.45 thf(fact_2_knows4,axiom,
% 0.18/0.45 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.18/0.45 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.18/0.45 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K2 ) )
% 0.18/0.45 & ( knowle731562421_knows @ A @ ( enc @ K1 @ E ) ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.18/0.45
% 0.18/0.45 % knows4
% 0.18/0.45 thf(fact_3_knows5,axiom,
% 0.18/0.45 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.18/0.45 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.18/0.45 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K1 ) )
% 0.18/0.45 & ( knowle731562421_knows @ A @ ( sign @ K2 @ E ) ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.18/0.45
% 0.18/0.45 % knows5
% 0.18/0.45 thf(fact_4_knows6,axiom,
% 0.18/0.45 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.18/0.45 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.18/0.45 & ( knowle731562421_knows @ A @ E1 ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ ( enc @ K @ E1 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % knows6
% 0.18/0.45 thf(fact_5_knows7,axiom,
% 0.18/0.45 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.18/0.45 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.18/0.45 & ( knowle731562421_knows @ A @ E1 ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ ( sign @ K @ E1 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % knows7
% 0.18/0.45 thf(fact_6_know2knows__k,axiom,
% 0.18/0.45 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.18/0.45 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % know2knows_k
% 0.18/0.45 thf(fact_7_know1k,axiom,
% 0.18/0.45 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 0.18/0.45 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ nil_Se901661471ession ) )
% 0.18/0.45 = ( knowle945212990e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % know1k
% 0.18/0.45 thf(fact_8_eoutKnowCorrect__L1k,axiom,
% 0.18/0.45 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.18/0.45 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 0.18/0.45 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.18/0.45 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.18/0.45 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eoutKnowCorrect_L1k
% 0.18/0.45 thf(fact_9_eout__know__k,axiom,
% 0.18/0.45 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.18/0.45 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 0.18/0.45 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.18/0.45 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.18/0.45 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eout_know_k
% 0.18/0.45 thf(fact_10_know_Osimps_I1_J,axiom,
% 0.18/0.45 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.18/0.45 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.18/0.45 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.18/0.45 | ( member_Secrecy_KS2 @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % know.simps(1)
% 0.18/0.45 thf(fact_11_Expression_Oinject_I1_J,axiom,
% 0.18/0.45 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.18/0.45 ( ( ( secrecy_kE @ X1 )
% 0.18/0.45 = ( secrecy_kE @ Y1 ) )
% 0.18/0.45 = ( X1 = Y1 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Expression.inject(1)
% 0.18/0.45 thf(fact_12_knows__emptyexpression,axiom,
% 0.18/0.45 ! [C: secrecy_specID] : ( knowle731562421_knows @ C @ nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % knows_emptyexpression
% 0.18/0.45 thf(fact_13_KS2Expression_Osimps_I1_J,axiom,
% 0.18/0.45 ! [M: secrecy_Keys] :
% 0.18/0.45 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.18/0.45 = ( secrecy_kE @ M ) ) ).
% 0.18/0.45
% 0.18/0.45 % KS2Expression.simps(1)
% 0.18/0.45 thf(fact_14_list_Oinject,axiom,
% 0.18/0.45 ! [X21: secrecy_KS,X22: list_Secrecy_KS,Y21: secrecy_KS,Y22: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( cons_Secrecy_KS @ X21 @ X22 )
% 0.18/0.45 = ( cons_Secrecy_KS @ Y21 @ Y22 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inject
% 0.18/0.45 thf(fact_15_list_Oinject,axiom,
% 0.18/0.45 ! [X21: list_S529945141ession,X22: list_l425507653ession,Y21: list_S529945141ession,Y22: list_l425507653ession] :
% 0.18/0.45 ( ( ( cons_l533358079ession @ X21 @ X22 )
% 0.18/0.45 = ( cons_l533358079ession @ Y21 @ Y22 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inject
% 0.18/0.45 thf(fact_16_list_Oinject,axiom,
% 0.18/0.45 ! [X21: list_Secrecy_KS,X22: list_list_Secrecy_KS,Y21: list_Secrecy_KS,Y22: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( ( cons_list_Secrecy_KS @ X21 @ X22 )
% 0.18/0.45 = ( cons_list_Secrecy_KS @ Y21 @ Y22 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inject
% 0.18/0.45 thf(fact_17_list_Oinject,axiom,
% 0.18/0.45 ! [X21: secrecy_Secrets,X22: list_Secrecy_Secrets,Y21: secrecy_Secrets,Y22: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( ( cons_Secrecy_Secrets @ X21 @ X22 )
% 0.18/0.45 = ( cons_Secrecy_Secrets @ Y21 @ Y22 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inject
% 0.18/0.45 thf(fact_18_list_Oinject,axiom,
% 0.18/0.45 ! [X21: secrecy_Keys,X22: list_Secrecy_Keys,Y21: secrecy_Keys,Y22: list_Secrecy_Keys] :
% 0.18/0.45 ( ( ( cons_Secrecy_Keys @ X21 @ X22 )
% 0.18/0.45 = ( cons_Secrecy_Keys @ Y21 @ Y22 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inject
% 0.18/0.45 thf(fact_19_list_Oinject,axiom,
% 0.18/0.45 ! [X21: secrecy_Expression,X22: list_S529945141ession,Y21: secrecy_Expression,Y22: list_S529945141ession] :
% 0.18/0.45 ( ( ( cons_S112077679ession @ X21 @ X22 )
% 0.18/0.45 = ( cons_S112077679ession @ Y21 @ Y22 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inject
% 0.18/0.45 thf(fact_20_know1s,axiom,
% 0.18/0.45 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 0.18/0.45 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ nil_Se901661471ession ) )
% 0.18/0.45 = ( knowle945212990e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % know1s
% 0.18/0.45 thf(fact_21_list_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X21: list_S529945141ession,X22: list_l425507653ession] :
% 0.18/0.45 ( nil_li311616943ession
% 0.18/0.45 != ( cons_l533358079ession @ X21 @ X22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.distinct(1)
% 0.18/0.45 thf(fact_22_list_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X21: list_Secrecy_KS,X22: list_list_Secrecy_KS] :
% 0.18/0.45 ( nil_list_Secrecy_KS
% 0.18/0.45 != ( cons_list_Secrecy_KS @ X21 @ X22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.distinct(1)
% 0.18/0.45 thf(fact_23_list_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X21: secrecy_Secrets,X22: list_Secrecy_Secrets] :
% 0.18/0.45 ( nil_Secrecy_Secrets
% 0.18/0.45 != ( cons_Secrecy_Secrets @ X21 @ X22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.distinct(1)
% 0.18/0.45 thf(fact_24_list_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X21: secrecy_Keys,X22: list_Secrecy_Keys] :
% 0.18/0.45 ( nil_Secrecy_Keys
% 0.18/0.45 != ( cons_Secrecy_Keys @ X21 @ X22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.distinct(1)
% 0.18/0.45 thf(fact_25_list_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X21: secrecy_KS,X22: list_Secrecy_KS] :
% 0.18/0.45 ( nil_Secrecy_KS
% 0.18/0.45 != ( cons_Secrecy_KS @ X21 @ X22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.distinct(1)
% 0.18/0.45 thf(fact_26_list_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X21: secrecy_Expression,X22: list_S529945141ession] :
% 0.18/0.45 ( nil_Se901661471ession
% 0.18/0.45 != ( cons_S112077679ession @ X21 @ X22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.distinct(1)
% 0.18/0.45 thf(fact_27_list_OdiscI,axiom,
% 0.18/0.45 ! [List: list_l425507653ession,X21: list_S529945141ession,X22: list_l425507653ession] :
% 0.18/0.45 ( ( List
% 0.18/0.45 = ( cons_l533358079ession @ X21 @ X22 ) )
% 0.18/0.45 => ( List != nil_li311616943ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.discI
% 0.18/0.45 thf(fact_28_list_OdiscI,axiom,
% 0.18/0.45 ! [List: list_list_Secrecy_KS,X21: list_Secrecy_KS,X22: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( List
% 0.18/0.45 = ( cons_list_Secrecy_KS @ X21 @ X22 ) )
% 0.18/0.45 => ( List != nil_list_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.discI
% 0.18/0.45 thf(fact_29_list_OdiscI,axiom,
% 0.18/0.45 ! [List: list_Secrecy_Secrets,X21: secrecy_Secrets,X22: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( List
% 0.18/0.45 = ( cons_Secrecy_Secrets @ X21 @ X22 ) )
% 0.18/0.45 => ( List != nil_Secrecy_Secrets ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.discI
% 0.18/0.45 thf(fact_30_list_OdiscI,axiom,
% 0.18/0.45 ! [List: list_Secrecy_Keys,X21: secrecy_Keys,X22: list_Secrecy_Keys] :
% 0.18/0.45 ( ( List
% 0.18/0.45 = ( cons_Secrecy_Keys @ X21 @ X22 ) )
% 0.18/0.45 => ( List != nil_Secrecy_Keys ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.discI
% 0.18/0.45 thf(fact_31_list_OdiscI,axiom,
% 0.18/0.45 ! [List: list_Secrecy_KS,X21: secrecy_KS,X22: list_Secrecy_KS] :
% 0.18/0.45 ( ( List
% 0.18/0.45 = ( cons_Secrecy_KS @ X21 @ X22 ) )
% 0.18/0.45 => ( List != nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.discI
% 0.18/0.45 thf(fact_32_list_OdiscI,axiom,
% 0.18/0.45 ! [List: list_S529945141ession,X21: secrecy_Expression,X22: list_S529945141ession] :
% 0.18/0.45 ( ( List
% 0.18/0.45 = ( cons_S112077679ession @ X21 @ X22 ) )
% 0.18/0.45 => ( List != nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.discI
% 0.18/0.45 thf(fact_33_list_Oexhaust,axiom,
% 0.18/0.45 ! [Y: list_l425507653ession] :
% 0.18/0.45 ( ( Y != nil_li311616943ession )
% 0.18/0.45 => ~ ! [X212: list_S529945141ession,X222: list_l425507653ession] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( cons_l533358079ession @ X212 @ X222 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.exhaust
% 0.18/0.45 thf(fact_34_list_Oexhaust,axiom,
% 0.18/0.45 ! [Y: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( Y != nil_list_Secrecy_KS )
% 0.18/0.45 => ~ ! [X212: list_Secrecy_KS,X222: list_list_Secrecy_KS] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( cons_list_Secrecy_KS @ X212 @ X222 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.exhaust
% 0.18/0.45 thf(fact_35_list_Oexhaust,axiom,
% 0.18/0.45 ! [Y: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( Y != nil_Secrecy_Secrets )
% 0.18/0.45 => ~ ! [X212: secrecy_Secrets,X222: list_Secrecy_Secrets] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( cons_Secrecy_Secrets @ X212 @ X222 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.exhaust
% 0.18/0.45 thf(fact_36_list_Oexhaust,axiom,
% 0.18/0.45 ! [Y: list_Secrecy_Keys] :
% 0.18/0.45 ( ( Y != nil_Secrecy_Keys )
% 0.18/0.45 => ~ ! [X212: secrecy_Keys,X222: list_Secrecy_Keys] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( cons_Secrecy_Keys @ X212 @ X222 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.exhaust
% 0.18/0.45 thf(fact_37_list_Oexhaust,axiom,
% 0.18/0.45 ! [Y: list_Secrecy_KS] :
% 0.18/0.45 ( ( Y != nil_Secrecy_KS )
% 0.18/0.45 => ~ ! [X212: secrecy_KS,X222: list_Secrecy_KS] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( cons_Secrecy_KS @ X212 @ X222 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.exhaust
% 0.18/0.45 thf(fact_38_list_Oexhaust,axiom,
% 0.18/0.45 ! [Y: list_S529945141ession] :
% 0.18/0.45 ( ( Y != nil_Se901661471ession )
% 0.18/0.45 => ~ ! [X212: secrecy_Expression,X222: list_S529945141ession] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( cons_S112077679ession @ X212 @ X222 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.exhaust
% 0.18/0.45 thf(fact_39_list_Oinducts,axiom,
% 0.18/0.45 ! [P: list_l425507653ession > $o,List: list_l425507653ession] :
% 0.18/0.45 ( ( P @ nil_li311616943ession )
% 0.18/0.45 => ( ! [X12: list_S529945141ession,X2: list_l425507653ession] :
% 0.18/0.45 ( ( P @ X2 )
% 0.18/0.45 => ( P @ ( cons_l533358079ession @ X12 @ X2 ) ) )
% 0.18/0.45 => ( P @ List ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inducts
% 0.18/0.45 thf(fact_40_list_Oinducts,axiom,
% 0.18/0.45 ! [P: list_list_Secrecy_KS > $o,List: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_list_Secrecy_KS )
% 0.18/0.45 => ( ! [X12: list_Secrecy_KS,X2: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ X2 )
% 0.18/0.45 => ( P @ ( cons_list_Secrecy_KS @ X12 @ X2 ) ) )
% 0.18/0.45 => ( P @ List ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inducts
% 0.18/0.45 thf(fact_41_list_Oinducts,axiom,
% 0.18/0.45 ! [P: list_Secrecy_Secrets > $o,List: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( P @ nil_Secrecy_Secrets )
% 0.18/0.45 => ( ! [X12: secrecy_Secrets,X2: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( P @ X2 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_Secrets @ X12 @ X2 ) ) )
% 0.18/0.45 => ( P @ List ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inducts
% 0.18/0.45 thf(fact_42_list_Oinducts,axiom,
% 0.18/0.45 ! [P: list_Secrecy_Keys > $o,List: list_Secrecy_Keys] :
% 0.18/0.45 ( ( P @ nil_Secrecy_Keys )
% 0.18/0.45 => ( ! [X12: secrecy_Keys,X2: list_Secrecy_Keys] :
% 0.18/0.45 ( ( P @ X2 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_Keys @ X12 @ X2 ) ) )
% 0.18/0.45 => ( P @ List ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inducts
% 0.18/0.45 thf(fact_43_list_Oinducts,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > $o,List: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X12: secrecy_KS,X2: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ X2 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X12 @ X2 ) ) )
% 0.18/0.45 => ( P @ List ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inducts
% 0.18/0.45 thf(fact_44_list_Oinducts,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > $o,List: list_S529945141ession] :
% 0.18/0.45 ( ( P @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X12: secrecy_Expression,X2: list_S529945141ession] :
% 0.18/0.45 ( ( P @ X2 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X12 @ X2 ) ) )
% 0.18/0.45 => ( P @ List ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inducts
% 0.18/0.45 thf(fact_45_neq__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_l425507653ession] :
% 0.18/0.45 ( ( Xs != nil_li311616943ession )
% 0.18/0.45 = ( ? [Y2: list_S529945141ession,Ys: list_l425507653ession] :
% 0.18/0.45 ( Xs
% 0.18/0.45 = ( cons_l533358079ession @ Y2 @ Ys ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_Nil_conv
% 0.18/0.45 thf(fact_46_neq__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs != nil_list_Secrecy_KS )
% 0.18/0.45 = ( ? [Y2: list_Secrecy_KS,Ys: list_list_Secrecy_KS] :
% 0.18/0.45 ( Xs
% 0.18/0.45 = ( cons_list_Secrecy_KS @ Y2 @ Ys ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_Nil_conv
% 0.18/0.45 thf(fact_47_neq__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_Secrets )
% 0.18/0.45 = ( ? [Y2: secrecy_Secrets,Ys: list_Secrecy_Secrets] :
% 0.18/0.45 ( Xs
% 0.18/0.45 = ( cons_Secrecy_Secrets @ Y2 @ Ys ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_Nil_conv
% 0.18/0.45 thf(fact_48_neq__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_Keys] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_Keys )
% 0.18/0.45 = ( ? [Y2: secrecy_Keys,Ys: list_Secrecy_Keys] :
% 0.18/0.45 ( Xs
% 0.18/0.45 = ( cons_Secrecy_Keys @ Y2 @ Ys ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_Nil_conv
% 0.18/0.45 thf(fact_49_neq__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 = ( ? [Y2: secrecy_KS,Ys: list_Secrecy_KS] :
% 0.18/0.45 ( Xs
% 0.18/0.45 = ( cons_Secrecy_KS @ Y2 @ Ys ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_Nil_conv
% 0.18/0.45 thf(fact_50_neq__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession] :
% 0.18/0.45 ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 = ( ? [Y2: secrecy_Expression,Ys: list_S529945141ession] :
% 0.18/0.45 ( Xs
% 0.18/0.45 = ( cons_S112077679ession @ Y2 @ Ys ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_Nil_conv
% 0.18/0.45 thf(fact_51_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_Secrecy_Keys > list_Secrecy_KS > $o,Xs: list_Secrecy_Keys,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Secrecy_Keys @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [Y3: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Secrecy_Keys @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_52_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_Secrecy_Keys > list_l425507653ession > $o,Xs: list_Secrecy_Keys,Ys2: list_l425507653ession] :
% 0.18/0.45 ( ( P @ nil_Secrecy_Keys @ nil_li311616943ession )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_li311616943ession )
% 0.18/0.45 => ( ! [Y3: list_S529945141ession,Ys3: list_l425507653ession] : ( P @ nil_Secrecy_Keys @ ( cons_l533358079ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: list_S529945141ession,Ys3: list_l425507653ession] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_l533358079ession @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_53_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_Secrecy_Keys > list_list_Secrecy_KS > $o,Xs: list_Secrecy_Keys,Ys2: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Secrecy_Keys @ nil_list_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_list_Secrecy_KS )
% 0.18/0.45 => ( ! [Y3: list_Secrecy_KS,Ys3: list_list_Secrecy_KS] : ( P @ nil_Secrecy_Keys @ ( cons_list_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: list_Secrecy_KS,Ys3: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_list_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_54_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_Secrecy_Keys > list_Secrecy_Secrets > $o,Xs: list_Secrecy_Keys,Ys2: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( P @ nil_Secrecy_Keys @ nil_Secrecy_Secrets )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_Secrecy_Secrets )
% 0.18/0.45 => ( ! [Y3: secrecy_Secrets,Ys3: list_Secrecy_Secrets] : ( P @ nil_Secrecy_Keys @ ( cons_Secrecy_Secrets @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: secrecy_Secrets,Ys3: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_Secrecy_Secrets @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_55_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_Secrecy_Keys > list_Secrecy_Keys > $o,Xs: list_Secrecy_Keys,Ys2: list_Secrecy_Keys] :
% 0.18/0.45 ( ( P @ nil_Secrecy_Keys @ nil_Secrecy_Keys )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_Secrecy_Keys )
% 0.18/0.45 => ( ! [Y3: secrecy_Keys,Ys3: list_Secrecy_Keys] : ( P @ nil_Secrecy_Keys @ ( cons_Secrecy_Keys @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: secrecy_Keys,Ys3: list_Secrecy_Keys] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_Secrecy_Keys @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_56_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [Y3: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_57_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > list_S529945141ession > $o,Xs: list_Secrecy_KS,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [Y3: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Secrecy_KS @ ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y3: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_58_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > list_Secrecy_KS > $o,Xs: list_S529945141ession,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [Y3: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Se901661471ession @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_59_list__induct2_H,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > list_S529945141ession > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [Y3: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Se901661471ession @ ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y3: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_induct2'
% 0.18/0.45 thf(fact_60_splice_Oinduct,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 0.18/0.45 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Ys3 @ Xs2 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % splice.induct
% 0.18/0.45 thf(fact_61_splice_Oinduct,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 0.18/0.45 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( P @ Ys3 @ Xs2 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % splice.induct
% 0.18/0.45 thf(fact_62_induct__list012,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.18/0.45 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Zs: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Zs )
% 0.18/0.45 => ( ( P @ ( cons_Secrecy_KS @ Y3 @ Zs ) )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Zs ) ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % induct_list012
% 0.18/0.45 thf(fact_63_induct__list012,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( P @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Zs: list_S529945141ession] :
% 0.18/0.45 ( ( P @ Zs )
% 0.18/0.45 => ( ( P @ ( cons_S112077679ession @ Y3 @ Zs ) )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Zs ) ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % induct_list012
% 0.18/0.45 thf(fact_64_KS_Oinject_I2_J,axiom,
% 0.18/0.45 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 0.18/0.45 ( ( ( secrecy_sKS @ X23 )
% 0.18/0.45 = ( secrecy_sKS @ Y23 ) )
% 0.18/0.45 = ( X23 = Y23 ) ) ).
% 0.18/0.45
% 0.18/0.45 % KS.inject(2)
% 0.18/0.45 thf(fact_65_KS_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 0.18/0.45 ( ( secrecy_kKS @ X1 )
% 0.18/0.45 != ( secrecy_sKS @ X23 ) ) ).
% 0.18/0.45
% 0.18/0.45 % KS.distinct(1)
% 0.18/0.45 thf(fact_66_KS_Oinduct,axiom,
% 0.18/0.45 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.18/0.45 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 0.18/0.45 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 0.18/0.45 => ( P @ KS ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % KS.induct
% 0.18/0.45 thf(fact_67_KS_Oexhaust,axiom,
% 0.18/0.45 ! [Y: secrecy_KS] :
% 0.18/0.45 ( ! [X12: secrecy_Keys] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( secrecy_kKS @ X12 ) )
% 0.18/0.45 => ~ ! [X2: secrecy_Secrets] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( secrecy_sKS @ X2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % KS.exhaust
% 0.18/0.45 thf(fact_68_not__Cons__self2,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( cons_S112077679ession @ X3 @ Xs )
% 0.18/0.45 != Xs ) ).
% 0.18/0.45
% 0.18/0.45 % not_Cons_self2
% 0.18/0.45 thf(fact_69_map__tailrec__rev_Oinduct,axiom,
% 0.18/0.45 ! [P: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,A0: secrecy_KS > secrecy_Expression,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 0.18/0.45 ( ! [F: secrecy_KS > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Secrecy_KS @ X_1 )
% 0.18/0.45 => ( ! [F: secrecy_KS > secrecy_Expression,A3: secrecy_KS,As: list_Secrecy_KS,Bs: list_S529945141ession] :
% 0.18/0.45 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 0.18/0.45 => ( P @ F @ ( cons_Secrecy_KS @ A3 @ As ) @ Bs ) )
% 0.18/0.45 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % map_tailrec_rev.induct
% 0.18/0.45 thf(fact_70_map__tailrec__rev_Oinduct,axiom,
% 0.18/0.45 ! [P: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.18/0.45 ( ! [F: secrecy_Expression > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Se901661471ession @ X_1 )
% 0.18/0.45 => ( ! [F: secrecy_Expression > secrecy_Expression,A3: secrecy_Expression,As: list_S529945141ession,Bs: list_S529945141ession] :
% 0.18/0.45 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 0.18/0.45 => ( P @ F @ ( cons_S112077679ession @ A3 @ As ) @ Bs ) )
% 0.18/0.45 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % map_tailrec_rev.induct
% 0.18/0.45 thf(fact_71_list__nonempty__induct,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs2 != nil_Secrecy_KS )
% 0.18/0.45 => ( ( P @ Xs2 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_nonempty_induct
% 0.18/0.45 thf(fact_72_list__nonempty__induct,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 0.18/0.45 ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( Xs2 != nil_Se901661471ession )
% 0.18/0.45 => ( ( P @ Xs2 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_nonempty_induct
% 0.18/0.45 thf(fact_73_successively_Oinduct,axiom,
% 0.18/0.45 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 0.18/0.45 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS] : ( P @ P2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.18/0.45 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ P2 @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) )
% 0.18/0.45 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % successively.induct
% 0.18/0.45 thf(fact_74_successively_Oinduct,axiom,
% 0.18/0.45 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 0.18/0.45 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression] : ( P @ P2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.18/0.45 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( P @ P2 @ ( cons_S112077679ession @ Y3 @ Xs2 ) )
% 0.18/0.45 => ( P @ P2 @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % successively.induct
% 0.18/0.45 thf(fact_75_remdups__adj_Oinduct,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > $o,A0: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.18/0.45 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( X = Y3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) )
% 0.18/0.45 => ( ( ( X != Y3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) ) ) )
% 0.18/0.45 => ( P @ A0 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % remdups_adj.induct
% 0.18/0.45 thf(fact_76_remdups__adj_Oinduct,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > $o,A0: list_S529945141ession] :
% 0.18/0.45 ( ( P @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( ( X = Y3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) )
% 0.18/0.45 => ( ( ( X != Y3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) ) ) )
% 0.18/0.45 => ( P @ A0 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % remdups_adj.induct
% 0.18/0.45 thf(fact_77_sorted__wrt_Oinduct,axiom,
% 0.18/0.45 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 0.18/0.45 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ P2 @ Ys3 )
% 0.18/0.45 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ Ys3 ) ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sorted_wrt.induct
% 0.18/0.45 thf(fact_78_sorted__wrt_Oinduct,axiom,
% 0.18/0.45 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 0.18/0.45 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( P @ P2 @ Ys3 )
% 0.18/0.45 => ( P @ P2 @ ( cons_S112077679ession @ X @ Ys3 ) ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sorted_wrt.induct
% 0.18/0.45 thf(fact_79_remdups__adj_Ocases,axiom,
% 0.18/0.45 ! [X3: list_Secrecy_KS] :
% 0.18/0.45 ( ( X3 != nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.18/0.45 => ~ ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % remdups_adj.cases
% 0.18/0.45 thf(fact_80_remdups__adj_Ocases,axiom,
% 0.18/0.45 ! [X3: list_S529945141ession] :
% 0.18/0.45 ( ( X3 != nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.18/0.45 => ~ ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % remdups_adj.cases
% 0.18/0.45 thf(fact_81_transpose_Ocases,axiom,
% 0.18/0.45 ! [X3: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( X3 != nil_list_Secrecy_KS )
% 0.18/0.45 => ( ! [Xss: list_list_Secrecy_KS] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ Xss ) )
% 0.18/0.45 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Xss: list_list_Secrecy_KS] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_list_Secrecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % transpose.cases
% 0.18/0.45 thf(fact_82_transpose_Ocases,axiom,
% 0.18/0.45 ! [X3: list_l425507653ession] :
% 0.18/0.45 ( ( X3 != nil_li311616943ession )
% 0.18/0.45 => ( ! [Xss: list_l425507653ession] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_l533358079ession @ nil_Se901661471ession @ Xss ) )
% 0.18/0.45 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession,Xss: list_l425507653ession] :
% 0.18/0.45 ( X3
% 0.18/0.45 != ( cons_l533358079ession @ ( cons_S112077679ession @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % transpose.cases
% 0.18/0.45 thf(fact_83_mem__Collect__eq,axiom,
% 0.18/0.45 ! [A4: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.18/0.45 ( ( member_Secrecy_Keys @ A4 @ ( collect_Secrecy_Keys @ P ) )
% 0.18/0.45 = ( P @ A4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem_Collect_eq
% 0.18/0.45 thf(fact_84_mem__Collect__eq,axiom,
% 0.18/0.45 ! [A4: secrecy_KS,P: secrecy_KS > $o] :
% 0.18/0.45 ( ( member_Secrecy_KS2 @ A4 @ ( collect_Secrecy_KS @ P ) )
% 0.18/0.45 = ( P @ A4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem_Collect_eq
% 0.18/0.45 thf(fact_85_mem__Collect__eq,axiom,
% 0.18/0.45 ! [A4: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.18/0.45 ( ( member2138796287ecrets @ A4 @ ( collec836099393ecrets @ P ) )
% 0.18/0.45 = ( P @ A4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem_Collect_eq
% 0.18/0.45 thf(fact_86_Collect__mem__eq,axiom,
% 0.18/0.45 ! [A: set_Secrecy_Keys] :
% 0.18/0.45 ( ( collect_Secrecy_Keys
% 0.18/0.45 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_mem_eq
% 0.18/0.45 thf(fact_87_Collect__mem__eq,axiom,
% 0.18/0.45 ! [A: set_Secrecy_KS] :
% 0.18/0.45 ( ( collect_Secrecy_KS
% 0.18/0.45 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS2 @ X4 @ A ) )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_mem_eq
% 0.18/0.45 thf(fact_88_Collect__mem__eq,axiom,
% 0.18/0.45 ! [A: set_Secrecy_Secrets] :
% 0.18/0.45 ( ( collec836099393ecrets
% 0.18/0.45 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_mem_eq
% 0.18/0.45 thf(fact_89_shuffles_Oinduct,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 0.18/0.45 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.18/0.45 => ( ! [Xs2: list_Secrecy_KS] : ( P @ Xs2 @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Xs2 @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % shuffles.induct
% 0.18/0.45 thf(fact_90_shuffles_Oinduct,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 0.18/0.45 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.18/0.45 => ( ! [Xs2: list_S529945141ession] : ( P @ Xs2 @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y3: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( P @ Xs2 @ ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) )
% 0.18/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % shuffles.induct
% 0.18/0.45 thf(fact_91_know_Osimps_I2_J,axiom,
% 0.18/0.45 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.18/0.45 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.18/0.45 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.18/0.45 | ( member_Secrecy_KS2 @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % know.simps(2)
% 0.18/0.45 thf(fact_92_Expression2KSL_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( secrec1371625429on2KSL @ nil_Se901661471ession )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % Expression2KSL.simps(1)
% 0.18/0.45 thf(fact_93_insert__Nil,axiom,
% 0.18/0.45 ! [X3: secrecy_KS] :
% 0.18/0.45 ( ( insert_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 0.18/0.45 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_Nil
% 0.18/0.45 thf(fact_94_insert__Nil,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression] :
% 0.18/0.45 ( ( insert1173886601ession @ X3 @ nil_Se901661471ession )
% 0.18/0.45 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_Nil
% 0.18/0.45 thf(fact_95_list__ex1__simps_I1_J,axiom,
% 0.18/0.45 ! [P: secrecy_Expression > $o] :
% 0.18/0.45 ~ ( list_e1486860828ession @ P @ nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % list_ex1_simps(1)
% 0.18/0.45 thf(fact_96_list__ex1__simps_I1_J,axiom,
% 0.18/0.45 ! [P: secrecy_KS > $o] :
% 0.18/0.45 ~ ( list_ex1_Secrecy_KS @ P @ nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % list_ex1_simps(1)
% 0.18/0.45 thf(fact_97_eoutKnowsECorrect__def,axiom,
% 0.18/0.45 ( knowle1268625169orrect
% 0.18/0.45 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 0.18/0.45 ( ( eout @ C2 @ E2 )
% 0.18/0.45 = ( ? [K3: secrecy_Keys] :
% 0.18/0.45 ( ( E2
% 0.18/0.45 = ( secrecy_kE @ K3 ) )
% 0.18/0.45 & ( member_Secrecy_Keys @ K3 @ ( specKeys @ C2 ) ) )
% 0.18/0.45 | ? [S: secrecy_Secrets] :
% 0.18/0.45 ( ( E2
% 0.18/0.45 = ( secrecy_sE @ S ) )
% 0.18/0.45 & ( member2138796287ecrets @ S @ ( specSecrets @ C2 ) ) )
% 0.18/0.45 | ( knowle731562421_knows @ C2 @ ( cons_S112077679ession @ E2 @ nil_Se901661471ession ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eoutKnowsECorrect_def
% 0.18/0.45 thf(fact_98_eoutKnowsECorrect__L1,axiom,
% 0.18/0.45 ! [C: secrecy_specID,E: secrecy_Expression] :
% 0.18/0.45 ( ( knowle1268625169orrect @ C @ E )
% 0.18/0.45 => ( ( eout @ C @ E )
% 0.18/0.45 => ( ? [K4: secrecy_Keys] :
% 0.18/0.45 ( ( E
% 0.18/0.45 = ( secrecy_kE @ K4 ) )
% 0.18/0.45 & ( member_Secrecy_Keys @ K4 @ ( specKeys @ C ) ) )
% 0.18/0.45 | ? [S2: secrecy_Secrets] :
% 0.18/0.45 ( ( E
% 0.18/0.45 = ( secrecy_sE @ S2 ) )
% 0.18/0.45 & ( member2138796287ecrets @ S2 @ ( specSecrets @ C ) ) )
% 0.18/0.45 | ( knowle731562421_knows @ C @ ( cons_S112077679ession @ E @ nil_Se901661471ession ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eoutKnowsECorrect_L1
% 0.18/0.45 thf(fact_99_map__tailrec__rev_Oelims,axiom,
% 0.18/0.45 ! [X3: secrecy_KS > secrecy_Expression,Xa: list_Secrecy_KS,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 0.18/0.45 ( ( ( map_ta623472337ession @ X3 @ Xa @ Xb )
% 0.18/0.45 = Y )
% 0.18/0.45 => ( ( ( Xa = nil_Secrecy_KS )
% 0.18/0.45 => ( Y != Xb ) )
% 0.18/0.45 => ~ ! [A3: secrecy_KS,As: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xa
% 0.18/0.45 = ( cons_Secrecy_KS @ A3 @ As ) )
% 0.18/0.45 => ( Y
% 0.18/0.45 != ( map_ta623472337ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % map_tailrec_rev.elims
% 0.18/0.45 thf(fact_100_map__tailrec__rev_Oelims,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression > secrecy_Expression,Xa: list_S529945141ession,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 0.18/0.45 ( ( ( map_ta1624757057ession @ X3 @ Xa @ Xb )
% 0.18/0.45 = Y )
% 0.18/0.45 => ( ( ( Xa = nil_Se901661471ession )
% 0.18/0.45 => ( Y != Xb ) )
% 0.18/0.45 => ~ ! [A3: secrecy_Expression,As: list_S529945141ession] :
% 0.18/0.45 ( ( Xa
% 0.18/0.45 = ( cons_S112077679ession @ A3 @ As ) )
% 0.18/0.45 => ( Y
% 0.18/0.45 != ( map_ta1624757057ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % map_tailrec_rev.elims
% 0.18/0.45 thf(fact_101_notSpecKeysSecretsExpr__L1,axiom,
% 0.18/0.45 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 0.18/0.45 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 0.18/0.45 => ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ nil_Se901661471ession ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % notSpecKeysSecretsExpr_L1
% 0.18/0.45 thf(fact_102_Expression_Oinject_I2_J,axiom,
% 0.18/0.45 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 0.18/0.45 ( ( ( secrecy_sE @ X23 )
% 0.18/0.45 = ( secrecy_sE @ Y23 ) )
% 0.18/0.45 = ( X23 = Y23 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Expression.inject(2)
% 0.18/0.45 thf(fact_103_Expression_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 0.18/0.45 ( ( secrecy_kE @ X1 )
% 0.18/0.45 != ( secrecy_sE @ X23 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Expression.distinct(1)
% 0.18/0.45 thf(fact_104_notSpecKeysSecretsExpr__L2,axiom,
% 0.18/0.45 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 0.18/0.45 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 0.18/0.45 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 0.18/0.45
% 0.18/0.45 % notSpecKeysSecretsExpr_L2
% 0.18/0.45 thf(fact_105_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.18/0.45 ! [F2: secrecy_Expression > secrecy_Expression,A4: secrecy_Expression,As2: list_S529945141ession,Bs2: list_S529945141ession] :
% 0.18/0.45 ( ( map_ta1624757057ession @ F2 @ ( cons_S112077679ession @ A4 @ As2 ) @ Bs2 )
% 0.18/0.45 = ( map_ta1624757057ession @ F2 @ As2 @ ( cons_S112077679ession @ ( F2 @ A4 ) @ Bs2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % map_tailrec_rev.simps(2)
% 0.18/0.45 thf(fact_106_KS2Expression_Osimps_I2_J,axiom,
% 0.18/0.45 ! [M: secrecy_Secrets] :
% 0.18/0.45 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.18/0.45 = ( secrecy_sE @ M ) ) ).
