%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP089^1 : 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 : n001.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 08:55:27 AM UTC 2026
% Result : Theorem 2.81s 1.95s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 259 ( 85 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 477 ( 59 ~; 40 |; 0 &; 354 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 91 usr; 12 con; 0-3 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
secrecy_specID: $tType ).
thf(type_def_6,type,
set_Secrecy_KS: $tType ).
thf(type_def_8,type,
secrecy_KS: $tType ).
thf(type_def_9,type,
set_Secrecy_Keys: $tType ).
thf(type_def_10,type,
set_Secrecy_Secrets: $tType ).
thf(type_def_11,type,
set_Secrecy_chanID: $tType ).
thf(type_def_12,type,
set_Secrecy_specID: $tType ).
thf(type_def_13,type,
secrecy_Expression: $tType ).
thf(type_def_14,type,
list_S529945141ession: $tType ).
thf(type_def_15,type,
secrecy_Keys: $tType ).
thf(type_def_16,type,
secrecy_Secrets: $tType ).
thf(type_def_17,type,
secrecy_chanID: $tType ).
thf(type_def_18,type,
nat: $tType ).
thf(func_def_0,type,
list_S529945141ession: $tType ).
thf(func_def_1,type,
set_Secrecy_Secrets: $tType ).
thf(func_def_2,type,
set_Secrecy_specID: $tType ).
thf(func_def_3,type,
set_Secrecy_chanID: $tType ).
thf(func_def_4,type,
set_Secrecy_Keys: $tType ).
thf(func_def_5,type,
set_Secrecy_KS: $tType ).
thf(func_def_6,type,
secrecy_Expression: $tType ).
thf(func_def_7,type,
secrecy_Secrets: $tType ).
thf(func_def_8,type,
secrecy_specID: $tType ).
thf(func_def_9,type,
secrecy_chanID: $tType ).
thf(func_def_10,type,
secrecy_Keys: $tType ).
thf(func_def_11,type,
secrecy_KS: $tType ).
thf(func_def_12,type,
nat: $tType ).
thf(func_def_13,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_14,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(func_def_15,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(func_def_16,type,
sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_17,type,
sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_18,type,
sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_19,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_20,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_21,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_22,type,
bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
thf(func_def_23,type,
bot_bo2072920570Keys_o: secrecy_Keys > $o ).
thf(func_def_24,type,
bot_bo1909946299rets_o: secrecy_Secrets > $o ).
thf(func_def_25,type,
bot_bo1012329985anID_o: secrecy_chanID > $o ).
thf(func_def_26,type,
bot_bo1767780696ecID_o: secrecy_specID > $o ).
thf(func_def_27,type,
bot_bo1943466239ecy_KS: set_Secrecy_KS ).
thf(func_def_28,type,
bot_bo701486667y_Keys: set_Secrecy_Keys ).
thf(func_def_29,type,
bot_bo1124690338ecrets: set_Secrecy_Secrets ).
thf(func_def_30,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(func_def_31,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(func_def_32,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_33,type,
correctCompositionKS: secrecy_specID > $o ).
thf(func_def_34,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_35,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_36,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_37,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_38,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_39,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_40,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_41,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_42,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_43,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_44,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_45,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_46,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_47,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_48,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_49,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_50,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_51,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_52,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_53,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_54,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_55,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(func_def_56,type,
collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
thf(func_def_57,type,
insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_58,type,
insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_59,type,
insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_60,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_61,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_62,type,
is_emp928984296chanID: set_Secrecy_chanID > $o ).
thf(func_def_63,type,
is_emp1849217361specID: set_Secrecy_specID > $o ).
thf(func_def_64,type,
is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
thf(func_def_65,type,
is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
thf(func_def_66,type,
is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
thf(func_def_67,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(func_def_68,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(func_def_69,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_70,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(func_def_71,type,
correctCompositionIn: secrecy_specID > $o ).
thf(func_def_72,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(func_def_73,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(func_def_74,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_75,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_76,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_77,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_78,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_79,type,
outStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_80,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(func_def_81,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(func_def_82,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(func_def_83,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(func_def_84,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_85,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(func_def_86,type,
p: secrecy_specID ).
thf(func_def_87,type,
pq: secrecy_specID ).
thf(func_def_88,type,
q: secrecy_specID ).
thf(func_def_89,type,
m: secrecy_KS ).
thf(func_def_90,type,
secret: secrecy_Secrets ).
thf(func_def_106,type,
sK0: ( secrecy_KS > $o ) > secrecy_Keys ).
thf(func_def_107,type,
sK1: ( secrecy_KS > $o ) > secrecy_Secrets ).
thf(func_def_108,type,
sK2: secrecy_specID > secrecy_Keys > secrecy_chanID ).
thf(func_def_109,type,
sK3: secrecy_Secrets > secrecy_specID > secrecy_chanID ).
thf(func_def_110,type,
sK4: secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Keys ).
thf(func_def_111,type,
sK5: secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Secrets ).
thf(func_def_112,type,
sK6: secrecy_KS > secrecy_Keys ).
thf(func_def_113,type,
sK7: secrecy_KS > secrecy_Secrets ).
thf(func_def_114,type,
sK8: secrecy_specID > secrecy_Secrets > secrecy_chanID ).
thf(func_def_115,type,
sK9: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets ).
thf(func_def_116,type,
sK10: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys ).
thf(func_def_117,type,
sK11: secrecy_Keys > secrecy_specID > secrecy_chanID ).
thf(func_def_119,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f1737,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1736,f1136]) ).
thf(f1136,plain,
( ( correc965049635ionLoc @ pq )
= $true ),
inference(cnf_transformation,[status(thm)],[f382]) ).
thf(f382,plain,
( ( correc965049635ionLoc @ pq )
= $true ),
inference(fool_elimination,[status(thm)],[f381]) ).
thf(f381,plain,
correc965049635ionLoc @ pq,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
correc965049635ionLoc @ pq,
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_0_cCompLoc) ).
thf(f1736,plain,
( ( correc965049635ionLoc @ pq )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f1735,f1113]) ).
thf(f1113,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f985]) ).
thf(f985,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
!= $true ),
inference(flattening,[status(thm)],[f454]) ).
thf(f454,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f453]) ).
thf(f453,plain,
~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_4_sg2b) ).
thf(f1735,plain,
( ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
= $true )
| ( ( correc965049635ionLoc @ pq )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1734,f1130]) ).
thf(f1130,plain,
( ( ine @ q @ ( secrecy_sE @ secret ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f999]) ).
thf(f999,plain,
( ( ine @ q @ ( secrecy_sE @ secret ) )
!= $true ),
inference(flattening,[status(thm)],[f870]) ).
thf(f870,plain,
( ( ine @ q @ ( secrecy_sE @ secret ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f869]) ).
thf(f869,plain,
~ ( ine @ q @ ( secrecy_sE @ secret ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
~ ( ine @ q @ ( secrecy_sE @ secret ) ),
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_2_sg2a) ).
thf(f1734,plain,
( ( ( ine @ q @ ( secrecy_sE @ secret ) )
= $true )
| ( ( correc965049635ionLoc @ pq )
!= $true )
| ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1733,f1086]) ).
thf(f1086,plain,
( ( ine @ p @ ( secrecy_sE @ secret ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1000]) ).
thf(f1000,plain,
( ( ine @ p @ ( secrecy_sE @ secret ) )
!= $true ),
inference(flattening,[status(thm)],[f856]) ).
thf(f856,plain,
( ( ine @ p @ ( secrecy_sE @ secret ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f855]) ).
thf(f855,plain,
~ ( ine @ p @ ( secrecy_sE @ secret ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
~ ( ine @ p @ ( secrecy_sE @ secret ) ),
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_1_sg1a) ).
thf(f1733,plain,
( ( ( ine @ p @ ( secrecy_sE @ secret ) )
= $true )
| ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
= $true )
| ( ( correc965049635ionLoc @ pq )
!= $true )
| ( ( ine @ q @ ( secrecy_sE @ secret ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1732,f1085]) ).
thf(f1085,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f984]) ).
thf(f984,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) )
!= $true ),
inference(flattening,[status(thm)],[f497]) ).
thf(f497,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f496]) ).
thf(f496,plain,
~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) ),
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_3_sg1b) ).
thf(f1732,plain,
( ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) )
= $true )
| ( ( ine @ p @ ( secrecy_sE @ secret ) )
= $true )
| ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
= $true )
| ( ( correc965049635ionLoc @ pq )
!= $true )
| ( ( ine @ q @ ( secrecy_sE @ secret ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1731]) ).
thf(f1731,plain,
( ( ( ine @ q @ ( secrecy_sE @ secret ) )
= $true )
| ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
= $true )
| ( $true != $true )
| ( ( ine @ p @ ( secrecy_sE @ secret ) )
= $true )
| ( ( subcomponents @ pq )
!= ( subcomponents @ pq ) )
| ( ( correc965049635ionLoc @ pq )
!= $true )
| ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) )
= $true ) ),
inference(superposition,[status(thm)],[f1255,f1084]) ).