% 0.18/0.45
% 0.18/0.45 % KS2Expression.simps(2)
% 0.18/0.45 thf(fact_107_eoutKnowCorrect__L1s,axiom,
% 0.18/0.45 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.18/0.45 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 0.18/0.45 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.18/0.45 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 0.18/0.45 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eoutKnowCorrect_L1s
% 0.18/0.45 thf(fact_108_eout__know__s,axiom,
% 0.18/0.45 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.18/0.45 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 0.18/0.45 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.18/0.45 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 0.18/0.45 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eout_know_s
% 0.18/0.45 thf(fact_109_product__lists_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( produc1450295286ession @ nil_li311616943ession )
% 0.18/0.45 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % product_lists.simps(1)
% 0.18/0.45 thf(fact_110_product__lists_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( produc713695622ecy_KS @ nil_list_Secrecy_KS )
% 0.18/0.45 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % product_lists.simps(1)
% 0.18/0.45 thf(fact_111_subseqs_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( subseq348280080ession @ nil_Se901661471ession )
% 0.18/0.45 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % subseqs.simps(1)
% 0.18/0.45 thf(fact_112_subseqs_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( subseqs_Secrecy_KS @ nil_Secrecy_KS )
% 0.18/0.45 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % subseqs.simps(1)
% 0.18/0.45 thf(fact_113_DecrEnc,axiom,
% 0.18/0.45 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 0.18/0.45 ( ( encrDecrKeys @ K12 @ K22 )
% 0.18/0.45 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 0.18/0.45 = E3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % DecrEnc
% 0.18/0.45 thf(fact_114_ExtSign,axiom,
% 0.18/0.45 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 0.18/0.45 ( ( encrDecrKeys @ K12 @ K22 )
% 0.18/0.45 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 0.18/0.45 = E3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % ExtSign
% 0.18/0.45 thf(fact_115_notSpecKeysSecretsExpr__def,axiom,
% 0.18/0.45 ( notSpe1586871396tsExpr
% 0.18/0.45 = ( ^ [P3: secrecy_specID,E2: list_S529945141ession] :
% 0.18/0.45 ( ! [X4: secrecy_Keys] :
% 0.18/0.45 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E2 )
% 0.18/0.45 => ~ ( member_Secrecy_KS2 @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 0.18/0.45 & ! [Y2: secrecy_Secrets] :
% 0.18/0.45 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y2 ) @ E2 )
% 0.18/0.45 => ~ ( member_Secrecy_KS2 @ ( secrecy_sKS @ Y2 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % notSpecKeysSecretsExpr_def
% 0.18/0.45 thf(fact_116_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.18/0.45 ! [Less: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ~ ( lexord948960489ecy_KS @ Less @ ( cons_Secrecy_KS @ X3 @ Xs ) @ nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_simps(3)
% 0.18/0.45 thf(fact_117_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.45 ~ ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_simps(3)
% 0.18/0.45 thf(fact_118_bind__simps_I1_J,axiom,
% 0.18/0.45 ! [F2: secrecy_Expression > list_S529945141ession] :
% 0.18/0.45 ( ( bind_S815874003ession @ nil_Se901661471ession @ F2 )
% 0.18/0.45 = nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % bind_simps(1)
% 0.18/0.45 thf(fact_119_bind__simps_I1_J,axiom,
% 0.18/0.45 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 0.18/0.45 ( ( bind_S1823644515ecy_KS @ nil_Se901661471ession @ F2 )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % bind_simps(1)
% 0.18/0.45 thf(fact_120_bind__simps_I1_J,axiom,
% 0.18/0.45 ! [F2: secrecy_KS > list_S529945141ession] :
% 0.18/0.45 ( ( bind_S711229283ession @ nil_Secrecy_KS @ F2 )
% 0.18/0.45 = nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % bind_simps(1)
% 0.18/0.45 thf(fact_121_bind__simps_I1_J,axiom,
% 0.18/0.45 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 0.18/0.45 ( ( bind_S645462771ecy_KS @ nil_Secrecy_KS @ F2 )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % bind_simps(1)
% 0.18/0.45 thf(fact_122_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) )
% 0.18/0.45 = ( ( Less @ X3 @ Y )
% 0.18/0.45 | ( ~ ( Less @ Y @ X3 )
% 0.18/0.45 & ( lexord1123423577ession @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_simps(4)
% 0.18/0.45 thf(fact_123_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_simps(1)
% 0.18/0.45 thf(fact_124_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.18/0.45 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_simps(1)
% 0.18/0.45 thf(fact_125_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( lexord1123423577ession @ Less @ Xs @ nil_Se901661471ession )
% 0.18/0.45 = ( Xs = nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_simps(2)
% 0.18/0.45 thf(fact_126_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.18/0.45 ! [Less: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( lexord948960489ecy_KS @ Less @ Xs @ nil_Secrecy_KS )
% 0.18/0.45 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_simps(2)
% 0.18/0.45 thf(fact_127_ord_Olexordp__eq_OCons__eq,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ~ ( Less @ X3 @ Y )
% 0.18/0.45 => ( ~ ( Less @ Y @ X3 )
% 0.18/0.45 => ( ( lexord1123423577ession @ Less @ Xs @ Ys2 )
% 0.18/0.45 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.Cons_eq
% 0.18/0.45 thf(fact_128_ord_Olexordp__eq_OCons,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( Less @ X3 @ Y )
% 0.18/0.45 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.Cons
% 0.18/0.45 thf(fact_129_ord_Olexordp__eq_ONil,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.Nil
% 0.18/0.45 thf(fact_130_ord_Olexordp__eq_ONil,axiom,
% 0.18/0.45 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.Nil
% 0.18/0.45 thf(fact_131_ord_Olexordp__eq_Oinducts,axiom,
% 0.18/0.45 ! [Less: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X23: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 0.18/0.45 ( ( lexord948960489ecy_KS @ Less @ X1 @ X23 )
% 0.18/0.45 => ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.18/0.45 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( Less @ X @ Y3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ~ ( Less @ X @ Y3 )
% 0.18/0.45 => ( ~ ( Less @ Y3 @ X )
% 0.18/0.45 => ( ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 )
% 0.18/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) ) ) )
% 0.18/0.45 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.inducts
% 0.18/0.45 thf(fact_132_ord_Olexordp__eq_Oinducts,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X23: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 0.18/0.45 ( ( lexord1123423577ession @ Less @ X1 @ X23 )
% 0.18/0.45 => ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( Less @ X @ Y3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ~ ( Less @ X @ Y3 )
% 0.18/0.45 => ( ~ ( Less @ Y3 @ X )
% 0.18/0.45 => ( ( lexord1123423577ession @ Less @ Xs2 @ Ys3 )
% 0.18/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) ) ) )
% 0.18/0.45 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.inducts
% 0.18/0.45 thf(fact_133_ord_Olexordp__eq_Osimps,axiom,
% 0.18/0.45 ( lexord948960489ecy_KS
% 0.18/0.45 = ( ^ [Less2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 0.18/0.45 ( ? [Ys: list_Secrecy_KS] :
% 0.18/0.45 ( ( A12 = nil_Secrecy_KS )
% 0.18/0.45 & ( A22 = Ys ) )
% 0.18/0.45 | ? [X4: secrecy_KS,Y2: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 0.18/0.45 & ( Less2 @ X4 @ Y2 ) )
% 0.18/0.45 | ? [X4: secrecy_KS,Y2: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 0.18/0.45 & ~ ( Less2 @ X4 @ Y2 )
% 0.18/0.45 & ~ ( Less2 @ Y2 @ X4 )
% 0.18/0.45 & ( lexord948960489ecy_KS @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.simps
% 0.18/0.45 thf(fact_134_ord_Olexordp__eq_Osimps,axiom,
% 0.18/0.45 ( lexord1123423577ession
% 0.18/0.45 = ( ^ [Less2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 0.18/0.45 ( ? [Ys: list_S529945141ession] :
% 0.18/0.45 ( ( A12 = nil_Se901661471ession )
% 0.18/0.45 & ( A22 = Ys ) )
% 0.18/0.45 | ? [X4: secrecy_Expression,Y2: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 0.18/0.45 & ( Less2 @ X4 @ Y2 ) )
% 0.18/0.45 | ? [X4: secrecy_Expression,Y2: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 0.18/0.45 & ~ ( Less2 @ X4 @ Y2 )
% 0.18/0.45 & ~ ( Less2 @ Y2 @ X4 )
% 0.18/0.45 & ( lexord1123423577ession @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.simps
% 0.18/0.45 thf(fact_135_ord_Olexordp__eq_Ocases,axiom,
% 0.18/0.45 ! [Less: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 0.18/0.45 ( ( lexord948960489ecy_KS @ Less @ A1 @ A2 )
% 0.18/0.45 => ( ( A1 != nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS] :
% 0.18/0.45 ( ? [Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( A1
% 0.18/0.45 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.18/0.45 => ! [Y3: secrecy_KS] :
% 0.18/0.45 ( ? [Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( A2
% 0.18/0.45 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ~ ( Less @ X @ Y3 ) ) )
% 0.18/0.45 => ~ ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( A1
% 0.18/0.45 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.18/0.45 => ! [Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ~ ( Less @ X @ Y3 )
% 0.18/0.45 => ( ~ ( Less @ Y3 @ X )
% 0.18/0.45 => ~ ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.cases
% 0.18/0.45 thf(fact_136_ord_Olexordp__eq_Ocases,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.18/0.45 ( ( lexord1123423577ession @ Less @ A1 @ A2 )
% 0.18/0.45 => ( ( A1 != nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression] :
% 0.18/0.45 ( ? [Xs2: list_S529945141ession] :
% 0.18/0.45 ( A1
% 0.18/0.45 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.18/0.45 => ! [Y3: secrecy_Expression] :
% 0.18/0.45 ( ? [Ys3: list_S529945141ession] :
% 0.18/0.45 ( A2
% 0.18/0.45 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ~ ( Less @ X @ Y3 ) ) )
% 0.18/0.45 => ~ ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( A1
% 0.18/0.45 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.18/0.45 => ! [Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ~ ( Less @ X @ Y3 )
% 0.18/0.45 => ( ~ ( Less @ Y3 @ X )
% 0.18/0.45 => ~ ( lexord1123423577ession @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq.cases
% 0.18/0.45 thf(fact_137_mem_Osimps_I1_J,axiom,
% 0.18/0.45 ! [X3: secrecy_KS] :
% 0.18/0.45 ~ ( mem_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % mem.simps(1)
% 0.18/0.45 thf(fact_138_mem_Osimps_I1_J,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression] :
% 0.18/0.45 ~ ( mem_Se1967555118ession @ X3 @ nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % mem.simps(1)
% 0.18/0.45 thf(fact_139_mem_Osimps_I2_J,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Y: secrecy_Expression,L: list_S529945141ession] :
% 0.18/0.45 ( ( mem_Se1967555118ession @ X3 @ ( cons_S112077679ession @ Y @ L ) )
% 0.18/0.45 = ( ( X3 = Y )
% 0.18/0.45 | ( mem_Se1967555118ession @ X3 @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem.simps(2)
% 0.18/0.45 thf(fact_140_listrelp_Oinducts,axiom,
% 0.18/0.45 ! [R: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X23: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 0.18/0.45 ( ( listre788412843ecy_KS @ R @ X1 @ X23 )
% 0.18/0.45 => ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( R @ X @ Y3 )
% 0.18/0.45 => ( ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 )
% 0.18/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) ) )
% 0.18/0.45 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.inducts
% 0.18/0.45 thf(fact_141_listrelp_Oinducts,axiom,
% 0.18/0.45 ! [R: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X23: list_S529945141ession,P: list_Secrecy_KS > list_S529945141ession > $o] :
% 0.18/0.45 ( ( listre1601064475ession @ R @ X1 @ X23 )
% 0.18/0.45 => ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_KS,Y3: secrecy_Expression,Xs2: list_Secrecy_KS,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( R @ X @ Y3 )
% 0.18/0.45 => ( ( listre1601064475ession @ R @ Xs2 @ Ys3 )
% 0.18/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) ) )
% 0.18/0.45 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.inducts
% 0.18/0.45 thf(fact_142_listrelp_Oinducts,axiom,
% 0.18/0.45 ! [R: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X23: list_Secrecy_KS,P: list_S529945141ession > list_Secrecy_KS > $o] :
% 0.18/0.45 ( ( listre565996059ecy_KS @ R @ X1 @ X23 )
% 0.18/0.45 => ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Y3: secrecy_KS,Xs2: list_S529945141ession,Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( R @ X @ Y3 )
% 0.18/0.45 => ( ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 )
% 0.18/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) ) )
% 0.18/0.45 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.inducts
% 0.18/0.45 thf(fact_143_listrelp_Oinducts,axiom,
% 0.18/0.45 ! [R: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X23: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 0.18/0.45 ( ( listre84909707ession @ R @ X1 @ X23 )
% 0.18/0.45 => ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( R @ X @ Y3 )
% 0.18/0.45 => ( ( listre84909707ession @ R @ Xs2 @ Ys3 )
% 0.18/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.18/0.45 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) ) )
% 0.18/0.45 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.inducts
% 0.18/0.45 thf(fact_144_listrelp_Osimps,axiom,
% 0.18/0.45 ( listre788412843ecy_KS
% 0.18/0.45 = ( ^ [R2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( A12 = nil_Secrecy_KS )
% 0.18/0.45 & ( A22 = nil_Secrecy_KS ) )
% 0.18/0.45 | ? [X4: secrecy_KS,Y2: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 0.18/0.45 & ( R2 @ X4 @ Y2 )
% 0.18/0.45 & ( listre788412843ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.simps
% 0.18/0.45 thf(fact_145_listrelp_Osimps,axiom,
% 0.18/0.45 ( listre1601064475ession
% 0.18/0.45 = ( ^ [R2: secrecy_KS > secrecy_Expression > $o,A12: list_Secrecy_KS,A22: list_S529945141ession] :
% 0.18/0.45 ( ( ( A12 = nil_Secrecy_KS )
% 0.18/0.45 & ( A22 = nil_Se901661471ession ) )
% 0.18/0.45 | ? [X4: secrecy_KS,Y2: secrecy_Expression,Xs3: list_Secrecy_KS,Ys: list_S529945141ession] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 0.18/0.45 & ( R2 @ X4 @ Y2 )
% 0.18/0.45 & ( listre1601064475ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.simps
% 0.18/0.45 thf(fact_146_listrelp_Osimps,axiom,
% 0.18/0.45 ( listre565996059ecy_KS
% 0.18/0.45 = ( ^ [R2: secrecy_Expression > secrecy_KS > $o,A12: list_S529945141ession,A22: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( A12 = nil_Se901661471ession )
% 0.18/0.45 & ( A22 = nil_Secrecy_KS ) )
% 0.18/0.45 | ? [X4: secrecy_Expression,Y2: secrecy_KS,Xs3: list_S529945141ession,Ys: list_Secrecy_KS] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 0.18/0.45 & ( R2 @ X4 @ Y2 )
% 0.18/0.45 & ( listre565996059ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.simps
% 0.18/0.45 thf(fact_147_listrelp_Osimps,axiom,
% 0.18/0.45 ( listre84909707ession
% 0.18/0.45 = ( ^ [R2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 0.18/0.45 ( ( ( A12 = nil_Se901661471ession )
% 0.18/0.45 & ( A22 = nil_Se901661471ession ) )
% 0.18/0.45 | ? [X4: secrecy_Expression,Y2: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.18/0.45 ( ( A12
% 0.18/0.45 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.18/0.45 & ( A22
% 0.18/0.45 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 0.18/0.45 & ( R2 @ X4 @ Y2 )
% 0.18/0.45 & ( listre84909707ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.simps
% 0.18/0.45 thf(fact_148_listrelp_Ocases,axiom,
% 0.18/0.45 ! [R: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 0.18/0.45 ( ( listre788412843ecy_KS @ R @ A1 @ A2 )
% 0.18/0.45 => ( ( ( A1 = nil_Secrecy_KS )
% 0.18/0.45 => ( A2 != nil_Secrecy_KS ) )
% 0.18/0.45 => ~ ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( A1
% 0.18/0.45 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.18/0.45 => ! [Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ( R @ X @ Y3 )
% 0.18/0.45 => ~ ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.cases
% 0.18/0.45 thf(fact_149_listrelp_Ocases,axiom,
% 0.18/0.45 ! [R: secrecy_KS > secrecy_Expression > $o,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 0.18/0.45 ( ( listre1601064475ession @ R @ A1 @ A2 )
% 0.18/0.45 => ( ( ( A1 = nil_Secrecy_KS )
% 0.18/0.45 => ( A2 != nil_Se901661471ession ) )
% 0.18/0.45 => ~ ! [X: secrecy_KS,Y3: secrecy_Expression,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( A1
% 0.18/0.45 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.18/0.45 => ! [Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ( R @ X @ Y3 )
% 0.18/0.45 => ~ ( listre1601064475ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.cases
% 0.18/0.45 thf(fact_150_listrelp_Ocases,axiom,
% 0.18/0.45 ! [R: secrecy_Expression > secrecy_KS > $o,A1: list_S529945141ession,A2: list_Secrecy_KS] :
% 0.18/0.45 ( ( listre565996059ecy_KS @ R @ A1 @ A2 )
% 0.18/0.45 => ( ( ( A1 = nil_Se901661471ession )
% 0.18/0.45 => ( A2 != nil_Secrecy_KS ) )
% 0.18/0.45 => ~ ! [X: secrecy_Expression,Y3: secrecy_KS,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( A1
% 0.18/0.45 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.18/0.45 => ! [Ys3: list_Secrecy_KS] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ( R @ X @ Y3 )
% 0.18/0.45 => ~ ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.cases
% 0.18/0.45 thf(fact_151_listrelp_Ocases,axiom,
% 0.18/0.45 ! [R: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.18/0.45 ( ( listre84909707ession @ R @ A1 @ A2 )
% 0.18/0.45 => ( ( ( A1 = nil_Se901661471ession )
% 0.18/0.45 => ( A2 != nil_Se901661471ession ) )
% 0.18/0.45 => ~ ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( A1
% 0.18/0.45 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.18/0.45 => ! [Ys3: list_S529945141ession] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 0.18/0.45 => ( ( R @ X @ Y3 )
% 0.18/0.45 => ~ ( listre84909707ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.cases
% 0.18/0.45 thf(fact_152_listrelp_OCons,axiom,
% 0.18/0.45 ! [R: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( R @ X3 @ Y )
% 0.18/0.45 => ( ( listre84909707ession @ R @ Xs @ Ys2 )
% 0.18/0.45 => ( listre84909707ession @ R @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.Cons
% 0.18/0.45 thf(fact_153_listrelp_ONil,axiom,
% 0.18/0.45 ! [R: secrecy_Expression > secrecy_Expression > $o] : ( listre84909707ession @ R @ nil_Se901661471ession @ nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.Nil
% 0.18/0.45 thf(fact_154_listrelp_ONil,axiom,
% 0.18/0.45 ! [R: secrecy_Expression > secrecy_KS > $o] : ( listre565996059ecy_KS @ R @ nil_Se901661471ession @ nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.Nil
% 0.18/0.45 thf(fact_155_listrelp_ONil,axiom,
% 0.18/0.45 ! [R: secrecy_KS > secrecy_Expression > $o] : ( listre1601064475ession @ R @ nil_Secrecy_KS @ nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.Nil
% 0.18/0.45 thf(fact_156_listrelp_ONil,axiom,
% 0.18/0.45 ! [R: secrecy_KS > secrecy_KS > $o] : ( listre788412843ecy_KS @ R @ nil_Secrecy_KS @ nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % listrelp.Nil
% 0.18/0.45 thf(fact_157_mem__memS__eq,axiom,
% 0.18/0.45 mem_Se1967555118ession = memS_S2026082737ession ).
% 0.18/0.45
% 0.18/0.45 % mem_memS_eq
% 0.18/0.45 thf(fact_158_mem__notdisjoint,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,L1: list_S529945141ession,L2: list_S529945141ession] :
% 0.18/0.45 ( ( mem_Se1967555118ession @ X3 @ L1 )
% 0.18/0.45 => ( ( mem_Se1967555118ession @ X3 @ L2 )
% 0.18/0.45 => ~ ( disjoi1945222607ession @ L1 @ L2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem_notdisjoint
% 0.18/0.45 thf(fact_159_member__rec_I2_J,axiom,
% 0.18/0.45 ! [Y: secrecy_Expression] :
% 0.18/0.45 ~ ( member2020590922ession @ nil_Se901661471ession @ Y ) ).
% 0.18/0.45
% 0.18/0.45 % member_rec(2)
% 0.18/0.45 thf(fact_160_member__rec_I2_J,axiom,
% 0.18/0.45 ! [Y: secrecy_KS] :
% 0.18/0.45 ~ ( member_Secrecy_KS @ nil_Secrecy_KS @ Y ) ).
% 0.18/0.45
% 0.18/0.45 % member_rec(2)
% 0.18/0.45 thf(fact_161_member__rec_I1_J,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression] :
% 0.18/0.45 ( ( member2020590922ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Y )
% 0.18/0.45 = ( ( X3 = Y )
% 0.18/0.45 | ( member2020590922ession @ Xs @ Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % member_rec(1)
% 0.18/0.45 thf(fact_162_splice_Oelims,axiom,
% 0.18/0.45 ! [X3: list_Secrecy_KS,Xa: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( splice_Secrecy_KS @ X3 @ Xa )
% 0.18/0.45 = Y )
% 0.18/0.45 => ( ( ( X3 = nil_Secrecy_KS )
% 0.18/0.45 => ( Y != Xa ) )
% 0.18/0.45 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( X3
% 0.18/0.45 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.18/0.45 => ( Y
% 0.18/0.45 != ( cons_Secrecy_KS @ X @ ( splice_Secrecy_KS @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % splice.elims
% 0.18/0.45 thf(fact_163_splice_Oelims,axiom,
% 0.18/0.45 ! [X3: list_S529945141ession,Xa: list_S529945141ession,Y: list_S529945141ession] :
% 0.18/0.45 ( ( ( splice1390717708ession @ X3 @ Xa )
% 0.18/0.45 = Y )
% 0.18/0.45 => ( ( ( X3 = nil_Se901661471ession )
% 0.18/0.45 => ( Y != Xa ) )
% 0.18/0.45 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( X3
% 0.18/0.45 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.18/0.45 => ( Y
% 0.18/0.45 != ( cons_S112077679ession @ X @ ( splice1390717708ession @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % splice.elims
% 0.18/0.45 thf(fact_164_append_Oassoc,axiom,
% 0.18/0.45 ! [A4: list_S529945141ession,B: list_S529945141ession,C3: list_S529945141ession] :
% 0.18/0.45 ( ( append2089414218ession @ ( append2089414218ession @ A4 @ B ) @ C3 )
% 0.18/0.45 = ( append2089414218ession @ A4 @ ( append2089414218ession @ B @ C3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append.assoc
% 0.18/0.45 thf(fact_165_append__assoc,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.18/0.45 ( ( append2089414218ession @ ( append2089414218ession @ Xs @ Ys2 ) @ Zs2 )
% 0.18/0.45 = ( append2089414218ession @ Xs @ ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_assoc
% 0.18/0.45 thf(fact_166_append__same__eq,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Ys2 @ Xs )
% 0.18/0.45 = ( append2089414218ession @ Zs2 @ Xs ) )
% 0.18/0.45 = ( Ys2 = Zs2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_same_eq
% 0.18/0.45 thf(fact_167_same__append__eq,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.18/0.45 = ( append2089414218ession @ Xs @ Zs2 ) )
% 0.18/0.45 = ( Ys2 = Zs2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % same_append_eq
% 0.18/0.45 thf(fact_168_append_Oright__neutral,axiom,
% 0.18/0.45 ! [A4: list_S529945141ession] :
% 0.18/0.45 ( ( append2089414218ession @ A4 @ nil_Se901661471ession )
% 0.18/0.45 = A4 ) ).
% 0.18/0.45
% 0.18/0.45 % append.right_neutral
% 0.18/0.45 thf(fact_169_append_Oright__neutral,axiom,
% 0.18/0.45 ! [A4: list_Secrecy_KS] :
% 0.18/0.45 ( ( append_Secrecy_KS @ A4 @ nil_Secrecy_KS )
% 0.18/0.45 = A4 ) ).
% 0.18/0.45
% 0.18/0.45 % append.right_neutral
% 0.18/0.45 thf(fact_170_append__is__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.18/0.45 = nil_Se901661471ession )
% 0.18/0.45 = ( ( Xs = nil_Se901661471ession )
% 0.18/0.45 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_is_Nil_conv
% 0.18/0.45 thf(fact_171_append__is__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.18/0.45 = nil_Secrecy_KS )
% 0.18/0.45 = ( ( Xs = nil_Secrecy_KS )
% 0.18/0.45 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_is_Nil_conv
% 0.18/0.45 thf(fact_172_Nil__is__append__conv,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( nil_Se901661471ession
% 0.18/0.45 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( ( Xs = nil_Se901661471ession )
% 0.18/0.45 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Nil_is_append_conv
% 0.18/0.45 thf(fact_173_Nil__is__append__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( nil_Secrecy_KS
% 0.18/0.45 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( ( Xs = nil_Secrecy_KS )
% 0.18/0.45 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Nil_is_append_conv
% 0.18/0.45 thf(fact_174_self__append__conv2,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( Ys2
% 0.18/0.45 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( Xs = nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % self_append_conv2
% 0.18/0.45 thf(fact_175_self__append__conv2,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( Ys2
% 0.18/0.45 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % self_append_conv2
% 0.18/0.45 thf(fact_176_append__self__conv2,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 = ( Xs = nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_self_conv2
% 0.18/0.45 thf(fact_177_append__self__conv2,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_self_conv2
% 0.18/0.45 thf(fact_178_self__append__conv,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( Xs
% 0.18/0.45 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( Ys2 = nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % self_append_conv
% 0.18/0.45 thf(fact_179_self__append__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs
% 0.18/0.45 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % self_append_conv
% 0.18/0.45 thf(fact_180_append__self__conv,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.18/0.45 = Xs )
% 0.18/0.45 = ( Ys2 = nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_self_conv
% 0.18/0.45 thf(fact_181_append__self__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.18/0.45 = Xs )
% 0.18/0.45 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_self_conv
% 0.18/0.45 thf(fact_182_append__Nil2,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession] :
% 0.18/0.45 ( ( append2089414218ession @ Xs @ nil_Se901661471ession )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % append_Nil2
% 0.18/0.45 thf(fact_183_append__Nil2,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( append_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % append_Nil2
% 0.18/0.45 thf(fact_184_split__Nil__iff,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( ( splice1390717708ession @ Xs @ Ys2 )
% 0.18/0.45 = nil_Se901661471ession )
% 0.18/0.45 = ( ( Xs = nil_Se901661471ession )
% 0.18/0.45 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % split_Nil_iff
% 0.18/0.45 thf(fact_185_split__Nil__iff,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( splice_Secrecy_KS @ Xs @ Ys2 )
% 0.18/0.45 = nil_Secrecy_KS )
% 0.18/0.45 = ( ( Xs = nil_Secrecy_KS )
% 0.18/0.45 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % split_Nil_iff
% 0.18/0.45 thf(fact_186_splice__Nil2,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession] :
% 0.18/0.45 ( ( splice1390717708ession @ Xs @ nil_Se901661471ession )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % splice_Nil2
% 0.18/0.45 thf(fact_187_splice__Nil2,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( splice_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % splice_Nil2
% 0.18/0.45 thf(fact_188_append1__eq__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS,Y: secrecy_KS] :
% 0.18/0.45 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.18/0.45 = ( append_Secrecy_KS @ Ys2 @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) )
% 0.18/0.45 = ( ( Xs = Ys2 )
% 0.18/0.45 & ( X3 = Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append1_eq_conv
% 0.18/0.45 thf(fact_189_append1__eq__conv,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession,Y: secrecy_Expression] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.18/0.45 = ( append2089414218ession @ Ys2 @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) )
% 0.18/0.45 = ( ( Xs = Ys2 )
% 0.18/0.45 & ( X3 = Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append1_eq_conv
% 0.18/0.45 thf(fact_190_bind__simps_I2_J,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs: list_S529945141ession,F2: secrecy_Expression > list_S529945141ession] :
% 0.18/0.45 ( ( bind_S815874003ession @ ( cons_S112077679ession @ X3 @ Xs ) @ F2 )
% 0.18/0.45 = ( append2089414218ession @ ( F2 @ X3 ) @ ( bind_S815874003ession @ Xs @ F2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % bind_simps(2)
% 0.18/0.45 thf(fact_191_append__eq__appendI,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Xs1: list_S529945141ession,Zs2: list_S529945141ession,Ys2: list_S529945141ession,Us: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ Xs1 )
% 0.18/0.45 = Zs2 )
% 0.18/0.45 => ( ( Ys2
% 0.18/0.45 = ( append2089414218ession @ Xs1 @ Us ) )
% 0.18/0.45 => ( ( append2089414218ession @ Xs @ Ys2 )
% 0.18/0.45 = ( append2089414218ession @ Zs2 @ Us ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_eq_appendI
% 0.18/0.45 thf(fact_192_append__eq__append__conv2,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession,Ts: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.18/0.45 = ( append2089414218ession @ Zs2 @ Ts ) )
% 0.18/0.45 = ( ? [Us2: list_S529945141ession] :
% 0.18/0.45 ( ( ( Xs
% 0.18/0.45 = ( append2089414218ession @ Zs2 @ Us2 ) )
% 0.18/0.45 & ( ( append2089414218ession @ Us2 @ Ys2 )
% 0.18/0.45 = Ts ) )
% 0.18/0.45 | ( ( ( append2089414218ession @ Xs @ Us2 )
% 0.18/0.45 = Zs2 )
% 0.18/0.45 & ( Ys2
% 0.18/0.45 = ( append2089414218ession @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_eq_append_conv2
% 0.18/0.45 thf(fact_193_eq__Nil__appendI,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( Xs = Ys2 )
% 0.18/0.45 => ( Xs
% 0.18/0.45 = ( append2089414218ession @ nil_Se901661471ession @ Ys2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eq_Nil_appendI
% 0.18/0.45 thf(fact_194_eq__Nil__appendI,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs = Ys2 )
% 0.18/0.45 => ( Xs
% 0.18/0.45 = ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eq_Nil_appendI
% 0.18/0.45 thf(fact_195_append__Nil,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( append2089414218ession @ nil_Se901661471ession @ Ys2 )
% 0.18/0.45 = Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % append_Nil
% 0.18/0.45 thf(fact_196_append__Nil,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 0.18/0.45 = Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % append_Nil
% 0.18/0.45 thf(fact_197_append_Oleft__neutral,axiom,
% 0.18/0.45 ! [A4: list_S529945141ession] :
% 0.18/0.45 ( ( append2089414218ession @ nil_Se901661471ession @ A4 )
% 0.18/0.45 = A4 ) ).
% 0.18/0.45
% 0.18/0.45 % append.left_neutral
% 0.18/0.45 thf(fact_198_append_Oleft__neutral,axiom,
% 0.18/0.45 ! [A4: list_Secrecy_KS] :
% 0.18/0.45 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ A4 )
% 0.18/0.45 = A4 ) ).
% 0.18/0.45
% 0.18/0.45 % append.left_neutral
% 0.18/0.45 thf(fact_199_Cons__eq__appendI,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs1: list_S529945141ession,Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.18/0.45 ( ( ( cons_S112077679ession @ X3 @ Xs1 )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 => ( ( Xs
% 0.18/0.45 = ( append2089414218ession @ Xs1 @ Zs2 ) )
% 0.18/0.45 => ( ( cons_S112077679ession @ X3 @ Xs )
% 0.18/0.45 = ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Cons_eq_appendI
% 0.18/0.45 thf(fact_200_append__Cons,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( append2089414218ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 0.18/0.45 = ( cons_S112077679ession @ X3 @ ( append2089414218ession @ Xs @ Ys2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_Cons
% 0.18/0.45 thf(fact_201_ord_Olexordp__eq__pref,axiom,
% 0.18/0.45 ! [Less: secrecy_Expression > secrecy_Expression > $o,U: list_S529945141ession,V: list_S529945141ession] : ( lexord1123423577ession @ Less @ U @ ( append2089414218ession @ U @ V ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord.lexordp_eq_pref
% 0.18/0.45 thf(fact_202_knows2b,axiom,
% 0.18/0.45 ! [A: secrecy_specID,E: list_S529945141ession,E1: list_S529945141ession] :
% 0.18/0.45 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E @ E1 ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.18/0.45
% 0.18/0.45 % knows2b
% 0.18/0.45 thf(fact_203_knows2a,axiom,
% 0.18/0.45 ! [A: secrecy_specID,E1: list_S529945141ession,E: list_S529945141ession] :
% 0.18/0.45 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.18/0.45
% 0.18/0.45 % knows2a
% 0.18/0.45 thf(fact_204_knows3,axiom,
% 0.18/0.45 ! [A: secrecy_specID,E1: list_S529945141ession,E22: list_S529945141ession] :
% 0.18/0.45 ( ( ( knowle731562421_knows @ A @ E1 )
% 0.18/0.45 & ( knowle731562421_knows @ A @ E22 ) )
% 0.18/0.45 => ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % knows3
% 0.18/0.45 thf(fact_205_splice_Osimps_I2_J,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( splice1390717708ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 0.18/0.45 = ( cons_S112077679ession @ X3 @ ( splice1390717708ession @ Ys2 @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % splice.simps(2)
% 0.18/0.45 thf(fact_206_splice_Osimps_I1_J,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( splice1390717708ession @ nil_Se901661471ession @ Ys2 )
% 0.18/0.45 = Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % splice.simps(1)
% 0.18/0.45 thf(fact_207_splice_Osimps_I1_J,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( splice_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 0.18/0.45 = Ys2 ) ).