thf(f1084,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f965]) ).
thf(f965,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) )
= $true ),
inference(flattening,[status(thm)],[f648]) ).
thf(f648,plain,
~ ( ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f647]) ).
thf(f647,plain,
~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ),
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',conj_0) ).
thf(f1255,plain,
! [X0: secrecy_specID,X1: secrecy_Secrets] :
( ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X1 ) @ ( localSecrets @ X0 ) ) )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X1 ) @ ( localSecrets @ q ) ) )
| ( ( correc965049635ionLoc @ X0 )
!= $true )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X1 ) @ ( localSecrets @ p ) ) )
| ( $true
= ( ine @ q @ ( secrecy_sE @ X1 ) ) )
| ( $true
= ( ine @ p @ ( secrecy_sE @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f1101,f1135]) ).
thf(f1135,plain,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_5_subPQ) ).
thf(f1101,plain,
! [X2: secrecy_specID,X3: secrecy_specID,X0: secrecy_Secrets,X1: secrecy_specID] :
( ( ( subcomponents @ X2 )
!= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
| ( ( correc965049635ionLoc @ X2 )
!= $true )
| ( ( ine @ X3 @ ( secrecy_sE @ X0 ) )
= $true )
| ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X2 ) ) )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X3 ) ) )
| ( $true
= ( ine @ X1 @ ( secrecy_sE @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1004]) ).
thf(f1004,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( ine @ X3 @ ( secrecy_sE @ X0 ) )
= $true )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
| ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X2 ) ) )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X3 ) ) )
| ( $true
= ( ine @ X1 @ ( secrecy_sE @ X0 ) ) )
| ( ( correc965049635ionLoc @ X2 )
!= $true )
| ( ( subcomponents @ X2 )
!= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ),
inference(flattening,[status(thm)],[f1003]) ).
thf(f1003,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_specID] :
( ( $true
= ( ine @ X1 @ ( secrecy_sE @ X0 ) ) )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X3 ) ) )
| ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
| ( ( ine @ X3 @ ( secrecy_sE @ X0 ) )
= $true )
| ( ( correc965049635ionLoc @ X2 )
!= $true )
| ( ( subcomponents @ X2 )
!= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
| ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f979]) ).
thf(f979,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_specID] :
( ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X2 ) ) )
=> ( ( ( subcomponents @ X2 )
= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( ( correc965049635ionLoc @ X2 )
= $true )
=> ( ( ( ine @ X3 @ ( secrecy_sE @ X0 ) )
!= $true )
=> ( ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
=> ( ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X3 ) ) )
=> ( $true
= ( ine @ X1 @ ( secrecy_sE @ X0 ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f630]) ).
thf(f630,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_specID] :
( ( $true
= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X2 ) ) )
=> ( ( ( subcomponents @ X2 )
= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( ( correc965049635ionLoc @ X2 )
= $true )
=> ( ( ( ine @ X3 @ ( secrecy_sE @ X0 ) )
!= $true )
=> ( ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
=> ( ( $true
!= ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X3 ) ) )
=> ( $true
= ( ine @ X1 @ ( secrecy_sE @ X0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f629]) ).
thf(f629,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID,X2: secrecy_specID,X3: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X2 ) )
=> ( ( ( subcomponents @ X2 )
= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ X2 )
=> ( ~ ( ine @ X3 @ ( secrecy_sE @ X0 ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X3 ) )
=> ( ine @ X1 @ ( secrecy_sE @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X4: secrecy_Secrets,X6: secrecy_specID,X5: secrecy_specID,X7: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ X4 ) @ ( localSecrets @ X5 ) )
=> ( ( ( subcomponents @ X5 )
= ( insert1671894227specID @ X6 @ ( insert1671894227specID @ X7 @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ X5 )
=> ( ~ ( ine @ X7 @ ( secrecy_sE @ X4 ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ X4 ) @ ( localSecrets @ X6 ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ X4 ) @ ( localSecrets @ X7 ) )
=> ( ine @ X6 @ ( secrecy_sE @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_13_LocalSecretsComposition__ine1__s) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP089^1 : 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
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:26:35 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : ITP089^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.47 % Domain : Interactive Theorem Proving
% 0.31/0.47 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_396__3295470_1
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Des21]
% 0.31/0.47 % Names : KnowledgeKeysSecrets/prob_396__3295470_1 [Des21]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.23 v8.1.0, 0.36 v7.5.0
% 0.31/0.47 % Syntax : Number of formulae : 447 ( 176 unt; 91 typ; 0 def)
% 0.31/0.47 % Number of atoms : 1273 ( 451 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 13 ( 3 avg)
% 0.31/0.47 % Number of connectives : 3885 ( 296 ~; 51 |; 125 &;2857 @)
% 0.31/0.47 % ( 0 <=>; 556 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 19 ( 7 avg)
% 0.31/0.47 % Number of types : 14 ( 13 usr)
% 0.31/0.47 % Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 79 ( 78 usr; 10 con; 0-3 aty)
% 0.31/0.47 % Number of variables : 994 ( 56 ^; 893 !; 45 ?; 994 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:35:26.675
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % Could-be-implicit typings (13)
% 0.31/0.47 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.31/0.47 list_S529945141ession: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.31/0.47 set_Secrecy_Secrets: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.31/0.47 set_Secrecy_specID: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.47 set_Secrecy_chanID: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.31/0.47 set_Secrecy_Keys: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.31/0.47 set_Secrecy_KS: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.31/0.47 secrecy_Expression: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.31/0.47 secrecy_Secrets: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.31/0.47 secrecy_specID: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Secrecy____types__OchanID,type,
% 0.31/0.47 secrecy_chanID: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.31/0.47 secrecy_Keys: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.31/0.47 secrecy_KS: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.31/0.47 nat: $tType ).
% 0.31/0.47
% 0.31/0.47 % Explicit typings (78)
% 0.31/0.47 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.31/0.47 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.31/0.47 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.31/0.47 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.31/0.47 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.31/0.47 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.31/0.47 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.47 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.31/0.47 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.31/0.47 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 0.31/0.47 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 0.31/0.47 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 0.31/0.47 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 0.31/0.47 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 0.31/0.47 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.31/0.47 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.31/0.47 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.31/0.47 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.47 bot_bo443197316chanID: set_Secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.31/0.47 bot_bo1785112429specID: set_Secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.47 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.31/0.47 correctCompositionKS: secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_Oeout,type,
% 0.31/0.47 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OeoutM,type,
% 0.31/0.47 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OexprChannel,type,
% 0.31/0.47 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_Oine,type,
% 0.31/0.47 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OineM,type,
% 0.31/0.47 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.31/0.47 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.31/0.47 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.31/0.47 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.31/0.47 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.31/0.47 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OspecKeys,type,
% 0.31/0.47 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.31/0.47 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.31/0.47 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.31/0.47 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.31/0.47 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.31/0.47 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.31/0.47 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.31/0.47 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.31/0.47 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.31/0.47 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.31/0.47 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 0.31/0.47 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 0.31/0.47 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 0.31/0.47 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 0.31/0.47 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 0.31/0.47 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 0.31/0.47 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 0.31/0.47 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 0.31/0.47 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 0.31/0.47 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 0.31/0.47 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 0.31/0.47 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 0.31/0.47 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 0.31/0.47 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 0.31/0.47 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 0.31/0.47 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 0.31/0.47 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.31/0.47 correctCompositionIn: secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.31/0.47 correc965049635ionLoc: secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.31/0.47 correc990227761ionOut: secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_OinStream,type,
% 0.31/0.47 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_Oins,type,
% 0.31/0.47 ins: secrecy_specID > set_Secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_Oloc,type,
% 0.31/0.47 loc: secrecy_specID > set_Secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_OlocStream,type,
% 0.31/0.47 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_Oout,type,
% 0.31/0.47 out: secrecy_specID > set_Secrecy_chanID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_OoutStream,type,
% 0.31/0.47 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_inout_Osubcomponents,type,
% 0.31/0.47 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.31/0.47 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.31/0.47 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.31/0.47 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 0.31/0.47 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 0.31/0.47 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_P,type,
% 0.31/0.47 p: secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_PQ,type,
% 0.31/0.47 pq: secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_Q,type,
% 0.31/0.47 q: secrecy_specID ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_m,type,
% 0.31/0.47 m: secrecy_KS ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_secret____,type,
% 0.31/0.47 secret: secrecy_Secrets ).
% 0.31/0.47
% 0.31/0.47 % Relevant facts (355)
% 0.31/0.47 thf(fact_0_cCompLoc,axiom,
% 0.31/0.47 correc965049635ionLoc @ pq ).
% 0.31/0.47
% 0.31/0.47 % cCompLoc
% 0.31/0.47 thf(fact_1_sg1a,axiom,
% 0.31/0.47 ~ ( ine @ p @ ( secrecy_sE @ secret ) ) ).
% 0.31/0.47
% 0.31/0.47 % sg1a
% 0.31/0.47 thf(fact_2_sg2a,axiom,
% 0.31/0.47 ~ ( ine @ q @ ( secrecy_sE @ secret ) ) ).
% 0.31/0.47
% 0.31/0.47 % sg2a
% 0.31/0.47 thf(fact_3_sg1b,axiom,
% 0.31/0.47 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) ) ).
% 0.31/0.47
% 0.31/0.47 % sg1b
% 0.31/0.47 thf(fact_4_sg2b,axiom,
% 0.31/0.47 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ).
% 0.31/0.47
% 0.31/0.47 % sg2b
% 0.31/0.47 thf(fact_5_subPQ,axiom,
% 0.31/0.47 ( ( subcomponents @ pq )
% 0.31/0.47 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subPQ
% 0.31/0.47 thf(fact_6_a2,axiom,
% 0.31/0.47 ( m
% 0.31/0.47 = ( secrecy_sKS @ secret ) ) ).
% 0.31/0.47
% 0.31/0.47 % a2
% 0.31/0.47 thf(fact_7_cCompI,axiom,
% 0.31/0.47 correctCompositionIn @ pq ).
% 0.31/0.47
% 0.31/0.47 % cCompI
% 0.31/0.47 thf(fact_8_sg3,axiom,
% 0.31/0.47 ~ ( ine @ pq @ ( secrecy_sE @ secret ) ) ).
% 0.31/0.47
% 0.31/0.47 % sg3
% 0.31/0.47 thf(fact_9_KS_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.31/0.47 ( ( ( secrecy_sKS @ X2 )
% 0.31/0.47 = ( secrecy_sKS @ Y2 ) )
% 0.31/0.47 = ( X2 = Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % KS.inject(2)
% 0.31/0.47 thf(fact_10_sg1,axiom,
% 0.31/0.47 ~ ( knowle945212990e_know @ p @ ( secrecy_sKS @ secret ) ) ).
% 0.31/0.47
% 0.31/0.47 % sg1
% 0.31/0.47 thf(fact_11_sg2,axiom,
% 0.31/0.47 ~ ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) ) ).
% 0.31/0.47
% 0.31/0.47 % sg2
% 0.31/0.47 thf(fact_12_know_Osimps_I2_J,axiom,
% 0.31/0.47 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.31/0.47 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % know.simps(2)
% 0.31/0.47 thf(fact_13_LocalSecretsComposition__ine1__s,axiom,
% 0.31/0.47 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.47 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_ine1_s
% 0.31/0.47 thf(fact_14_LocalSecretsComposition__ine2__s,axiom,
% 0.31/0.47 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.47 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_ine2_s
% 0.31/0.47 thf(fact_15_LocalSecretsComposition__neg1__s,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg1_s
% 0.31/0.47 thf(fact_16_KS2Expression_Osimps_I2_J,axiom,
% 0.31/0.47 ! [M: secrecy_Secrets] :
% 0.31/0.47 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.31/0.47 = ( secrecy_sE @ M ) ) ).
% 0.31/0.47
% 0.31/0.47 % KS2Expression.simps(2)
% 0.31/0.47 thf(fact_17_LocalSecretsComposition1,axiom,
% 0.31/0.47 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition1
% 0.31/0.47 thf(fact_18_not__know__s__not__ine,axiom,
% 0.31/0.47 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_know_s_not_ine
% 0.31/0.47 thf(fact_19_notknowQ,axiom,
% 0.31/0.47 ~ ( knowle945212990e_know @ q @ m ) ).
% 0.31/0.47
% 0.31/0.47 % notknowQ
% 0.31/0.47 thf(fact_20_notknowP,axiom,
% 0.31/0.47 ~ ( knowle945212990e_know @ p @ m ) ).
% 0.31/0.47
% 0.31/0.47 % notknowP
% 0.31/0.47 thf(fact_21_Expression_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.31/0.47 ( ( ( secrecy_sE @ X2 )
% 0.31/0.47 = ( secrecy_sE @ Y2 ) )
% 0.31/0.47 = ( X2 = Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Expression.inject(2)
% 0.31/0.47 thf(fact_22_know__composition__neg__ine__s,axiom,
% 0.31/0.47 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ~ ( knowle945212990e_know @ P @ ( secrecy_sKS @ Secret ) )
% 0.31/0.47 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % know_composition_neg_ine_s
% 0.31/0.47 thf(fact_23_TBtheorem1a,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( ine @ PQ @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( ine @ P @ E )
% 0.31/0.47 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem1a
% 0.31/0.47 thf(fact_24_TBtheorem3a,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ~ ( ine @ P @ E )
% 0.31/0.47 => ( ~ ( ine @ Q @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem3a
% 0.31/0.47 thf(fact_25_singletonI,axiom,
% 0.31/0.47 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_26_singletonI,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_27_singletonI,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_28_singletonI,axiom,
% 0.31/0.47 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_29_singletonI,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_30_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.31/0.47 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_31_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.31/0.47 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_32_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.31/0.47 ( ( ~ ( member740727610specID @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_33_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.31/0.47 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_34_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.31/0.47 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_35_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_36_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_37_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member740727610specID @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_38_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_39_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_40_insert__absorb2,axiom,
% 0.31/0.47 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A ) )
% 0.31/0.47 = ( insert1671894227specID @ X @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb2
% 0.31/0.47 thf(fact_41_insert__absorb2,axiom,
% 0.31/0.47 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A ) )
% 0.31/0.47 = ( insert751661162chanID @ X @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb2
% 0.31/0.47 thf(fact_42_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_KS] :
% 0.31/0.47 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_43_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_Secrets] :
% 0.31/0.47 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_44_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_Keys] :
% 0.31/0.47 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_45_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_specID] :
% 0.31/0.47 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_46_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_chanID] :
% 0.31/0.47 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_47_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ( ! [X3: secrecy_KS] :
% 0.31/0.47 ~ ( member_Secrecy_KS @ X3 @ A ) )
% 0.31/0.47 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_48_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( ! [X3: secrecy_Secrets] :
% 0.31/0.47 ~ ( member2138796287ecrets @ X3 @ A ) )
% 0.31/0.47 = ( A = bot_bo1124690338ecrets ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_49_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( ! [X3: secrecy_Keys] :
% 0.31/0.47 ~ ( member_Secrecy_Keys @ X3 @ A ) )
% 0.31/0.47 = ( A = bot_bo701486667y_Keys ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_50_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ( ! [X3: secrecy_specID] :
% 0.31/0.47 ~ ( member740727610specID @ X3 @ A ) )
% 0.31/0.47 = ( A = bot_bo1785112429specID ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_51_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ! [X3: secrecy_chanID] :
% 0.31/0.47 ~ ( member1967978193chanID @ X3 @ A ) )
% 0.31/0.47 = ( A = bot_bo443197316chanID ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_52_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P: secrecy_specID > $o] :
% 0.31/0.47 ( ( ( collec1545797240specID @ P )
% 0.31/0.47 = bot_bo1785112429specID )
% 0.31/0.47 = ( ! [X3: secrecy_specID] :
% 0.31/0.47 ~ ( P @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_53_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P: secrecy_chanID > $o] :
% 0.31/0.47 ( ( ( collec625564175chanID @ P )
% 0.31/0.47 = bot_bo443197316chanID )
% 0.31/0.47 = ( ! [X3: secrecy_chanID] :
% 0.31/0.47 ~ ( P @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_54_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P: secrecy_specID > $o] :
% 0.31/0.47 ( ( bot_bo1785112429specID
% 0.31/0.47 = ( collec1545797240specID @ P ) )
% 0.31/0.47 = ( ! [X3: secrecy_specID] :
% 0.31/0.47 ~ ( P @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_55_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P: secrecy_chanID > $o] :
% 0.31/0.47 ( ( bot_bo443197316chanID
% 0.31/0.47 = ( collec625564175chanID @ P ) )
% 0.31/0.47 = ( ! [X3: secrecy_chanID] :
% 0.31/0.47 ~ ( P @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_56_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ( ? [X3: secrecy_KS] : ( member_Secrecy_KS @ X3 @ A ) )
% 0.31/0.47 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_57_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( ? [X3: secrecy_Secrets] : ( member2138796287ecrets @ X3 @ A ) )
% 0.31/0.47 = ( A != bot_bo1124690338ecrets ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_58_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( ? [X3: secrecy_Keys] : ( member_Secrecy_Keys @ X3 @ A ) )
% 0.31/0.47 = ( A != bot_bo701486667y_Keys ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_59_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ( ? [X3: secrecy_specID] : ( member740727610specID @ X3 @ A ) )
% 0.31/0.47 = ( A != bot_bo1785112429specID ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_60_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ? [X3: secrecy_chanID] : ( member1967978193chanID @ X3 @ A ) )