% 0.18/0.45
% 0.18/0.45 % splice.simps(1)
% 0.18/0.45 thf(fact_208_rev__nonempty__induct,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs2 != nil_Secrecy_KS )
% 0.18/0.45 => ( ( P @ Xs2 )
% 0.18/0.45 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rev_nonempty_induct
% 0.18/0.45 thf(fact_209_rev__nonempty__induct,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 0.18/0.45 ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( Xs2 != nil_Se901661471ession )
% 0.18/0.45 => ( ( P @ Xs2 )
% 0.18/0.45 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rev_nonempty_induct
% 0.18/0.45 thf(fact_210_append__eq__Cons__conv,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( append_Secrecy_KS @ Ys2 @ Zs2 )
% 0.18/0.45 = ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = ( ( ( Ys2 = nil_Secrecy_KS )
% 0.18/0.45 & ( Zs2
% 0.18/0.45 = ( cons_Secrecy_KS @ X3 @ Xs ) ) )
% 0.18/0.45 | ? [Ys4: list_Secrecy_KS] :
% 0.18/0.45 ( ( Ys2
% 0.18/0.45 = ( cons_Secrecy_KS @ X3 @ Ys4 ) )
% 0.18/0.45 & ( ( append_Secrecy_KS @ Ys4 @ Zs2 )
% 0.18/0.45 = Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_eq_Cons_conv
% 0.18/0.45 thf(fact_211_append__eq__Cons__conv,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession,Zs2: list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Ys2 @ Zs2 )
% 0.18/0.45 = ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = ( ( ( Ys2 = nil_Se901661471ession )
% 0.18/0.45 & ( Zs2
% 0.18/0.45 = ( cons_S112077679ession @ X3 @ Xs ) ) )
% 0.18/0.45 | ? [Ys4: list_S529945141ession] :
% 0.18/0.45 ( ( Ys2
% 0.18/0.45 = ( cons_S112077679ession @ X3 @ Ys4 ) )
% 0.18/0.45 & ( ( append2089414218ession @ Ys4 @ Zs2 )
% 0.18/0.45 = Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_eq_Cons_conv
% 0.18/0.45 thf(fact_212_Cons__eq__append__conv,axiom,
% 0.18/0.45 ! [X3: secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( cons_Secrecy_KS @ X3 @ Xs )
% 0.18/0.45 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 0.18/0.45 = ( ( ( Ys2 = nil_Secrecy_KS )
% 0.18/0.45 & ( ( cons_Secrecy_KS @ X3 @ Xs )
% 0.18/0.45 = Zs2 ) )
% 0.18/0.45 | ? [Ys4: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( cons_Secrecy_KS @ X3 @ Ys4 )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 & ( Xs
% 0.18/0.45 = ( append_Secrecy_KS @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Cons_eq_append_conv
% 0.18/0.45 thf(fact_213_Cons__eq__append__conv,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.18/0.45 ( ( ( cons_S112077679ession @ X3 @ Xs )
% 0.18/0.45 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.18/0.45 = ( ( ( Ys2 = nil_Se901661471ession )
% 0.18/0.45 & ( ( cons_S112077679ession @ X3 @ Xs )
% 0.18/0.45 = Zs2 ) )
% 0.18/0.45 | ? [Ys4: list_S529945141ession] :
% 0.18/0.45 ( ( ( cons_S112077679ession @ X3 @ Ys4 )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 & ( Xs
% 0.18/0.45 = ( append2089414218ession @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Cons_eq_append_conv
% 0.18/0.45 thf(fact_214_rev__exhaust,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 => ~ ! [Ys3: list_Secrecy_KS,Y3: secrecy_KS] :
% 0.18/0.45 ( Xs
% 0.18/0.45 != ( append_Secrecy_KS @ Ys3 @ ( cons_Secrecy_KS @ Y3 @ nil_Secrecy_KS ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rev_exhaust
% 0.18/0.45 thf(fact_215_rev__exhaust,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession] :
% 0.18/0.45 ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 => ~ ! [Ys3: list_S529945141ession,Y3: secrecy_Expression] :
% 0.18/0.45 ( Xs
% 0.18/0.45 != ( append2089414218ession @ Ys3 @ ( cons_S112077679ession @ Y3 @ nil_Se901661471ession ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rev_exhaust
% 0.18/0.45 thf(fact_216_rev__induct,axiom,
% 0.18/0.45 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ nil_Secrecy_KS )
% 0.18/0.45 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( P @ Xs2 )
% 0.18/0.45 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rev_induct
% 0.18/0.45 thf(fact_217_rev__induct,axiom,
% 0.18/0.45 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( P @ nil_Se901661471ession )
% 0.18/0.45 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.18/0.45 ( ( P @ Xs2 )
% 0.18/0.45 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) )
% 0.18/0.45 => ( P @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rev_induct
% 0.18/0.45 thf(fact_218_maps__simps_I1_J,axiom,
% 0.18/0.45 ! [F2: secrecy_Expression > list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( maps_S599402637ession @ F2 @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = ( append2089414218ession @ ( F2 @ X3 ) @ ( maps_S599402637ession @ F2 @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % maps_simps(1)
% 0.18/0.45 thf(fact_219_concat__eq__append__conv,axiom,
% 0.18/0.45 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.18/0.45 ( ( ( concat388015140ession @ Xss2 )
% 0.18/0.45 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.18/0.45 = ( ( ( Xss2 = nil_li311616943ession )
% 0.18/0.45 => ( ( Ys2 = nil_Se901661471ession )
% 0.18/0.45 & ( Zs2 = nil_Se901661471ession ) ) )
% 0.18/0.45 & ( ( Xss2 != nil_li311616943ession )
% 0.18/0.45 => ? [Xss1: list_l425507653ession,Xs3: list_S529945141ession,Xs4: list_S529945141ession,Xss22: list_l425507653ession] :
% 0.18/0.45 ( ( Xss2
% 0.18/0.45 = ( append1105297242ession @ Xss1 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.18/0.45 & ( Ys2
% 0.18/0.45 = ( append2089414218ession @ ( concat388015140ession @ Xss1 ) @ Xs3 ) )
% 0.18/0.45 & ( Zs2
% 0.18/0.45 = ( append2089414218ession @ Xs4 @ ( concat388015140ession @ Xss22 ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % concat_eq_append_conv
% 0.18/0.45 thf(fact_220_concat__eq__append__conv,axiom,
% 0.18/0.45 ! [Xss2: list_list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( concat_Secrecy_KS @ Xss2 )
% 0.18/0.45 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 0.18/0.45 = ( ( ( Xss2 = nil_list_Secrecy_KS )
% 0.18/0.45 => ( ( Ys2 = nil_Secrecy_KS )
% 0.18/0.45 & ( Zs2 = nil_Secrecy_KS ) ) )
% 0.18/0.45 & ( ( Xss2 != nil_list_Secrecy_KS )
% 0.18/0.45 => ? [Xss1: list_list_Secrecy_KS,Xs3: list_Secrecy_KS,Xs4: list_Secrecy_KS,Xss22: list_list_Secrecy_KS] :
% 0.18/0.45 ( ( Xss2
% 0.18/0.45 = ( append1376766698ecy_KS @ Xss1 @ ( cons_list_Secrecy_KS @ ( append_Secrecy_KS @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.18/0.45 & ( Ys2
% 0.18/0.45 = ( append_Secrecy_KS @ ( concat_Secrecy_KS @ Xss1 ) @ Xs3 ) )
% 0.18/0.45 & ( Zs2
% 0.18/0.45 = ( append_Secrecy_KS @ Xs4 @ ( concat_Secrecy_KS @ Xss22 ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % concat_eq_append_conv
% 0.18/0.45 thf(fact_221_rotate1_Osimps_I2_J,axiom,
% 0.18/0.45 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( rotate1_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rotate1.simps(2)
% 0.18/0.45 thf(fact_222_rotate1_Osimps_I2_J,axiom,
% 0.18/0.45 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( rotate1237234450ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % rotate1.simps(2)
% 0.18/0.45 thf(fact_223_butlast__snoc,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.18/0.45 ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % butlast_snoc
% 0.18/0.45 thf(fact_224_butlast__snoc,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.18/0.45 ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % butlast_snoc
% 0.18/0.45 thf(fact_225_rotate1__is__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession] :
% 0.18/0.45 ( ( ( rotate1237234450ession @ Xs )
% 0.18/0.45 = nil_Se901661471ession )
% 0.18/0.45 = ( Xs = nil_Se901661471ession ) ) ).
% 0.18/0.45
% 0.18/0.45 % rotate1_is_Nil_conv
% 0.18/0.45 thf(fact_226_rotate1__is__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( rotate1_Secrecy_KS @ Xs )
% 0.18/0.45 = nil_Secrecy_KS )
% 0.18/0.45 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.18/0.45
% 0.18/0.45 % rotate1_is_Nil_conv
% 0.18/0.45 thf(fact_227_concat__append,axiom,
% 0.18/0.45 ! [Xs: list_l425507653ession,Ys2: list_l425507653ession] :
% 0.18/0.45 ( ( concat388015140ession @ ( append1105297242ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( append2089414218ession @ ( concat388015140ession @ Xs ) @ ( concat388015140ession @ Ys2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % concat_append
% 0.18/0.45 thf(fact_228_butlast_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( butlas171474643ession @ nil_Se901661471ession )
% 0.18/0.45 = nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % butlast.simps(1)
% 0.18/0.45 thf(fact_229_butlast_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( butlast_Secrecy_KS @ nil_Secrecy_KS )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % butlast.simps(1)
% 0.18/0.45 thf(fact_230_rotate1_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( rotate1237234450ession @ nil_Se901661471ession )
% 0.18/0.45 = nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % rotate1.simps(1)
% 0.18/0.45 thf(fact_231_rotate1_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( rotate1_Secrecy_KS @ nil_Secrecy_KS )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % rotate1.simps(1)
% 0.18/0.45 thf(fact_232_butlast_Osimps_I2_J,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.18/0.45 ( ( ( Xs = nil_Secrecy_KS )
% 0.18/0.45 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = nil_Secrecy_KS ) )
% 0.18/0.45 & ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = ( cons_Secrecy_KS @ X3 @ ( butlast_Secrecy_KS @ Xs ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % butlast.simps(2)
% 0.18/0.45 thf(fact_233_butlast_Osimps_I2_J,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.18/0.45 ( ( ( Xs = nil_Se901661471ession )
% 0.18/0.45 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = nil_Se901661471ession ) )
% 0.18/0.45 & ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = ( cons_S112077679ession @ X3 @ ( butlas171474643ession @ Xs ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % butlast.simps(2)
% 0.18/0.45 thf(fact_234_concat_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( concat388015140ession @ nil_li311616943ession )
% 0.18/0.45 = nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % concat.simps(1)
% 0.18/0.45 thf(fact_235_concat_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( concat_Secrecy_KS @ nil_list_Secrecy_KS )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % concat.simps(1)
% 0.18/0.45 thf(fact_236_butlast__append,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( ( Ys2 = nil_Se901661471ession )
% 0.18/0.45 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( butlas171474643ession @ Xs ) ) )
% 0.18/0.45 & ( ( Ys2 != nil_Se901661471ession )
% 0.18/0.45 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( append2089414218ession @ Xs @ ( butlas171474643ession @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % butlast_append
% 0.18/0.45 thf(fact_237_butlast__append,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( Ys2 = nil_Secrecy_KS )
% 0.18/0.45 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( butlast_Secrecy_KS @ Xs ) ) )
% 0.18/0.45 & ( ( Ys2 != nil_Secrecy_KS )
% 0.18/0.45 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( append_Secrecy_KS @ Xs @ ( butlast_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % butlast_append
% 0.18/0.45 thf(fact_238_concat_Osimps_I2_J,axiom,
% 0.18/0.45 ! [X3: list_S529945141ession,Xs: list_l425507653ession] :
% 0.18/0.45 ( ( concat388015140ession @ ( cons_l533358079ession @ X3 @ Xs ) )
% 0.18/0.45 = ( append2089414218ession @ X3 @ ( concat388015140ession @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % concat.simps(2)
% 0.18/0.45 thf(fact_239_maps__simps_I2_J,axiom,
% 0.18/0.45 ! [F2: secrecy_Expression > list_S529945141ession] :
% 0.18/0.45 ( ( maps_S599402637ession @ F2 @ nil_Se901661471ession )
% 0.18/0.45 = nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % maps_simps(2)
% 0.18/0.45 thf(fact_240_maps__simps_I2_J,axiom,
% 0.18/0.45 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 0.18/0.45 ( ( maps_S399472669ecy_KS @ F2 @ nil_Se901661471ession )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % maps_simps(2)
% 0.18/0.45 thf(fact_241_maps__simps_I2_J,axiom,
% 0.18/0.45 ! [F2: secrecy_KS > list_S529945141ession] :
% 0.18/0.45 ( ( maps_S1434541085ession @ F2 @ nil_Secrecy_KS )
% 0.18/0.45 = nil_Se901661471ession ) ).
% 0.18/0.45
% 0.18/0.45 % maps_simps(2)
% 0.18/0.45 thf(fact_242_maps__simps_I2_J,axiom,
% 0.18/0.45 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 0.18/0.45 ( ( maps_S377605037ecy_KS @ F2 @ nil_Secrecy_KS )
% 0.18/0.45 = nil_Secrecy_KS ) ).
% 0.18/0.45
% 0.18/0.45 % maps_simps(2)
% 0.18/0.45 thf(fact_243_concat__eq__appendD,axiom,
% 0.18/0.45 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.18/0.45 ( ( ( concat388015140ession @ Xss2 )
% 0.18/0.45 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.18/0.45 => ( ( Xss2 != nil_li311616943ession )
% 0.18/0.45 => ? [Xss12: list_l425507653ession,Xs2: list_S529945141ession,Xs5: list_S529945141ession,Xss23: list_l425507653ession] :
% 0.18/0.45 ( ( Xss2
% 0.18/0.45 = ( append1105297242ession @ Xss12 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.18/0.45 & ( Ys2
% 0.18/0.45 = ( append2089414218ession @ ( concat388015140ession @ Xss12 ) @ Xs2 ) )
% 0.18/0.45 & ( Zs2
% 0.18/0.45 = ( append2089414218ession @ Xs5 @ ( concat388015140ession @ Xss23 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % concat_eq_appendD
% 0.18/0.45 thf(fact_244_append__butlast__last__id,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 => ( ( append_Secrecy_KS @ ( butlast_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( last_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) )
% 0.18/0.45 = Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_butlast_last_id
% 0.18/0.45 thf(fact_245_append__butlast__last__id,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession] :
% 0.18/0.45 ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 => ( ( append2089414218ession @ ( butlas171474643ession @ Xs ) @ ( cons_S112077679ession @ ( last_S1532390982ession @ Xs ) @ nil_Se901661471ession ) )
% 0.18/0.45 = Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_butlast_last_id
% 0.18/0.45 thf(fact_246_snoc__eq__iff__butlast,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 = ( ( Ys2 != nil_Secrecy_KS )
% 0.18/0.45 & ( ( butlast_Secrecy_KS @ Ys2 )
% 0.18/0.45 = Xs )
% 0.18/0.45 & ( ( last_Secrecy_KS @ Ys2 )
% 0.18/0.45 = X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % snoc_eq_iff_butlast
% 0.18/0.45 thf(fact_247_snoc__eq__iff__butlast,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.18/0.45 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 = ( ( Ys2 != nil_Se901661471ession )
% 0.18/0.45 & ( ( butlas171474643ession @ Ys2 )
% 0.18/0.45 = Xs )
% 0.18/0.45 & ( ( last_S1532390982ession @ Ys2 )
% 0.18/0.45 = X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % snoc_eq_iff_butlast
% 0.18/0.45 thf(fact_248_last__snoc,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.18/0.45 ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 0.18/0.45 = X3 ) ).
% 0.18/0.45
% 0.18/0.45 % last_snoc
% 0.18/0.45 thf(fact_249_last__snoc,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.18/0.45 ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 0.18/0.45 = X3 ) ).
% 0.18/0.45
% 0.18/0.45 % last_snoc
% 0.18/0.45 thf(fact_250_last__appendR,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( Ys2 != nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_S1532390982ession @ Ys2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_appendR
% 0.18/0.45 thf(fact_251_last__appendR,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( Ys2 != nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_Secrecy_KS @ Ys2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_appendR
% 0.18/0.45 thf(fact_252_last__appendL,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( Ys2 = nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_appendL
% 0.18/0.45 thf(fact_253_last__appendL,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( Ys2 = nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_appendL
% 0.18/0.45 thf(fact_254_last__ConsR,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.18/0.45 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_ConsR
% 0.18/0.45 thf(fact_255_last__ConsR,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.18/0.45 ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_ConsR
% 0.18/0.45 thf(fact_256_last__ConsL,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.18/0.45 ( ( Xs = nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_ConsL
% 0.18/0.45 thf(fact_257_last__ConsL,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.18/0.45 ( ( Xs = nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_ConsL
% 0.18/0.45 thf(fact_258_last_Osimps,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.18/0.45 ( ( ( Xs = nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = X3 ) )
% 0.18/0.45 & ( ( Xs != nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.45 = ( last_Secrecy_KS @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last.simps
% 0.18/0.45 thf(fact_259_last_Osimps,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.18/0.45 ( ( ( Xs = nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = X3 ) )
% 0.18/0.45 & ( ( Xs != nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.45 = ( last_S1532390982ession @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last.simps
% 0.18/0.45 thf(fact_260_last__append,axiom,
% 0.18/0.45 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.18/0.45 ( ( ( Ys2 = nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_S1532390982ession @ Xs ) ) )
% 0.18/0.45 & ( ( Ys2 != nil_Se901661471ession )
% 0.18/0.45 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_S1532390982ession @ Ys2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_append
% 0.18/0.45 thf(fact_261_last__append,axiom,
% 0.18/0.45 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.45 ( ( ( Ys2 = nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_Secrecy_KS @ Xs ) ) )
% 0.18/0.45 & ( ( Ys2 != nil_Secrecy_KS )
% 0.18/0.45 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.45 = ( last_Secrecy_KS @ Ys2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % last_append
% 0.18/0.45 thf(fact_262_longest__common__suffix,axiom,
% 0.18/0.45 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.45 ? [Ss: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 0.18/0.45 ( ( Xs
% 0.18/0.45 = ( append2089414218ession @ Xs5 @ Ss ) )
% 0.18/0.45 & ( Ys2
% 0.18/0.45 = ( append2089414218ession @ Ys5 @ Ss ) )
% 0.18/0.45 & ( ( Xs5 = nil_Se901661471ession )
% 0.18/0.45 | ( Ys5 = nil_Se901661471ession )
% 0.18/0.45 | ( ( last_S1532390982ession @ Xs5 )
% 0.18/0.45 != ( last_S1532390982ession @ Ys5 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % longest_common_suffix
% 0.18/0.45 thf(fact_263_longest__common__suffix,axiom,
% 0.18/0.45 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.45 ? [Ss: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.18/0.45 ( ( Xs
% 0.18/0.45 = ( append_Secrecy_KS @ Xs5 @ Ss ) )
% 0.18/0.45 & ( Ys2
% 0.18/0.45 = ( append_Secrecy_KS @ Ys5 @ Ss ) )
% 0.18/0.45 & ( ( Xs5 = nil_Secrecy_KS )
% 0.18/0.45 | ( Ys5 = nil_Secrecy_KS )
% 0.18/0.45 | ( ( last_Secrecy_KS @ Xs5 )
% 0.18/0.45 != ( last_Secrecy_KS @ Ys5 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % longest_common_suffix
% 0.18/0.45 thf(fact_264_concat__conv__foldr,axiom,
% 0.18/0.45 ( concat388015140ession
% 0.18/0.45 = ( ^ [Xss3: list_l425507653ession] : ( foldr_1531709715ession @ append2089414218ession @ Xss3 @ nil_Se901661471ession ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % concat_conv_foldr
% 0.18/0.45 thf(fact_265_concat__conv__foldr,axiom,
% 0.18/0.45 ( concat_Secrecy_KS
% 0.18/0.45 = ( ^ [Xss3: list_list_Secrecy_KS] : ( foldr_1711005747ecy_KS @ append_Secrecy_KS @ Xss3 @ nil_Secrecy_KS ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % concat_conv_foldr
% 0.18/0.45 thf(fact_266_SuccD,axiom,
% 0.18/0.45 ! [K: secrecy_Keys,Kl: set_li849033543y_Keys,Kl2: list_Secrecy_Keys] :
% 0.18/0.45 ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl @ Kl2 ) )
% 0.18/0.45 => ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl2 @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl ) ) ).
% 0.18/0.45
% 0.18/0.45 % SuccD
% 0.18/0.45 thf(fact_267_SuccD,axiom,
% 0.18/0.45 ! [K: secrecy_Secrets,Kl: set_li2007071804ecrets,Kl2: list_Secrecy_Secrets] :
% 0.18/0.45 ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl @ Kl2 ) )
% 0.18/0.45 => ( member1138497285ecrets @ ( append186372209ecrets @ Kl2 @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl ) ) ).
% 0.18/0.45
% 0.18/0.45 % SuccD
% 0.18/0.45 thf(fact_268_SuccD,axiom,
% 0.18/0.45 ! [K: secrecy_KS,Kl: set_list_Secrecy_KS,Kl2: list_Secrecy_KS] :
% 0.18/0.45 ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl @ Kl2 ) )
% 0.18/0.45 => ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl2 @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl ) ) ).
% 0.18/0.45
% 0.18/0.45 % SuccD
% 0.18/0.45 thf(fact_269_SuccD,axiom,
% 0.18/0.45 ! [K: secrecy_Expression,Kl: set_li185139947ession,Kl2: list_S529945141ession] :
% 0.18/0.45 ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl @ Kl2 ) )
% 0.18/0.45 => ( member249235532ession @ ( append2089414218ession @ Kl2 @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl ) ) ).
% 0.18/0.45
% 0.18/0.45 % SuccD
% 0.18/0.45 thf(fact_270_SuccI,axiom,
% 0.18/0.45 ! [Kl2: list_Secrecy_Keys,K: secrecy_Keys,Kl: set_li849033543y_Keys] :
% 0.18/0.45 ( ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl2 @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl )
% 0.18/0.45 => ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl @ Kl2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % SuccI
% 0.18/0.45 thf(fact_271_SuccI,axiom,
% 0.18/0.45 ! [Kl2: list_Secrecy_Secrets,K: secrecy_Secrets,Kl: set_li2007071804ecrets] :
% 0.18/0.45 ( ( member1138497285ecrets @ ( append186372209ecrets @ Kl2 @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl )
% 0.18/0.45 => ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl @ Kl2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % SuccI
% 0.18/0.45 thf(fact_272_SuccI,axiom,
% 0.18/0.46 ! [Kl2: list_Secrecy_KS,K: secrecy_KS,Kl: set_list_Secrecy_KS] :
% 0.18/0.46 ( ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl2 @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl )
% 0.18/0.46 => ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl @ Kl2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % SuccI
% 0.18/0.46 thf(fact_273_SuccI,axiom,
% 0.18/0.46 ! [Kl2: list_S529945141ession,K: secrecy_Expression,Kl: set_li185139947ession] :
% 0.18/0.46 ( ( member249235532ession @ ( append2089414218ession @ Kl2 @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl )
% 0.18/0.46 => ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl @ Kl2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % SuccI
% 0.18/0.46 thf(fact_274_empty__Shift,axiom,
% 0.18/0.46 ! [Kl: set_li849033543y_Keys,K: secrecy_Keys] :
% 0.18/0.46 ( ( member341114536y_Keys @ nil_Secrecy_Keys @ Kl )
% 0.18/0.46 => ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl @ nil_Secrecy_Keys ) )
% 0.18/0.46 => ( member341114536y_Keys @ nil_Secrecy_Keys @ ( bNF_Gr414702370y_Keys @ Kl @ K ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_Shift
% 0.18/0.46 thf(fact_275_empty__Shift,axiom,
% 0.18/0.46 ! [Kl: set_li2007071804ecrets,K: secrecy_Secrets] :
% 0.18/0.46 ( ( member1138497285ecrets @ nil_Secrecy_Secrets @ Kl )
% 0.18/0.46 => ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl @ nil_Secrecy_Secrets ) )
% 0.18/0.46 => ( member1138497285ecrets @ nil_Secrecy_Secrets @ ( bNF_Gr28627573ecrets @ Kl @ K ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_Shift
% 0.18/0.46 thf(fact_276_empty__Shift,axiom,
% 0.18/0.46 ! [Kl: set_li185139947ession,K: secrecy_Expression] :
% 0.18/0.46 ( ( member249235532ession @ nil_Se901661471ession @ Kl )
% 0.18/0.46 => ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl @ nil_Se901661471ession ) )
% 0.18/0.46 => ( member249235532ession @ nil_Se901661471ession @ ( bNF_Gr275623750ession @ Kl @ K ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_Shift
% 0.18/0.46 thf(fact_277_empty__Shift,axiom,
% 0.18/0.46 ! [Kl: set_list_Secrecy_KS,K: secrecy_KS] :
% 0.18/0.46 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ Kl )
% 0.18/0.46 => ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl @ nil_Secrecy_KS ) )
% 0.18/0.46 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( bNF_Gr660123862ecy_KS @ Kl @ K ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_Shift
% 0.18/0.46 thf(fact_278_ShiftD,axiom,
% 0.18/0.46 ! [Kl2: list_S529945141ession,Kl: set_li185139947ession,K: secrecy_Expression] :
% 0.18/0.46 ( ( member249235532ession @ Kl2 @ ( bNF_Gr275623750ession @ Kl @ K ) )
% 0.18/0.46 => ( member249235532ession @ ( cons_S112077679ession @ K @ Kl2 ) @ Kl ) ) ).
% 0.18/0.46
% 0.18/0.46 % ShiftD
% 0.18/0.46 thf(fact_279_Succ__Shift,axiom,
% 0.18/0.46 ! [Kl: set_li185139947ession,K: secrecy_Expression,Kl2: list_S529945141ession] :
% 0.18/0.46 ( ( bNF_Gr979629770ession @ ( bNF_Gr275623750ession @ Kl @ K ) @ Kl2 )
% 0.18/0.46 = ( bNF_Gr979629770ession @ Kl @ ( cons_S112077679ession @ K @ Kl2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Succ_Shift
% 0.18/0.46 thf(fact_280_rev__eq__Cons__iff,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,Y: secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( ( rev_Secrecy_KS @ Xs )
% 0.18/0.46 = ( cons_Secrecy_KS @ Y @ Ys2 ) )
% 0.18/0.46 = ( Xs
% 0.18/0.46 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Ys2 ) @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_eq_Cons_iff
% 0.18/0.46 thf(fact_281_rev__eq__Cons__iff,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( ( rev_Se1073238207ession @ Xs )
% 0.18/0.46 = ( cons_S112077679ession @ Y @ Ys2 ) )
% 0.18/0.46 = ( Xs
% 0.18/0.46 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_eq_Cons_iff
% 0.18/0.46 thf(fact_282_append_Omonoid__axioms,axiom,
% 0.18/0.46 monoid929671412ession @ append2089414218ession @ nil_Se901661471ession ).
% 0.18/0.46
% 0.18/0.46 % append.monoid_axioms
% 0.18/0.46 thf(fact_283_append_Omonoid__axioms,axiom,
% 0.18/0.46 monoid1528146052ecy_KS @ append_Secrecy_KS @ nil_Secrecy_KS ).
% 0.18/0.46
% 0.18/0.46 % append.monoid_axioms
% 0.18/0.46 thf(fact_284_rev__is__Nil__conv,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( ( rev_Se1073238207ession @ Xs )
% 0.18/0.46 = nil_Se901661471ession )
% 0.18/0.46 = ( Xs = nil_Se901661471ession ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_is_Nil_conv
% 0.18/0.46 thf(fact_285_rev__is__Nil__conv,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( ( rev_Secrecy_KS @ Xs )
% 0.18/0.46 = nil_Secrecy_KS )
% 0.18/0.46 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_is_Nil_conv
% 0.18/0.46 thf(fact_286_Nil__is__rev__conv,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( nil_Se901661471ession
% 0.18/0.46 = ( rev_Se1073238207ession @ Xs ) )
% 0.18/0.46 = ( Xs = nil_Se901661471ession ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nil_is_rev_conv
% 0.18/0.46 thf(fact_287_Nil__is__rev__conv,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( nil_Secrecy_KS
% 0.18/0.46 = ( rev_Secrecy_KS @ Xs ) )
% 0.18/0.46 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nil_is_rev_conv
% 0.18/0.46 thf(fact_288_rev__append,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( rev_Se1073238207ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( rev_Se1073238207ession @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_append
% 0.18/0.46 thf(fact_289_singleton__rev__conv,axiom,
% 0.18/0.46 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 0.18/0.46 = ( rev_Secrecy_KS @ Xs ) )
% 0.18/0.46 = ( Xs
% 0.18/0.46 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_rev_conv
% 0.18/0.46 thf(fact_290_singleton__rev__conv,axiom,
% 0.18/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.46 ( ( ( cons_S112077679ession @ X3 @ nil_Se901661471ession )
% 0.18/0.46 = ( rev_Se1073238207ession @ Xs ) )
% 0.18/0.46 = ( Xs
% 0.18/0.46 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_rev_conv
% 0.18/0.46 thf(fact_291_rev__singleton__conv,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.18/0.46 ( ( ( rev_Secrecy_KS @ Xs )
% 0.18/0.46 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.18/0.46 = ( Xs
% 0.18/0.46 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_singleton_conv
% 0.18/0.46 thf(fact_292_rev__singleton__conv,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.18/0.46 ( ( ( rev_Se1073238207ession @ Xs )
% 0.18/0.46 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.18/0.46 = ( Xs
% 0.18/0.46 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_singleton_conv
% 0.18/0.46 thf(fact_293_rev_Osimps_I1_J,axiom,
% 0.18/0.46 ( ( rev_Se1073238207ession @ nil_Se901661471ession )
% 0.18/0.46 = nil_Se901661471ession ) ).
% 0.18/0.46
% 0.18/0.46 % rev.simps(1)
% 0.18/0.46 thf(fact_294_rev_Osimps_I1_J,axiom,
% 0.18/0.46 ( ( rev_Secrecy_KS @ nil_Secrecy_KS )
% 0.18/0.46 = nil_Secrecy_KS ) ).
% 0.18/0.46
% 0.18/0.46 % rev.simps(1)
% 0.18/0.46 thf(fact_295_rev_Osimps_I2_J,axiom,
% 0.18/0.46 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( rev_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.46 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev.simps(2)
% 0.18/0.46 thf(fact_296_rev_Osimps_I2_J,axiom,
% 0.18/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.46 ( ( rev_Se1073238207ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.46 = ( append2089414218ession @ ( rev_Se1073238207ession @ Xs ) @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev.simps(2)
% 0.18/0.46 thf(fact_297_hd__rev,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 => ( ( hd_Sec357328890ession @ ( rev_Se1073238207ession @ Xs ) )
% 0.18/0.46 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_rev
% 0.18/0.46 thf(fact_298_hd__rev,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 => ( ( hd_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 0.18/0.46 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_rev
% 0.18/0.46 thf(fact_299_hd__append2,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_append2
% 0.18/0.46 thf(fact_300_hd__append2,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_append2
% 0.18/0.46 thf(fact_301_hd__concat,axiom,
% 0.18/0.46 ! [Xs: list_l425507653ession] :
% 0.18/0.46 ( ( Xs != nil_li311616943ession )
% 0.18/0.46 => ( ( ( hd_lis1623417098ession @ Xs )
% 0.18/0.46 != nil_Se901661471ession )
% 0.18/0.46 => ( ( hd_Sec357328890ession @ ( concat388015140ession @ Xs ) )
% 0.18/0.46 = ( hd_Sec357328890ession @ ( hd_lis1623417098ession @ Xs ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_concat
% 0.18/0.46 thf(fact_302_hd__concat,axiom,
% 0.18/0.46 ! [Xs: list_list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs != nil_list_Secrecy_KS )
% 0.18/0.46 => ( ( ( hd_list_Secrecy_KS @ Xs )
% 0.18/0.46 != nil_Secrecy_KS )
% 0.18/0.46 => ( ( hd_Secrecy_KS @ ( concat_Secrecy_KS @ Xs ) )
% 0.18/0.46 = ( hd_Secrecy_KS @ ( hd_list_Secrecy_KS @ Xs ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_concat
% 0.18/0.46 thf(fact_303_list_Osel_I1_J,axiom,
% 0.18/0.46 ! [X21: secrecy_Expression,X22: list_S529945141ession] :
% 0.18/0.46 ( ( hd_Sec357328890ession @ ( cons_S112077679ession @ X21 @ X22 ) )
% 0.18/0.46 = X21 ) ).
% 0.18/0.46
% 0.18/0.46 % list.sel(1)
% 0.18/0.46 thf(fact_304_longest__common__prefix,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ? [Ps: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 0.18/0.46 ( ( Xs
% 0.18/0.46 = ( append2089414218ession @ Ps @ Xs5 ) )
% 0.18/0.46 & ( Ys2
% 0.18/0.46 = ( append2089414218ession @ Ps @ Ys5 ) )
% 0.18/0.46 & ( ( Xs5 = nil_Se901661471ession )
% 0.18/0.46 | ( Ys5 = nil_Se901661471ession )
% 0.18/0.46 | ( ( hd_Sec357328890ession @ Xs5 )
% 0.18/0.46 != ( hd_Sec357328890ession @ Ys5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % longest_common_prefix
% 0.18/0.46 thf(fact_305_longest__common__prefix,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ? [Ps: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs
% 0.18/0.46 = ( append_Secrecy_KS @ Ps @ Xs5 ) )
% 0.18/0.46 & ( Ys2
% 0.18/0.46 = ( append_Secrecy_KS @ Ps @ Ys5 ) )
% 0.18/0.46 & ( ( Xs5 = nil_Secrecy_KS )
% 0.18/0.46 | ( Ys5 = nil_Secrecy_KS )
% 0.18/0.46 | ( ( hd_Secrecy_KS @ Xs5 )
% 0.18/0.46 != ( hd_Secrecy_KS @ Ys5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % longest_common_prefix
% 0.18/0.46 thf(fact_306_hd__append,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( hd_Sec357328890ession @ Ys2 ) ) )
% 0.18/0.46 & ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( hd_Sec357328890ession @ Xs ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_append
% 0.18/0.46 thf(fact_307_hd__append,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( hd_Secrecy_KS @ Ys2 ) ) )
% 0.18/0.46 & ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( hd_Secrecy_KS @ Xs ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_append
% 0.18/0.46 thf(fact_308_last__rev,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 => ( ( last_S1532390982ession @ ( rev_Se1073238207ession @ Xs ) )
% 0.18/0.46 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % last_rev
% 0.18/0.46 thf(fact_309_last__rev,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 => ( ( last_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 0.18/0.46 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % last_rev
% 0.18/0.46 thf(fact_310_rotate1__hd__tl,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 => ( ( rotate1_Secrecy_KS @ Xs )
% 0.18/0.46 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rotate1_hd_tl
% 0.18/0.46 thf(fact_311_rotate1__hd__tl,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 => ( ( rotate1237234450ession @ Xs )
% 0.18/0.46 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ nil_Se901661471ession ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rotate1_hd_tl
% 0.18/0.46 thf(fact_312_distinct__adj__append__iff,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( distin1076152135ession @ Xs )
% 0.18/0.46 & ( distin1076152135ession @ Ys2 )
% 0.18/0.46 & ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 | ( Ys2 = nil_Se901661471ession )
% 0.18/0.46 | ( ( last_S1532390982ession @ Xs )
% 0.18/0.46 != ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_append_iff
% 0.18/0.46 thf(fact_313_distinct__adj__append__iff,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( distin1495927511ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( distin1495927511ecy_KS @ Xs )
% 0.18/0.46 & ( distin1495927511ecy_KS @ Ys2 )
% 0.18/0.46 & ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 | ( Ys2 = nil_Secrecy_KS )
% 0.18/0.46 | ( ( last_Secrecy_KS @ Xs )
% 0.18/0.46 != ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_append_iff
% 0.18/0.46 thf(fact_314_distinct__adj__Cons__Cons,axiom,
% 0.18/0.46 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.46 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.18/0.46 = ( ( X3 != Y )
% 0.18/0.46 & ( distin1076152135ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_Cons_Cons
% 0.18/0.46 thf(fact_315_tl__append2,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 => ( ( tl_Sec1905266422ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % tl_append2
% 0.18/0.46 thf(fact_316_tl__append2,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 => ( ( tl_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % tl_append2
% 0.18/0.46 thf(fact_317_list_Ocollapse,axiom,
% 0.18/0.46 ! [List: list_Secrecy_KS] :
% 0.18/0.46 ( ( List != nil_Secrecy_KS )
% 0.18/0.46 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) )
% 0.18/0.46 = List ) ) ).
% 0.18/0.46
% 0.18/0.46 % list.collapse
% 0.18/0.46 thf(fact_318_list_Ocollapse,axiom,
% 0.18/0.46 ! [List: list_S529945141ession] :
% 0.18/0.46 ( ( List != nil_Se901661471ession )
% 0.18/0.46 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) )
% 0.18/0.46 = List ) ) ).
% 0.18/0.46
% 0.18/0.46 % list.collapse
% 0.18/0.46 thf(fact_319_hd__Cons__tl,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ ( tl_Secrecy_KS @ Xs ) )
% 0.18/0.46 = Xs ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_Cons_tl
% 0.18/0.46 thf(fact_320_hd__Cons__tl,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ ( tl_Sec1905266422ession @ Xs ) )
% 0.18/0.46 = Xs ) ) ).
% 0.18/0.46
% 0.18/0.46 % hd_Cons_tl
% 0.18/0.46 thf(fact_321_list_Oexpand,axiom,
% 0.18/0.46 ! [List: list_S529945141ession,List2: list_S529945141ession] :
% 0.18/0.46 ( ( ( List = nil_Se901661471ession )
% 0.18/0.46 = ( List2 = nil_Se901661471ession ) )
% 0.18/0.46 => ( ( ( List != nil_Se901661471ession )
% 0.18/0.46 => ( ( List2 != nil_Se901661471ession )
% 0.18/0.46 => ( ( ( hd_Sec357328890ession @ List )
% 0.18/0.46 = ( hd_Sec357328890ession @ List2 ) )
% 0.18/0.46 & ( ( tl_Sec1905266422ession @ List )
% 0.18/0.46 = ( tl_Sec1905266422ession @ List2 ) ) ) ) )
% 0.18/0.46 => ( List = List2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % list.expand
% 0.18/0.46 thf(fact_322_list_Oexpand,axiom,
% 0.18/0.46 ! [List: list_Secrecy_KS,List2: list_Secrecy_KS] :
% 0.18/0.46 ( ( ( List = nil_Secrecy_KS )
% 0.18/0.46 = ( List2 = nil_Secrecy_KS ) )
% 0.18/0.46 => ( ( ( List != nil_Secrecy_KS )
% 0.18/0.46 => ( ( List2 != nil_Secrecy_KS )
% 0.18/0.46 => ( ( ( hd_Secrecy_KS @ List )
% 0.18/0.46 = ( hd_Secrecy_KS @ List2 ) )
% 0.18/0.46 & ( ( tl_Secrecy_KS @ List )
% 0.18/0.46 = ( tl_Secrecy_KS @ List2 ) ) ) ) )
% 0.18/0.46 => ( List = List2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % list.expand
% 0.18/0.46 thf(fact_323_distinct__adj__singleton,axiom,
% 0.18/0.46 ! [X3: secrecy_KS] : ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_singleton
% 0.18/0.46 thf(fact_324_distinct__adj__singleton,axiom,
% 0.18/0.46 ! [X3: secrecy_Expression] : ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_singleton
% 0.18/0.46 thf(fact_325_tl__Nil,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( ( tl_Secrecy_KS @ Xs )
% 0.18/0.46 = nil_Secrecy_KS )
% 0.18/0.46 = ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 | ? [X4: secrecy_KS] :
% 0.18/0.46 ( Xs
% 0.18/0.46 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % tl_Nil
% 0.18/0.46 thf(fact_326_tl__Nil,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( ( tl_Sec1905266422ession @ Xs )
% 0.18/0.46 = nil_Se901661471ession )
% 0.18/0.46 = ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 | ? [X4: secrecy_Expression] :
% 0.18/0.46 ( Xs
% 0.18/0.46 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % tl_Nil
% 0.18/0.46 thf(fact_327_Nil__tl,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( nil_Secrecy_KS
% 0.18/0.46 = ( tl_Secrecy_KS @ Xs ) )
% 0.18/0.46 = ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 | ? [X4: secrecy_KS] :
% 0.18/0.46 ( Xs
% 0.18/0.46 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nil_tl
% 0.18/0.46 thf(fact_328_Nil__tl,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( nil_Se901661471ession
% 0.18/0.46 = ( tl_Sec1905266422ession @ Xs ) )
% 0.18/0.46 = ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 | ? [X4: secrecy_Expression] :
% 0.18/0.46 ( Xs
% 0.18/0.46 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nil_tl
% 0.18/0.46 thf(fact_329_distinct__adj__ConsD,axiom,
% 0.18/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.46 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.46 => ( distin1076152135ession @ Xs ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_ConsD
% 0.18/0.46 thf(fact_330_distinct__adj__Nil,axiom,
% 0.18/0.46 distin1076152135ession @ nil_Se901661471ession ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_Nil
% 0.18/0.46 thf(fact_331_distinct__adj__Nil,axiom,
% 0.18/0.46 distin1495927511ecy_KS @ nil_Secrecy_KS ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_Nil
% 0.18/0.46 thf(fact_332_list_Osel_I3_J,axiom,
% 0.18/0.46 ! [X21: secrecy_Expression,X22: list_S529945141ession] :
% 0.18/0.46 ( ( tl_Sec1905266422ession @ ( cons_S112077679ession @ X21 @ X22 ) )
% 0.18/0.46 = X22 ) ).