% 0.31/0.47 = ( A != bot_bo443197316chanID ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_61_equals0I,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ! [Y: secrecy_KS] :
% 0.31/0.47 ~ ( member_Secrecy_KS @ Y @ A )
% 0.31/0.48 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0I
% 0.31/0.48 thf(fact_62_equals0I,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ! [Y: secrecy_Secrets] :
% 0.31/0.48 ~ ( member2138796287ecrets @ Y @ A )
% 0.31/0.48 => ( A = bot_bo1124690338ecrets ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0I
% 0.31/0.48 thf(fact_63_equals0I,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Keys] :
% 0.31/0.48 ( ! [Y: secrecy_Keys] :
% 0.31/0.48 ~ ( member_Secrecy_Keys @ Y @ A )
% 0.31/0.48 => ( A = bot_bo701486667y_Keys ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0I
% 0.31/0.48 thf(fact_64_equals0I,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID] :
% 0.31/0.48 ( ! [Y: secrecy_specID] :
% 0.31/0.48 ~ ( member740727610specID @ Y @ A )
% 0.31/0.48 => ( A = bot_bo1785112429specID ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0I
% 0.31/0.48 thf(fact_65_equals0I,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID] :
% 0.31/0.48 ( ! [Y: secrecy_chanID] :
% 0.31/0.48 ~ ( member1967978193chanID @ Y @ A )
% 0.31/0.48 => ( A = bot_bo443197316chanID ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0I
% 0.31/0.48 thf(fact_66_equals0D,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 0.31/0.48 ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.48 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0D
% 0.31/0.48 thf(fact_67_equals0D,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 0.31/0.48 ( ( A = bot_bo1124690338ecrets )
% 0.31/0.48 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0D
% 0.31/0.48 thf(fact_68_equals0D,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 0.31/0.48 ( ( A = bot_bo701486667y_Keys )
% 0.31/0.48 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0D
% 0.31/0.48 thf(fact_69_equals0D,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 0.31/0.48 ( ( A = bot_bo1785112429specID )
% 0.31/0.48 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0D
% 0.31/0.48 thf(fact_70_equals0D,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 0.31/0.48 ( ( A = bot_bo443197316chanID )
% 0.31/0.48 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0D
% 0.31/0.48 thf(fact_71_emptyE,axiom,
% 0.31/0.48 ! [A2: secrecy_KS] :
% 0.31/0.48 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 0.31/0.48
% 0.31/0.48 % emptyE
% 0.31/0.48 thf(fact_72_emptyE,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets] :
% 0.31/0.48 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 0.31/0.48
% 0.31/0.48 % emptyE
% 0.31/0.48 thf(fact_73_emptyE,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys] :
% 0.31/0.48 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 0.31/0.48
% 0.31/0.48 % emptyE
% 0.31/0.48 thf(fact_74_emptyE,axiom,
% 0.31/0.48 ! [A2: secrecy_specID] :
% 0.31/0.48 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 0.31/0.48
% 0.31/0.48 % emptyE
% 0.31/0.48 thf(fact_75_emptyE,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID] :
% 0.31/0.48 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 0.31/0.48
% 0.31/0.48 % emptyE
% 0.31/0.48 thf(fact_76_mk__disjoint__insert,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ A2 @ A )
% 0.31/0.48 => ? [B3: set_Secrecy_KS] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 0.31/0.48 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_disjoint_insert
% 0.31/0.48 thf(fact_77_mk__disjoint__insert,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ A2 @ A )
% 0.31/0.48 => ? [B3: set_Secrecy_chanID] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert751661162chanID @ A2 @ B3 ) )
% 0.31/0.48 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_disjoint_insert
% 0.31/0.48 thf(fact_78_mk__disjoint__insert,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ A2 @ A )
% 0.31/0.48 => ? [B3: set_Secrecy_specID] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert1671894227specID @ A2 @ B3 ) )
% 0.31/0.48 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_disjoint_insert
% 0.31/0.48 thf(fact_79_mk__disjoint__insert,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ A2 @ A )
% 0.31/0.48 => ? [B3: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert565337510ecrets @ A2 @ B3 ) )
% 0.31/0.48 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_disjoint_insert
% 0.31/0.48 thf(fact_80_mk__disjoint__insert,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.31/0.48 => ? [B3: set_Secrecy_Keys] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 0.31/0.48 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_disjoint_insert
% 0.31/0.48 thf(fact_81_insert__commute,axiom,
% 0.31/0.48 ! [X: secrecy_specID,Y3: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y3 @ A ) )
% 0.31/0.48 = ( insert1671894227specID @ Y3 @ ( insert1671894227specID @ X @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_commute
% 0.31/0.48 thf(fact_82_insert__commute,axiom,
% 0.31/0.48 ! [X: secrecy_chanID,Y3: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y3 @ A ) )
% 0.31/0.48 = ( insert751661162chanID @ Y3 @ ( insert751661162chanID @ X @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_commute
% 0.31/0.48 thf(fact_83_insert__eq__iff,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 0.31/0.48 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 0.31/0.48 = ( insert_Secrecy_KS @ B2 @ B ) )
% 0.31/0.48 = ( ( ( A2 = B2 )
% 0.31/0.48 => ( A = B ) )
% 0.31/0.48 & ( ( A2 != B2 )
% 0.31/0.48 => ? [C2: set_Secrecy_KS] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 0.31/0.48 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 0.31/0.48 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_eq_iff
% 0.31/0.48 thf(fact_84_insert__eq__iff,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ~ ( member1967978193chanID @ A2 @ A )
% 0.31/0.48 => ( ~ ( member1967978193chanID @ B2 @ B )
% 0.31/0.48 => ( ( ( insert751661162chanID @ A2 @ A )
% 0.31/0.48 = ( insert751661162chanID @ B2 @ B ) )
% 0.31/0.48 = ( ( ( A2 = B2 )
% 0.31/0.48 => ( A = B ) )
% 0.31/0.48 & ( ( A2 != B2 )
% 0.31/0.48 => ? [C2: set_Secrecy_chanID] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert751661162chanID @ B2 @ C2 ) )
% 0.31/0.48 & ~ ( member1967978193chanID @ B2 @ C2 )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert751661162chanID @ A2 @ C2 ) )
% 0.31/0.48 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_eq_iff
% 0.31/0.48 thf(fact_85_insert__eq__iff,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ~ ( member740727610specID @ A2 @ A )
% 0.31/0.48 => ( ~ ( member740727610specID @ B2 @ B )
% 0.31/0.48 => ( ( ( insert1671894227specID @ A2 @ A )
% 0.31/0.48 = ( insert1671894227specID @ B2 @ B ) )
% 0.31/0.48 = ( ( ( A2 = B2 )
% 0.31/0.48 => ( A = B ) )
% 0.31/0.48 & ( ( A2 != B2 )
% 0.31/0.48 => ? [C2: set_Secrecy_specID] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert1671894227specID @ B2 @ C2 ) )
% 0.31/0.48 & ~ ( member740727610specID @ B2 @ C2 )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert1671894227specID @ A2 @ C2 ) )
% 0.31/0.48 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_eq_iff
% 0.31/0.48 thf(fact_86_insert__eq__iff,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.48 ( ~ ( member2138796287ecrets @ A2 @ A )
% 0.31/0.48 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 0.31/0.48 => ( ( ( insert565337510ecrets @ A2 @ A )
% 0.31/0.48 = ( insert565337510ecrets @ B2 @ B ) )
% 0.31/0.48 = ( ( ( A2 = B2 )
% 0.31/0.48 => ( A = B ) )
% 0.31/0.48 & ( ( A2 != B2 )
% 0.31/0.48 => ? [C2: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert565337510ecrets @ B2 @ C2 ) )
% 0.31/0.48 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert565337510ecrets @ A2 @ C2 ) )
% 0.31/0.48 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_eq_iff
% 0.31/0.48 thf(fact_87_insert__eq__iff,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.48 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 0.31/0.48 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 0.31/0.48 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.31/0.48 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 0.31/0.48 = ( ( ( A2 = B2 )
% 0.31/0.48 => ( A = B ) )
% 0.31/0.48 & ( ( A2 != B2 )
% 0.31/0.48 => ? [C2: set_Secrecy_Keys] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 0.31/0.48 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 0.31/0.48 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_eq_iff
% 0.31/0.48 thf(fact_88_insert__absorb,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ A2 @ A )
% 0.31/0.48 => ( ( insert_Secrecy_KS @ A2 @ A )
% 0.31/0.48 = A ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_absorb
% 0.31/0.48 thf(fact_89_insert__absorb,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ A2 @ A )
% 0.31/0.48 => ( ( insert751661162chanID @ A2 @ A )
% 0.31/0.48 = A ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_absorb
% 0.31/0.48 thf(fact_90_insert__absorb,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ A2 @ A )
% 0.31/0.48 => ( ( insert1671894227specID @ A2 @ A )
% 0.31/0.48 = A ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_absorb
% 0.31/0.48 thf(fact_91_insert__absorb,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ A2 @ A )
% 0.31/0.48 => ( ( insert565337510ecrets @ A2 @ A )
% 0.31/0.48 = A ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_absorb