% 0.18/0.46
% 0.18/0.46 % list.sel(3)
% 0.18/0.46 thf(fact_333_list_Osel_I2_J,axiom,
% 0.18/0.46 ( ( tl_Sec1905266422ession @ nil_Se901661471ession )
% 0.18/0.46 = nil_Se901661471ession ) ).
% 0.18/0.46
% 0.18/0.46 % list.sel(2)
% 0.18/0.46 thf(fact_334_list_Osel_I2_J,axiom,
% 0.18/0.46 ( ( tl_Secrecy_KS @ nil_Secrecy_KS )
% 0.18/0.46 = nil_Secrecy_KS ) ).
% 0.18/0.46
% 0.18/0.46 % list.sel(2)
% 0.18/0.46 thf(fact_335_distinct__adj__appendD1,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 => ( distin1076152135ession @ Xs ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_appendD1
% 0.18/0.46 thf(fact_336_distinct__adj__appendD2,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 => ( distin1076152135ession @ Ys2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_appendD2
% 0.18/0.46 thf(fact_337_last__tl,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession] :
% 0.18/0.46 ( ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 | ( ( tl_Sec1905266422ession @ Xs )
% 0.18/0.46 != nil_Se901661471ession ) )
% 0.18/0.46 => ( ( last_S1532390982ession @ ( tl_Sec1905266422ession @ Xs ) )
% 0.18/0.46 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % last_tl
% 0.18/0.46 thf(fact_338_last__tl,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 | ( ( tl_Secrecy_KS @ Xs )
% 0.18/0.46 != nil_Secrecy_KS ) )
% 0.18/0.46 => ( ( last_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) )
% 0.18/0.46 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % last_tl
% 0.18/0.46 thf(fact_339_list_Oexhaust__sel,axiom,
% 0.18/0.46 ! [List: list_Secrecy_KS] :
% 0.18/0.46 ( ( List != nil_Secrecy_KS )
% 0.18/0.46 => ( List
% 0.18/0.46 = ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % list.exhaust_sel
% 0.18/0.46 thf(fact_340_list_Oexhaust__sel,axiom,
% 0.18/0.46 ! [List: list_S529945141ession] :
% 0.18/0.46 ( ( List != nil_Se901661471ession )
% 0.18/0.46 => ( List
% 0.18/0.46 = ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % list.exhaust_sel
% 0.18/0.46 thf(fact_341_distinct__adj__Cons,axiom,
% 0.18/0.46 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.18/0.46 ( ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.18/0.46 = ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 | ( ( X3
% 0.18/0.46 != ( hd_Secrecy_KS @ Xs ) )
% 0.18/0.46 & ( distin1495927511ecy_KS @ Xs ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_Cons
% 0.18/0.46 thf(fact_342_distinct__adj__Cons,axiom,
% 0.18/0.46 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.18/0.46 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.18/0.46 = ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 | ( ( X3
% 0.18/0.46 != ( hd_Sec357328890ession @ Xs ) )
% 0.18/0.46 & ( distin1076152135ession @ Xs ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % distinct_adj_Cons
% 0.18/0.46 thf(fact_343_successively__append__iff,axiom,
% 0.18/0.46 ! [P: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( succes1388047762ession @ P @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( succes1388047762ession @ P @ Xs )
% 0.18/0.46 & ( succes1388047762ession @ P @ Ys2 )
% 0.18/0.46 & ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 | ( Ys2 = nil_Se901661471ession )
% 0.18/0.46 | ( P @ ( last_S1532390982ession @ Xs ) @ ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % successively_append_iff
% 0.18/0.46 thf(fact_344_successively__append__iff,axiom,
% 0.18/0.46 ! [P: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( succes590251810ecy_KS @ P @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( succes590251810ecy_KS @ P @ Xs )
% 0.18/0.46 & ( succes590251810ecy_KS @ P @ Ys2 )
% 0.18/0.46 & ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 | ( Ys2 = nil_Secrecy_KS )
% 0.18/0.46 | ( P @ ( last_Secrecy_KS @ Xs ) @ ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % successively_append_iff
% 0.18/0.46 thf(fact_345_Cons__in__shuffles__iff,axiom,
% 0.18/0.46 ! [Z: secrecy_KS,Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( member193705948ecy_KS @ ( cons_Secrecy_KS @ Z @ Zs2 ) @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( ( Xs != nil_Secrecy_KS )
% 0.18/0.46 & ( ( hd_Secrecy_KS @ Xs )
% 0.18/0.46 = Z )
% 0.18/0.46 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) )
% 0.18/0.46 | ( ( Ys2 != nil_Secrecy_KS )
% 0.18/0.46 & ( ( hd_Secrecy_KS @ Ys2 )
% 0.18/0.46 = Z )
% 0.18/0.46 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ ( tl_Secrecy_KS @ Ys2 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Cons_in_shuffles_iff
% 0.18/0.46 thf(fact_346_Cons__in__shuffles__iff,axiom,
% 0.18/0.46 ! [Z: secrecy_Expression,Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( ( Xs != nil_Se901661471ession )
% 0.18/0.46 & ( ( hd_Sec357328890ession @ Xs )
% 0.18/0.46 = Z )
% 0.18/0.46 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) )
% 0.18/0.46 | ( ( Ys2 != nil_Se901661471ession )
% 0.18/0.46 & ( ( hd_Sec357328890ession @ Ys2 )
% 0.18/0.46 = Z )
% 0.18/0.46 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ ( tl_Sec1905266422ession @ Ys2 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Cons_in_shuffles_iff
% 0.18/0.46 thf(fact_347_Nil__in__shuffles,axiom,
% 0.18/0.46 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( Xs = nil_Se901661471ession )
% 0.18/0.46 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nil_in_shuffles
% 0.18/0.46 thf(fact_348_Nil__in__shuffles,axiom,
% 0.18/0.46 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 = ( ( Xs = nil_Secrecy_KS )
% 0.18/0.46 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nil_in_shuffles
% 0.18/0.46 thf(fact_349_shufflesE,axiom,
% 0.18/0.46 ! [Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.18/0.46 ( ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.18/0.46 => ( ( ( Zs2 = Xs )
% 0.18/0.46 => ( Ys2 != nil_Secrecy_KS ) )
% 0.18/0.46 => ( ( ( Zs2 = Ys2 )
% 0.18/0.46 => ( Xs != nil_Secrecy_KS ) )
% 0.18/0.46 => ( ! [X: secrecy_KS,Xs5: list_Secrecy_KS] :
% 0.18/0.46 ( ( Xs
% 0.18/0.46 = ( cons_Secrecy_KS @ X @ Xs5 ) )
% 0.18/0.46 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 0.18/0.46 ( ( Zs2
% 0.18/0.46 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 0.18/0.46 => ( ( X = Z2 )
% 0.18/0.46 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs5 @ Ys2 ) ) ) ) )
% 0.18/0.46 => ~ ! [Y3: secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.18/0.46 ( ( Ys2
% 0.18/0.46 = ( cons_Secrecy_KS @ Y3 @ Ys5 ) )
% 0.18/0.46 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 0.18/0.46 ( ( Zs2
% 0.18/0.46 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 0.18/0.46 => ( ( Y3 = Z2 )
% 0.18/0.46 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % shufflesE
% 0.18/0.46 thf(fact_350_shufflesE,axiom,
% 0.18/0.46 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.18/0.46 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.18/0.46 => ( ( ( Zs2 = Xs )
% 0.18/0.46 => ( Ys2 != nil_Se901661471ession ) )
% 0.18/0.46 => ( ( ( Zs2 = Ys2 )
% 0.18/0.46 => ( Xs != nil_Se901661471ession ) )
% 0.18/0.46 => ( ! [X: secrecy_Expression,Xs5: list_S529945141ession] :
% 0.18/0.46 ( ( Xs
% 0.18/0.46 = ( cons_S112077679ession @ X @ Xs5 ) )
% 0.18/0.46 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 0.18/0.46 ( ( Zs2
% 0.18/0.46 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 0.18/0.46 => ( ( X = Z2 )
% 0.18/0.46 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs5 @ Ys2 ) ) ) ) )
% 0.18/0.46 => ~ ! [Y3: secrecy_Expression,Ys5: list_S529945141ession] :
% 0.18/0.46 ( ( Ys2
% 0.18/0.46 = ( cons_S112077679ession @ Y3 @ Ys5 ) )
% 0.18/0.46 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 0.18/0.46 ( ( Zs2
% 0.18/0.46 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 0.18/0.46 => ( ( Y3 = Z2 )
% 0.18/0.46 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % shufflesE
% 0.18/0.46
% 0.18/0.46 % Conjectures (1)
% 0.18/0.46 thf(conj_0,conjecture,
% 0.18/0.46 knowle945212990e_know @ a @ ( secrecy_kKS @ m ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 2.95/1.73 ---- Embedded in THF ---
% 2.95/1.74 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.95/1.74 %%% Generated on Tue Feb 24 08:25:41 EST 2026
% 2.95/1.74 %%% using '$$dhol' embedding, version 1.3.0.
% 2.95/1.74 %%% Logic specification used:
% 2.95/1.74 %%% thf(spec, logic, $$dhol).
% 2.95/1.74
% 2.95/1.74 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2DTF26818.p
% See solution above
% 2.95/1.74 ------------------------
% 2.95/1.77 ---- Cleaned THF ---
% 2.95/1.77 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 2.95/1.77 list_l425507653ession: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 2.95/1.77 set_li185139947ession: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OSecrets_J_J,type,
% 2.95/1.77 set_li2007071804ecrets: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKeys_J_J,type,
% 2.95/1.77 set_li849033543y_Keys: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 2.95/1.77 list_list_Secrecy_KS: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 2.95/1.77 set_list_Secrecy_KS: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 list_S529945141ession: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 set_Se1942955227ession: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 2.95/1.77 list_Secrecy_Secrets: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.95/1.77 set_Secrecy_Secrets: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 2.95/1.77 list_Secrecy_Keys: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.95/1.77 set_Secrecy_Keys: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 list_Secrecy_KS: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 set_Secrecy_KS: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Secrecy____types__OExpression,type,
% 2.95/1.77 secrecy_Expression: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 2.95/1.77 secrecy_Secrets: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Secrecy____types__OspecID,type,
% 2.95/1.77 secrecy_specID: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Secrecy____types__OKeys,type,
% 2.95/1.77 secrecy_Keys: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(ty_n_t__Secrecy____types__OKS,type,
% 2.95/1.77 secrecy_KS: $tType ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKS,type,
% 2.95/1.77 bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKeys,type,
% 2.95/1.77 bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OSecrets,type,
% 2.95/1.77 bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKS,type,
% 2.95/1.77 bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OKeys,type,
% 2.95/1.77 bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OSecrets,type,
% 2.95/1.77 bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.95/1.77 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Groups_Omonoid_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 monoid929671412ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Groups_Omonoid_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 monoid1528146052ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 2.95/1.77 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowsECorrect,type,
% 2.95/1.77 knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 2.95/1.77 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknows,type,
% 2.95/1.77 knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_ListExtras_Odisjoint_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 disjoi1945222607ession: list_S529945141ession > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_ListExtras_OmemS_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 memS_S2026082737ession: secrecy_Expression > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OKS,type,
% 2.95/1.77 mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oappend_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oappend_001t__Secrecy____types__OKS,type,
% 2.95/1.77 append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oappend_001t__Secrecy____types__OKeys,type,
% 2.95/1.77 append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oappend_001t__Secrecy____types__OSecrets,type,
% 2.95/1.77 append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Obind_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 2.95/1.77 bind_S1823644515ecy_KS: list_S529945141ession > ( secrecy_Expression > list_Secrecy_KS ) > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 bind_S711229283ession: list_Secrecy_KS > ( secrecy_KS > list_S529945141ession ) > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Obind_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 2.95/1.77 bind_S645462771ecy_KS: list_Secrecy_KS > ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Obutlast_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 butlas171474643ession: list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Obutlast_001t__Secrecy____types__OKS,type,
% 2.95/1.77 butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oconcat_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 concat388015140ession: list_l425507653ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oconcat_001t__Secrecy____types__OKS,type,
% 2.95/1.77 concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 distin1076152135ession: list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OKS,type,
% 2.95/1.77 distin1495927511ecy_KS: list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OExpression_J_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 foldr_1531709715ession: ( list_S529945141ession > list_S529945141ession > list_S529945141ession ) > list_l425507653ession > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OKS_J_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 foldr_1711005747ecy_KS: ( list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oinsert_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oinsert_001t__Secrecy____types__OKS,type,
% 2.95/1.77 insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olast_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 last_S1532390982ession: list_S529945141ession > secrecy_Expression ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olast_001t__Secrecy____types__OKS,type,
% 2.95/1.77 last_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKS,type,
% 2.95/1.77 cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OKeys,type,
% 2.95/1.77 cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_OCons_001t__Secrecy____types__OSecrets,type,
% 2.95/1.77 cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 nil_li311616943ession: list_l425507653ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 nil_list_Secrecy_KS: list_list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 nil_Se901661471ession: list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKS,type,
% 2.95/1.77 nil_Secrecy_KS: list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OKeys,type,
% 2.95/1.77 nil_Secrecy_Keys: list_Secrecy_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_ONil_001t__Secrecy____types__OSecrets,type,
% 2.95/1.77 nil_Secrecy_Secrets: list_Secrecy_Secrets ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 hd_lis1623417098ession: list_l425507653ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_Ohd_001t__Secrecy____types__OKS,type,
% 2.95/1.77 hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OKS,type,
% 2.95/1.77 tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olist__ex1_001t__Secrecy____types__OKS,type,
% 2.95/1.77 list_ex1_Secrecy_KS: ( secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 2.95/1.77 listre565996059ecy_KS: ( secrecy_Expression > secrecy_KS > $o ) > list_S529945141ession > list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 2.95/1.77 listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 2.95/1.77 maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 2.95/1.77 maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omember_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Omember_001t__Secrecy____types__OKS,type,
% 2.95/1.77 member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OKS,type,
% 2.95/1.77 lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 produc1450295286ession: list_l425507653ession > list_l425507653ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OKS,type,
% 2.95/1.77 produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Orev_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Orev_001t__Secrecy____types__OKS,type,
% 2.95/1.77 rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Orotate1_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Orotate1_001t__Secrecy____types__OKS,type,
% 2.95/1.77 rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OKS,type,
% 2.95/1.77 shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Osplice_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Osplice_001t__Secrecy____types__OKS,type,
% 2.95/1.77 splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 subseq348280080ession: list_S529945141ession > list_l425507653ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OKS,type,
% 2.95/1.77 subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OKS,type,
% 2.95/1.77 succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_ODecr,type,
% 2.95/1.77 decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OEnc,type,
% 2.95/1.77 enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 2.95/1.77 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OExt,type,
% 2.95/1.77 ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OSign,type,
% 2.95/1.77 sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_Oeout,type,
% 2.95/1.77 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_Oine,type,
% 2.95/1.77 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 2.95/1.77 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OspecKeys,type,
% 2.95/1.77 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 2.95/1.77 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy_OspecSecrets,type,
% 2.95/1.77 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 2.95/1.77 secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 2.95/1.77 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 2.95/1.77 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 2.95/1.77 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 2.95/1.77 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 2.95/1.77 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 2.95/1.77 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 2.95/1.77 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 2.95/1.77 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.95/1.77 member249235532ession: list_S529945141ession > set_li185139947ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 2.95/1.77 member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 2.95/1.77 member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 2.95/1.77 member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__Secrecy____types__OExpression,type,
% 2.95/1.77 member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 2.95/1.77 member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 2.95/1.77 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 2.95/1.77 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 2.95/1.77
% 2.95/1.77 thf(sy_v_A,type,
% 2.95/1.77 a: secrecy_specID ).
% 2.95/1.77
% 2.95/1.77 thf(sy_v_m,type,
% 2.95/1.77 m: secrecy_Keys ).
% 2.95/1.77
% 2.95/1.77 thf(fact_0_assms,axiom,
% 2.95/1.77 knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_kE @ m ) @ nil_Se901661471ession ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_1_KS_Oinject_I1_J,axiom,
% 2.95/1.77 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.95/1.77 ( ( ( secrecy_kKS @ X1 )
% 2.95/1.77 = ( secrecy_kKS @ Y1 ) )
% 2.95/1.77 = ( X1 = Y1 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_2_knows4,axiom,
% 2.95/1.77 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 2.95/1.77 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.95/1.77 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K2 ) )
% 2.95/1.77 & ( knowle731562421_knows @ A @ ( enc @ K1 @ E ) ) )
% 2.95/1.77 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_3_knows5,axiom,
% 2.95/1.77 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 2.95/1.77 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.95/1.77 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K1 ) )
% 2.95/1.77 & ( knowle731562421_knows @ A @ ( sign @ K2 @ E ) ) )
% 2.95/1.77 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_4_knows6,axiom,
% 2.95/1.77 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 2.95/1.77 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 2.95/1.77 & ( knowle731562421_knows @ A @ E1 ) )
% 2.95/1.77 => ( knowle731562421_knows @ A @ ( enc @ K @ E1 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_5_knows7,axiom,
% 2.95/1.77 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 2.95/1.77 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 2.95/1.77 & ( knowle731562421_knows @ A @ E1 ) )
% 2.95/1.77 => ( knowle731562421_knows @ A @ ( sign @ K @ E1 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_6_know2knows__k,axiom,
% 2.95/1.77 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.95/1.77 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.95/1.77 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_7_know1k,axiom,
% 2.95/1.77 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 2.95/1.77 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ nil_Se901661471ession ) )
% 2.95/1.77 = ( knowle945212990e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_8_eoutKnowCorrect__L1k,axiom,
% 2.95/1.77 ! [C: secrecy_specID,M: secrecy_Keys] :
% 2.95/1.77 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 2.95/1.77 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 2.95/1.77 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 2.95/1.77 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_9_eout__know__k,axiom,
% 2.95/1.77 ! [C: secrecy_specID,M: secrecy_Keys] :
% 2.95/1.77 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 2.95/1.77 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 2.95/1.77 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 2.95/1.77 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_10_know_Osimps_I1_J,axiom,
% 2.95/1.77 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.95/1.77 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.95/1.77 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 2.95/1.77 | ( member_Secrecy_KS2 @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_11_Expression_Oinject_I1_J,axiom,
% 2.95/1.77 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.95/1.77 ( ( ( secrecy_kE @ X1 )
% 2.95/1.77 = ( secrecy_kE @ Y1 ) )
% 2.95/1.77 = ( X1 = Y1 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_12_knows__emptyexpression,axiom,
% 2.95/1.77 ! [C: secrecy_specID] : ( knowle731562421_knows @ C @ nil_Se901661471ession ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_13_KS2Expression_Osimps_I1_J,axiom,
% 2.95/1.77 ! [M: secrecy_Keys] :
% 2.95/1.77 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 2.95/1.77 = ( secrecy_kE @ M ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_14_list_Oinject,axiom,
% 2.95/1.77 ! [X21: secrecy_KS,X22: list_Secrecy_KS,Y21: secrecy_KS,Y22: list_Secrecy_KS] :
% 2.95/1.77 ( ( ( cons_Secrecy_KS @ X21 @ X22 )
% 2.95/1.77 = ( cons_Secrecy_KS @ Y21 @ Y22 ) )
% 2.95/1.77 = ( ( X21 = Y21 )
% 2.95/1.77 & ( X22 = Y22 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_15_list_Oinject,axiom,
% 2.95/1.77 ! [X21: list_S529945141ession,X22: list_l425507653ession,Y21: list_S529945141ession,Y22: list_l425507653ession] :
% 2.95/1.77 ( ( ( cons_l533358079ession @ X21 @ X22 )
% 2.95/1.77 = ( cons_l533358079ession @ Y21 @ Y22 ) )
% 2.95/1.77 = ( ( X21 = Y21 )
% 2.95/1.77 & ( X22 = Y22 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_16_list_Oinject,axiom,
% 2.95/1.77 ! [X21: list_Secrecy_KS,X22: list_list_Secrecy_KS,Y21: list_Secrecy_KS,Y22: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( ( cons_list_Secrecy_KS @ X21 @ X22 )
% 2.95/1.77 = ( cons_list_Secrecy_KS @ Y21 @ Y22 ) )
% 2.95/1.77 = ( ( X21 = Y21 )
% 2.95/1.77 & ( X22 = Y22 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_17_list_Oinject,axiom,
% 2.95/1.77 ! [X21: secrecy_Secrets,X22: list_Secrecy_Secrets,Y21: secrecy_Secrets,Y22: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( ( cons_Secrecy_Secrets @ X21 @ X22 )
% 2.95/1.77 = ( cons_Secrecy_Secrets @ Y21 @ Y22 ) )
% 2.95/1.77 = ( ( X21 = Y21 )
% 2.95/1.77 & ( X22 = Y22 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_18_list_Oinject,axiom,
% 2.95/1.77 ! [X21: secrecy_Keys,X22: list_Secrecy_Keys,Y21: secrecy_Keys,Y22: list_Secrecy_Keys] :
% 2.95/1.77 ( ( ( cons_Secrecy_Keys @ X21 @ X22 )
% 2.95/1.77 = ( cons_Secrecy_Keys @ Y21 @ Y22 ) )
% 2.95/1.77 = ( ( X21 = Y21 )
% 2.95/1.77 & ( X22 = Y22 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_19_list_Oinject,axiom,
% 2.95/1.77 ! [X21: secrecy_Expression,X22: list_S529945141ession,Y21: secrecy_Expression,Y22: list_S529945141ession] :
% 2.95/1.77 ( ( ( cons_S112077679ession @ X21 @ X22 )
% 2.95/1.77 = ( cons_S112077679ession @ Y21 @ Y22 ) )
% 2.95/1.77 = ( ( X21 = Y21 )
% 2.95/1.77 & ( X22 = Y22 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_20_know1s,axiom,
% 2.95/1.77 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 2.95/1.77 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ nil_Se901661471ession ) )
% 2.95/1.77 = ( knowle945212990e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_21_list_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X21: list_S529945141ession,X22: list_l425507653ession] :
% 2.95/1.77 ( nil_li311616943ession
% 2.95/1.77 != ( cons_l533358079ession @ X21 @ X22 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_22_list_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X21: list_Secrecy_KS,X22: list_list_Secrecy_KS] :
% 2.95/1.77 ( nil_list_Secrecy_KS
% 2.95/1.77 != ( cons_list_Secrecy_KS @ X21 @ X22 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_23_list_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X21: secrecy_Secrets,X22: list_Secrecy_Secrets] :
% 2.95/1.77 ( nil_Secrecy_Secrets
% 2.95/1.77 != ( cons_Secrecy_Secrets @ X21 @ X22 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_24_list_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X21: secrecy_Keys,X22: list_Secrecy_Keys] :
% 2.95/1.77 ( nil_Secrecy_Keys
% 2.95/1.77 != ( cons_Secrecy_Keys @ X21 @ X22 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_25_list_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X21: secrecy_KS,X22: list_Secrecy_KS] :
% 2.95/1.77 ( nil_Secrecy_KS
% 2.95/1.77 != ( cons_Secrecy_KS @ X21 @ X22 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_26_list_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X21: secrecy_Expression,X22: list_S529945141ession] :
% 2.95/1.77 ( nil_Se901661471ession
% 2.95/1.77 != ( cons_S112077679ession @ X21 @ X22 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_27_list_OdiscI,axiom,
% 2.95/1.77 ! [List: list_l425507653ession,X21: list_S529945141ession,X22: list_l425507653ession] :
% 2.95/1.77 ( ( List
% 2.95/1.77 = ( cons_l533358079ession @ X21 @ X22 ) )
% 2.95/1.77 => ( List != nil_li311616943ession ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_28_list_OdiscI,axiom,
% 2.95/1.77 ! [List: list_list_Secrecy_KS,X21: list_Secrecy_KS,X22: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( List
% 2.95/1.77 = ( cons_list_Secrecy_KS @ X21 @ X22 ) )
% 2.95/1.77 => ( List != nil_list_Secrecy_KS ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_29_list_OdiscI,axiom,
% 2.95/1.77 ! [List: list_Secrecy_Secrets,X21: secrecy_Secrets,X22: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( List
% 2.95/1.77 = ( cons_Secrecy_Secrets @ X21 @ X22 ) )
% 2.95/1.77 => ( List != nil_Secrecy_Secrets ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_30_list_OdiscI,axiom,
% 2.95/1.77 ! [List: list_Secrecy_Keys,X21: secrecy_Keys,X22: list_Secrecy_Keys] :
% 2.95/1.77 ( ( List
% 2.95/1.77 = ( cons_Secrecy_Keys @ X21 @ X22 ) )
% 2.95/1.77 => ( List != nil_Secrecy_Keys ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_31_list_OdiscI,axiom,
% 2.95/1.77 ! [List: list_Secrecy_KS,X21: secrecy_KS,X22: list_Secrecy_KS] :
% 2.95/1.77 ( ( List
% 2.95/1.77 = ( cons_Secrecy_KS @ X21 @ X22 ) )
% 2.95/1.77 => ( List != nil_Secrecy_KS ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_32_list_OdiscI,axiom,
% 2.95/1.77 ! [List: list_S529945141ession,X21: secrecy_Expression,X22: list_S529945141ession] :
% 2.95/1.77 ( ( List
% 2.95/1.77 = ( cons_S112077679ession @ X21 @ X22 ) )
% 2.95/1.77 => ( List != nil_Se901661471ession ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_33_list_Oexhaust,axiom,
% 2.95/1.77 ! [Y: list_l425507653ession] :
% 2.95/1.77 ( ( Y != nil_li311616943ession )
% 2.95/1.77 => ~ ! [X212: list_S529945141ession,X222: list_l425507653ession] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( cons_l533358079ession @ X212 @ X222 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_34_list_Oexhaust,axiom,
% 2.95/1.77 ! [Y: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( Y != nil_list_Secrecy_KS )
% 2.95/1.77 => ~ ! [X212: list_Secrecy_KS,X222: list_list_Secrecy_KS] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( cons_list_Secrecy_KS @ X212 @ X222 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_35_list_Oexhaust,axiom,
% 2.95/1.77 ! [Y: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( Y != nil_Secrecy_Secrets )
% 2.95/1.77 => ~ ! [X212: secrecy_Secrets,X222: list_Secrecy_Secrets] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( cons_Secrecy_Secrets @ X212 @ X222 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_36_list_Oexhaust,axiom,
% 2.95/1.77 ! [Y: list_Secrecy_Keys] :
% 2.95/1.77 ( ( Y != nil_Secrecy_Keys )
% 2.95/1.77 => ~ ! [X212: secrecy_Keys,X222: list_Secrecy_Keys] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( cons_Secrecy_Keys @ X212 @ X222 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_37_list_Oexhaust,axiom,
% 2.95/1.77 ! [Y: list_Secrecy_KS] :
% 2.95/1.77 ( ( Y != nil_Secrecy_KS )
% 2.95/1.77 => ~ ! [X212: secrecy_KS,X222: list_Secrecy_KS] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( cons_Secrecy_KS @ X212 @ X222 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_38_list_Oexhaust,axiom,
% 2.95/1.77 ! [Y: list_S529945141ession] :
% 2.95/1.77 ( ( Y != nil_Se901661471ession )
% 2.95/1.77 => ~ ! [X212: secrecy_Expression,X222: list_S529945141ession] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( cons_S112077679ession @ X212 @ X222 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_39_list_Oinducts,axiom,
% 2.95/1.77 ! [P: list_l425507653ession > $o,List: list_l425507653ession] :
% 2.95/1.77 ( ( P @ nil_li311616943ession )
% 2.95/1.77 => ( ! [X12: list_S529945141ession,X2: list_l425507653ession] :
% 2.95/1.77 ( ( P @ X2 )
% 2.95/1.77 => ( P @ ( cons_l533358079ession @ X12 @ X2 ) ) )
% 2.95/1.77 => ( P @ List ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_40_list_Oinducts,axiom,
% 2.95/1.77 ! [P: list_list_Secrecy_KS > $o,List: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_list_Secrecy_KS )
% 2.95/1.77 => ( ! [X12: list_Secrecy_KS,X2: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ X2 )
% 2.95/1.77 => ( P @ ( cons_list_Secrecy_KS @ X12 @ X2 ) ) )
% 2.95/1.77 => ( P @ List ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_41_list_Oinducts,axiom,
% 2.95/1.77 ! [P: list_Secrecy_Secrets > $o,List: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( P @ nil_Secrecy_Secrets )
% 2.95/1.77 => ( ! [X12: secrecy_Secrets,X2: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( P @ X2 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_Secrets @ X12 @ X2 ) ) )
% 2.95/1.77 => ( P @ List ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_42_list_Oinducts,axiom,
% 2.95/1.77 ! [P: list_Secrecy_Keys > $o,List: list_Secrecy_Keys] :
% 2.95/1.77 ( ( P @ nil_Secrecy_Keys )
% 2.95/1.77 => ( ! [X12: secrecy_Keys,X2: list_Secrecy_Keys] :
% 2.95/1.77 ( ( P @ X2 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_Keys @ X12 @ X2 ) ) )
% 2.95/1.77 => ( P @ List ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_43_list_Oinducts,axiom,
% 2.95/1.77 ! [P: list_Secrecy_KS > $o,List: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X12: secrecy_KS,X2: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ X2 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X12 @ X2 ) ) )
% 2.95/1.77 => ( P @ List ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_44_list_Oinducts,axiom,
% 2.95/1.77 ! [P: list_S529945141ession > $o,List: list_S529945141ession] :
% 2.95/1.77 ( ( P @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X12: secrecy_Expression,X2: list_S529945141ession] :
% 2.95/1.77 ( ( P @ X2 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X12 @ X2 ) ) )
% 2.95/1.77 => ( P @ List ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_45_neq__Nil__conv,axiom,
% 2.95/1.77 ! [Xs: list_l425507653ession] :
% 2.95/1.77 ( ( Xs != nil_li311616943ession )
% 2.95/1.77 = ( ? [Y2: list_S529945141ession,Ys: list_l425507653ession] :
% 2.95/1.77 ( Xs
% 2.95/1.77 = ( cons_l533358079ession @ Y2 @ Ys ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_46_neq__Nil__conv,axiom,
% 2.95/1.77 ! [Xs: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( Xs != nil_list_Secrecy_KS )
% 2.95/1.77 = ( ? [Y2: list_Secrecy_KS,Ys: list_list_Secrecy_KS] :
% 2.95/1.77 ( Xs
% 2.95/1.77 = ( cons_list_Secrecy_KS @ Y2 @ Ys ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_47_neq__Nil__conv,axiom,
% 2.95/1.77 ! [Xs: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( Xs != nil_Secrecy_Secrets )
% 2.95/1.77 = ( ? [Y2: secrecy_Secrets,Ys: list_Secrecy_Secrets] :
% 2.95/1.77 ( Xs
% 2.95/1.77 = ( cons_Secrecy_Secrets @ Y2 @ Ys ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_48_neq__Nil__conv,axiom,
% 2.95/1.77 ! [Xs: list_Secrecy_Keys] :
% 2.95/1.77 ( ( Xs != nil_Secrecy_Keys )
% 2.95/1.77 = ( ? [Y2: secrecy_Keys,Ys: list_Secrecy_Keys] :
% 2.95/1.77 ( Xs
% 2.95/1.77 = ( cons_Secrecy_Keys @ Y2 @ Ys ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_49_neq__Nil__conv,axiom,
% 2.95/1.77 ! [Xs: list_Secrecy_KS] :
% 2.95/1.77 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.77 = ( ? [Y2: secrecy_KS,Ys: list_Secrecy_KS] :
% 2.95/1.77 ( Xs
% 2.95/1.77 = ( cons_Secrecy_KS @ Y2 @ Ys ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_50_neq__Nil__conv,axiom,
% 2.95/1.77 ! [Xs: list_S529945141ession] :
% 2.95/1.77 ( ( Xs != nil_Se901661471ession )
% 2.95/1.77 = ( ? [Y2: secrecy_Expression,Ys: list_S529945141ession] :
% 2.95/1.77 ( Xs
% 2.95/1.77 = ( cons_S112077679ession @ Y2 @ Ys ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_51_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_Secrecy_Keys > list_Secrecy_KS > $o,Xs: list_Secrecy_Keys,Ys2: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_Secrecy_Keys @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [Y3: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Secrecy_Keys @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_52_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_Secrecy_Keys > list_l425507653ession > $o,Xs: list_Secrecy_Keys,Ys2: list_l425507653ession] :
% 2.95/1.77 ( ( P @ nil_Secrecy_Keys @ nil_li311616943ession )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_li311616943ession )
% 2.95/1.77 => ( ! [Y3: list_S529945141ession,Ys3: list_l425507653ession] : ( P @ nil_Secrecy_Keys @ ( cons_l533358079ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: list_S529945141ession,Ys3: list_l425507653ession] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_l533358079ession @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_53_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_Secrecy_Keys > list_list_Secrecy_KS > $o,Xs: list_Secrecy_Keys,Ys2: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_Secrecy_Keys @ nil_list_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_list_Secrecy_KS )
% 2.95/1.77 => ( ! [Y3: list_Secrecy_KS,Ys3: list_list_Secrecy_KS] : ( P @ nil_Secrecy_Keys @ ( cons_list_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: list_Secrecy_KS,Ys3: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_list_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_54_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_Secrecy_Keys > list_Secrecy_Secrets > $o,Xs: list_Secrecy_Keys,Ys2: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( P @ nil_Secrecy_Keys @ nil_Secrecy_Secrets )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_Secrecy_Secrets )