% 0.31/0.48 thf(fact_92_insert__absorb,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.31/0.48 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.31/0.48 = A ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_absorb
% 0.31/0.48 thf(fact_93_insert__ident,axiom,
% 0.31/0.48 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ~ ( member_Secrecy_KS @ X @ A )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ X @ B )
% 0.31/0.48 => ( ( ( insert_Secrecy_KS @ X @ A )
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ B ) )
% 0.31/0.48 = ( A = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_ident
% 0.31/0.48 thf(fact_94_insert__ident,axiom,
% 0.31/0.48 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ~ ( member1967978193chanID @ X @ A )
% 0.31/0.48 => ( ~ ( member1967978193chanID @ X @ B )
% 0.31/0.48 => ( ( ( insert751661162chanID @ X @ A )
% 0.31/0.48 = ( insert751661162chanID @ X @ B ) )
% 0.31/0.48 = ( A = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_ident
% 0.31/0.48 thf(fact_95_insert__ident,axiom,
% 0.31/0.48 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ~ ( member740727610specID @ X @ A )
% 0.31/0.48 => ( ~ ( member740727610specID @ X @ B )
% 0.31/0.48 => ( ( ( insert1671894227specID @ X @ A )
% 0.31/0.48 = ( insert1671894227specID @ X @ B ) )
% 0.31/0.48 = ( A = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_ident
% 0.31/0.48 thf(fact_96_insert__ident,axiom,
% 0.31/0.48 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.48 ( ~ ( member2138796287ecrets @ X @ A )
% 0.31/0.48 => ( ~ ( member2138796287ecrets @ X @ B )
% 0.31/0.48 => ( ( ( insert565337510ecrets @ X @ A )
% 0.31/0.48 = ( insert565337510ecrets @ X @ B ) )
% 0.31/0.48 = ( A = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_ident
% 0.31/0.48 thf(fact_97_insert__ident,axiom,
% 0.31/0.48 ! [X: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.48 ( ~ ( member_Secrecy_Keys @ X @ A )
% 0.31/0.48 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 0.31/0.48 => ( ( ( insert_Secrecy_Keys @ X @ A )
% 0.31/0.48 = ( insert_Secrecy_Keys @ X @ B ) )
% 0.31/0.48 = ( A = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_ident
% 0.31/0.48 thf(fact_98_Set_Oset__insert,axiom,
% 0.31/0.48 ! [X: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X @ A )
% 0.31/0.48 => ~ ! [B3: set_Secrecy_KS] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ B3 ) )
% 0.31/0.48 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.set_insert
% 0.31/0.48 thf(fact_99_Set_Oset__insert,axiom,
% 0.31/0.48 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X @ A )
% 0.31/0.48 => ~ ! [B3: set_Secrecy_chanID] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert751661162chanID @ X @ B3 ) )
% 0.31/0.48 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.set_insert
% 0.31/0.48 thf(fact_100_Set_Oset__insert,axiom,
% 0.31/0.48 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ X @ A )
% 0.31/0.48 => ~ ! [B3: set_Secrecy_specID] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert1671894227specID @ X @ B3 ) )
% 0.31/0.48 => ( member740727610specID @ X @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.set_insert
% 0.31/0.48 thf(fact_101_Set_Oset__insert,axiom,
% 0.31/0.48 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ X @ A )
% 0.31/0.48 => ~ ! [B3: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert565337510ecrets @ X @ B3 ) )
% 0.31/0.48 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.set_insert
% 0.31/0.48 thf(fact_102_Set_Oset__insert,axiom,
% 0.31/0.48 ! [X: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ X @ A )
% 0.31/0.48 => ~ ! [B3: set_Secrecy_Keys] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 0.31/0.48 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.set_insert
% 0.31/0.48 thf(fact_103_mem__Collect__eq,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 0.31/0.48 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 0.31/0.48 = ( P @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % mem_Collect_eq
% 0.31/0.48 thf(fact_104_mem__Collect__eq,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 0.31/0.48 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 0.31/0.48 = ( P @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % mem_Collect_eq
% 0.31/0.48 thf(fact_105_mem__Collect__eq,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 0.31/0.48 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 0.31/0.48 = ( P @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % mem_Collect_eq
% 0.31/0.48 thf(fact_106_mem__Collect__eq,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.31/0.48 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 0.31/0.48 = ( P @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % mem_Collect_eq
% 0.31/0.48 thf(fact_107_mem__Collect__eq,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 0.31/0.48 = ( P @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % mem_Collect_eq
% 0.31/0.48 thf(fact_108_Collect__mem__eq,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS] :
% 0.31/0.48 ( ( collect_Secrecy_KS
% 0.31/0.48 @ ^ [X3: secrecy_KS] : ( member_Secrecy_KS @ X3 @ A ) )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_mem_eq
% 0.31/0.48 thf(fact_109_Collect__mem__eq,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( collec625564175chanID
% 0.31/0.48 @ ^ [X3: secrecy_chanID] : ( member1967978193chanID @ X3 @ A ) )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_mem_eq
% 0.31/0.48 thf(fact_110_Collect__mem__eq,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID] :
% 0.31/0.48 ( ( collec1545797240specID
% 0.31/0.48 @ ^ [X3: secrecy_specID] : ( member740727610specID @ X3 @ A ) )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_mem_eq
% 0.31/0.48 thf(fact_111_Collect__mem__eq,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( collec836099393ecrets
% 0.31/0.48 @ ^ [X3: secrecy_Secrets] : ( member2138796287ecrets @ X3 @ A ) )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_mem_eq
% 0.31/0.48 thf(fact_112_Collect__mem__eq,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( collect_Secrecy_Keys
% 0.31/0.48 @ ^ [X3: secrecy_Keys] : ( member_Secrecy_Keys @ X3 @ A ) )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_mem_eq
% 0.31/0.48 thf(fact_113_insertI2,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ A2 @ B )
% 0.31/0.48 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI2
% 0.31/0.48 thf(fact_114_insertI2,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ A2 @ B )
% 0.31/0.48 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI2
% 0.31/0.48 thf(fact_115_insertI2,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ A2 @ B )
% 0.31/0.48 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI2
% 0.31/0.48 thf(fact_116_insertI2,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ A2 @ B )
% 0.31/0.48 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI2
% 0.31/0.48 thf(fact_117_insertI2,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ A2 @ B )
% 0.31/0.48 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI2
% 0.31/0.48 thf(fact_118_insertI1,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI1
% 0.31/0.48 thf(fact_119_insertI1,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI1
% 0.31/0.48 thf(fact_120_insertI1,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI1
% 0.31/0.48 thf(fact_121_insertI1,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI1
% 0.31/0.48 thf(fact_122_insertI1,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI1
% 0.31/0.48 thf(fact_123_insertE,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.31/0.48 => ( ( A2 != B2 )
% 0.31/0.48 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertE
% 0.31/0.48 thf(fact_124_insertE,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.31/0.48 => ( ( A2 != B2 )
% 0.31/0.48 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertE
% 0.31/0.48 thf(fact_125_insertE,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.31/0.48 => ( ( A2 != B2 )
% 0.31/0.48 => ( member740727610specID @ A2 @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertE
% 0.31/0.48 thf(fact_126_insertE,axiom,
% 0.31/0.48 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.31/0.48 => ( ( A2 != B2 )
% 0.31/0.48 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertE
% 0.31/0.48 thf(fact_127_insertE,axiom,
% 0.31/0.48 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.31/0.48 => ( ( A2 != B2 )
% 0.31/0.48 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertE
% 0.31/0.48 thf(fact_128_singleton__inject,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 0.31/0.48 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 0.31/0.48 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.31/0.48 => ( A2 = B2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_inject
% 0.31/0.48 thf(fact_129_singleton__inject,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 0.31/0.48 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 0.31/0.48 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.31/0.48 => ( A2 = B2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_inject
% 0.31/0.48 thf(fact_130_insert__not__empty,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( insert1671894227specID @ A2 @ A )
% 0.31/0.48 != bot_bo1785112429specID ) ).
% 0.31/0.48
% 0.31/0.48 % insert_not_empty
% 0.31/0.48 thf(fact_131_insert__not__empty,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( insert751661162chanID @ A2 @ A )
% 0.31/0.48 != bot_bo443197316chanID ) ).
% 0.31/0.48
% 0.31/0.48 % insert_not_empty
% 0.31/0.48 thf(fact_132_doubleton__eq__iff,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 0.31/0.48 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.31/0.48 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 0.31/0.48 = ( ( ( A2 = C )
% 0.31/0.48 & ( B2 = D ) )
% 0.31/0.48 | ( ( A2 = D )
% 0.31/0.48 & ( B2 = C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % doubleton_eq_iff
% 0.31/0.48 thf(fact_133_doubleton__eq__iff,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 0.31/0.48 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.31/0.48 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 0.31/0.48 = ( ( ( A2 = C )
% 0.31/0.48 & ( B2 = D ) )
% 0.31/0.48 | ( ( A2 = D )
% 0.31/0.48 & ( B2 = C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % doubleton_eq_iff
% 0.31/0.48 thf(fact_134_singleton__iff,axiom,
% 0.31/0.48 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.31/0.48 = ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_iff
% 0.31/0.48 thf(fact_135_singleton__iff,axiom,
% 0.31/0.48 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.31/0.48 = ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_iff
% 0.31/0.48 thf(fact_136_singleton__iff,axiom,
% 0.31/0.48 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.31/0.48 = ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_iff
% 0.31/0.48 thf(fact_137_singleton__iff,axiom,
% 0.31/0.48 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.31/0.48 = ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_iff
% 0.31/0.48 thf(fact_138_singleton__iff,axiom,
% 0.31/0.48 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.31/0.48 = ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_iff
% 0.31/0.48 thf(fact_139_singletonD,axiom,
% 0.31/0.48 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.31/0.48 => ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singletonD
% 0.31/0.48 thf(fact_140_singletonD,axiom,
% 0.31/0.48 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.31/0.48 => ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singletonD
% 0.31/0.48 thf(fact_141_singletonD,axiom,
% 0.31/0.48 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.31/0.48 => ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singletonD
% 0.31/0.48 thf(fact_142_singletonD,axiom,
% 0.31/0.48 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.31/0.48 => ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singletonD
% 0.31/0.48 thf(fact_143_singletonD,axiom,
% 0.31/0.48 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.31/0.48 => ( B2 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singletonD
% 0.31/0.48 thf(fact_144_the__elem__eq,axiom,
% 0.31/0.48 ! [X: secrecy_specID] :
% 0.31/0.48 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.48 = X ) ).
% 0.31/0.48
% 0.31/0.48 % the_elem_eq
% 0.31/0.48 thf(fact_145_the__elem__eq,axiom,
% 0.31/0.48 ! [X: secrecy_chanID] :
% 0.31/0.48 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.48 = X ) ).
% 0.31/0.48
% 0.31/0.48 % the_elem_eq
% 0.31/0.48 thf(fact_146_is__singletonI,axiom,
% 0.31/0.48 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI
% 0.31/0.48 thf(fact_147_is__singletonI,axiom,
% 0.31/0.48 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI
% 0.31/0.48 thf(fact_148_TBtheorem4a__empty,axiom,
% 0.31/0.48 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ( ( ine @ P @ E )
% 0.31/0.48 | ( ine @ Q @ E ) )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( ( loc @ PQ )
% 0.31/0.48 = bot_bo443197316chanID )
% 0.31/0.48 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4a_empty
% 0.31/0.48 thf(fact_149_TBtheorem3b,axiom,
% 0.31/0.48 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ~ ( ineM @ P @ M2 @ E )
% 0.31/0.48 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem3b
% 0.31/0.48 thf(fact_150_TBtheorem1b,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.48 ( ( ineM @ PQ @ M2 @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( ineM @ P @ M2 @ E )
% 0.31/0.48 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem1b
% 0.31/0.48 thf(fact_151_Set_Ois__empty__def,axiom,
% 0.31/0.48 ( is_emp1849217361specID
% 0.31/0.48 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.is_empty_def
% 0.31/0.48 thf(fact_152_Set_Ois__empty__def,axiom,
% 0.31/0.48 ( is_emp928984296chanID
% 0.31/0.48 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.is_empty_def
% 0.31/0.48 thf(fact_153_correctCompositionIn__prop1,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.31/0.48 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionIn_prop1
% 0.31/0.48 thf(fact_154_correctCompositionIn__L2,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionIn_L2
% 0.31/0.48 thf(fact_155_bot__set__def,axiom,
% 0.31/0.48 ( bot_bo1785112429specID
% 0.31/0.48 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_set_def
% 0.31/0.48 thf(fact_156_bot__set__def,axiom,
% 0.31/0.48 ( bot_bo443197316chanID
% 0.31/0.48 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_set_def
% 0.31/0.48 thf(fact_157_ineM__ine,axiom,
% 0.31/0.48 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.48 ( ( ineM @ P @ M2 @ E )
% 0.31/0.48 => ( ine @ P @ E ) ) ).
% 0.31/0.48
% 0.31/0.48 % ineM_ine
% 0.31/0.48 thf(fact_158_not__ine__ineM,axiom,
% 0.31/0.48 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 0.31/0.48 ( ~ ( ine @ P @ E )
% 0.31/0.48 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 0.31/0.48
% 0.31/0.48 % not_ine_ineM
% 0.31/0.48 thf(fact_159_is__singleton__the__elem,axiom,
% 0.31/0.48 ( is_sin1501507247specID
% 0.31/0.48 = ( ^ [A3: set_Secrecy_specID] :
% 0.31/0.48 ( A3
% 0.31/0.48 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singleton_the_elem
% 0.31/0.48 thf(fact_160_is__singleton__the__elem,axiom,
% 0.31/0.48 ( is_sin581274182chanID
% 0.31/0.48 = ( ^ [A3: set_Secrecy_chanID] :
% 0.31/0.48 ( A3
% 0.31/0.48 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singleton_the_elem
% 0.31/0.48 thf(fact_161_correctCompositionIn__L1,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionIn_L1
% 0.31/0.48 thf(fact_162_is__singletonI_H,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS] :
% 0.31/0.48 ( ( A != bot_bo1943466239ecy_KS )
% 0.31/0.48 => ( ! [X4: secrecy_KS,Y: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X4 @ A )
% 0.31/0.48 => ( ( member_Secrecy_KS @ Y @ A )
% 0.31/0.48 => ( X4 = Y ) ) )
% 0.31/0.48 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI'
% 0.31/0.48 thf(fact_163_is__singletonI_H,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( A != bot_bo1124690338ecrets )
% 0.31/0.48 => ( ! [X4: secrecy_Secrets,Y: secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ X4 @ A )
% 0.31/0.48 => ( ( member2138796287ecrets @ Y @ A )
% 0.31/0.48 => ( X4 = Y ) ) )
% 0.31/0.48 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI'
% 0.31/0.48 thf(fact_164_is__singletonI_H,axiom,
% 0.31/0.48 ! [A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( A != bot_bo701486667y_Keys )
% 0.31/0.48 => ( ! [X4: secrecy_Keys,Y: secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ X4 @ A )
% 0.31/0.48 => ( ( member_Secrecy_Keys @ Y @ A )
% 0.31/0.48 => ( X4 = Y ) ) )
% 0.31/0.48 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI'
% 0.31/0.48 thf(fact_165_is__singletonI_H,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID] :
% 0.31/0.48 ( ( A != bot_bo1785112429specID )
% 0.31/0.48 => ( ! [X4: secrecy_specID,Y: secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ X4 @ A )
% 0.31/0.48 => ( ( member740727610specID @ Y @ A )
% 0.31/0.48 => ( X4 = Y ) ) )
% 0.31/0.48 => ( is_sin1501507247specID @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI'
% 0.31/0.48 thf(fact_166_is__singletonI_H,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( A != bot_bo443197316chanID )
% 0.31/0.48 => ( ! [X4: secrecy_chanID,Y: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ A )
% 0.31/0.48 => ( ( member1967978193chanID @ Y @ A )
% 0.31/0.48 => ( X4 = Y ) ) )
% 0.31/0.48 => ( is_sin581274182chanID @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI'
% 0.31/0.48 thf(fact_167_is__singletonE,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID] :
% 0.31/0.48 ( ( is_sin1501507247specID @ A )
% 0.31/0.48 => ~ ! [X4: secrecy_specID] :
% 0.31/0.48 ( A
% 0.31/0.48 != ( insert1671894227specID @ X4 @ bot_bo1785112429specID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonE
% 0.31/0.48 thf(fact_168_is__singletonE,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( is_sin581274182chanID @ A )
% 0.31/0.48 => ~ ! [X4: secrecy_chanID] :
% 0.31/0.48 ( A
% 0.31/0.48 != ( insert751661162chanID @ X4 @ bot_bo443197316chanID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonE
% 0.31/0.48 thf(fact_169_is__singleton__def,axiom,
% 0.31/0.48 ( is_sin1501507247specID
% 0.31/0.48 = ( ^ [A3: set_Secrecy_specID] :
% 0.31/0.48 ? [X3: secrecy_specID] :
% 0.31/0.48 ( A3
% 0.31/0.48 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singleton_def
% 0.31/0.48 thf(fact_170_is__singleton__def,axiom,
% 0.31/0.48 ( is_sin581274182chanID
% 0.31/0.48 = ( ^ [A3: set_Secrecy_chanID] :
% 0.31/0.48 ? [X3: secrecy_chanID] :
% 0.31/0.48 ( A3
% 0.31/0.48 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singleton_def
% 0.31/0.48 thf(fact_171_subcomponents__loc,axiom,
% 0.31/0.48 ! [X: secrecy_specID] :
% 0.31/0.48 ( ( correc965049635ionLoc @ X )
% 0.31/0.48 => ( ( ( subcomponents @ X )
% 0.31/0.48 = bot_bo1785112429specID )
% 0.31/0.48 => ( ( loc @ X )
% 0.31/0.48 = bot_bo443197316chanID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % subcomponents_loc
% 0.31/0.48 thf(fact_172_TBtheorem4b__notP1,axiom,
% 0.31/0.48 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ( ineM @ P @ M2 @ E )
% 0.31/0.48 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.48 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.31/0.48 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.31/0.48 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4b_notP1
% 0.31/0.48 thf(fact_173_TBtheorem4a__notP1,axiom,
% 0.31/0.48 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ( ine @ P @ E )