% 2.95/1.77 => ( ! [Y3: secrecy_Secrets,Ys3: list_Secrecy_Secrets] : ( P @ nil_Secrecy_Keys @ ( cons_Secrecy_Secrets @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: secrecy_Secrets,Ys3: list_Secrecy_Secrets] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_Secrecy_Secrets @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_55_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_Secrecy_Keys > list_Secrecy_Keys > $o,Xs: list_Secrecy_Keys,Ys2: list_Secrecy_Keys] :
% 2.95/1.77 ( ( P @ nil_Secrecy_Keys @ nil_Secrecy_Keys )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys] : ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ nil_Secrecy_Keys )
% 2.95/1.77 => ( ! [Y3: secrecy_Keys,Ys3: list_Secrecy_Keys] : ( P @ nil_Secrecy_Keys @ ( cons_Secrecy_Keys @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_Keys,Xs2: list_Secrecy_Keys,Y3: secrecy_Keys,Ys3: list_Secrecy_Keys] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_Keys @ X @ Xs2 ) @ ( cons_Secrecy_Keys @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_56_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [Y3: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_57_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_Secrecy_KS > list_S529945141ession > $o,Xs: list_Secrecy_KS,Ys2: list_S529945141ession] :
% 2.95/1.77 ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [Y3: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Secrecy_KS @ ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y3: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_58_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_S529945141ession > list_Secrecy_KS > $o,Xs: list_S529945141ession,Ys2: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [Y3: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Se901661471ession @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_59_list__induct2_H,axiom,
% 2.95/1.77 ! [P: list_S529945141ession > list_S529945141ession > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.77 ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [Y3: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Se901661471ession @ ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y3: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_60_splice_Oinduct,axiom,
% 2.95/1.77 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 2.95/1.77 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 2.95/1.77 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ Ys3 @ Xs2 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_61_splice_Oinduct,axiom,
% 2.95/1.77 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 2.95/1.77 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( P @ Ys3 @ Xs2 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_62_induct__list012,axiom,
% 2.95/1.77 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.95/1.77 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Zs: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ Zs )
% 2.95/1.77 => ( ( P @ ( cons_Secrecy_KS @ Y3 @ Zs ) )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Zs ) ) ) ) )
% 2.95/1.77 => ( P @ Xs ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_63_induct__list012,axiom,
% 2.95/1.77 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 2.95/1.77 ( ( P @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Zs: list_S529945141ession] :
% 2.95/1.77 ( ( P @ Zs )
% 2.95/1.77 => ( ( P @ ( cons_S112077679ession @ Y3 @ Zs ) )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Zs ) ) ) ) )
% 2.95/1.77 => ( P @ Xs ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_64_KS_Oinject_I2_J,axiom,
% 2.95/1.77 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 2.95/1.77 ( ( ( secrecy_sKS @ X23 )
% 2.95/1.77 = ( secrecy_sKS @ Y23 ) )
% 2.95/1.77 = ( X23 = Y23 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_65_KS_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 2.95/1.77 ( ( secrecy_kKS @ X1 )
% 2.95/1.77 != ( secrecy_sKS @ X23 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_66_KS_Oinduct,axiom,
% 2.95/1.77 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 2.95/1.77 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 2.95/1.77 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 2.95/1.77 => ( P @ KS ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_67_KS_Oexhaust,axiom,
% 2.95/1.77 ! [Y: secrecy_KS] :
% 2.95/1.77 ( ! [X12: secrecy_Keys] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( secrecy_kKS @ X12 ) )
% 2.95/1.77 => ~ ! [X2: secrecy_Secrets] :
% 2.95/1.77 ( Y
% 2.95/1.77 != ( secrecy_sKS @ X2 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_68_not__Cons__self2,axiom,
% 2.95/1.77 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.77 ( ( cons_S112077679ession @ X3 @ Xs )
% 2.95/1.77 != Xs ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_69_map__tailrec__rev_Oinduct,axiom,
% 2.95/1.77 ! [P: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,A0: secrecy_KS > secrecy_Expression,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 2.95/1.77 ( ! [F: secrecy_KS > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Secrecy_KS @ X_1 )
% 2.95/1.77 => ( ! [F: secrecy_KS > secrecy_Expression,A3: secrecy_KS,As: list_Secrecy_KS,Bs: list_S529945141ession] :
% 2.95/1.77 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 2.95/1.77 => ( P @ F @ ( cons_Secrecy_KS @ A3 @ As ) @ Bs ) )
% 2.95/1.77 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_70_map__tailrec__rev_Oinduct,axiom,
% 2.95/1.77 ! [P: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression,A1: list_S529945141ession,A2: list_S529945141ession] :
% 2.95/1.77 ( ! [F: secrecy_Expression > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Se901661471ession @ X_1 )
% 2.95/1.77 => ( ! [F: secrecy_Expression > secrecy_Expression,A3: secrecy_Expression,As: list_S529945141ession,Bs: list_S529945141ession] :
% 2.95/1.77 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 2.95/1.77 => ( P @ F @ ( cons_S112077679ession @ A3 @ As ) @ Bs ) )
% 2.95/1.77 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_71_list__nonempty__induct,axiom,
% 2.95/1.77 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 2.95/1.77 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.95/1.77 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( ( Xs2 != nil_Secrecy_KS )
% 2.95/1.77 => ( ( P @ Xs2 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 2.95/1.77 => ( P @ Xs ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_72_list__nonempty__induct,axiom,
% 2.95/1.77 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 2.95/1.77 ( ( Xs != nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.77 ( ( Xs2 != nil_Se901661471ession )
% 2.95/1.77 => ( ( P @ Xs2 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 2.95/1.77 => ( P @ Xs ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_73_successively_Oinduct,axiom,
% 2.95/1.77 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 2.95/1.77 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS] : ( P @ P2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.95/1.77 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ P2 @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) )
% 2.95/1.77 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_74_successively_Oinduct,axiom,
% 2.95/1.77 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 2.95/1.77 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression] : ( P @ P2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.95/1.77 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.77 ( ( P @ P2 @ ( cons_S112077679ession @ Y3 @ Xs2 ) )
% 2.95/1.77 => ( P @ P2 @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_75_remdups__adj_Oinduct,axiom,
% 2.95/1.77 ! [P: list_Secrecy_KS > $o,A0: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.95/1.77 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( ( ( X = Y3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) )
% 2.95/1.77 => ( ( ( X != Y3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) ) ) )
% 2.95/1.77 => ( P @ A0 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_76_remdups__adj_Oinduct,axiom,
% 2.95/1.77 ! [P: list_S529945141ession > $o,A0: list_S529945141ession] :
% 2.95/1.77 ( ( P @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.77 ( ( ( X = Y3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) )
% 2.95/1.77 => ( ( ( X != Y3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) ) ) )
% 2.95/1.77 => ( P @ A0 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_77_sorted__wrt_Oinduct,axiom,
% 2.95/1.77 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 2.95/1.77 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ P2 @ Ys3 )
% 2.95/1.77 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ Ys3 ) ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_78_sorted__wrt_Oinduct,axiom,
% 2.95/1.77 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 2.95/1.77 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( P @ P2 @ Ys3 )
% 2.95/1.77 => ( P @ P2 @ ( cons_S112077679ession @ X @ Ys3 ) ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_79_remdups__adj_Ocases,axiom,
% 2.95/1.77 ! [X3: list_Secrecy_KS] :
% 2.95/1.77 ( ( X3 != nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.95/1.77 => ~ ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_80_remdups__adj_Ocases,axiom,
% 2.95/1.77 ! [X3: list_S529945141ession] :
% 2.95/1.77 ( ( X3 != nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.95/1.77 => ~ ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_81_transpose_Ocases,axiom,
% 2.95/1.77 ! [X3: list_list_Secrecy_KS] :
% 2.95/1.77 ( ( X3 != nil_list_Secrecy_KS )
% 2.95/1.77 => ( ! [Xss: list_list_Secrecy_KS] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ Xss ) )
% 2.95/1.77 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Xss: list_list_Secrecy_KS] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_list_Secrecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_82_transpose_Ocases,axiom,
% 2.95/1.77 ! [X3: list_l425507653ession] :
% 2.95/1.77 ( ( X3 != nil_li311616943ession )
% 2.95/1.77 => ( ! [Xss: list_l425507653ession] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_l533358079ession @ nil_Se901661471ession @ Xss ) )
% 2.95/1.77 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession,Xss: list_l425507653ession] :
% 2.95/1.77 ( X3
% 2.95/1.77 != ( cons_l533358079ession @ ( cons_S112077679ession @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_83_mem__Collect__eq,axiom,
% 2.95/1.77 ! [A4: secrecy_Keys,P: secrecy_Keys > $o] :
% 2.95/1.77 ( ( member_Secrecy_Keys @ A4 @ ( collect_Secrecy_Keys @ P ) )
% 2.95/1.77 = ( P @ A4 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_84_mem__Collect__eq,axiom,
% 2.95/1.77 ! [A4: secrecy_KS,P: secrecy_KS > $o] :
% 2.95/1.77 ( ( member_Secrecy_KS2 @ A4 @ ( collect_Secrecy_KS @ P ) )
% 2.95/1.77 = ( P @ A4 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_85_mem__Collect__eq,axiom,
% 2.95/1.77 ! [A4: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 2.95/1.77 ( ( member2138796287ecrets @ A4 @ ( collec836099393ecrets @ P ) )
% 2.95/1.77 = ( P @ A4 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_86_Collect__mem__eq,axiom,
% 2.95/1.77 ! [A: set_Secrecy_Keys] :
% 2.95/1.77 ( ( collect_Secrecy_Keys
% 2.95/1.77 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 2.95/1.77 = A ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_87_Collect__mem__eq,axiom,
% 2.95/1.77 ! [A: set_Secrecy_KS] :
% 2.95/1.77 ( ( collect_Secrecy_KS
% 2.95/1.77 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS2 @ X4 @ A ) )
% 2.95/1.77 = A ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_88_Collect__mem__eq,axiom,
% 2.95/1.77 ! [A: set_Secrecy_Secrets] :
% 2.95/1.77 ( ( collec836099393ecrets
% 2.95/1.77 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 2.95/1.77 = A ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_89_shuffles_Oinduct,axiom,
% 2.95/1.77 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 2.95/1.77 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 2.95/1.77 => ( ! [Xs2: list_Secrecy_KS] : ( P @ Xs2 @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y3: secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( P @ Xs2 @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_90_shuffles_Oinduct,axiom,
% 2.95/1.77 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 2.95/1.77 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 2.95/1.77 => ( ! [Xs2: list_S529945141ession] : ( P @ Xs2 @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y3: secrecy_Expression,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( P @ Xs2 @ ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) )
% 2.95/1.77 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_91_know_Osimps_I2_J,axiom,
% 2.95/1.77 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.95/1.77 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.95/1.77 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 2.95/1.77 | ( member_Secrecy_KS2 @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_92_Expression2KSL_Osimps_I1_J,axiom,
% 2.95/1.77 ( ( secrec1371625429on2KSL @ nil_Se901661471ession )
% 2.95/1.77 = nil_Secrecy_KS ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_93_insert__Nil,axiom,
% 2.95/1.77 ! [X3: secrecy_KS] :
% 2.95/1.77 ( ( insert_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 2.95/1.77 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_94_insert__Nil,axiom,
% 2.95/1.77 ! [X3: secrecy_Expression] :
% 2.95/1.77 ( ( insert1173886601ession @ X3 @ nil_Se901661471ession )
% 2.95/1.77 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_95_list__ex1__simps_I1_J,axiom,
% 2.95/1.77 ! [P: secrecy_Expression > $o] :
% 2.95/1.77 ~ ( list_e1486860828ession @ P @ nil_Se901661471ession ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_96_list__ex1__simps_I1_J,axiom,
% 2.95/1.77 ! [P: secrecy_KS > $o] :
% 2.95/1.77 ~ ( list_ex1_Secrecy_KS @ P @ nil_Secrecy_KS ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_97_eoutKnowsECorrect__def,axiom,
% 2.95/1.77 ( knowle1268625169orrect
% 2.95/1.77 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 2.95/1.77 ( ( eout @ C2 @ E2 )
% 2.95/1.77 = ( ? [K3: secrecy_Keys] :
% 2.95/1.77 ( ( E2
% 2.95/1.77 = ( secrecy_kE @ K3 ) )
% 2.95/1.77 & ( member_Secrecy_Keys @ K3 @ ( specKeys @ C2 ) ) )
% 2.95/1.77 | ? [S: secrecy_Secrets] :
% 2.95/1.77 ( ( E2
% 2.95/1.77 = ( secrecy_sE @ S ) )
% 2.95/1.77 & ( member2138796287ecrets @ S @ ( specSecrets @ C2 ) ) )
% 2.95/1.77 | ( knowle731562421_knows @ C2 @ ( cons_S112077679ession @ E2 @ nil_Se901661471ession ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_98_eoutKnowsECorrect__L1,axiom,
% 2.95/1.77 ! [C: secrecy_specID,E: secrecy_Expression] :
% 2.95/1.77 ( ( knowle1268625169orrect @ C @ E )
% 2.95/1.77 => ( ( eout @ C @ E )
% 2.95/1.77 => ( ? [K4: secrecy_Keys] :
% 2.95/1.77 ( ( E
% 2.95/1.77 = ( secrecy_kE @ K4 ) )
% 2.95/1.77 & ( member_Secrecy_Keys @ K4 @ ( specKeys @ C ) ) )
% 2.95/1.77 | ? [S2: secrecy_Secrets] :
% 2.95/1.77 ( ( E
% 2.95/1.77 = ( secrecy_sE @ S2 ) )
% 2.95/1.77 & ( member2138796287ecrets @ S2 @ ( specSecrets @ C ) ) )
% 2.95/1.77 | ( knowle731562421_knows @ C @ ( cons_S112077679ession @ E @ nil_Se901661471ession ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_99_map__tailrec__rev_Oelims,axiom,
% 2.95/1.77 ! [X3: secrecy_KS > secrecy_Expression,Xa: list_Secrecy_KS,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 2.95/1.77 ( ( ( map_ta623472337ession @ X3 @ Xa @ Xb )
% 2.95/1.77 = Y )
% 2.95/1.77 => ( ( ( Xa = nil_Secrecy_KS )
% 2.95/1.77 => ( Y != Xb ) )
% 2.95/1.77 => ~ ! [A3: secrecy_KS,As: list_Secrecy_KS] :
% 2.95/1.77 ( ( Xa
% 2.95/1.77 = ( cons_Secrecy_KS @ A3 @ As ) )
% 2.95/1.77 => ( Y
% 2.95/1.77 != ( map_ta623472337ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_100_map__tailrec__rev_Oelims,axiom,
% 2.95/1.77 ! [X3: secrecy_Expression > secrecy_Expression,Xa: list_S529945141ession,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 2.95/1.77 ( ( ( map_ta1624757057ession @ X3 @ Xa @ Xb )
% 2.95/1.77 = Y )
% 2.95/1.77 => ( ( ( Xa = nil_Se901661471ession )
% 2.95/1.77 => ( Y != Xb ) )
% 2.95/1.77 => ~ ! [A3: secrecy_Expression,As: list_S529945141ession] :
% 2.95/1.77 ( ( Xa
% 2.95/1.77 = ( cons_S112077679ession @ A3 @ As ) )
% 2.95/1.77 => ( Y
% 2.95/1.77 != ( map_ta1624757057ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_101_notSpecKeysSecretsExpr__L1,axiom,
% 2.95/1.77 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 2.95/1.77 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 2.95/1.77 => ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ nil_Se901661471ession ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_102_Expression_Oinject_I2_J,axiom,
% 2.95/1.77 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 2.95/1.77 ( ( ( secrecy_sE @ X23 )
% 2.95/1.77 = ( secrecy_sE @ Y23 ) )
% 2.95/1.77 = ( X23 = Y23 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_103_Expression_Odistinct_I1_J,axiom,
% 2.95/1.77 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 2.95/1.77 ( ( secrecy_kE @ X1 )
% 2.95/1.77 != ( secrecy_sE @ X23 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_104_notSpecKeysSecretsExpr__L2,axiom,
% 2.95/1.77 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 2.95/1.77 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 2.95/1.77 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_105_map__tailrec__rev_Osimps_I2_J,axiom,
% 2.95/1.77 ! [F2: secrecy_Expression > secrecy_Expression,A4: secrecy_Expression,As2: list_S529945141ession,Bs2: list_S529945141ession] :
% 2.95/1.77 ( ( map_ta1624757057ession @ F2 @ ( cons_S112077679ession @ A4 @ As2 ) @ Bs2 )
% 2.95/1.77 = ( map_ta1624757057ession @ F2 @ As2 @ ( cons_S112077679ession @ ( F2 @ A4 ) @ Bs2 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_106_KS2Expression_Osimps_I2_J,axiom,
% 2.95/1.77 ! [M: secrecy_Secrets] :
% 2.95/1.77 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 2.95/1.77 = ( secrecy_sE @ M ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_107_eoutKnowCorrect__L1s,axiom,
% 2.95/1.77 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 2.95/1.77 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 2.95/1.77 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 2.95/1.77 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 2.95/1.77 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_108_eout__know__s,axiom,
% 2.95/1.77 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 2.95/1.77 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 2.95/1.77 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 2.95/1.77 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 2.95/1.77 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_109_product__lists_Osimps_I1_J,axiom,
% 2.95/1.77 ( ( produc1450295286ession @ nil_li311616943ession )
% 2.95/1.77 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_110_product__lists_Osimps_I1_J,axiom,
% 2.95/1.77 ( ( produc713695622ecy_KS @ nil_list_Secrecy_KS )
% 2.95/1.77 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_111_subseqs_Osimps_I1_J,axiom,
% 2.95/1.77 ( ( subseq348280080ession @ nil_Se901661471ession )
% 2.95/1.77 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_112_subseqs_Osimps_I1_J,axiom,
% 2.95/1.77 ( ( subseqs_Secrecy_KS @ nil_Secrecy_KS )
% 2.95/1.77 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_113_DecrEnc,axiom,
% 2.95/1.77 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 2.95/1.77 ( ( encrDecrKeys @ K12 @ K22 )
% 2.95/1.77 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 2.95/1.77 = E3 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_114_ExtSign,axiom,
% 2.95/1.77 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 2.95/1.77 ( ( encrDecrKeys @ K12 @ K22 )
% 2.95/1.77 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 2.95/1.77 = E3 ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_115_notSpecKeysSecretsExpr__def,axiom,
% 2.95/1.77 ( notSpe1586871396tsExpr
% 2.95/1.77 = ( ^ [P3: secrecy_specID,E2: list_S529945141ession] :
% 2.95/1.77 ( ! [X4: secrecy_Keys] :
% 2.95/1.77 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E2 )
% 2.95/1.77 => ~ ( member_Secrecy_KS2 @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 2.95/1.77 & ! [Y2: secrecy_Secrets] :
% 2.95/1.77 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y2 ) @ E2 )
% 2.95/1.77 => ~ ( member_Secrecy_KS2 @ ( secrecy_sKS @ Y2 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_116_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.95/1.77 ! [Less: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.77 ~ ( lexord948960489ecy_KS @ Less @ ( cons_Secrecy_KS @ X3 @ Xs ) @ nil_Secrecy_KS ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_117_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.77 ~ ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ nil_Se901661471ession ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_118_bind__simps_I1_J,axiom,
% 2.95/1.77 ! [F2: secrecy_Expression > list_S529945141ession] :
% 2.95/1.77 ( ( bind_S815874003ession @ nil_Se901661471ession @ F2 )
% 2.95/1.77 = nil_Se901661471ession ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_119_bind__simps_I1_J,axiom,
% 2.95/1.77 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 2.95/1.77 ( ( bind_S1823644515ecy_KS @ nil_Se901661471ession @ F2 )
% 2.95/1.77 = nil_Secrecy_KS ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_120_bind__simps_I1_J,axiom,
% 2.95/1.77 ! [F2: secrecy_KS > list_S529945141ession] :
% 2.95/1.77 ( ( bind_S711229283ession @ nil_Secrecy_KS @ F2 )
% 2.95/1.77 = nil_Se901661471ession ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_121_bind__simps_I1_J,axiom,
% 2.95/1.77 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 2.95/1.77 ( ( bind_S645462771ecy_KS @ nil_Secrecy_KS @ F2 )
% 2.95/1.77 = nil_Secrecy_KS ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_122_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 2.95/1.77 ( ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) )
% 2.95/1.77 = ( ( Less @ X3 @ Y )
% 2.95/1.77 | ( ~ ( Less @ Y @ X3 )
% 2.95/1.77 & ( lexord1123423577ession @ Less @ Xs @ Ys2 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_123_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_124_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.95/1.77 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_125_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession] :
% 2.95/1.77 ( ( lexord1123423577ession @ Less @ Xs @ nil_Se901661471ession )
% 2.95/1.77 = ( Xs = nil_Se901661471ession ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_126_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.95/1.77 ! [Less: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 2.95/1.77 ( ( lexord948960489ecy_KS @ Less @ Xs @ nil_Secrecy_KS )
% 2.95/1.77 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_127_ord_Olexordp__eq_OCons__eq,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.77 ( ~ ( Less @ X3 @ Y )
% 2.95/1.77 => ( ~ ( Less @ Y @ X3 )
% 2.95/1.77 => ( ( lexord1123423577ession @ Less @ Xs @ Ys2 )
% 2.95/1.77 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_128_ord_Olexordp__eq_OCons,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.77 ( ( Less @ X3 @ Y )
% 2.95/1.77 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_129_ord_Olexordp__eq_ONil,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_130_ord_Olexordp__eq_ONil,axiom,
% 2.95/1.77 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_131_ord_Olexordp__eq_Oinducts,axiom,
% 2.95/1.77 ! [Less: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X23: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 2.95/1.77 ( ( lexord948960489ecy_KS @ Less @ X1 @ X23 )
% 2.95/1.77 => ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 2.95/1.77 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( Less @ X @ Y3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ~ ( Less @ X @ Y3 )
% 2.95/1.77 => ( ~ ( Less @ Y3 @ X )
% 2.95/1.77 => ( ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 )
% 2.95/1.77 => ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) ) ) )
% 2.95/1.77 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_132_ord_Olexordp__eq_Oinducts,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X23: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 2.95/1.77 ( ( lexord1123423577ession @ Less @ X1 @ X23 )
% 2.95/1.77 => ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( Less @ X @ Y3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ~ ( Less @ X @ Y3 )
% 2.95/1.77 => ( ~ ( Less @ Y3 @ X )
% 2.95/1.77 => ( ( lexord1123423577ession @ Less @ Xs2 @ Ys3 )
% 2.95/1.77 => ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) ) ) )
% 2.95/1.77 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_133_ord_Olexordp__eq_Osimps,axiom,
% 2.95/1.77 ( lexord948960489ecy_KS
% 2.95/1.77 = ( ^ [Less2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 2.95/1.77 ( ? [Ys: list_Secrecy_KS] :
% 2.95/1.77 ( ( A12 = nil_Secrecy_KS )
% 2.95/1.77 & ( A22 = Ys ) )
% 2.95/1.77 | ? [X4: secrecy_KS,Y2: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 2.95/1.77 & ( Less2 @ X4 @ Y2 ) )
% 2.95/1.77 | ? [X4: secrecy_KS,Y2: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 2.95/1.77 & ~ ( Less2 @ X4 @ Y2 )
% 2.95/1.77 & ~ ( Less2 @ Y2 @ X4 )
% 2.95/1.77 & ( lexord948960489ecy_KS @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_134_ord_Olexordp__eq_Osimps,axiom,
% 2.95/1.77 ( lexord1123423577ession
% 2.95/1.77 = ( ^ [Less2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 2.95/1.77 ( ? [Ys: list_S529945141ession] :
% 2.95/1.77 ( ( A12 = nil_Se901661471ession )
% 2.95/1.77 & ( A22 = Ys ) )
% 2.95/1.77 | ? [X4: secrecy_Expression,Y2: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 2.95/1.77 & ( Less2 @ X4 @ Y2 ) )
% 2.95/1.77 | ? [X4: secrecy_Expression,Y2: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 2.95/1.77 & ~ ( Less2 @ X4 @ Y2 )
% 2.95/1.77 & ~ ( Less2 @ Y2 @ X4 )
% 2.95/1.77 & ( lexord1123423577ession @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_135_ord_Olexordp__eq_Ocases,axiom,
% 2.95/1.77 ! [Less: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 2.95/1.77 ( ( lexord948960489ecy_KS @ Less @ A1 @ A2 )
% 2.95/1.77 => ( ( A1 != nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS] :
% 2.95/1.77 ( ? [Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( A1
% 2.95/1.77 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.95/1.77 => ! [Y3: secrecy_KS] :
% 2.95/1.77 ( ? [Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( A2
% 2.95/1.77 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ~ ( Less @ X @ Y3 ) ) )
% 2.95/1.77 => ~ ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( ( A1
% 2.95/1.77 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.95/1.77 => ! [Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( A2
% 2.95/1.77 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ~ ( Less @ X @ Y3 )
% 2.95/1.77 => ( ~ ( Less @ Y3 @ X )
% 2.95/1.77 => ~ ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_136_ord_Olexordp__eq_Ocases,axiom,
% 2.95/1.77 ! [Less: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 2.95/1.77 ( ( lexord1123423577ession @ Less @ A1 @ A2 )
% 2.95/1.77 => ( ( A1 != nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression] :
% 2.95/1.77 ( ? [Xs2: list_S529945141ession] :
% 2.95/1.77 ( A1
% 2.95/1.77 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.95/1.77 => ! [Y3: secrecy_Expression] :
% 2.95/1.77 ( ? [Ys3: list_S529945141ession] :
% 2.95/1.77 ( A2
% 2.95/1.77 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ~ ( Less @ X @ Y3 ) ) )
% 2.95/1.77 => ~ ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.77 ( ( A1
% 2.95/1.77 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.95/1.77 => ! [Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( A2
% 2.95/1.77 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ~ ( Less @ X @ Y3 )
% 2.95/1.77 => ( ~ ( Less @ Y3 @ X )
% 2.95/1.77 => ~ ( lexord1123423577ession @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_137_mem_Osimps_I1_J,axiom,
% 2.95/1.77 ! [X3: secrecy_KS] :
% 2.95/1.77 ~ ( mem_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_138_mem_Osimps_I1_J,axiom,
% 2.95/1.77 ! [X3: secrecy_Expression] :
% 2.95/1.77 ~ ( mem_Se1967555118ession @ X3 @ nil_Se901661471ession ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_139_mem_Osimps_I2_J,axiom,
% 2.95/1.77 ! [X3: secrecy_Expression,Y: secrecy_Expression,L: list_S529945141ession] :
% 2.95/1.77 ( ( mem_Se1967555118ession @ X3 @ ( cons_S112077679ession @ Y @ L ) )
% 2.95/1.77 = ( ( X3 = Y )
% 2.95/1.77 | ( mem_Se1967555118ession @ X3 @ L ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_140_listrelp_Oinducts,axiom,
% 2.95/1.77 ! [R: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X23: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 2.95/1.77 ( ( listre788412843ecy_KS @ R @ X1 @ X23 )
% 2.95/1.77 => ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( R @ X @ Y3 )
% 2.95/1.77 => ( ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 )
% 2.95/1.77 => ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) ) )
% 2.95/1.77 => ( P @ X1 @ X23 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_141_listrelp_Oinducts,axiom,
% 2.95/1.77 ! [R: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X23: list_S529945141ession,P: list_Secrecy_KS > list_S529945141ession > $o] :
% 2.95/1.77 ( ( listre1601064475ession @ R @ X1 @ X23 )
% 2.95/1.77 => ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_KS,Y3: secrecy_Expression,Xs2: list_Secrecy_KS,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( R @ X @ Y3 )
% 2.95/1.77 => ( ( listre1601064475ession @ R @ Xs2 @ Ys3 )
% 2.95/1.77 => ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) ) )
% 2.95/1.77 => ( P @ X1 @ X23 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_142_listrelp_Oinducts,axiom,
% 2.95/1.77 ! [R: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X23: list_Secrecy_KS,P: list_S529945141ession > list_Secrecy_KS > $o] :
% 2.95/1.77 ( ( listre565996059ecy_KS @ R @ X1 @ X23 )
% 2.95/1.77 => ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Y3: secrecy_KS,Xs2: list_S529945141ession,Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( R @ X @ Y3 )
% 2.95/1.77 => ( ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 )
% 2.95/1.77 => ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y3 @ Ys3 ) ) ) ) )
% 2.95/1.77 => ( P @ X1 @ X23 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_143_listrelp_Oinducts,axiom,
% 2.95/1.77 ! [R: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X23: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 2.95/1.77 ( ( listre84909707ession @ R @ X1 @ X23 )
% 2.95/1.77 => ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 2.95/1.77 => ( ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( R @ X @ Y3 )
% 2.95/1.77 => ( ( listre84909707ession @ R @ Xs2 @ Ys3 )
% 2.95/1.77 => ( ( P @ Xs2 @ Ys3 )
% 2.95/1.77 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y3 @ Ys3 ) ) ) ) )
% 2.95/1.77 => ( P @ X1 @ X23 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_144_listrelp_Osimps,axiom,
% 2.95/1.77 ( listre788412843ecy_KS
% 2.95/1.77 = ( ^ [R2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 2.95/1.77 ( ( ( A12 = nil_Secrecy_KS )
% 2.95/1.77 & ( A22 = nil_Secrecy_KS ) )
% 2.95/1.77 | ? [X4: secrecy_KS,Y2: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 2.95/1.77 & ( R2 @ X4 @ Y2 )
% 2.95/1.77 & ( listre788412843ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_145_listrelp_Osimps,axiom,
% 2.95/1.77 ( listre1601064475ession
% 2.95/1.77 = ( ^ [R2: secrecy_KS > secrecy_Expression > $o,A12: list_Secrecy_KS,A22: list_S529945141ession] :
% 2.95/1.77 ( ( ( A12 = nil_Secrecy_KS )
% 2.95/1.77 & ( A22 = nil_Se901661471ession ) )
% 2.95/1.77 | ? [X4: secrecy_KS,Y2: secrecy_Expression,Xs3: list_Secrecy_KS,Ys: list_S529945141ession] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 2.95/1.77 & ( R2 @ X4 @ Y2 )
% 2.95/1.77 & ( listre1601064475ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_146_listrelp_Osimps,axiom,
% 2.95/1.77 ( listre565996059ecy_KS
% 2.95/1.77 = ( ^ [R2: secrecy_Expression > secrecy_KS > $o,A12: list_S529945141ession,A22: list_Secrecy_KS] :
% 2.95/1.77 ( ( ( A12 = nil_Se901661471ession )
% 2.95/1.77 & ( A22 = nil_Secrecy_KS ) )
% 2.95/1.77 | ? [X4: secrecy_Expression,Y2: secrecy_KS,Xs3: list_S529945141ession,Ys: list_Secrecy_KS] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_Secrecy_KS @ Y2 @ Ys ) )
% 2.95/1.77 & ( R2 @ X4 @ Y2 )
% 2.95/1.77 & ( listre565996059ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_147_listrelp_Osimps,axiom,
% 2.95/1.77 ( listre84909707ession
% 2.95/1.77 = ( ^ [R2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 2.95/1.77 ( ( ( A12 = nil_Se901661471ession )
% 2.95/1.77 & ( A22 = nil_Se901661471ession ) )
% 2.95/1.77 | ? [X4: secrecy_Expression,Y2: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 2.95/1.77 ( ( A12
% 2.95/1.77 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 2.95/1.77 & ( A22
% 2.95/1.77 = ( cons_S112077679ession @ Y2 @ Ys ) )
% 2.95/1.77 & ( R2 @ X4 @ Y2 )
% 2.95/1.77 & ( listre84909707ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_148_listrelp_Ocases,axiom,
% 2.95/1.77 ! [R: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 2.95/1.77 ( ( listre788412843ecy_KS @ R @ A1 @ A2 )
% 2.95/1.77 => ( ( ( A1 = nil_Secrecy_KS )
% 2.95/1.77 => ( A2 != nil_Secrecy_KS ) )
% 2.95/1.77 => ~ ! [X: secrecy_KS,Y3: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( ( A1
% 2.95/1.77 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.95/1.77 => ! [Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( A2
% 2.95/1.77 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ( R @ X @ Y3 )
% 2.95/1.77 => ~ ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_149_listrelp_Ocases,axiom,
% 2.95/1.77 ! [R: secrecy_KS > secrecy_Expression > $o,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 2.95/1.77 ( ( listre1601064475ession @ R @ A1 @ A2 )
% 2.95/1.77 => ( ( ( A1 = nil_Secrecy_KS )
% 2.95/1.77 => ( A2 != nil_Se901661471ession ) )
% 2.95/1.77 => ~ ! [X: secrecy_KS,Y3: secrecy_Expression,Xs2: list_Secrecy_KS] :
% 2.95/1.77 ( ( A1
% 2.95/1.77 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.95/1.77 => ! [Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( A2
% 2.95/1.77 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ( R @ X @ Y3 )
% 2.95/1.77 => ~ ( listre1601064475ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_150_listrelp_Ocases,axiom,
% 2.95/1.77 ! [R: secrecy_Expression > secrecy_KS > $o,A1: list_S529945141ession,A2: list_Secrecy_KS] :
% 2.95/1.77 ( ( listre565996059ecy_KS @ R @ A1 @ A2 )
% 2.95/1.77 => ( ( ( A1 = nil_Se901661471ession )
% 2.95/1.77 => ( A2 != nil_Secrecy_KS ) )
% 2.95/1.77 => ~ ! [X: secrecy_Expression,Y3: secrecy_KS,Xs2: list_S529945141ession] :
% 2.95/1.77 ( ( A1
% 2.95/1.77 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.95/1.77 => ! [Ys3: list_Secrecy_KS] :
% 2.95/1.77 ( ( A2
% 2.95/1.77 = ( cons_Secrecy_KS @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ( R @ X @ Y3 )
% 2.95/1.77 => ~ ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_151_listrelp_Ocases,axiom,
% 2.95/1.77 ! [R: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 2.95/1.77 ( ( listre84909707ession @ R @ A1 @ A2 )
% 2.95/1.77 => ( ( ( A1 = nil_Se901661471ession )
% 2.95/1.77 => ( A2 != nil_Se901661471ession ) )
% 2.95/1.77 => ~ ! [X: secrecy_Expression,Y3: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.77 ( ( A1
% 2.95/1.77 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.95/1.77 => ! [Ys3: list_S529945141ession] :
% 2.95/1.77 ( ( A2
% 2.95/1.77 = ( cons_S112077679ession @ Y3 @ Ys3 ) )
% 2.95/1.77 => ( ( R @ X @ Y3 )
% 2.95/1.77 => ~ ( listre84909707ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_152_listrelp_OCons,axiom,
% 2.95/1.77 ! [R: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.77 ( ( R @ X3 @ Y )
% 2.95/1.77 => ( ( listre84909707ession @ R @ Xs @ Ys2 )
% 2.95/1.77 => ( listre84909707ession @ R @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ).
% 2.95/1.77
% 2.95/1.77 thf(fact_153_listrelp_ONil,axiom,
% 2.95/1.77 ! [R: secrecy_Expression > secrecy_Expression > $o] : ( listre84909707ession @ R @ nil_Se901661471ession @ nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_154_listrelp_ONil,axiom,
% 2.95/1.78 ! [R: secrecy_Expression > secrecy_KS > $o] : ( listre565996059ecy_KS @ R @ nil_Se901661471ession @ nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_155_listrelp_ONil,axiom,
% 2.95/1.78 ! [R: secrecy_KS > secrecy_Expression > $o] : ( listre1601064475ession @ R @ nil_Secrecy_KS @ nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_156_listrelp_ONil,axiom,
% 2.95/1.78 ! [R: secrecy_KS > secrecy_KS > $o] : ( listre788412843ecy_KS @ R @ nil_Secrecy_KS @ nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_157_mem__memS__eq,axiom,
% 2.95/1.78 mem_Se1967555118ession = memS_S2026082737ession ).
% 2.95/1.78
% 2.95/1.78 thf(fact_158_mem__notdisjoint,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,L1: list_S529945141ession,L2: list_S529945141ession] :
% 2.95/1.78 ( ( mem_Se1967555118ession @ X3 @ L1 )
% 2.95/1.78 => ( ( mem_Se1967555118ession @ X3 @ L2 )
% 2.95/1.78 => ~ ( disjoi1945222607ession @ L1 @ L2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_159_member__rec_I2_J,axiom,
% 2.95/1.78 ! [Y: secrecy_Expression] :
% 2.95/1.78 ~ ( member2020590922ession @ nil_Se901661471ession @ Y ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_160_member__rec_I2_J,axiom,
% 2.95/1.78 ! [Y: secrecy_KS] :
% 2.95/1.78 ~ ( member_Secrecy_KS @ nil_Secrecy_KS @ Y ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_161_member__rec_I1_J,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression] :
% 2.95/1.78 ( ( member2020590922ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Y )
% 2.95/1.78 = ( ( X3 = Y )
% 2.95/1.78 | ( member2020590922ession @ Xs @ Y ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_162_splice_Oelims,axiom,
% 2.95/1.78 ! [X3: list_Secrecy_KS,Xa: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( splice_Secrecy_KS @ X3 @ Xa )
% 2.95/1.78 = Y )
% 2.95/1.78 => ( ( ( X3 = nil_Secrecy_KS )
% 2.95/1.78 => ( Y != Xa ) )
% 2.95/1.78 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.78 ( ( X3
% 2.95/1.78 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 2.95/1.78 => ( Y
% 2.95/1.78 != ( cons_Secrecy_KS @ X @ ( splice_Secrecy_KS @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_163_splice_Oelims,axiom,
% 2.95/1.78 ! [X3: list_S529945141ession,Xa: list_S529945141ession,Y: list_S529945141ession] :
% 2.95/1.78 ( ( ( splice1390717708ession @ X3 @ Xa )
% 2.95/1.78 = Y )
% 2.95/1.78 => ( ( ( X3 = nil_Se901661471ession )
% 2.95/1.78 => ( Y != Xa ) )
% 2.95/1.78 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.78 ( ( X3
% 2.95/1.78 = ( cons_S112077679ession @ X @ Xs2 ) )
% 2.95/1.78 => ( Y
% 2.95/1.78 != ( cons_S112077679ession @ X @ ( splice1390717708ession @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_164_append_Oassoc,axiom,
% 2.95/1.78 ! [A4: list_S529945141ession,B: list_S529945141ession,C3: list_S529945141ession] :
% 2.95/1.78 ( ( append2089414218ession @ ( append2089414218ession @ A4 @ B ) @ C3 )
% 2.95/1.78 = ( append2089414218ession @ A4 @ ( append2089414218ession @ B @ C3 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_165_append__assoc,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.95/1.78 ( ( append2089414218ession @ ( append2089414218ession @ Xs @ Ys2 ) @ Zs2 )
% 2.95/1.78 = ( append2089414218ession @ Xs @ ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_166_append__same__eq,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Ys2 @ Xs )
% 2.95/1.78 = ( append2089414218ession @ Zs2 @ Xs ) )
% 2.95/1.78 = ( Ys2 = Zs2 ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_167_same__append__eq,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.95/1.78 = ( append2089414218ession @ Xs @ Zs2 ) )
% 2.95/1.78 = ( Ys2 = Zs2 ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_168_append_Oright__neutral,axiom,
% 2.95/1.78 ! [A4: list_S529945141ession] :
% 2.95/1.78 ( ( append2089414218ession @ A4 @ nil_Se901661471ession )
% 2.95/1.78 = A4 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_169_append_Oright__neutral,axiom,
% 2.95/1.78 ! [A4: list_Secrecy_KS] :
% 2.95/1.78 ( ( append_Secrecy_KS @ A4 @ nil_Secrecy_KS )
% 2.95/1.78 = A4 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_170_append__is__Nil__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.95/1.78 = nil_Se901661471ession )
% 2.95/1.78 = ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_171_append__is__Nil__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 2.95/1.78 = nil_Secrecy_KS )
% 2.95/1.78 = ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_172_Nil__is__append__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( nil_Se901661471ession
% 2.95/1.78 = ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_173_Nil__is__append__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( nil_Secrecy_KS
% 2.95/1.78 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_174_self__append__conv2,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Ys2
% 2.95/1.78 = ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( Xs = nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_175_self__append__conv2,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Ys2
% 2.95/1.78 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_176_append__self__conv2,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.95/1.78 = Ys2 )
% 2.95/1.78 = ( Xs = nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_177_append__self__conv2,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 2.95/1.78 = Ys2 )
% 2.95/1.78 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_178_self__append__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( Ys2 = nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_179_self__append__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_180_append__self__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.95/1.78 = Xs )
% 2.95/1.78 = ( Ys2 = nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_181_append__self__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 2.95/1.78 = Xs )
% 2.95/1.78 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_182_append__Nil2,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( append2089414218ession @ Xs @ nil_Se901661471ession )
% 2.95/1.78 = Xs ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_183_append__Nil2,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( append_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 2.95/1.78 = Xs ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_184_split__Nil__iff,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( ( splice1390717708ession @ Xs @ Ys2 )
% 2.95/1.78 = nil_Se901661471ession )
% 2.95/1.78 = ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_185_split__Nil__iff,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( splice_Secrecy_KS @ Xs @ Ys2 )
% 2.95/1.78 = nil_Secrecy_KS )
% 2.95/1.78 = ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_186_splice__Nil2,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( splice1390717708ession @ Xs @ nil_Se901661471ession )
% 2.95/1.78 = Xs ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_187_splice__Nil2,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( splice_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 2.95/1.78 = Xs ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_188_append1__eq__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS,Y: secrecy_KS] :
% 2.95/1.78 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 2.95/1.78 = ( append_Secrecy_KS @ Ys2 @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) )
% 2.95/1.78 = ( ( Xs = Ys2 )
% 2.95/1.78 & ( X3 = Y ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_189_append1__eq__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession,Y: secrecy_Expression] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 2.95/1.78 = ( append2089414218ession @ Ys2 @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) )
% 2.95/1.78 = ( ( Xs = Ys2 )
% 2.95/1.78 & ( X3 = Y ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_190_bind__simps_I2_J,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession,F2: secrecy_Expression > list_S529945141ession] :
% 2.95/1.78 ( ( bind_S815874003ession @ ( cons_S112077679ession @ X3 @ Xs ) @ F2 )
% 2.95/1.78 = ( append2089414218ession @ ( F2 @ X3 ) @ ( bind_S815874003ession @ Xs @ F2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_191_append__eq__appendI,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Xs1: list_S529945141ession,Zs2: list_S529945141ession,Ys2: list_S529945141ession,Us: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ Xs1 )
% 2.95/1.78 = Zs2 )
% 2.95/1.78 => ( ( Ys2
% 2.95/1.78 = ( append2089414218ession @ Xs1 @ Us ) )
% 2.95/1.78 => ( ( append2089414218ession @ Xs @ Ys2 )
% 2.95/1.78 = ( append2089414218ession @ Zs2 @ Us ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_192_append__eq__append__conv2,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession,Ts: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 2.95/1.78 = ( append2089414218ession @ Zs2 @ Ts ) )
% 2.95/1.78 = ( ? [Us2: list_S529945141ession] :
% 2.95/1.78 ( ( ( Xs
% 2.95/1.78 = ( append2089414218ession @ Zs2 @ Us2 ) )
% 2.95/1.78 & ( ( append2089414218ession @ Us2 @ Ys2 )
% 2.95/1.78 = Ts ) )
% 2.95/1.78 | ( ( ( append2089414218ession @ Xs @ Us2 )
% 2.95/1.78 = Zs2 )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append2089414218ession @ Us2 @ Ts ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_193_eq__Nil__appendI,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( Xs = Ys2 )
% 2.95/1.78 => ( Xs
% 2.95/1.78 = ( append2089414218ession @ nil_Se901661471ession @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_194_eq__Nil__appendI,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs = Ys2 )
% 2.95/1.78 => ( Xs
% 2.95/1.78 = ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_195_append__Nil,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( append2089414218ession @ nil_Se901661471ession @ Ys2 )
% 2.95/1.78 = Ys2 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_196_append__Nil,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 2.95/1.78 = Ys2 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_197_append_Oleft__neutral,axiom,
% 2.95/1.78 ! [A4: list_S529945141ession] :
% 2.95/1.78 ( ( append2089414218ession @ nil_Se901661471ession @ A4 )
% 2.95/1.78 = A4 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_198_append_Oleft__neutral,axiom,
% 2.95/1.78 ! [A4: list_Secrecy_KS] :
% 2.95/1.78 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ A4 )
% 2.95/1.78 = A4 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_199_Cons__eq__appendI,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs1: list_S529945141ession,Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.95/1.78 ( ( ( cons_S112077679ession @ X3 @ Xs1 )
% 2.95/1.78 = Ys2 )
% 2.95/1.78 => ( ( Xs
% 2.95/1.78 = ( append2089414218ession @ Xs1 @ Zs2 ) )
% 2.95/1.78 => ( ( cons_S112077679ession @ X3 @ Xs )
% 2.95/1.78 = ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_200_append__Cons,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( append2089414218ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ ( append2089414218ession @ Xs @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_201_ord_Olexordp__eq__pref,axiom,
% 2.95/1.78 ! [Less: secrecy_Expression > secrecy_Expression > $o,U: list_S529945141ession,V: list_S529945141ession] : ( lexord1123423577ession @ Less @ U @ ( append2089414218ession @ U @ V ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_202_knows2b,axiom,
% 2.95/1.78 ! [A: secrecy_specID,E: list_S529945141ession,E1: list_S529945141ession] :
% 2.95/1.78 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E @ E1 ) )
% 2.95/1.78 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_203_knows2a,axiom,
% 2.95/1.78 ! [A: secrecy_specID,E1: list_S529945141ession,E: list_S529945141ession] :
% 2.95/1.78 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E ) )
% 2.95/1.78 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_204_knows3,axiom,
% 2.95/1.78 ! [A: secrecy_specID,E1: list_S529945141ession,E22: list_S529945141ession] :
% 2.95/1.78 ( ( ( knowle731562421_knows @ A @ E1 )
% 2.95/1.78 & ( knowle731562421_knows @ A @ E22 ) )
% 2.95/1.78 => ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E22 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_205_splice_Osimps_I2_J,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( splice1390717708ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ ( splice1390717708ession @ Ys2 @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_206_splice_Osimps_I1_J,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( splice1390717708ession @ nil_Se901661471ession @ Ys2 )
% 2.95/1.78 = Ys2 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_207_splice_Osimps_I1_J,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( splice_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 2.95/1.78 = Ys2 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_208_rev__nonempty__induct,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 2.95/1.78 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs2 != nil_Secrecy_KS )
% 2.95/1.78 => ( ( P @ Xs2 )
% 2.95/1.78 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) ) )
% 2.95/1.78 => ( P @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_209_rev__nonempty__induct,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 2.95/1.78 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.78 ( ( Xs2 != nil_Se901661471ession )
% 2.95/1.78 => ( ( P @ Xs2 )
% 2.95/1.78 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) ) )
% 2.95/1.78 => ( P @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_210_append__eq__Cons__conv,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( append_Secrecy_KS @ Ys2 @ Zs2 )
% 2.95/1.78 = ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = ( ( ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 & ( Zs2
% 2.95/1.78 = ( cons_Secrecy_KS @ X3 @ Xs ) ) )
% 2.95/1.78 | ? [Ys4: list_Secrecy_KS] :
% 2.95/1.78 ( ( Ys2
% 2.95/1.78 = ( cons_Secrecy_KS @ X3 @ Ys4 ) )
% 2.95/1.78 & ( ( append_Secrecy_KS @ Ys4 @ Zs2 )
% 2.95/1.78 = Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_211_append__eq__Cons__conv,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession,Zs2: list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Ys2 @ Zs2 )
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( ( ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 & ( Zs2
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ Xs ) ) )
% 2.95/1.78 | ? [Ys4: list_S529945141ession] :
% 2.95/1.78 ( ( Ys2
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ Ys4 ) )
% 2.95/1.78 & ( ( append2089414218ession @ Ys4 @ Zs2 )
% 2.95/1.78 = Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_212_Cons__eq__append__conv,axiom,
% 2.95/1.78 ! [X3: secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( cons_Secrecy_KS @ X3 @ Xs )
% 2.95/1.78 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 2.95/1.78 = ( ( ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 & ( ( cons_Secrecy_KS @ X3 @ Xs )
% 2.95/1.78 = Zs2 ) )
% 2.95/1.78 | ? [Ys4: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( cons_Secrecy_KS @ X3 @ Ys4 )
% 2.95/1.78 = Ys2 )
% 2.95/1.78 & ( Xs
% 2.95/1.78 = ( append_Secrecy_KS @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_213_Cons__eq__append__conv,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.95/1.78 ( ( ( cons_S112077679ession @ X3 @ Xs )
% 2.95/1.78 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 2.95/1.78 = ( ( ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 & ( ( cons_S112077679ession @ X3 @ Xs )
% 2.95/1.78 = Zs2 ) )
% 2.95/1.78 | ? [Ys4: list_S529945141ession] :
% 2.95/1.78 ( ( ( cons_S112077679ession @ X3 @ Ys4 )
% 2.95/1.78 = Ys2 )
% 2.95/1.78 & ( Xs
% 2.95/1.78 = ( append2089414218ession @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_214_rev__exhaust,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ~ ! [Ys3: list_Secrecy_KS,Y3: secrecy_KS] :
% 2.95/1.78 ( Xs
% 2.95/1.78 != ( append_Secrecy_KS @ Ys3 @ ( cons_Secrecy_KS @ Y3 @ nil_Secrecy_KS ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_215_rev__exhaust,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ~ ! [Ys3: list_S529945141ession,Y3: secrecy_Expression] :
% 2.95/1.78 ( Xs
% 2.95/1.78 != ( append2089414218ession @ Ys3 @ ( cons_S112077679ession @ Y3 @ nil_Se901661471ession ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_216_rev__induct,axiom,
% 2.95/1.78 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( P @ nil_Secrecy_KS )
% 2.95/1.78 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 2.95/1.78 ( ( P @ Xs2 )
% 2.95/1.78 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) )
% 2.95/1.78 => ( P @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_217_rev__induct,axiom,
% 2.95/1.78 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( P @ nil_Se901661471ession )
% 2.95/1.78 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 2.95/1.78 ( ( P @ Xs2 )
% 2.95/1.78 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) )
% 2.95/1.78 => ( P @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_218_maps__simps_I1_J,axiom,
% 2.95/1.78 ! [F2: secrecy_Expression > list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( maps_S599402637ession @ F2 @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( append2089414218ession @ ( F2 @ X3 ) @ ( maps_S599402637ession @ F2 @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_219_concat__eq__append__conv,axiom,
% 2.95/1.78 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.95/1.78 ( ( ( concat388015140ession @ Xss2 )
% 2.95/1.78 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 2.95/1.78 = ( ( ( Xss2 = nil_li311616943ession )
% 2.95/1.78 => ( ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 & ( Zs2 = nil_Se901661471ession ) ) )
% 2.95/1.78 & ( ( Xss2 != nil_li311616943ession )
% 2.95/1.78 => ? [Xss1: list_l425507653ession,Xs3: list_S529945141ession,Xs4: list_S529945141ession,Xss22: list_l425507653ession] :
% 2.95/1.78 ( ( Xss2
% 2.95/1.78 = ( append1105297242ession @ Xss1 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append2089414218ession @ ( concat388015140ession @ Xss1 ) @ Xs3 ) )
% 2.95/1.78 & ( Zs2
% 2.95/1.78 = ( append2089414218ession @ Xs4 @ ( concat388015140ession @ Xss22 ) ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_220_concat__eq__append__conv,axiom,
% 2.95/1.78 ! [Xss2: list_list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( concat_Secrecy_KS @ Xss2 )
% 2.95/1.78 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 2.95/1.78 = ( ( ( Xss2 = nil_list_Secrecy_KS )
% 2.95/1.78 => ( ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 & ( Zs2 = nil_Secrecy_KS ) ) )
% 2.95/1.78 & ( ( Xss2 != nil_list_Secrecy_KS )
% 2.95/1.78 => ? [Xss1: list_list_Secrecy_KS,Xs3: list_Secrecy_KS,Xs4: list_Secrecy_KS,Xss22: list_list_Secrecy_KS] :
% 2.95/1.78 ( ( Xss2
% 2.95/1.78 = ( append1376766698ecy_KS @ Xss1 @ ( cons_list_Secrecy_KS @ ( append_Secrecy_KS @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append_Secrecy_KS @ ( concat_Secrecy_KS @ Xss1 ) @ Xs3 ) )
% 2.95/1.78 & ( Zs2
% 2.95/1.78 = ( append_Secrecy_KS @ Xs4 @ ( concat_Secrecy_KS @ Xss22 ) ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_221_rotate1_Osimps_I2_J,axiom,
% 2.95/1.78 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( rotate1_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_222_rotate1_Osimps_I2_J,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( rotate1237234450ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_223_butlast__snoc,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.95/1.78 ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 2.95/1.78 = Xs ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_224_butlast__snoc,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.95/1.78 ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 2.95/1.78 = Xs ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_225_rotate1__is__Nil__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( rotate1237234450ession @ Xs )
% 2.95/1.78 = nil_Se901661471ession )
% 2.95/1.78 = ( Xs = nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_226_rotate1__is__Nil__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( rotate1_Secrecy_KS @ Xs )
% 2.95/1.78 = nil_Secrecy_KS )
% 2.95/1.78 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_227_concat__append,axiom,
% 2.95/1.78 ! [Xs: list_l425507653ession,Ys2: list_l425507653ession] :
% 2.95/1.78 ( ( concat388015140ession @ ( append1105297242ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( append2089414218ession @ ( concat388015140ession @ Xs ) @ ( concat388015140ession @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_228_butlast_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( butlas171474643ession @ nil_Se901661471ession )
% 2.95/1.78 = nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_229_butlast_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( butlast_Secrecy_KS @ nil_Secrecy_KS )
% 2.95/1.78 = nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_230_rotate1_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( rotate1237234450ession @ nil_Se901661471ession )
% 2.95/1.78 = nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_231_rotate1_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( rotate1_Secrecy_KS @ nil_Secrecy_KS )
% 2.95/1.78 = nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_232_butlast_Osimps_I2_J,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.95/1.78 ( ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = nil_Secrecy_KS ) )
% 2.95/1.78 & ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = ( cons_Secrecy_KS @ X3 @ ( butlast_Secrecy_KS @ Xs ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_233_butlast_Osimps_I2_J,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.95/1.78 ( ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = nil_Se901661471ession ) )
% 2.95/1.78 & ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ ( butlas171474643ession @ Xs ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_234_concat_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( concat388015140ession @ nil_li311616943ession )
% 2.95/1.78 = nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_235_concat_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( concat_Secrecy_KS @ nil_list_Secrecy_KS )
% 2.95/1.78 = nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_236_butlast__append,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( butlas171474643ession @ Xs ) ) )
% 2.95/1.78 & ( ( Ys2 != nil_Se901661471ession )
% 2.95/1.78 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( append2089414218ession @ Xs @ ( butlas171474643ession @ Ys2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_237_butlast__append,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( butlast_Secrecy_KS @ Xs ) ) )
% 2.95/1.78 & ( ( Ys2 != nil_Secrecy_KS )
% 2.95/1.78 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( append_Secrecy_KS @ Xs @ ( butlast_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_238_concat_Osimps_I2_J,axiom,
% 2.95/1.78 ! [X3: list_S529945141ession,Xs: list_l425507653ession] :
% 2.95/1.78 ( ( concat388015140ession @ ( cons_l533358079ession @ X3 @ Xs ) )
% 2.95/1.78 = ( append2089414218ession @ X3 @ ( concat388015140ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_239_maps__simps_I2_J,axiom,
% 2.95/1.78 ! [F2: secrecy_Expression > list_S529945141ession] :
% 2.95/1.78 ( ( maps_S599402637ession @ F2 @ nil_Se901661471ession )
% 2.95/1.78 = nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_240_maps__simps_I2_J,axiom,
% 2.95/1.78 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 2.95/1.78 ( ( maps_S399472669ecy_KS @ F2 @ nil_Se901661471ession )
% 2.95/1.78 = nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_241_maps__simps_I2_J,axiom,
% 2.95/1.78 ! [F2: secrecy_KS > list_S529945141ession] :
% 2.95/1.78 ( ( maps_S1434541085ession @ F2 @ nil_Secrecy_KS )
% 2.95/1.78 = nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_242_maps__simps_I2_J,axiom,
% 2.95/1.78 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 2.95/1.78 ( ( maps_S377605037ecy_KS @ F2 @ nil_Secrecy_KS )
% 2.95/1.78 = nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_243_concat__eq__appendD,axiom,
% 2.95/1.78 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 2.95/1.78 ( ( ( concat388015140ession @ Xss2 )
% 2.95/1.78 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 2.95/1.78 => ( ( Xss2 != nil_li311616943ession )
% 2.95/1.78 => ? [Xss12: list_l425507653ession,Xs2: list_S529945141ession,Xs5: list_S529945141ession,Xss23: list_l425507653ession] :
% 2.95/1.78 ( ( Xss2
% 2.95/1.78 = ( append1105297242ession @ Xss12 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append2089414218ession @ ( concat388015140ession @ Xss12 ) @ Xs2 ) )
% 2.95/1.78 & ( Zs2
% 2.95/1.78 = ( append2089414218ession @ Xs5 @ ( concat388015140ession @ Xss23 ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_244_append__butlast__last__id,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( append_Secrecy_KS @ ( butlast_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( last_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) )
% 2.95/1.78 = Xs ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_245_append__butlast__last__id,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( append2089414218ession @ ( butlas171474643ession @ Xs ) @ ( cons_S112077679ession @ ( last_S1532390982ession @ Xs ) @ nil_Se901661471ession ) )
% 2.95/1.78 = Xs ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_246_snoc__eq__iff__butlast,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 2.95/1.78 = Ys2 )
% 2.95/1.78 = ( ( Ys2 != nil_Secrecy_KS )
% 2.95/1.78 & ( ( butlast_Secrecy_KS @ Ys2 )
% 2.95/1.78 = Xs )
% 2.95/1.78 & ( ( last_Secrecy_KS @ Ys2 )
% 2.95/1.78 = X3 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_247_snoc__eq__iff__butlast,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 2.95/1.78 = Ys2 )
% 2.95/1.78 = ( ( Ys2 != nil_Se901661471ession )
% 2.95/1.78 & ( ( butlas171474643ession @ Ys2 )
% 2.95/1.78 = Xs )
% 2.95/1.78 & ( ( last_S1532390982ession @ Ys2 )
% 2.95/1.78 = X3 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_248_last__snoc,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.95/1.78 ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 2.95/1.78 = X3 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_249_last__snoc,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.95/1.78 ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 2.95/1.78 = X3 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_250_last__appendR,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Ys2 != nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_S1532390982ession @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_251_last__appendR,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Ys2 != nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_252_last__appendL,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_253_last__appendL,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_254_last__ConsR,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_255_last__ConsR,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_256_last__ConsL,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.95/1.78 ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = X3 ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_257_last__ConsL,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.95/1.78 ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = X3 ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_258_last_Osimps,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.95/1.78 ( ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = X3 ) )
% 2.95/1.78 & ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_259_last_Osimps,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.95/1.78 ( ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = X3 ) )
% 2.95/1.78 & ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( last_S1532390982ession @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_260_last__append,axiom,
% 2.95/1.78 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_S1532390982ession @ Xs ) ) )
% 2.95/1.78 & ( ( Ys2 != nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_S1532390982ession @ Ys2 ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_261_last__append,axiom,
% 2.95/1.78 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Xs ) ) )
% 2.95/1.78 & ( ( Ys2 != nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Ys2 ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_262_longest__common__suffix,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ? [Ss: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( append2089414218ession @ Xs5 @ Ss ) )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append2089414218ession @ Ys5 @ Ss ) )
% 2.95/1.78 & ( ( Xs5 = nil_Se901661471ession )
% 2.95/1.78 | ( Ys5 = nil_Se901661471ession )
% 2.95/1.78 | ( ( last_S1532390982ession @ Xs5 )
% 2.95/1.78 != ( last_S1532390982ession @ Ys5 ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_263_longest__common__suffix,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ? [Ss: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( append_Secrecy_KS @ Xs5 @ Ss ) )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append_Secrecy_KS @ Ys5 @ Ss ) )
% 2.95/1.78 & ( ( Xs5 = nil_Secrecy_KS )
% 2.95/1.78 | ( Ys5 = nil_Secrecy_KS )
% 2.95/1.78 | ( ( last_Secrecy_KS @ Xs5 )
% 2.95/1.78 != ( last_Secrecy_KS @ Ys5 ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_264_concat__conv__foldr,axiom,
% 2.95/1.78 ( concat388015140ession
% 2.95/1.78 = ( ^ [Xss3: list_l425507653ession] : ( foldr_1531709715ession @ append2089414218ession @ Xss3 @ nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_265_concat__conv__foldr,axiom,
% 2.95/1.78 ( concat_Secrecy_KS
% 2.95/1.78 = ( ^ [Xss3: list_list_Secrecy_KS] : ( foldr_1711005747ecy_KS @ append_Secrecy_KS @ Xss3 @ nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_266_SuccD,axiom,
% 2.95/1.78 ! [K: secrecy_Keys,Kl: set_li849033543y_Keys,Kl2: list_Secrecy_Keys] :
% 2.95/1.78 ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl @ Kl2 ) )
% 2.95/1.78 => ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl2 @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_267_SuccD,axiom,
% 2.95/1.78 ! [K: secrecy_Secrets,Kl: set_li2007071804ecrets,Kl2: list_Secrecy_Secrets] :
% 2.95/1.78 ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl @ Kl2 ) )
% 2.95/1.78 => ( member1138497285ecrets @ ( append186372209ecrets @ Kl2 @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_268_SuccD,axiom,
% 2.95/1.78 ! [K: secrecy_KS,Kl: set_list_Secrecy_KS,Kl2: list_Secrecy_KS] :
% 2.95/1.78 ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl @ Kl2 ) )
% 2.95/1.78 => ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl2 @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_269_SuccD,axiom,
% 2.95/1.78 ! [K: secrecy_Expression,Kl: set_li185139947ession,Kl2: list_S529945141ession] :
% 2.95/1.78 ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl @ Kl2 ) )
% 2.95/1.78 => ( member249235532ession @ ( append2089414218ession @ Kl2 @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_270_SuccI,axiom,
% 2.95/1.78 ! [Kl2: list_Secrecy_Keys,K: secrecy_Keys,Kl: set_li849033543y_Keys] :
% 2.95/1.78 ( ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl2 @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl )
% 2.95/1.78 => ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl @ Kl2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_271_SuccI,axiom,
% 2.95/1.78 ! [Kl2: list_Secrecy_Secrets,K: secrecy_Secrets,Kl: set_li2007071804ecrets] :
% 2.95/1.78 ( ( member1138497285ecrets @ ( append186372209ecrets @ Kl2 @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl )
% 2.95/1.78 => ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl @ Kl2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_272_SuccI,axiom,
% 2.95/1.78 ! [Kl2: list_Secrecy_KS,K: secrecy_KS,Kl: set_list_Secrecy_KS] :
% 2.95/1.78 ( ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl2 @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl )
% 2.95/1.78 => ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl @ Kl2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_273_SuccI,axiom,
% 2.95/1.78 ! [Kl2: list_S529945141ession,K: secrecy_Expression,Kl: set_li185139947ession] :
% 2.95/1.78 ( ( member249235532ession @ ( append2089414218ession @ Kl2 @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl )
% 2.95/1.78 => ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl @ Kl2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_274_empty__Shift,axiom,
% 2.95/1.78 ! [Kl: set_li849033543y_Keys,K: secrecy_Keys] :
% 2.95/1.78 ( ( member341114536y_Keys @ nil_Secrecy_Keys @ Kl )
% 2.95/1.78 => ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl @ nil_Secrecy_Keys ) )
% 2.95/1.78 => ( member341114536y_Keys @ nil_Secrecy_Keys @ ( bNF_Gr414702370y_Keys @ Kl @ K ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_275_empty__Shift,axiom,
% 2.95/1.78 ! [Kl: set_li2007071804ecrets,K: secrecy_Secrets] :
% 2.95/1.78 ( ( member1138497285ecrets @ nil_Secrecy_Secrets @ Kl )
% 2.95/1.78 => ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl @ nil_Secrecy_Secrets ) )
% 2.95/1.78 => ( member1138497285ecrets @ nil_Secrecy_Secrets @ ( bNF_Gr28627573ecrets @ Kl @ K ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_276_empty__Shift,axiom,
% 2.95/1.78 ! [Kl: set_li185139947ession,K: secrecy_Expression] :
% 2.95/1.78 ( ( member249235532ession @ nil_Se901661471ession @ Kl )
% 2.95/1.78 => ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl @ nil_Se901661471ession ) )
% 2.95/1.78 => ( member249235532ession @ nil_Se901661471ession @ ( bNF_Gr275623750ession @ Kl @ K ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_277_empty__Shift,axiom,
% 2.95/1.78 ! [Kl: set_list_Secrecy_KS,K: secrecy_KS] :
% 2.95/1.78 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ Kl )
% 2.95/1.78 => ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl @ nil_Secrecy_KS ) )
% 2.95/1.78 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( bNF_Gr660123862ecy_KS @ Kl @ K ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_278_ShiftD,axiom,
% 2.95/1.78 ! [Kl2: list_S529945141ession,Kl: set_li185139947ession,K: secrecy_Expression] :
% 2.95/1.78 ( ( member249235532ession @ Kl2 @ ( bNF_Gr275623750ession @ Kl @ K ) )
% 2.95/1.78 => ( member249235532ession @ ( cons_S112077679ession @ K @ Kl2 ) @ Kl ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_279_Succ__Shift,axiom,
% 2.95/1.78 ! [Kl: set_li185139947ession,K: secrecy_Expression,Kl2: list_S529945141ession] :
% 2.95/1.78 ( ( bNF_Gr979629770ession @ ( bNF_Gr275623750ession @ Kl @ K ) @ Kl2 )
% 2.95/1.78 = ( bNF_Gr979629770ession @ Kl @ ( cons_S112077679ession @ K @ Kl2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_280_rev__eq__Cons__iff,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Y: secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( rev_Secrecy_KS @ Xs )
% 2.95/1.78 = ( cons_Secrecy_KS @ Y @ Ys2 ) )
% 2.95/1.78 = ( Xs
% 2.95/1.78 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Ys2 ) @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_281_rev__eq__Cons__iff,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( ( rev_Se1073238207ession @ Xs )
% 2.95/1.78 = ( cons_S112077679ession @ Y @ Ys2 ) )
% 2.95/1.78 = ( Xs
% 2.95/1.78 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_282_append_Omonoid__axioms,axiom,
% 2.95/1.78 monoid929671412ession @ append2089414218ession @ nil_Se901661471ession ).
% 2.95/1.78
% 2.95/1.78 thf(fact_283_append_Omonoid__axioms,axiom,
% 2.95/1.78 monoid1528146052ecy_KS @ append_Secrecy_KS @ nil_Secrecy_KS ).
% 2.95/1.78
% 2.95/1.78 thf(fact_284_rev__is__Nil__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( rev_Se1073238207ession @ Xs )
% 2.95/1.78 = nil_Se901661471ession )
% 2.95/1.78 = ( Xs = nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_285_rev__is__Nil__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( rev_Secrecy_KS @ Xs )
% 2.95/1.78 = nil_Secrecy_KS )
% 2.95/1.78 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_286_Nil__is__rev__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( nil_Se901661471ession
% 2.95/1.78 = ( rev_Se1073238207ession @ Xs ) )
% 2.95/1.78 = ( Xs = nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_287_Nil__is__rev__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( nil_Secrecy_KS
% 2.95/1.78 = ( rev_Secrecy_KS @ Xs ) )
% 2.95/1.78 = ( Xs = nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_288_rev__append,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( rev_Se1073238207ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( rev_Se1073238207ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_289_singleton__rev__conv,axiom,
% 2.95/1.78 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 2.95/1.78 = ( rev_Secrecy_KS @ Xs ) )
% 2.95/1.78 = ( Xs
% 2.95/1.78 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_290_singleton__rev__conv,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( cons_S112077679ession @ X3 @ nil_Se901661471ession )
% 2.95/1.78 = ( rev_Se1073238207ession @ Xs ) )
% 2.95/1.78 = ( Xs
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_291_rev__singleton__conv,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 2.95/1.78 ( ( ( rev_Secrecy_KS @ Xs )
% 2.95/1.78 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 2.95/1.78 = ( Xs
% 2.95/1.78 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_292_rev__singleton__conv,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 2.95/1.78 ( ( ( rev_Se1073238207ession @ Xs )
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 2.95/1.78 = ( Xs
% 2.95/1.78 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_293_rev_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( rev_Se1073238207ession @ nil_Se901661471ession )
% 2.95/1.78 = nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_294_rev_Osimps_I1_J,axiom,
% 2.95/1.78 ( ( rev_Secrecy_KS @ nil_Secrecy_KS )
% 2.95/1.78 = nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_295_rev_Osimps_I2_J,axiom,
% 2.95/1.78 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( rev_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_296_rev_Osimps_I2_J,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( rev_Se1073238207ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( append2089414218ession @ ( rev_Se1073238207ession @ Xs ) @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_297_hd__rev,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( hd_Sec357328890ession @ ( rev_Se1073238207ession @ Xs ) )
% 2.95/1.78 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_298_hd__rev,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( hd_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_299_hd__append2,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_300_hd__append2,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_301_hd__concat,axiom,
% 2.95/1.78 ! [Xs: list_l425507653ession] :
% 2.95/1.78 ( ( Xs != nil_li311616943ession )
% 2.95/1.78 => ( ( ( hd_lis1623417098ession @ Xs )
% 2.95/1.78 != nil_Se901661471ession )
% 2.95/1.78 => ( ( hd_Sec357328890ession @ ( concat388015140ession @ Xs ) )
% 2.95/1.78 = ( hd_Sec357328890ession @ ( hd_lis1623417098ession @ Xs ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_302_hd__concat,axiom,
% 2.95/1.78 ! [Xs: list_list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_list_Secrecy_KS )
% 2.95/1.78 => ( ( ( hd_list_Secrecy_KS @ Xs )
% 2.95/1.78 != nil_Secrecy_KS )
% 2.95/1.78 => ( ( hd_Secrecy_KS @ ( concat_Secrecy_KS @ Xs ) )
% 2.95/1.78 = ( hd_Secrecy_KS @ ( hd_list_Secrecy_KS @ Xs ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_303_list_Osel_I1_J,axiom,
% 2.95/1.78 ! [X21: secrecy_Expression,X22: list_S529945141ession] :
% 2.95/1.78 ( ( hd_Sec357328890ession @ ( cons_S112077679ession @ X21 @ X22 ) )
% 2.95/1.78 = X21 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_304_longest__common__prefix,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ? [Ps: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( append2089414218ession @ Ps @ Xs5 ) )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append2089414218ession @ Ps @ Ys5 ) )
% 2.95/1.78 & ( ( Xs5 = nil_Se901661471ession )
% 2.95/1.78 | ( Ys5 = nil_Se901661471ession )
% 2.95/1.78 | ( ( hd_Sec357328890ession @ Xs5 )
% 2.95/1.78 != ( hd_Sec357328890ession @ Ys5 ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_305_longest__common__prefix,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ? [Ps: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( append_Secrecy_KS @ Ps @ Xs5 ) )
% 2.95/1.78 & ( Ys2
% 2.95/1.78 = ( append_Secrecy_KS @ Ps @ Ys5 ) )
% 2.95/1.78 & ( ( Xs5 = nil_Secrecy_KS )
% 2.95/1.78 | ( Ys5 = nil_Secrecy_KS )
% 2.95/1.78 | ( ( hd_Secrecy_KS @ Xs5 )
% 2.95/1.78 != ( hd_Secrecy_KS @ Ys5 ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_306_hd__append,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( hd_Sec357328890ession @ Ys2 ) ) )
% 2.95/1.78 & ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( hd_Sec357328890ession @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_307_hd__append,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( hd_Secrecy_KS @ Ys2 ) ) )
% 2.95/1.78 & ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( hd_Secrecy_KS @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_308_last__rev,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( rev_Se1073238207ession @ Xs ) )
% 2.95/1.78 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_309_last__rev,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 2.95/1.78 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_310_rotate1__hd__tl,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( rotate1_Secrecy_KS @ Xs )
% 2.95/1.78 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_311_rotate1__hd__tl,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( rotate1237234450ession @ Xs )
% 2.95/1.78 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ nil_Se901661471ession ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_312_distinct__adj__append__iff,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( distin1076152135ession @ Xs )
% 2.95/1.78 & ( distin1076152135ession @ Ys2 )
% 2.95/1.78 & ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 | ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 | ( ( last_S1532390982ession @ Xs )
% 2.95/1.78 != ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_313_distinct__adj__append__iff,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( distin1495927511ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( distin1495927511ecy_KS @ Xs )
% 2.95/1.78 & ( distin1495927511ecy_KS @ Ys2 )
% 2.95/1.78 & ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 | ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 | ( ( last_Secrecy_KS @ Xs )
% 2.95/1.78 != ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_314_distinct__adj__Cons__Cons,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 2.95/1.78 = ( ( X3 != Y )
% 2.95/1.78 & ( distin1076152135ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_315_tl__append2,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( tl_Sec1905266422ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_316_tl__append2,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( tl_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_317_list_Ocollapse,axiom,
% 2.95/1.78 ! [List: list_Secrecy_KS] :
% 2.95/1.78 ( ( List != nil_Secrecy_KS )
% 2.95/1.78 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) )
% 2.95/1.78 = List ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_318_list_Ocollapse,axiom,
% 2.95/1.78 ! [List: list_S529945141ession] :
% 2.95/1.78 ( ( List != nil_Se901661471ession )
% 2.95/1.78 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) )
% 2.95/1.78 = List ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_319_hd__Cons__tl,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ ( tl_Secrecy_KS @ Xs ) )
% 2.95/1.78 = Xs ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_320_hd__Cons__tl,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ ( tl_Sec1905266422ession @ Xs ) )
% 2.95/1.78 = Xs ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_321_list_Oexpand,axiom,
% 2.95/1.78 ! [List: list_S529945141ession,List2: list_S529945141ession] :
% 2.95/1.78 ( ( ( List = nil_Se901661471ession )
% 2.95/1.78 = ( List2 = nil_Se901661471ession ) )
% 2.95/1.78 => ( ( ( List != nil_Se901661471ession )
% 2.95/1.78 => ( ( List2 != nil_Se901661471ession )
% 2.95/1.78 => ( ( ( hd_Sec357328890ession @ List )
% 2.95/1.78 = ( hd_Sec357328890ession @ List2 ) )
% 2.95/1.78 & ( ( tl_Sec1905266422ession @ List )
% 2.95/1.78 = ( tl_Sec1905266422ession @ List2 ) ) ) ) )
% 2.95/1.78 => ( List = List2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_322_list_Oexpand,axiom,
% 2.95/1.78 ! [List: list_Secrecy_KS,List2: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( List = nil_Secrecy_KS )
% 2.95/1.78 = ( List2 = nil_Secrecy_KS ) )
% 2.95/1.78 => ( ( ( List != nil_Secrecy_KS )
% 2.95/1.78 => ( ( List2 != nil_Secrecy_KS )
% 2.95/1.78 => ( ( ( hd_Secrecy_KS @ List )
% 2.95/1.78 = ( hd_Secrecy_KS @ List2 ) )
% 2.95/1.78 & ( ( tl_Secrecy_KS @ List )
% 2.95/1.78 = ( tl_Secrecy_KS @ List2 ) ) ) ) )
% 2.95/1.78 => ( List = List2 ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_323_distinct__adj__singleton,axiom,
% 2.95/1.78 ! [X3: secrecy_KS] : ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_324_distinct__adj__singleton,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression] : ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_325_tl__Nil,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( tl_Secrecy_KS @ Xs )
% 2.95/1.78 = nil_Secrecy_KS )
% 2.95/1.78 = ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 | ? [X4: secrecy_KS] :
% 2.95/1.78 ( Xs
% 2.95/1.78 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_326_tl__Nil,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( tl_Sec1905266422ession @ Xs )
% 2.95/1.78 = nil_Se901661471ession )
% 2.95/1.78 = ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 | ? [X4: secrecy_Expression] :
% 2.95/1.78 ( Xs
% 2.95/1.78 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_327_Nil__tl,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( nil_Secrecy_KS
% 2.95/1.78 = ( tl_Secrecy_KS @ Xs ) )
% 2.95/1.78 = ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 | ? [X4: secrecy_KS] :
% 2.95/1.78 ( Xs
% 2.95/1.78 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_328_Nil__tl,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( nil_Se901661471ession
% 2.95/1.78 = ( tl_Sec1905266422ession @ Xs ) )
% 2.95/1.78 = ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 | ? [X4: secrecy_Expression] :
% 2.95/1.78 ( Xs
% 2.95/1.78 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_329_distinct__adj__ConsD,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 => ( distin1076152135ession @ Xs ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_330_distinct__adj__Nil,axiom,
% 2.95/1.78 distin1076152135ession @ nil_Se901661471ession ).