% 0.31/0.48 => ( ~ ( ine @ Q @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.48 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.31/0.48 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4a_notP1
% 0.31/0.48 thf(fact_174_TBtheorem4b__notP2,axiom,
% 0.31/0.48 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.48 ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.48 => ( ! [X4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.31/0.48 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4b_notP2
% 0.31/0.48 thf(fact_175_TBtheorem4b__notPQ,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.48 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.48 => ( ! [X4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.31/0.48 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ( ! [X4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.31/0.48 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4b_notPQ
% 0.31/0.48 thf(fact_176_TBtheorem4a__notP2,axiom,
% 0.31/0.48 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.48 ( ~ ( ine @ Q @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.48 => ( ! [X4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.31/0.48 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4a_notP2
% 0.31/0.48 thf(fact_177_TBtheorem4a__notPQ,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.48 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.48 => ( ! [X4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.31/0.48 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ( ! [X4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.31/0.48 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4a_notPQ
% 0.31/0.48 thf(fact_178_ine__exprChannelSingle__Set,axiom,
% 0.31/0.48 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.48 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.31/0.48 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_exprChannelSingle_Set
% 0.31/0.48 thf(fact_179_ine__exprChannelSet__Single,axiom,
% 0.31/0.48 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.48 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.31/0.48 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_exprChannelSet_Single
% 0.31/0.48 thf(fact_180_ine__empty__exprChannelSet,axiom,
% 0.31/0.48 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.48 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.48 => ( ( ChSet = bot_bo443197316chanID )
% 0.31/0.48 => ~ ( ine @ P @ E ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_empty_exprChannelSet
% 0.31/0.48 thf(fact_181_ine__nonempty__exprChannelSet,axiom,
% 0.31/0.48 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.48 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.48 => ( ( ChSet != bot_bo443197316chanID )
% 0.31/0.48 => ( ine @ P @ E ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_nonempty_exprChannelSet
% 0.31/0.48 thf(fact_182_locStream__def,axiom,
% 0.31/0.48 ( locStream
% 0.31/0.48 = ( ^ [X3: secrecy_specID] :
% 0.31/0.48 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.31/0.48 @ ( loc @ X3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % locStream_def
% 0.31/0.48 thf(fact_183_inStream__def,axiom,
% 0.31/0.48 ( inStream
% 0.31/0.48 = ( ^ [X3: secrecy_specID] :
% 0.31/0.48 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.31/0.48 @ ( ins @ X3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inStream_def
% 0.31/0.48 thf(fact_184_TBtheorem4b__PQ,axiom,
% 0.31/0.48 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ( ( ineM @ P @ M2 @ E )
% 0.31/0.48 | ( ineM @ Q @ M2 @ E ) )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.48 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.31/0.48 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.31/0.48 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.31/0.48 & ( exprChannel @ Ch2 @ E )
% 0.31/0.48 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4b_PQ
% 0.31/0.48 thf(fact_185_TBtheorem4b__P,axiom,
% 0.31/0.48 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.48 ( ( ineM @ P @ M2 @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 0.31/0.48 & ( exprChannel @ Ch2 @ E )
% 0.31/0.48 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.31/0.48 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 0.31/0.48 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4b_P
% 0.31/0.48 thf(fact_186_TBtheorem4a__PQ,axiom,
% 0.31/0.48 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ( ( ine @ P @ E )
% 0.31/0.48 | ( ine @ Q @ E ) )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.48 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.31/0.48 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.31/0.48 & ( exprChannel @ Ch2 @ E )
% 0.31/0.48 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4a_PQ
% 0.31/0.48 thf(fact_187_TBtheorem4a__P,axiom,
% 0.31/0.48 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.48 ( ( ine @ P @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.31/0.48 & ( exprChannel @ Ch2 @ E )
% 0.31/0.48 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.48 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBtheorem4a_P
% 0.31/0.48 thf(fact_188_ine__def,axiom,
% 0.31/0.48 ( ine
% 0.31/0.48 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.31/0.48 ? [Ch3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.31/0.48 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_def
% 0.31/0.48 thf(fact_189_ine__ins__neg1,axiom,
% 0.31/0.48 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 0.31/0.48 ( ~ ( ine @ P @ M )
% 0.31/0.48 => ( ( exprChannel @ X @ M )
% 0.31/0.48 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_ins_neg1
% 0.31/0.48 thf(fact_190_ineM__def,axiom,
% 0.31/0.48 ( ineM
% 0.31/0.48 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.48 ? [Ch3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.31/0.48 & ( member1967978193chanID @ Ch3 @ M3 )
% 0.31/0.48 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ineM_def
% 0.31/0.48 thf(fact_191_ineM__L1,axiom,
% 0.31/0.48 ! [Ch: secrecy_chanID,M2: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch @ M2 )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ E )
% 0.31/0.48 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ineM_L1
% 0.31/0.48 thf(fact_192_ine__exprChannelSet__def,axiom,
% 0.31/0.48 ( ine_exprChannelSet
% 0.31/0.48 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.48 ( ! [X3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X3 @ ChSet2 )
% 0.31/0.48 => ( ( member1967978193chanID @ X3 @ ( ins @ SP ) )
% 0.31/0.48 & ( exprChannel @ X3 @ E2 ) ) )
% 0.31/0.48 & ! [X3: secrecy_chanID] :
% 0.31/0.48 ( ( ~ ( member1967978193chanID @ X3 @ ChSet2 )
% 0.31/0.48 & ( member1967978193chanID @ X3 @ ( ins @ SP ) ) )
% 0.31/0.48 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_exprChannelSet_def
% 0.31/0.48 thf(fact_193_ine__exprChannelSingle__def,axiom,
% 0.31/0.48 ( ine_ex1303305700Single
% 0.31/0.48 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.31/0.48 & ( exprChannel @ Ch3 @ E2 )
% 0.31/0.48 & ! [X3: secrecy_chanID,T: nat] :
% 0.31/0.48 ( ( ( member1967978193chanID @ X3 @ ( ins @ SP ) )
% 0.31/0.48 & ( X3 != Ch3 ) )
% 0.31/0.48 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ine_exprChannelSingle_def
% 0.31/0.48 thf(fact_194_LocalSecretsComposition__exprChannel__s,axiom,
% 0.31/0.48 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.48 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.31/0.48 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.31/0.48 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.31/0.48 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.31/0.48 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % LocalSecretsComposition_exprChannel_s
% 0.31/0.48 thf(fact_195_correctCompositionInLoc__exprChannel,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ M )
% 0.31/0.48 => ( ! [X4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X4 @ ( ins @ PQ ) )
% 0.31/0.48 => ~ ( exprChannel @ X4 @ M ) )
% 0.31/0.48 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionInLoc_exprChannel
% 0.31/0.48 thf(fact_196_TBlemma3b,axiom,
% 0.31/0.48 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.48 ( ~ ( ineM @ P @ M2 @ E )
% 0.31/0.48 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ M2 )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.48 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % TBlemma3b
% 0.31/0.48 thf(fact_197_Collect__empty__eq__bot,axiom,
% 0.31/0.48 ! [P: secrecy_specID > $o] :
% 0.31/0.48 ( ( ( collec1545797240specID @ P )
% 0.31/0.48 = bot_bo1785112429specID )
% 0.31/0.48 = ( P = bot_bo1767780696ecID_o ) ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_empty_eq_bot
% 0.31/0.48 thf(fact_198_Collect__empty__eq__bot,axiom,
% 0.31/0.48 ! [P: secrecy_chanID > $o] :
% 0.31/0.48 ( ( ( collec625564175chanID @ P )
% 0.31/0.48 = bot_bo443197316chanID )
% 0.31/0.48 = ( P = bot_bo1012329985anID_o ) ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_empty_eq_bot
% 0.31/0.48 thf(fact_199_bot__empty__eq,axiom,
% 0.31/0.48 ( bot_bot_Secrecy_KS_o
% 0.31/0.48 = ( ^ [X3: secrecy_KS] : ( member_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_empty_eq
% 0.31/0.48 thf(fact_200_bot__empty__eq,axiom,
% 0.31/0.48 ( bot_bo1909946299rets_o
% 0.31/0.48 = ( ^ [X3: secrecy_Secrets] : ( member2138796287ecrets @ X3 @ bot_bo1124690338ecrets ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_empty_eq
% 0.31/0.48 thf(fact_201_bot__empty__eq,axiom,
% 0.31/0.48 ( bot_bo2072920570Keys_o
% 0.31/0.48 = ( ^ [X3: secrecy_Keys] : ( member_Secrecy_Keys @ X3 @ bot_bo701486667y_Keys ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_empty_eq
% 0.31/0.48 thf(fact_202_bot__empty__eq,axiom,
% 0.31/0.48 ( bot_bo1767780696ecID_o
% 0.31/0.48 = ( ^ [X3: secrecy_specID] : ( member740727610specID @ X3 @ bot_bo1785112429specID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_empty_eq
% 0.31/0.48 thf(fact_203_bot__empty__eq,axiom,
% 0.31/0.48 ( bot_bo1012329985anID_o
% 0.31/0.48 = ( ^ [X3: secrecy_chanID] : ( member1967978193chanID @ X3 @ bot_bo443197316chanID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_empty_eq