% 2.95/1.78
% 2.95/1.78 thf(fact_331_distinct__adj__Nil,axiom,
% 2.95/1.78 distin1495927511ecy_KS @ nil_Secrecy_KS ).
% 2.95/1.78
% 2.95/1.78 thf(fact_332_list_Osel_I3_J,axiom,
% 2.95/1.78 ! [X21: secrecy_Expression,X22: list_S529945141ession] :
% 2.95/1.78 ( ( tl_Sec1905266422ession @ ( cons_S112077679ession @ X21 @ X22 ) )
% 2.95/1.78 = X22 ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_333_list_Osel_I2_J,axiom,
% 2.95/1.78 ( ( tl_Sec1905266422ession @ nil_Se901661471ession )
% 2.95/1.78 = nil_Se901661471ession ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_334_list_Osel_I2_J,axiom,
% 2.95/1.78 ( ( tl_Secrecy_KS @ nil_Secrecy_KS )
% 2.95/1.78 = nil_Secrecy_KS ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_335_distinct__adj__appendD1,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 => ( distin1076152135ession @ Xs ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_336_distinct__adj__appendD2,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 => ( distin1076152135ession @ Ys2 ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_337_last__tl,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession] :
% 2.95/1.78 ( ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 | ( ( tl_Sec1905266422ession @ Xs )
% 2.95/1.78 != nil_Se901661471ession ) )
% 2.95/1.78 => ( ( last_S1532390982ession @ ( tl_Sec1905266422ession @ Xs ) )
% 2.95/1.78 = ( last_S1532390982ession @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_338_last__tl,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 | ( ( tl_Secrecy_KS @ Xs )
% 2.95/1.78 != nil_Secrecy_KS ) )
% 2.95/1.78 => ( ( last_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) )
% 2.95/1.78 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_339_list_Oexhaust__sel,axiom,
% 2.95/1.78 ! [List: list_Secrecy_KS] :
% 2.95/1.78 ( ( List != nil_Secrecy_KS )
% 2.95/1.78 => ( List
% 2.95/1.78 = ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_340_list_Oexhaust__sel,axiom,
% 2.95/1.78 ! [List: list_S529945141ession] :
% 2.95/1.78 ( ( List != nil_Se901661471ession )
% 2.95/1.78 => ( List
% 2.95/1.78 = ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_341_distinct__adj__Cons,axiom,
% 2.95/1.78 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 2.95/1.78 ( ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 2.95/1.78 = ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 | ( ( X3
% 2.95/1.78 != ( hd_Secrecy_KS @ Xs ) )
% 2.95/1.78 & ( distin1495927511ecy_KS @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_342_distinct__adj__Cons,axiom,
% 2.95/1.78 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 2.95/1.78 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 2.95/1.78 = ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 | ( ( X3
% 2.95/1.78 != ( hd_Sec357328890ession @ Xs ) )
% 2.95/1.78 & ( distin1076152135ession @ Xs ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_343_successively__append__iff,axiom,
% 2.95/1.78 ! [P: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( succes1388047762ession @ P @ ( append2089414218ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( succes1388047762ession @ P @ Xs )
% 2.95/1.78 & ( succes1388047762ession @ P @ Ys2 )
% 2.95/1.78 & ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 | ( Ys2 = nil_Se901661471ession )
% 2.95/1.78 | ( P @ ( last_S1532390982ession @ Xs ) @ ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_344_successively__append__iff,axiom,
% 2.95/1.78 ! [P: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( succes590251810ecy_KS @ P @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( succes590251810ecy_KS @ P @ Xs )
% 2.95/1.78 & ( succes590251810ecy_KS @ P @ Ys2 )
% 2.95/1.78 & ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 | ( Ys2 = nil_Secrecy_KS )
% 2.95/1.78 | ( P @ ( last_Secrecy_KS @ Xs ) @ ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_345_Cons__in__shuffles__iff,axiom,
% 2.95/1.78 ! [Z: secrecy_KS,Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( member193705948ecy_KS @ ( cons_Secrecy_KS @ Z @ Zs2 ) @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( ( Xs != nil_Secrecy_KS )
% 2.95/1.78 & ( ( hd_Secrecy_KS @ Xs )
% 2.95/1.78 = Z )
% 2.95/1.78 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) )
% 2.95/1.78 | ( ( Ys2 != nil_Secrecy_KS )
% 2.95/1.78 & ( ( hd_Secrecy_KS @ Ys2 )
% 2.95/1.78 = Z )
% 2.95/1.78 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ ( tl_Secrecy_KS @ Ys2 ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_346_Cons__in__shuffles__iff,axiom,
% 2.95/1.78 ! [Z: secrecy_Expression,Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( ( Xs != nil_Se901661471ession )
% 2.95/1.78 & ( ( hd_Sec357328890ession @ Xs )
% 2.95/1.78 = Z )
% 2.95/1.78 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) )
% 2.95/1.78 | ( ( Ys2 != nil_Se901661471ession )
% 2.95/1.78 & ( ( hd_Sec357328890ession @ Ys2 )
% 2.95/1.78 = Z )
% 2.95/1.78 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ ( tl_Sec1905266422ession @ Ys2 ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_347_Nil__in__shuffles,axiom,
% 2.95/1.78 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( Xs = nil_Se901661471ession )
% 2.95/1.78 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_348_Nil__in__shuffles,axiom,
% 2.95/1.78 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 = ( ( Xs = nil_Secrecy_KS )
% 2.95/1.78 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_349_shufflesE,axiom,
% 2.95/1.78 ! [Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 2.95/1.78 ( ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 2.95/1.78 => ( ( ( Zs2 = Xs )
% 2.95/1.78 => ( Ys2 != nil_Secrecy_KS ) )
% 2.95/1.78 => ( ( ( Zs2 = Ys2 )
% 2.95/1.78 => ( Xs != nil_Secrecy_KS ) )
% 2.95/1.78 => ( ! [X: secrecy_KS,Xs5: list_Secrecy_KS] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( cons_Secrecy_KS @ X @ Xs5 ) )
% 2.95/1.78 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 2.95/1.78 ( ( Zs2
% 2.95/1.78 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 2.95/1.78 => ( ( X = Z2 )
% 2.95/1.78 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs5 @ Ys2 ) ) ) ) )
% 2.95/1.78 => ~ ! [Y3: secrecy_KS,Ys5: list_Secrecy_KS] :
% 2.95/1.78 ( ( Ys2
% 2.95/1.78 = ( cons_Secrecy_KS @ Y3 @ Ys5 ) )
% 2.95/1.78 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 2.95/1.78 ( ( Zs2
% 2.95/1.78 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 2.95/1.78 => ( ( Y3 = Z2 )
% 2.95/1.78 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(fact_350_shufflesE,axiom,
% 2.95/1.78 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 2.95/1.78 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 2.95/1.78 => ( ( ( Zs2 = Xs )
% 2.95/1.78 => ( Ys2 != nil_Se901661471ession ) )
% 2.95/1.78 => ( ( ( Zs2 = Ys2 )
% 2.95/1.78 => ( Xs != nil_Se901661471ession ) )
% 2.95/1.78 => ( ! [X: secrecy_Expression,Xs5: list_S529945141ession] :
% 2.95/1.78 ( ( Xs
% 2.95/1.78 = ( cons_S112077679ession @ X @ Xs5 ) )
% 2.95/1.78 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 2.95/1.78 ( ( Zs2
% 2.95/1.78 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 2.95/1.78 => ( ( X = Z2 )
% 2.95/1.78 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs5 @ Ys2 ) ) ) ) )
% 2.95/1.78 => ~ ! [Y3: secrecy_Expression,Ys5: list_S529945141ession] :
% 2.95/1.78 ( ( Ys2
% 2.95/1.78 = ( cons_S112077679ession @ Y3 @ Ys5 ) )
% 2.95/1.78 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 2.95/1.78 ( ( Zs2
% 2.95/1.78 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 2.95/1.78 => ( ( Y3 = Z2 )
% 2.95/1.78 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 2.95/1.78
% 2.95/1.78 thf(conj_0,conjecture,
% 2.95/1.78 knowle945212990e_know @ a @ ( secrecy_kKS @ m ) ).
% 2.95/1.78 ------------------------
% 3.04/1.80 % (26932)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/183Mi)
% 3.04/1.80 % (26933)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_26818 for (2999ds/4Mi)
% 3.04/1.80 % (26936)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_26818 for (2999ds/2Mi)
% 3.04/1.80 % (26936)Instruction limit reached!
% 3.04/1.80 % (26936)------------------------------
% 3.04/1.80 % (26936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.80 % (26936)Termination reason: Unknown
% 3.04/1.80 % (26936)Termination phase: shuffling
% 3.04/1.80
% 3.04/1.80 % (26936)Memory used [KB]: 1407
% 3.04/1.80 % (26936)Time elapsed: 0.002 s
% 3.04/1.80 % (26936)Instructions burned: 2 (million)
% 3.04/1.80 % (26936)------------------------------
% 3.04/1.80 % (26936)------------------------------
% 3.04/1.80 % (26933)Instruction limit reached!
% 3.04/1.80 % (26933)------------------------------
% 3.04/1.80 % (26933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.80 % (26933)Termination reason: Unknown
% 3.04/1.80 % (26933)Termination phase: shuffling
% 3.04/1.80
% 3.04/1.80 % (26933)Memory used [KB]: 1535
% 3.04/1.80 % (26933)Time elapsed: 0.003 s
% 3.04/1.80 % (26933)Instructions burned: 6 (million)
% 3.04/1.80 % (26933)------------------------------
% 3.04/1.80 % (26933)------------------------------
% 3.04/1.81 % (26938)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/18Mi)
% 3.04/1.81 % (26937)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_26818 for (2999ds/275Mi)
% 3.04/1.81 % (26939)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/3Mi)
% 3.04/1.81 % (26934)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_26818 for (2999ds/27Mi)
% 3.04/1.81 % (26939)Instruction limit reached!
% 3.04/1.81 % (26939)------------------------------
% 3.04/1.81 % (26939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.81 % (26939)Termination reason: Unknown
% 3.04/1.81 % (26939)Termination phase: shuffling
% 3.04/1.81
% 3.04/1.81 % (26939)Memory used [KB]: 1535
% 3.04/1.81 % (26939)Time elapsed: 0.003 s
% 3.04/1.81 % (26939)Instructions burned: 5 (million)
% 3.04/1.81 % (26939)------------------------------
% 3.04/1.81 % (26939)------------------------------
% 3.04/1.81 % (26935)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/2Mi)
% 3.04/1.82 % (26935)Instruction limit reached!
% 3.04/1.82 % (26935)------------------------------
% 3.04/1.82 % (26935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.82 % (26935)Termination reason: Unknown
% 3.04/1.82 % (26935)Termination phase: shuffling
% 3.04/1.82
% 3.04/1.82 % (26935)Memory used [KB]: 1407
% 3.04/1.82 % (26935)Time elapsed: 0.003 s
% 3.04/1.82 % (26935)Instructions burned: 2 (million)
% 3.04/1.82 % (26935)------------------------------
% 3.04/1.82 % (26935)------------------------------
% 3.04/1.82 % (26938)Instruction limit reached!
% 3.04/1.82 % (26938)------------------------------
% 3.04/1.82 % (26938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.82 % (26938)Termination reason: Unknown
% 3.04/1.82 % (26938)Termination phase: shuffling
% 3.04/1.82
% 3.04/1.82 % (26938)Memory used [KB]: 1791
% 3.04/1.82 % (26938)Time elapsed: 0.010 s
% 3.04/1.82 % (26938)Instructions burned: 18 (million)
% 3.04/1.82 % (26938)------------------------------
% 3.04/1.82 % (26938)------------------------------
% 3.04/1.82 % (26934)Instruction limit reached!
% 3.04/1.82 % (26934)------------------------------
% 3.04/1.82 % (26934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.82 % (26934)Termination reason: Unknown
% 3.04/1.82 % (26934)Termination phase: Property scanning
% 3.04/1.82
% 3.04/1.82 % (26934)Memory used [KB]: 1918
% 3.04/1.82 % (26934)Time elapsed: 0.010 s
% 3.04/1.82 % (26934)Instructions burned: 29 (million)
% 3.04/1.82 % (26934)------------------------------
% 3.04/1.82 % (26934)------------------------------
% 3.04/1.82 % (26940)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_26818 for (2999ds/37Mi)
% 3.04/1.82 % (26941)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_26818 for (2999ds/15Mi)
% 3.04/1.83 % (26941)Instruction limit reached!
% 3.04/1.83 % (26941)------------------------------
% 3.04/1.83 % (26941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.83 % (26941)Termination reason: Unknown
% 3.04/1.83 % (26941)Termination phase: shuffling
% 3.04/1.83
% 3.04/1.83 % (26941)Memory used [KB]: 1791
% 3.04/1.83 % (26941)Time elapsed: 0.006 s
% 3.04/1.83 % (26941)Instructions burned: 15 (million)
% 3.04/1.83 % (26941)------------------------------
% 3.04/1.83 % (26941)------------------------------
% 3.04/1.83 % (26944)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/7Mi)
% 3.04/1.83 % (26944)Instruction limit reached!
% 3.04/1.83 % (26944)------------------------------
% 3.04/1.83 % (26944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.83 % (26944)Termination reason: Unknown
% 3.04/1.83 % (26944)Termination phase: shuffling
% 3.04/1.83
% 3.04/1.83 % (26944)Memory used [KB]: 1663
% 3.04/1.83 % (26944)Time elapsed: 0.004 s
% 3.04/1.83 % (26944)Instructions burned: 8 (million)
% 3.04/1.83 % (26944)------------------------------
% 3.04/1.83 % (26944)------------------------------
% 3.04/1.83 % (26942)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_26818 for (2999ds/3Mi)
% 3.04/1.84 % (26942)Instruction limit reached!
% 3.04/1.84 % (26942)------------------------------
% 3.04/1.84 % (26942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.84 % (26942)Termination reason: Unknown
% 3.04/1.84 % (26942)Termination phase: shuffling
% 3.04/1.84
% 3.04/1.84 % (26942)Memory used [KB]: 1535
% 3.04/1.84 % (26942)Time elapsed: 0.004 s
% 3.04/1.84 % (26942)Instructions burned: 3 (million)
% 3.04/1.84 % (26942)------------------------------
% 3.04/1.84 % (26942)------------------------------
% 3.04/1.84 % (26945)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/16Mi)
% 3.04/1.84 % (26943)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_26818 for (2999ds/1041Mi)
% 3.04/1.84 % (26940)Instruction limit reached!
% 3.04/1.84 % (26940)------------------------------
% 3.04/1.84 % (26940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.84 % (26940)Termination reason: Unknown
% 3.04/1.84 % (26940)Termination phase: shuffling
% 3.04/1.84
% 3.04/1.84 % (26940)Memory used [KB]: 2174
% 3.04/1.84 % (26940)Time elapsed: 0.022 s
% 3.04/1.84 % (26940)Instructions burned: 37 (million)
% 3.04/1.84 % (26940)------------------------------
% 3.04/1.84 % (26940)------------------------------
% 3.04/1.84 % (26946)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_26818 for (2999ds/3Mi)
% 3.04/1.84 % (26937)Refutation not found, incomplete strategy
% 3.04/1.84 % (26937)------------------------------
% 3.04/1.84 % (26937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.84 % (26937)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.84
% 3.04/1.84
% 3.04/1.84 % (26937)Memory used [KB]: 6652
% 3.04/1.84 % (26937)Time elapsed: 0.035 s
% 3.04/1.84 % (26937)Instructions burned: 58 (million)
% 3.04/1.84 % (26937)------------------------------
% 3.04/1.84 % (26937)------------------------------
% 3.04/1.84 % (26945)Instruction limit reached!
% 3.04/1.84 % (26945)------------------------------
% 3.04/1.84 % (26945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.84 % (26945)Termination reason: Unknown
% 3.04/1.84 % (26945)Termination phase: shuffling
% 3.04/1.84
% 3.04/1.84 % (26945)Memory used [KB]: 1791
% 3.04/1.84 % (26945)Time elapsed: 0.007 s
% 3.04/1.84 % (26945)Instructions burned: 19 (million)
% 3.04/1.84 % (26945)------------------------------
% 3.04/1.84 % (26945)------------------------------
% 3.04/1.84 % (26946)Instruction limit reached!
% 3.04/1.84 % (26946)------------------------------
% 3.04/1.84 % (26946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.84 % (26946)Termination reason: Unknown
% 3.04/1.84 % (26946)Termination phase: shuffling
% 3.04/1.84
% 3.04/1.84 % (26946)Memory used [KB]: 1535
% 3.04/1.84 % (26946)Time elapsed: 0.003 s
% 3.04/1.84 % (26946)Instructions burned: 6 (million)
% 3.04/1.84 % (26946)------------------------------
% 3.04/1.84 % (26946)------------------------------
% 3.04/1.85 % (26947)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_26818 for (2999ds/3Mi)
% 3.04/1.85 % (26947)Instruction limit reached!
% 3.04/1.85 % (26947)------------------------------
% 3.04/1.85 % (26947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.85 % (26947)Termination reason: Unknown
% 3.04/1.85 % (26947)Termination phase: shuffling
% 3.04/1.85
% 3.04/1.85 % (26947)Memory used [KB]: 1535
% 3.04/1.85 % (26947)Time elapsed: 0.002 s
% 3.04/1.85 % (26947)Instructions burned: 3 (million)
% 3.04/1.85 % (26947)------------------------------
% 3.04/1.85 % (26947)------------------------------
% 3.04/1.85 % (26932)Instruction limit reached!
% 3.04/1.85 % (26932)------------------------------
% 3.04/1.85 % (26932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.85 % (26932)Termination reason: Unknown
% 3.04/1.85 % (26932)Termination phase: Saturation
% 3.04/1.85
% 3.04/1.85 % (26932)Memory used [KB]: 7931
% 3.04/1.85 % (26932)Time elapsed: 0.052 s
% 3.04/1.85 % (26932)Instructions burned: 184 (million)
% 3.04/1.85 % (26932)------------------------------
% 3.04/1.85 % (26932)------------------------------
% 3.04/1.85 % (26949)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/3Mi)
% 3.04/1.85 % (26949)Instruction limit reached!
% 3.04/1.85 % (26949)------------------------------
% 3.04/1.85 % (26949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.85 % (26949)Termination reason: Unknown
% 3.04/1.85 % (26949)Termination phase: shuffling
% 3.04/1.85
% 3.04/1.85 % (26949)Memory used [KB]: 1535
% 3.04/1.85 % (26949)Time elapsed: 0.002 s
% 3.04/1.85 % (26949)Instructions burned: 3 (million)
% 3.04/1.85 % (26949)------------------------------
% 3.04/1.85 % (26949)------------------------------
% 3.04/1.85 % (26951)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/18Mi)
% 3.04/1.86 % (26952)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/710Mi)
% 3.04/1.86 % (26951)Instruction limit reached!
% 3.04/1.86 % (26951)------------------------------
% 3.04/1.86 % (26951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.86 % (26951)Termination reason: Unknown
% 3.04/1.86 % (26951)Termination phase: shuffling
% 3.04/1.86
% 3.04/1.86 % (26951)Memory used [KB]: 1791
% 3.04/1.86 % (26951)Time elapsed: 0.007 s
% 3.04/1.86 % (26951)Instructions burned: 20 (million)
% 3.04/1.86 % (26951)------------------------------
% 3.04/1.86 % (26951)------------------------------
% 3.04/1.86 % (26953)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/6Mi)
% 3.04/1.86 % (26948)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/7Mi)
% 3.04/1.86 % (26953)Instruction limit reached!
% 3.04/1.86 % (26953)------------------------------
% 3.04/1.86 % (26953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.86 % (26954)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_26818 for (2999ds/902Mi)
% 3.04/1.86 % (26953)Termination reason: Unknown
% 3.04/1.86 % (26953)Termination phase: shuffling
% 3.04/1.86
% 3.04/1.86 % (26953)Memory used [KB]: 1663
% 3.04/1.86 % (26953)Time elapsed: 0.003 s
% 3.04/1.86 % (26953)Instructions burned: 6 (million)
% 3.04/1.86 % (26953)------------------------------
% 3.04/1.86 % (26953)------------------------------
% 3.04/1.86 % (26950)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/4Mi)
% 3.04/1.86 % (26948)Instruction limit reached!
% 3.04/1.86 % (26948)------------------------------
% 3.04/1.86 % (26948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.87 % (26948)Termination reason: Unknown
% 3.04/1.87 % (26948)Termination phase: shuffling
% 3.04/1.87
% 3.04/1.87 % (26948)Memory used [KB]: 1663
% 3.04/1.87 % (26948)Time elapsed: 0.006 s
% 3.04/1.87 % (26948)Instructions burned: 7 (million)
% 3.04/1.87 % (26948)------------------------------
% 3.04/1.87 % (26948)------------------------------
% 3.04/1.87 % (26950)Instruction limit reached!
% 3.04/1.87 % (26950)------------------------------
% 3.04/1.87 % (26950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.87 % (26950)Termination reason: Unknown
% 3.04/1.87 % (26950)Termination phase: shuffling
% 3.04/1.87
% 3.04/1.87 % (26950)Memory used [KB]: 1535
% 3.04/1.87 % (26950)Time elapsed: 0.004 s
% 3.04/1.87 % (26950)Instructions burned: 4 (million)
% 3.04/1.87 % (26950)------------------------------
% 3.04/1.87 % (26950)------------------------------
% 3.04/1.87 % (26955)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_26818 for (2999ds/21Mi)
% 3.04/1.87 % (26952)Refutation not found, incomplete strategy
% 3.04/1.87 % (26952)------------------------------
% 3.04/1.87 % (26952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.87 % (26952)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.87
% 3.04/1.87
% 3.04/1.87 % (26952)Memory used [KB]: 6524
% 3.04/1.87 % (26952)Time elapsed: 0.015 s
% 3.04/1.87 % (26952)Instructions burned: 47 (million)
% 3.04/1.87 % (26952)------------------------------
% 3.04/1.87 % (26952)------------------------------
% 3.04/1.87 % (26956)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/5Mi)
% 3.04/1.87 % (26956)Instruction limit reached!
% 3.04/1.87 % (26956)------------------------------
% 3.04/1.87 % (26956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.87 % (26956)Termination reason: Unknown
% 3.04/1.87 % (26956)Termination phase: shuffling
% 3.04/1.87
% 3.04/1.87 % (26956)Memory used [KB]: 1663
% 3.04/1.87 % (26956)Time elapsed: 0.003 s
% 3.04/1.87 % (26956)Instructions burned: 7 (million)
% 3.04/1.87 % (26956)------------------------------
% 3.04/1.87 % (26956)------------------------------
% 3.04/1.88 % (26955)Instruction limit reached!
% 3.04/1.88 % (26955)------------------------------
% 3.04/1.88 % (26955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.88 % (26955)Termination reason: Unknown
% 3.04/1.88 % (26955)Termination phase: shuffling
% 3.04/1.88
% 3.04/1.88 % (26955)Memory used [KB]: 1918
% 3.04/1.88 % (26955)Time elapsed: 0.008 s
% 3.04/1.88 % (26955)Instructions burned: 23 (million)
% 3.04/1.88 % (26955)------------------------------
% 3.04/1.88 % (26955)------------------------------
% 3.04/1.88 % (26957)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_26818 for (2999ds/6Mi)
% 3.04/1.88 % (26957)Instruction limit reached!
% 3.04/1.88 % (26957)------------------------------
% 3.04/1.88 % (26957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.88 % (26957)Termination reason: Unknown
% 3.04/1.88 % (26957)Termination phase: shuffling
% 3.04/1.88
% 3.04/1.88 % (26957)Memory used [KB]: 1663
% 3.04/1.88 % (26957)Time elapsed: 0.003 s
% 3.04/1.88 % (26957)Instructions burned: 7 (million)
% 3.04/1.88 % (26957)------------------------------
% 3.04/1.88 % (26957)------------------------------
% 3.04/1.88 % (26960)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_26818 for (2998ds/19Mi)
% 3.04/1.88 % (26958)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26818 for (2999ds/377Mi)
% 3.04/1.89 % (26959)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_26818 for (2999ds/779Mi)
% 3.04/1.89 % (26960)Instruction limit reached!
% 3.04/1.89 % (26960)------------------------------
% 3.04/1.89 % (26960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.89 % (26960)Termination reason: Unknown
% 3.04/1.89 % (26960)Termination phase: shuffling
% 3.04/1.89
% 3.04/1.89 % (26960)Memory used [KB]: 1918
% 3.04/1.89 % (26960)Time elapsed: 0.007 s
% 3.04/1.89 % (26960)Instructions burned: 22 (million)
% 3.04/1.89 % (26960)------------------------------
% 3.04/1.89 % (26960)------------------------------
% 3.04/1.89 % (26962)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26818 for (2998ds/17Mi)
% 3.04/1.89 % (26961)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26818 for (2998ds/879Mi)
% 3.04/1.90 % (26962)Instruction limit reached!
% 3.04/1.90 % (26962)------------------------------
% 3.04/1.90 % (26962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.90 % (26962)Termination reason: Unknown
% 3.04/1.90 % (26962)Termination phase: shuffling
% 3.04/1.90
% 3.04/1.90 % (26962)Memory used [KB]: 1791
% 3.04/1.90 % (26962)Time elapsed: 0.007 s
% 3.04/1.90 % (26962)Instructions burned: 20 (million)
% 3.04/1.90 % (26962)------------------------------
% 3.04/1.90 % (26962)------------------------------
% 3.04/1.90 % (26963)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26818 for (2998ds/3Mi)
% 3.04/1.90 % (26963)Instruction limit reached!
% 3.04/1.90 % (26963)------------------------------
% 3.04/1.90 % (26963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.90 % (26963)Termination reason: Unknown
% 3.04/1.90 % (26963)Termination phase: shuffling
% 3.04/1.90
% 3.04/1.90 % (26963)Memory used [KB]: 1535
% 3.04/1.90 % (26963)Time elapsed: 0.002 s
% 3.04/1.90 % (26963)Instructions burned: 3 (million)
% 3.04/1.90 % (26963)------------------------------
% 3.04/1.90 % (26963)------------------------------
% 3.04/1.91 % (26964)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26818 for (2998ds/30Mi)
% 3.04/1.91 % (26965)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26818 for (2998ds/127Mi)
% 3.04/1.92 % (26964)Instruction limit reached!
% 3.04/1.92 % (26964)------------------------------
% 3.04/1.92 % (26964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.92 % (26964)Termination reason: Unknown
% 3.04/1.92 % (26964)Termination phase: shuffling
% 3.04/1.92
% 3.04/1.92 % (26964)Memory used [KB]: 2046
% 3.04/1.92 % (26964)Time elapsed: 0.010 s
% 3.04/1.92 % (26964)Instructions burned: 30 (million)
% 3.04/1.92 % (26964)------------------------------
% 3.04/1.92 % (26964)------------------------------
% 3.04/1.92 % (26954)Refutation not found, incomplete strategy
% 3.04/1.92 % (26954)------------------------------
% 3.04/1.92 % (26954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.92 % (26954)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.92
% 3.04/1.92
% 3.04/1.92 % (26954)Memory used [KB]: 8443
% 3.04/1.92 % (26954)Time elapsed: 0.054 s
% 3.04/1.92 % (26954)Instructions burned: 186 (million)
% 3.04/1.92 % (26954)------------------------------
% 3.04/1.92 % (26954)------------------------------
% 3.04/1.93 % (26966)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26818 for (2998ds/100Mi)
% 3.04/1.93 % (26967)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_26818 for (2998ds/3Mi)
% 3.04/1.93 % (26967)Instruction limit reached!
% 3.04/1.93 % (26967)------------------------------
% 3.04/1.93 % (26967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.93 % (26967)Termination reason: Unknown
% 3.04/1.93 % (26967)Termination phase: shuffling
% 3.04/1.93
% 3.04/1.93 % (26967)Memory used [KB]: 1535
% 3.04/1.93 % (26967)Time elapsed: 0.002 s
% 3.04/1.93 % (26967)Instructions burned: 3 (million)
% 3.04/1.93 % (26967)------------------------------
% 3.04/1.93 % (26967)------------------------------
% 3.04/1.94 % (26968)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_26818 for (2998ds/20Mi)
% 3.04/1.94 % (26968)Instruction limit reached!
% 3.04/1.94 % (26968)------------------------------
% 3.04/1.94 % (26968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.94 % (26968)Termination reason: Unknown
% 3.04/1.94 % (26968)Termination phase: shuffling
% 3.04/1.94
% 3.04/1.94 % (26968)Memory used [KB]: 1918
% 3.04/1.94 % (26968)Time elapsed: 0.008 s
% 3.04/1.94 % (26968)Instructions burned: 22 (million)
% 3.04/1.94 % (26968)------------------------------
% 3.04/1.94 % (26968)------------------------------
% 3.04/1.95 % (26966)Instruction limit reached!
% 3.04/1.95 % (26966)------------------------------
% 3.04/1.95 % (26966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.95 % (26966)Termination reason: Unknown
% 3.04/1.95 % (26966)Termination phase: Property scanning
% 3.04/1.95
% 3.04/1.95 % (26966)Memory used [KB]: 2814
% 3.04/1.95 % (26966)Time elapsed: 0.027 s
% 3.04/1.95 % (26966)Instructions burned: 101 (million)
% 3.04/1.95 % (26966)------------------------------
% 3.04/1.95 % (26966)------------------------------
% 3.04/1.95 % (26969)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_26818 for (2998ds/86Mi)
% 3.04/1.96 % (26970)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_26818 for (2998ds/107Mi)
% 3.04/1.98 % (26965)Instruction limit reached!
% 3.04/1.98 % (26965)------------------------------
% 3.04/1.98 % (26965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.98 % (26965)Termination reason: Unknown
% 3.04/1.98 % (26965)Termination phase: Property scanning
% 3.04/1.98
% 3.04/1.98 % (26965)Memory used [KB]: 2942
% 3.04/1.98 % (26965)Time elapsed: 0.069 s
% 3.04/1.98 % (26965)Instructions burned: 128 (million)
% 3.04/1.98 % (26965)------------------------------
% 3.04/1.98 % (26965)------------------------------
% 3.04/1.98 % (26969)Instruction limit reached!
% 3.04/1.98 % (26969)------------------------------
% 3.04/1.98 % (26969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.98 % (26969)Termination reason: Unknown
% 3.04/1.98 % (26969)Termination phase: Property scanning
% 3.04/1.98
% 3.04/1.98 % (26969)Memory used [KB]: 2814
% 3.04/1.98 % (26969)Time elapsed: 0.026 s
% 3.04/1.98 % (26969)Instructions burned: 90 (million)
% 3.04/1.98 % (26969)------------------------------
% 3.04/1.98 % (26969)------------------------------
% 3.04/1.99 % (26972)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_26818 for (2998ds/448Mi)
% 3.04/1.99 % (26970)Instruction limit reached!
% 3.04/1.99 % (26970)------------------------------
% 3.04/1.99 % (26970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.99 % (26970)Termination reason: Unknown
% 3.04/1.99 % (26970)Termination phase: Saturation
% 3.04/1.99
% 3.04/1.99 % (26970)Memory used [KB]: 7036
% 3.04/1.99 % (26970)Time elapsed: 0.031 s
% 3.04/1.99 % (26970)Instructions burned: 108 (million)
% 3.04/1.99 % (26970)------------------------------
% 3.04/1.99 % (26970)------------------------------
% 3.04/2.00 % (26971)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_26818 for (2998ds/39Mi)
% 3.04/2.00 % (26973)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_26818 for (2997ds/46Mi)
% 3.04/2.01 % (26973)Instruction limit reached!
% 3.04/2.01 % (26973)------------------------------
% 3.04/2.01 % (26973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/2.01 % (26973)Termination reason: Unknown
% 3.04/2.01 % (26973)Termination phase: SInE selection
% 3.04/2.01
% 3.04/2.01 % (26973)Memory used [KB]: 1918
% 3.04/2.01 % (26973)Time elapsed: 0.015 s
% 3.04/2.01 % (26973)Instructions burned: 48 (million)
% 3.04/2.01 % (26973)------------------------------
% 3.04/2.01 % (26973)------------------------------
% 3.04/2.02 % (26971)Instruction limit reached!
% 3.04/2.02 % (26971)------------------------------
% 3.04/2.02 % (26971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/2.02 % (26971)Termination reason: Unknown
% 3.04/2.02 % (26971)Termination phase: shuffling
% 3.04/2.02
% 3.04/2.02 % (26971)Memory used [KB]: 2302
% 3.04/2.02 % (26971)Time elapsed: 0.022 s
% 3.04/2.02 % (26971)Instructions burned: 40 (million)
% 3.04/2.02 % (26971)------------------------------
% 3.04/2.02 % (26971)------------------------------
% 4.56/2.02 % (26974)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_26818 for (2997ds/98Mi)
% 4.56/2.03 % (26975)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_26818 for (2997ds/507Mi)
% 4.56/2.05 % (26974)Instruction limit reached!
% 4.56/2.05 % (26974)------------------------------
% 4.56/2.05 % (26974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.56/2.05 % (26974)Termination reason: Unknown
% 4.56/2.05 % (26974)Termination phase: Property scanning
% 4.56/2.05
% 4.56/2.05 % (26974)Memory used [KB]: 2814
% 4.56/2.05 % (26974)Time elapsed: 0.029 s
% 4.56/2.05 % (26974)Instructions burned: 98 (million)
% 4.56/2.05 % (26974)------------------------------
% 4.56/2.05 % (26974)------------------------------
% 4.56/2.08 % (26976)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_26818 for (2997ds/149Mi)
% 4.56/2.10 % (26958)Instruction limit reached!
% 4.56/2.10 % (26958)------------------------------
% 4.56/2.10 % (26958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.56/2.10 % (26958)Termination reason: Unknown
% 4.56/2.10 % (26958)Termination phase: Saturation
% 4.56/2.10
% 4.56/2.10 % (26958)Memory used [KB]: 9083
% 4.56/2.10 % (26958)Time elapsed: 0.212 s
% 4.56/2.10 % (26958)Instructions burned: 377 (million)
% 4.56/2.10 % (26958)------------------------------
% 4.56/2.10 % (26958)------------------------------
% 4.56/2.10 % (26975)Refutation not found, incomplete strategy
% 4.56/2.10 % (26975)------------------------------
% 4.56/2.10 % (26975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.56/2.10 % (26975)Termination reason: Refutation not found, incomplete strategy
% 4.56/2.10
% 4.56/2.10
% 4.56/2.10 % (26975)Memory used [KB]: 8827
% 4.56/2.10 % (26975)Time elapsed: 0.066 s
% 4.56/2.10 % (26975)Instructions burned: 204 (million)
% 4.56/2.10 % (26975)------------------------------
% 4.56/2.10 % (26975)------------------------------
% 4.56/2.11 % (26978)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_26818 for (2996ds/6Mi)
% 4.56/2.11 % (26978)Instruction limit reached!
% 4.56/2.11 % (26978)------------------------------
% 4.56/2.11 % (26978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.56/2.11 % (26978)Termination reason: Unknown
% 4.56/2.11 % (26978)Termination phase: shuffling
% 4.56/2.11
% 4.56/2.11 % (26978)Memory used [KB]: 1663
% 4.56/2.11 % (26978)Time elapsed: 0.004 s
% 4.56/2.11 % (26978)Instructions burned: 9 (million)
% 4.56/2.11 % (26978)------------------------------
% 4.56/2.11 % (26978)------------------------------
% 4.56/2.11 % (26977)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26818 for (2996ds/39Mi)
% 4.56/2.12 % (26972)Instruction limit reached!
% 4.56/2.12 % (26972)------------------------------
% 4.56/2.12 % (26972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.56/2.12 % (26972)Termination reason: Unknown
% 4.56/2.12 % (26972)Termination phase: Saturation
% 4.56/2.12
% 4.56/2.12 % (26972)Memory used [KB]: 8059
% 4.56/2.12 % (26972)Time elapsed: 0.133 s
% 4.56/2.12 % (26972)Instructions burned: 448 (million)
% 4.56/2.12 % (26972)------------------------------
% 4.56/2.12 % (26972)------------------------------
% 4.56/2.12 % (26959)Instruction limit reached!
% 4.56/2.12 % (26959)------------------------------
% 4.56/2.12 % (26959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.56/2.12 % (26959)Termination reason: Unknown
% 4.56/2.12 % (26959)Termination phase: Saturation
% 4.56/2.12
% 4.56/2.12 % (26959)Memory used [KB]: 8827
% 4.56/2.12 % (26959)Time elapsed: 0.236 s
% 4.56/2.12 % (26959)Instructions burned: 781 (million)
% 4.56/2.12 % (26959)------------------------------
% 4.56/2.12 % (26959)------------------------------
% 4.56/2.12 % (26979)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_26818 for (2996ds/1087Mi)
% 5.18/2.13 % (26980)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26818 for (2996ds/47Mi)
% 5.18/2.13 % (26981)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_26818 for (2996ds/44Mi)
% 5.18/2.13 % (26977)Instruction limit reached!
% 5.18/2.13 % (26977)------------------------------
% 5.18/2.13 % (26977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.18/2.13 % (26977)Termination reason: Unknown
% 5.18/2.13 % (26977)Termination phase: Property scanning
% 5.18/2.13
% 5.18/2.13 % (26977)Memory used [KB]: 2046
% 5.18/2.13 % (26977)Time elapsed: 0.022 s
% 5.18/2.13 % (26977)Instructions burned: 39 (million)
% 5.18/2.13 % (26977)------------------------------
% 5.18/2.13 % (26977)------------------------------
% 5.18/2.14 % (26981)Instruction limit reached!
% 5.18/2.14 % (26981)------------------------------
% 5.18/2.14 % (26981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.18/2.14 % (26981)Termination reason: Unknown
% 5.18/2.14 % (26981)Termination phase: shuffling
% 5.18/2.14
% 5.18/2.14 % (26981)Memory used [KB]: 2302
% 5.18/2.14 % (26981)Time elapsed: 0.013 s
% 5.18/2.14 % (26981)Instructions burned: 44 (million)
% 5.18/2.14 % (26981)------------------------------
% 5.18/2.14 % (26981)------------------------------
% 5.18/2.14 % (26980)Instruction limit reached!
% 5.18/2.14 % (26980)------------------------------
% 5.18/2.14 % (26980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.18/2.14 % (26980)Termination reason: Unknown
% 5.18/2.14 % (26980)Termination phase: Preprocessing 1
% 5.18/2.14
% 5.18/2.14 % (26980)Memory used [KB]: 2174
% 5.18/2.14 % (26980)Time elapsed: 0.015 s
% 5.18/2.14 % (26980)Instructions burned: 48 (million)
% 5.18/2.14 % (26980)------------------------------
% 5.18/2.14 % (26980)------------------------------
% 5.18/2.15 % (26983)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26818 for (2996ds/62Mi)
% 5.18/2.15 % (26984)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_26818 for (2996ds/31Mi)
% 5.18/2.15 % (26982)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_26818 for (2996ds/432Mi)
% 5.18/2.16 % (26976)Instruction limit reached!
% 5.18/2.16 % (26976)------------------------------
% 5.18/2.16 % (26976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.18/2.16 % (26976)Termination reason: Unknown
% 5.18/2.16 % (26976)Termination phase: Property scanning
% 5.18/2.16
% 5.18/2.16 % (26976)Memory used [KB]: 2942
% 5.18/2.16 % (26976)Time elapsed: 0.078 s
% 5.18/2.16 % (26976)Instructions burned: 150 (million)
% 5.18/2.16 % (26976)------------------------------
% 5.18/2.16 % (26976)------------------------------
% 5.18/2.16 % (26984)Instruction limit reached!
% 5.18/2.16 % (26984)------------------------------
% 5.18/2.16 % (26984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.18/2.16 % (26984)Termination reason: Unknown
% 5.18/2.16 % (26984)Termination phase: Property scanning
% 5.18/2.16
% 5.18/2.16 % (26984)Memory used [KB]: 2046
% 5.18/2.16 % (26984)Time elapsed: 0.011 s
% 5.18/2.16 % (26984)Instructions burned: 33 (million)
% 5.18/2.16 % (26984)------------------------------
% 5.18/2.16 % (26984)------------------------------
% 5.18/2.17 % (26983)Instruction limit reached!
% 5.18/2.17 % (26983)------------------------------
% 5.18/2.17 % (26983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.18/2.17 % (26983)Termination reason: Unknown
% 5.18/2.17 % (26983)Termination phase: shuffling
% 5.18/2.17
% 5.18/2.17 % (26983)Memory used [KB]: 2686
% 5.18/2.17 % (26983)Time elapsed: 0.018 s
% 5.18/2.17 % (26983)Instructions burned: 63 (million)
% 5.18/2.17 % (26983)------------------------------
% 5.18/2.17 % (26983)------------------------------
% 5.18/2.17 % (26986)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_26818 for (2996ds/453Mi)
% 5.18/2.18 % (26985)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26818 for (2996ds/96Mi)
% 5.18/2.18 % (26987)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_26818 for (2996ds/71Mi)
% 5.54/2.20 % (26987)Instruction limit reached!
% 5.54/2.20 % (26987)------------------------------
% 5.54/2.20 % (26987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.20 % (26987)Termination reason: Unknown
% 5.54/2.20 % (26987)Termination phase: Preprocessing 3
% 5.54/2.20
% 5.54/2.20 % (26987)Memory used [KB]: 2686
% 5.54/2.20 % (26987)Time elapsed: 0.022 s
% 5.54/2.20 % (26987)Instructions burned: 72 (million)
% 5.54/2.20 % (26987)------------------------------
% 5.54/2.20 % (26987)------------------------------
% 5.54/2.21 % (26988)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26818 for (2995ds/83Mi)
% 5.54/2.21 % (26943)Instruction limit reached!
% 5.54/2.21 % (26943)------------------------------
% 5.54/2.21 % (26943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.21 % (26943)Termination reason: Unknown
% 5.54/2.21 % (26943)Termination phase: Saturation
% 5.54/2.21
% 5.54/2.21 % (26943)Memory used [KB]: 10490
% 5.54/2.21 % (26943)Time elapsed: 0.386 s
% 5.54/2.21 % (26943)Instructions burned: 1042 (million)
% 5.54/2.21 % (26943)------------------------------
% 5.54/2.21 % (26943)------------------------------
% 5.54/2.22 % (26989)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26818 for (2995ds/11Mi)
% 5.54/2.23 % (26985)Instruction limit reached!
% 5.54/2.23 % (26985)------------------------------
% 5.54/2.23 % (26985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.23 % (26985)Termination reason: Unknown
% 5.54/2.23 % (26985)Termination phase: Property scanning
% 5.54/2.23
% 5.54/2.23 % (26985)Memory used [KB]: 2814
% 5.54/2.23 % (26985)Time elapsed: 0.053 s
% 5.54/2.23 % (26985)Instructions burned: 97 (million)
% 5.54/2.23 % (26985)------------------------------
% 5.54/2.23 % (26985)------------------------------
% 5.54/2.23 % (26989)Instruction limit reached!
% 5.54/2.23 % (26989)------------------------------
% 5.54/2.23 % (26989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.23 % (26989)Termination reason: Unknown
% 5.54/2.23 % (26989)Termination phase: shuffling
% 5.54/2.23
% 5.54/2.23 % (26989)Memory used [KB]: 1663
% 5.54/2.23 % (26989)Time elapsed: 0.008 s
% 5.54/2.23 % (26989)Instructions burned: 12 (million)
% 5.54/2.23 % (26989)------------------------------
% 5.54/2.23 % (26989)------------------------------
% 5.54/2.23 % (26988)Instruction limit reached!
% 5.54/2.23 % (26988)------------------------------
% 5.54/2.23 % (26988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.23 % (26988)Termination reason: Unknown
% 5.54/2.23 % (26988)Termination phase: Saturation
% 5.54/2.23
% 5.54/2.23 % (26988)Memory used [KB]: 6780
% 5.54/2.23 % (26988)Time elapsed: 0.027 s
% 5.54/2.23 % (26988)Instructions burned: 85 (million)
% 5.54/2.23 % (26988)------------------------------
% 5.54/2.23 % (26988)------------------------------
% 5.54/2.24 % (26992)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26818 for (2995ds/150Mi)
% 5.54/2.25 % (26991)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26818 for (2995ds/6Mi)
% 5.54/2.25 % (26990)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_26818 for (2995ds/41Mi)
% 5.54/2.25 % (26991)Instruction limit reached!
% 5.54/2.25 % (26991)------------------------------
% 5.54/2.25 % (26991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.25 % (26991)Termination reason: Unknown
% 5.54/2.25 % (26991)Termination phase: shuffling
% 5.54/2.25
% 5.54/2.25 % (26991)Memory used [KB]: 1663
% 5.54/2.25 % (26991)Time elapsed: 0.006 s
% 5.54/2.25 % (26991)Instructions burned: 6 (million)
% 5.54/2.25 % (26991)------------------------------
% 5.54/2.25 % (26991)------------------------------
% 5.54/2.26 % (26993)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26818 for (2995ds/343Mi)
% 5.54/2.27 % (26990)Instruction limit reached!
% 5.54/2.27 % (26990)------------------------------
% 5.54/2.27 % (26990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.27 % (26990)Termination reason: Unknown
% 5.54/2.27 % (26990)Termination phase: shuffling
% 5.54/2.27
% 5.54/2.27 % (26990)Memory used [KB]: 2302
% 5.54/2.27 % (26990)Time elapsed: 0.023 s
% 5.54/2.27 % (26990)Instructions burned: 41 (million)
% 5.54/2.27 % (26990)------------------------------
% 5.54/2.27 % (26990)------------------------------
% 5.54/2.28 % (26961)Instruction limit reached!
% 5.54/2.28 % (26961)------------------------------
% 5.54/2.28 % (26961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.28 % (26961)Termination reason: Unknown
% 5.54/2.28 % (26961)Termination phase: Saturation
% 5.54/2.28
% 5.54/2.28 % (26961)Memory used [KB]: 7291
% 5.54/2.28 % (26961)Time elapsed: 0.388 s
% 5.54/2.28 % (26961)Instructions burned: 879 (million)
% 5.54/2.28 % (26961)------------------------------
% 5.54/2.28 % (26961)------------------------------
% 5.54/2.29 % (26992)Instruction limit reached!
% 5.54/2.29 % (26992)------------------------------
% 5.54/2.29 % (26992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.29 % (26992)Termination reason: Unknown
% 5.54/2.29 % (26992)Termination phase: Property scanning
% 5.54/2.29
% 5.54/2.29 % (26992)Memory used [KB]: 3198
% 5.54/2.29 % (26992)Time elapsed: 0.043 s
% 5.54/2.29 % (26992)Instructions burned: 153 (million)
% 5.54/2.29 % (26992)------------------------------
% 5.54/2.29 % (26992)------------------------------
% 5.54/2.29 % (26994)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_26818 for (2995ds/109Mi)
% 5.54/2.29 % (26986)Instruction limit reached!
% 5.54/2.29 % (26986)------------------------------
% 5.54/2.29 % (26986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.29 % (26986)Termination reason: Unknown
% 5.54/2.29 % (26986)Termination phase: Saturation
% 5.54/2.29
% 5.54/2.29 % (26986)Memory used [KB]: 8059
% 5.54/2.29 % (26986)Time elapsed: 0.118 s
% 5.54/2.29 % (26986)Instructions burned: 456 (million)
% 5.54/2.29 % (26986)------------------------------
% 5.54/2.29 % (26986)------------------------------
% 5.54/2.29 % (26995)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_26818 for (2995ds/253Mi)
% 5.54/2.30 % (26996)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26818 for (2995ds/140Mi)
% 6.06/2.30 % (26997)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_26818 for (2995ds/614Mi)
% 6.06/2.31 % (26995)Refutation not found, incomplete strategy
% 6.06/2.31 % (26995)------------------------------
% 6.06/2.31 % (26995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.31 % (26995)Termination reason: Refutation not found, incomplete strategy
% 6.06/2.31
% 6.06/2.31
% 6.06/2.31 % (26995)Memory used [KB]: 7036
% 6.06/2.31 % (26995)Time elapsed: 0.025 s
% 6.06/2.31 % (26995)Instructions burned: 76 (million)
% 6.06/2.31 % (26995)------------------------------
% 6.06/2.31 % (26995)------------------------------
% 6.06/2.32 % (26996)First to succeed.
% 6.06/2.32 % (26996)Refutation found. Thanks to Tanya!
% 6.06/2.32 % SZS status Theorem for DTF2THF_26818
% 6.06/2.32 % SZS output start Proof for DTF2THF_26818
% 6.06/2.32 thf(type_def_5, type, set_li185139947ession: $tType).
% 6.06/2.32 thf(type_def_6, type, secrecy_Expression: $tType).
% 6.06/2.32 thf(type_def_8, type, set_list_Secrecy_KS: $tType).
% 6.06/2.32 thf(type_def_9, type, secrecy_KS: $tType).
% 6.06/2.32 thf(type_def_10, type, set_li849033543y_Keys: $tType).
% 6.06/2.32 thf(type_def_11, type, secrecy_Keys: $tType).
% 6.06/2.32 thf(type_def_12, type, set_li2007071804ecrets: $tType).
% 6.06/2.32 thf(type_def_13, type, secrecy_Secrets: $tType).
% 6.06/2.32 thf(type_def_14, type, list_S529945141ession: $tType).
% 6.06/2.32 thf(type_def_15, type, set_Se1942955227ession: $tType).
% 6.06/2.32 thf(type_def_16, type, list_Secrecy_KS: $tType).
% 6.06/2.32 thf(type_def_17, type, set_Secrecy_KS: $tType).
% 6.06/2.32 thf(type_def_18, type, list_Secrecy_Keys: $tType).
% 6.06/2.32 thf(type_def_19, type, set_Secrecy_Keys: $tType).
% 6.06/2.32 thf(type_def_20, type, list_Secrecy_Secrets: $tType).
% 6.06/2.32 thf(type_def_21, type, set_Secrecy_Secrets: $tType).
% 6.06/2.32 thf(type_def_22, type, secrecy_specID: $tType).
% 6.06/2.32 thf(type_def_23, type, list_l425507653ession: $tType).
% 6.06/2.32 thf(type_def_24, type, list_list_Secrecy_KS: $tType).
% 6.06/2.32 thf(func_def_0, type, list_l425507653ession: $tType).
% 6.06/2.32 thf(func_def_1, type, set_li185139947ession: $tType).
% 6.06/2.32 thf(func_def_2, type, set_li2007071804ecrets: $tType).
% 6.06/2.32 thf(func_def_3, type, set_li849033543y_Keys: $tType).
% 6.06/2.32 thf(func_def_4, type, list_list_Secrecy_KS: $tType).
% 6.06/2.32 thf(func_def_5, type, set_list_Secrecy_KS: $tType).
% 6.06/2.32 thf(func_def_6, type, list_S529945141ession: $tType).
% 6.06/2.32 thf(func_def_7, type, set_Se1942955227ession: $tType).
% 6.06/2.32 thf(func_def_8, type, list_Secrecy_Secrets: $tType).
% 6.06/2.32 thf(func_def_9, type, set_Secrecy_Secrets: $tType).
% 6.06/2.32 thf(func_def_10, type, list_Secrecy_Keys: $tType).
% 6.06/2.32 thf(func_def_11, type, set_Secrecy_Keys: $tType).
% 6.06/2.32 thf(func_def_12, type, list_Secrecy_KS: $tType).
% 6.06/2.32 thf(func_def_13, type, set_Secrecy_KS: $tType).
% 6.06/2.32 thf(func_def_14, type, secrecy_Expression: $tType).
% 6.06/2.32 thf(func_def_15, type, secrecy_Secrets: $tType).
% 6.06/2.32 thf(func_def_16, type, secrecy_specID: $tType).
% 6.06/2.32 thf(func_def_17, type, secrecy_Keys: $tType).
% 6.06/2.32 thf(func_def_18, type, secrecy_KS: $tType).
% 6.06/2.32 thf(func_def_19, type, bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession).
% 6.06/2.32 thf(func_def_20, type, bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS).
% 6.06/2.32 thf(func_def_21, type, bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys).
% 6.06/2.32 thf(func_def_22, type, bNF_Gr28627573ecrets: set_li2007071804ecrets > secrecy_Secrets > set_li2007071804ecrets).
% 6.06/2.32 thf(func_def_23, type, bNF_Gr979629770ession: set_li185139947ession > list_S529945141ession > set_Se1942955227ession).
% 6.06/2.32 thf(func_def_24, type, bNF_Gr577175642ecy_KS: set_list_Secrecy_KS > list_Secrecy_KS > set_Secrecy_KS).
% 6.06/2.32 thf(func_def_25, type, bNF_Gr344893606y_Keys: set_li849033543y_Keys > list_Secrecy_Keys > set_Secrecy_Keys).
% 6.06/2.32 thf(func_def_26, type, bNF_Gr957048817ecrets: set_li2007071804ecrets > list_Secrecy_Secrets > set_Secrecy_Secrets).
% 6.06/2.32 thf(func_def_27, type, localSecrets: secrecy_specID > set_Secrecy_KS).
% 6.06/2.32 thf(func_def_28, type, monoid929671412ession: (list_S529945141ession > list_S529945141ession > list_S529945141ession) > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_29, type, monoid1528146052ecy_KS: (list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS) > list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_30, type, knowle233900195orrect: secrecy_specID > secrecy_KS > $o).
% 6.06/2.32 thf(func_def_31, type, knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o).
% 6.06/2.32 thf(func_def_32, type, knowle945212990e_know: secrecy_specID > secrecy_KS > $o).
% 6.06/2.32 thf(func_def_33, type, knowle731562421_knows: secrecy_specID > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_34, type, disjoi1945222607ession: list_S529945141ession > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_35, type, memS_S2026082737ession: secrecy_Expression > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_36, type, mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_37, type, mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_38, type, append1105297242ession: list_l425507653ession > list_l425507653ession > list_l425507653ession).
% 6.06/2.32 thf(func_def_39, type, append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS).
% 6.06/2.32 thf(func_def_40, type, append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_41, type, append_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_42, type, append_Secrecy_Keys: list_Secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys).
% 6.06/2.32 thf(func_def_43, type, append186372209ecrets: list_Secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets).
% 6.06/2.32 thf(func_def_44, type, bind_S815874003ession: list_S529945141ession > (secrecy_Expression > list_S529945141ession) > list_S529945141ession).
% 6.06/2.32 thf(func_def_45, type, bind_S1823644515ecy_KS: list_S529945141ession > (secrecy_Expression > list_Secrecy_KS) > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_46, type, bind_S711229283ession: list_Secrecy_KS > (secrecy_KS > list_S529945141ession) > list_S529945141ession).
% 6.06/2.32 thf(func_def_47, type, bind_S645462771ecy_KS: list_Secrecy_KS > (secrecy_KS > list_Secrecy_KS) > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_48, type, butlas171474643ession: list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_49, type, butlast_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_50, type, concat388015140ession: list_l425507653ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_51, type, concat_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_52, type, distin1076152135ession: list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_53, type, distin1495927511ecy_KS: list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_54, type, foldr_1531709715ession: (list_S529945141ession > list_S529945141ession > list_S529945141ession) > list_l425507653ession > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_55, type, foldr_1711005747ecy_KS: (list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS) > list_list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_56, type, insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_57, type, insert_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_58, type, last_S1532390982ession: list_S529945141ession > secrecy_Expression).
% 6.06/2.32 thf(func_def_59, type, last_Secrecy_KS: list_Secrecy_KS > secrecy_KS).
% 6.06/2.32 thf(func_def_60, type, cons_l533358079ession: list_S529945141ession > list_l425507653ession > list_l425507653ession).
% 6.06/2.32 thf(func_def_61, type, cons_list_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS).
% 6.06/2.32 thf(func_def_62, type, cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_63, type, cons_Secrecy_KS: secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_64, type, cons_Secrecy_Keys: secrecy_Keys > list_Secrecy_Keys > list_Secrecy_Keys).
% 6.06/2.32 thf(func_def_65, type, cons_Secrecy_Secrets: secrecy_Secrets > list_Secrecy_Secrets > list_Secrecy_Secrets).
% 6.06/2.32 thf(func_def_66, type, nil_li311616943ession: list_l425507653ession).
% 6.06/2.32 thf(func_def_67, type, nil_list_Secrecy_KS: list_list_Secrecy_KS).
% 6.06/2.32 thf(func_def_68, type, nil_Se901661471ession: list_S529945141ession).
% 6.06/2.32 thf(func_def_69, type, nil_Secrecy_KS: list_Secrecy_KS).
% 6.06/2.32 thf(func_def_70, type, nil_Secrecy_Keys: list_Secrecy_Keys).
% 6.06/2.32 thf(func_def_71, type, nil_Secrecy_Secrets: list_Secrecy_Secrets).
% 6.06/2.32 thf(func_def_72, type, hd_lis1623417098ession: list_l425507653ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_73, type, hd_list_Secrecy_KS: list_list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_74, type, hd_Sec357328890ession: list_S529945141ession > secrecy_Expression).
% 6.06/2.32 thf(func_def_75, type, hd_Secrecy_KS: list_Secrecy_KS > secrecy_KS).
% 6.06/2.32 thf(func_def_76, type, tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_77, type, tl_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_78, type, list_e1486860828ession: (secrecy_Expression > $o) > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_79, type, list_ex1_Secrecy_KS: (secrecy_KS > $o) > list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_80, type, listre84909707ession: (secrecy_Expression > secrecy_Expression > $o) > list_S529945141ession > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_81, type, listre565996059ecy_KS: (secrecy_Expression > secrecy_KS > $o) > list_S529945141ession > list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_82, type, listre1601064475ession: (secrecy_KS > secrecy_Expression > $o) > list_Secrecy_KS > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_83, type, listre788412843ecy_KS: (secrecy_KS > secrecy_KS > $o) > list_Secrecy_KS > list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_84, type, map_ta1624757057ession: (secrecy_Expression > secrecy_Expression) > list_S529945141ession > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_85, type, map_ta623472337ession: (secrecy_KS > secrecy_Expression) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_86, type, maps_S599402637ession: (secrecy_Expression > list_S529945141ession) > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_87, type, maps_S399472669ecy_KS: (secrecy_Expression > list_Secrecy_KS) > list_S529945141ession > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_88, type, maps_S1434541085ession: (secrecy_KS > list_S529945141ession) > list_Secrecy_KS > list_S529945141ession).
% 6.06/2.32 thf(func_def_89, type, maps_S377605037ecy_KS: (secrecy_KS > list_Secrecy_KS) > list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_90, type, member2020590922ession: list_S529945141ession > secrecy_Expression > $o).
% 6.06/2.32 thf(func_def_91, type, member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o).
% 6.06/2.32 thf(func_def_92, type, lexord1123423577ession: (secrecy_Expression > secrecy_Expression > $o) > list_S529945141ession > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_93, type, lexord948960489ecy_KS: (secrecy_KS > secrecy_KS > $o) > list_Secrecy_KS > list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_94, type, produc1450295286ession: list_l425507653ession > list_l425507653ession).
% 6.06/2.32 thf(func_def_95, type, produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS).
% 6.06/2.32 thf(func_def_96, type, rev_Se1073238207ession: list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_97, type, rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_98, type, rotate1237234450ession: list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_99, type, rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_100, type, shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession).
% 6.06/2.32 thf(func_def_101, type, shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS).
% 6.06/2.32 thf(func_def_102, type, splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_103, type, splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_104, type, subseq348280080ession: list_S529945141ession > list_l425507653ession).
% 6.06/2.32 thf(func_def_105, type, subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS).
% 6.06/2.32 thf(func_def_106, type, succes1388047762ession: (secrecy_Expression > secrecy_Expression > $o) > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_107, type, succes590251810ecy_KS: (secrecy_KS > secrecy_KS > $o) > list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_108, type, decr: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_109, type, enc: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_110, type, encrDecrKeys: secrecy_Keys > secrecy_Keys > $o).
% 6.06/2.32 thf(func_def_111, type, ext: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_112, type, sign: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 6.06/2.32 thf(func_def_113, type, eout: secrecy_specID > secrecy_Expression > $o).
% 6.06/2.32 thf(func_def_114, type, ine: secrecy_specID > secrecy_Expression > $o).
% 6.06/2.32 thf(func_def_115, type, notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o).
% 6.06/2.32 thf(func_def_116, type, specKeys: secrecy_specID > set_Secrecy_Keys).
% 6.06/2.32 thf(func_def_117, type, specKeysSecrets: secrecy_specID > set_Secrecy_KS).
% 6.06/2.32 thf(func_def_118, type, specSecrets: secrecy_specID > set_Secrecy_Secrets).
% 6.06/2.32 thf(func_def_119, type, secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS).
% 6.06/2.32 thf(func_def_120, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 6.06/2.32 thf(func_def_121, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 6.06/2.32 thf(func_def_122, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 6.06/2.32 thf(func_def_123, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 6.06/2.32 thf(func_def_124, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 6.06/2.32 thf(func_def_125, type, collect_Secrecy_KS: (secrecy_KS > $o) > set_Secrecy_KS).
% 6.06/2.32 thf(func_def_126, type, collect_Secrecy_Keys: (secrecy_Keys > $o) > set_Secrecy_Keys).
% 6.06/2.32 thf(func_def_127, type, collec836099393ecrets: (secrecy_Secrets > $o) > set_Secrecy_Secrets).
% 6.06/2.32 thf(func_def_128, type, member249235532ession: list_S529945141ession > set_li185139947ession > $o).
% 6.06/2.32 thf(func_def_129, type, member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_130, type, member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o).
% 6.06/2.32 thf(func_def_131, type, member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o).
% 6.06/2.32 thf(func_def_132, type, member279582780ession: secrecy_Expression > set_Se1942955227ession > $o).
% 6.06/2.32 thf(func_def_133, type, member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o).
% 6.06/2.32 thf(func_def_134, type, member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o).
% 6.06/2.32 thf(func_def_135, type, member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o).
% 6.06/2.32 thf(func_def_136, type, a: secrecy_specID).
% 6.06/2.32 thf(func_def_137, type, m: secrecy_Keys).
% 6.06/2.32 thf(func_def_156, type, sK0: secrecy_KS > secrecy_Secrets).
% 6.06/2.32 thf(func_def_157, type, sK1: secrecy_KS > secrecy_Keys).
% 6.06/2.32 thf(func_def_158, type, sK2: (secrecy_KS > $o) > secrecy_Secrets).
% 6.06/2.32 thf(func_def_159, type, sK3: (secrecy_KS > $o) > secrecy_Keys).
% 6.06/2.32 thf(func_def_161, type, ph5: !>[X0: $tType]:(X0)).
% 6.06/2.32 thf(f1114,plain,(
% 6.06/2.32 $false),
% 6.06/2.32 inference(subsumption_resolution,[status(thm)],[f1112,f1072])).
% 6.06/2.32 thf(f1072,plain,(
% 6.06/2.32 ((knowle945212990e_know @ a @ (secrecy_kKS @ m)) != $true)),
% 6.06/2.32 inference(cnf_transformation,[status(thm)],[f1043])).
% 6.06/2.32 thf(f1043,plain,(
% 6.06/2.32 ((knowle945212990e_know @ a @ (secrecy_kKS @ m)) != $true)),
% 6.06/2.32 inference(flattening,[status(thm)],[f770])).
% 6.06/2.32 thf(f770,plain,(
% 6.06/2.32 ~((knowle945212990e_know @ a @ (secrecy_kKS @ m)) = $true)),
% 6.06/2.32 inference(fool_elimination,[status(thm)],[f769])).
% 6.06/2.32 thf(f769,plain,(
% 6.06/2.32 ~(knowle945212990e_know @ a @ (secrecy_kKS @ m))),
% 6.06/2.32 inference(rectify,[status(thm)],[f353])).
% 6.06/2.32 thf(f353,negated_conjecture,(
% 6.06/2.32 ~(knowle945212990e_know @ a @ (secrecy_kKS @ m))),
% 6.06/2.32 inference(negated_conjecture,[status(cth)],[f352])).
% 6.06/2.32 thf(f352,conjecture,(
% 6.06/2.32 (knowle945212990e_know @ a @ (secrecy_kKS @ m))),
% 6.06/2.32 file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',conj_0)).
% 6.06/2.32 thf(f1112,plain,(
% 6.06/2.32 ((knowle945212990e_know @ a @ (secrecy_kKS @ m)) = $true)),
% 6.06/2.32 inference(superposition,[status(thm)],[f1089,f1070])).
% 6.06/2.32 thf(f1070,plain,(
% 6.06/2.32 ((knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_kE @ m) @ nil_Se901661471ession)) = $true)),
% 6.06/2.32 inference(cnf_transformation,[status(thm)],[f993])).
% 6.06/2.32 thf(f993,plain,(
% 6.06/2.32 ((knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_kE @ m) @ nil_Se901661471ession)) = $true)),
% 6.06/2.32 inference(fool_elimination,[status(thm)],[f992])).
% 6.06/2.32 thf(f992,plain,(
% 6.06/2.32 (knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_kE @ m) @ nil_Se901661471ession))),
% 6.06/2.32 inference(rectify,[status(thm)],[f1])).
% 6.06/2.32 thf(f1,axiom,(
% 6.06/2.32 (knowle731562421_knows @ a @ (cons_S112077679ession @ (secrecy_kE @ m) @ nil_Se901661471ession))),
% 6.06/2.32 file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',fact_0_assms)).
% 6.06/2.32 thf(f1089,plain,(
% 6.06/2.32 ( ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (((knowle731562421_knows @ X0 @ (cons_S112077679ession @ (secrecy_kE @ X1) @ nil_Se901661471ession)) = (knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)))) )),
% 6.06/2.32 inference(forward_demodulation,[status(thm)],[f1077,f1071])).
% 6.06/2.32 thf(f1071,plain,(
% 6.06/2.32 ( ! [X0 : secrecy_Keys] : (((secrecy_kE @ X0) = (secrec1016742679ession @ (secrecy_kKS @ X0)))) )),
% 6.06/2.32 inference(cnf_transformation,[status(thm)],[f665])).
% 6.06/2.32 thf(f665,plain,(
% 6.06/2.32 ! [X0 : secrecy_Keys] : ((secrecy_kE @ X0) = (secrec1016742679ession @ (secrecy_kKS @ X0)))),
% 6.06/2.32 inference(fool_elimination,[status(thm)],[f664])).
% 6.06/2.32 thf(f664,plain,(
% 6.06/2.32 ! [X0 : secrecy_Keys] : ((secrecy_kE @ X0) = (secrec1016742679ession @ (secrecy_kKS @ X0)))),
% 6.06/2.32 inference(rectify,[status(thm)],[f14])).
% 6.06/2.32 thf(f14,axiom,(
% 6.06/2.32 ! [X9 : secrecy_Keys] : ((secrecy_kE @ X9) = (secrec1016742679ession @ (secrecy_kKS @ X9)))),
% 6.06/2.32 file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',fact_13_KS2Expression_Osimps_I1_J)).
% 6.06/2.32 thf(f1077,plain,(
% 6.06/2.32 ( ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (((knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)) = (knowle731562421_knows @ X0 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil_Se901661471ession)))) )),
% 6.06/2.32 inference(cnf_transformation,[status(thm)],[f399])).
% 6.06/2.32 thf(f399,plain,(
% 6.06/2.32 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)) = (knowle731562421_knows @ X0 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil_Se901661471ession)))),
% 6.06/2.32 inference(fool_elimination,[status(thm)],[f398])).
% 6.06/2.32 thf(f398,plain,(
% 6.06/2.32 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)) = (knowle731562421_knows @ X0 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil_Se901661471ession)))),
% 6.06/2.32 inference(rectify,[status(thm)],[f8])).
% 6.06/2.32 thf(f8,axiom,(
% 6.06/2.32 ! [X10 : secrecy_specID,X11 : secrecy_Keys] : ((knowle731562421_knows @ X10 @ (cons_S112077679ession @ (secrec1016742679ession @ (secrecy_kKS @ X11)) @ nil_Se901661471ession)) = (knowle945212990e_know @ X10 @ (secrecy_kKS @ X11)))),
% 6.06/2.32 file('/export/starexec/sandbox/tmp/tmp.Q2cnibQHuu/DTF2THF_26818.p',fact_7_know1k)).
% 6.06/2.32 % SZS output end Proof for DTF2THF_26818
% 6.06/2.32 % (26996)------------------------------
% 6.06/2.32 % (26996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.32 % (26996)Termination reason: Refutation
% 6.06/2.32
% 6.06/2.32 % (26996)Memory used [KB]: 6908
% 6.06/2.32 % (26996)Time elapsed: 0.046 s
% 6.06/2.32 % (26996)Instructions burned: 77 (million)
% 6.06/2.32 % (26996)------------------------------
% 6.06/2.32 % (26996)------------------------------
% 6.06/2.32 % (26931)Success in time 0.53 s
%------------------------------------------------------------------------------