% 0.31/0.48 thf(fact_204_LocalSecretsComposition__neg__loc__s,axiom,
% 0.31/0.48 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.48 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % LocalSecretsComposition_neg_loc_s
% 0.31/0.48 thf(fact_205_correctCompositionKS__exprChannel__s__P,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_s_P
% 0.31/0.48 thf(fact_206_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_s_Q
% 0.31/0.48 thf(fact_207_correctCompositionKS__negQ,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_negQ
% 0.31/0.48 thf(fact_208_correctCompositionKS__negP,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_negP
% 0.31/0.48 thf(fact_209_correctCompositionKS__neg1,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.31/0.48 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_neg1
% 0.31/0.48 thf(fact_210_correctCompositionKS__PQ,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.48 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_PQ
% 0.31/0.48 thf(fact_211_know__composition2,axiom,
% 0.31/0.48 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.48 => ( ( knowle945212990e_know @ Q @ M )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % know_composition2
% 0.31/0.48 thf(fact_212_know__composition1,axiom,
% 0.31/0.48 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.48 => ( ( knowle945212990e_know @ P @ M )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % know_composition1
% 0.31/0.48 thf(fact_213_know__composition,axiom,
% 0.31/0.48 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.48 => ( ( ( knowle945212990e_know @ P @ M )
% 0.31/0.48 | ( knowle945212990e_know @ Q @ M ) )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % know_composition
% 0.31/0.48 thf(fact_214_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ? [Ch4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_s_Qex
% 0.31/0.48 thf(fact_215_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ? [Ch4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_s_Pex
% 0.31/0.48 thf(fact_216_LocalSecretsComposition__neg__s,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.31/0.48 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.31/0.48 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.48 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % LocalSecretsComposition_neg_s
% 0.31/0.48 thf(fact_217_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ? [Ch4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_k_Qex
% 0.31/0.48 thf(fact_218_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ? [Ch4: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_k_Pex
% 0.31/0.48 thf(fact_219_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_k_Q
% 0.31/0.48 thf(fact_220_correctCompositionKS__exprChannel__k__P,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.48 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % correctCompositionKS_exprChannel_k_P
% 0.31/0.48 thf(fact_221_Un__iff,axiom,
% 0.31/0.48 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.31/0.48 = ( ( member740727610specID @ C @ A )
% 0.31/0.48 | ( member740727610specID @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_iff
% 0.31/0.48 thf(fact_222_Un__iff,axiom,
% 0.31/0.48 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.31/0.48 = ( ( member2138796287ecrets @ C @ A )
% 0.31/0.48 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_iff
% 0.31/0.48 thf(fact_223_Un__iff,axiom,
% 0.31/0.48 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.31/0.48 = ( ( member_Secrecy_Keys @ C @ A )
% 0.31/0.48 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_iff
% 0.31/0.48 thf(fact_224_Un__iff,axiom,
% 0.31/0.48 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.48 = ( ( member_Secrecy_KS @ C @ A )
% 0.31/0.48 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_iff
% 0.31/0.48 thf(fact_225_Un__iff,axiom,
% 0.31/0.48 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.48 = ( ( member1967978193chanID @ C @ A )
% 0.31/0.48 | ( member1967978193chanID @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_iff
% 0.31/0.48 thf(fact_226_UnCI,axiom,
% 0.31/0.48 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( ~ ( member740727610specID @ C @ B )
% 0.31/0.48 => ( member740727610specID @ C @ A ) )
% 0.31/0.48 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnCI
% 0.31/0.48 thf(fact_227_UnCI,axiom,
% 0.31/0.48 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( ~ ( member2138796287ecrets @ C @ B )
% 0.31/0.48 => ( member2138796287ecrets @ C @ A ) )
% 0.31/0.48 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnCI
% 0.31/0.48 thf(fact_228_UnCI,axiom,
% 0.31/0.48 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 0.31/0.48 => ( member_Secrecy_Keys @ C @ A ) )
% 0.31/0.48 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnCI
% 0.31/0.48 thf(fact_229_UnCI,axiom,
% 0.31/0.48 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.48 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 0.31/0.48 => ( member_Secrecy_KS @ C @ A ) )
% 0.31/0.48 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnCI
% 0.31/0.48 thf(fact_230_UnCI,axiom,
% 0.31/0.48 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( ~ ( member1967978193chanID @ C @ B )
% 0.31/0.48 => ( member1967978193chanID @ C @ A ) )
% 0.31/0.48 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnCI
% 0.31/0.48 thf(fact_231_KS_Oinject_I1_J,axiom,
% 0.31/0.48 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.31/0.48 ( ( ( secrecy_kKS @ X1 )
% 0.31/0.48 = ( secrecy_kKS @ Y1 ) )
% 0.31/0.48 = ( X1 = Y1 ) ) ).
% 0.31/0.48
% 0.31/0.48 % KS.inject(1)
% 0.31/0.48 thf(fact_232_Expression_Oinject_I1_J,axiom,
% 0.31/0.48 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.31/0.48 ( ( ( secrecy_kE @ X1 )
% 0.31/0.48 = ( secrecy_kE @ Y1 ) )
% 0.31/0.48 = ( X1 = Y1 ) ) ).
% 0.31/0.48
% 0.31/0.48 % Expression.inject(1)
% 0.31/0.48 thf(fact_233_Un__empty,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.31/0.48 = bot_bo1943466239ecy_KS )
% 0.31/0.48 = ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.48 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty
% 0.31/0.48 thf(fact_234_Un__empty,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ( ( sup_su1712599557specID @ A @ B )
% 0.31/0.48 = bot_bo1785112429specID )
% 0.31/0.48 = ( ( A = bot_bo1785112429specID )
% 0.31/0.48 & ( B = bot_bo1785112429specID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty
% 0.31/0.48 thf(fact_235_Un__empty,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( ( sup_su370684444chanID @ A @ B )
% 0.31/0.48 = bot_bo443197316chanID )
% 0.31/0.48 = ( ( A = bot_bo443197316chanID )
% 0.31/0.48 & ( B = bot_bo443197316chanID ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty
% 0.31/0.48 thf(fact_236_Un__insert__left,axiom,
% 0.31/0.48 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 0.31/0.48 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 0.31/0.48 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_insert_left
% 0.31/0.48 thf(fact_237_Un__insert__left,axiom,
% 0.31/0.48 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 0.31/0.48 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_insert_left
% 0.31/0.48 thf(fact_238_Un__insert__left,axiom,
% 0.31/0.48 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 0.31/0.48 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_insert_left
% 0.31/0.48 thf(fact_239_Un__insert__right,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 0.31/0.48 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_insert_right
% 0.31/0.48 thf(fact_240_Un__insert__right,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 0.31/0.48 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_insert_right
% 0.31/0.48 thf(fact_241_Un__insert__right,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 0.31/0.48 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_insert_right
% 0.31/0.48 thf(fact_242_not__know__k__not__ine,axiom,
% 0.31/0.48 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.48 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.48 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % not_know_k_not_ine
% 0.31/0.48 thf(fact_243_Un__empty__right,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty_right
% 0.31/0.48 thf(fact_244_Un__empty__right,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID] :
% 0.31/0.48 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty_right
% 0.31/0.48 thf(fact_245_Un__empty__right,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty_right
% 0.31/0.48 thf(fact_246_Un__empty__left,axiom,
% 0.31/0.48 ! [B: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 0.31/0.48 = B ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty_left
% 0.31/0.48 thf(fact_247_Un__empty__left,axiom,
% 0.31/0.48 ! [B: set_Secrecy_specID] :
% 0.31/0.48 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 0.31/0.48 = B ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty_left
% 0.31/0.48 thf(fact_248_Un__empty__left,axiom,
% 0.31/0.48 ! [B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 0.31/0.48 = B ) ).
% 0.31/0.48
% 0.31/0.48 % Un_empty_left
% 0.31/0.48 thf(fact_249_KS2Expression_Osimps_I1_J,axiom,
% 0.31/0.48 ! [M: secrecy_Keys] :
% 0.31/0.48 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.31/0.48 = ( secrecy_kE @ M ) ) ).
% 0.31/0.48
% 0.31/0.48 % KS2Expression.simps(1)
% 0.31/0.48 thf(fact_250_Un__left__commute,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 0.31/0.48 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_left_commute
% 0.31/0.48 thf(fact_251_Un__left__commute,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 0.31/0.48 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_left_commute
% 0.31/0.48 thf(fact_252_Un__left__absorb,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.48 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_left_absorb
% 0.31/0.48 thf(fact_253_Un__left__absorb,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.48 = ( sup_su370684444chanID @ A @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_left_absorb
% 0.31/0.48 thf(fact_254_Un__commute,axiom,
% 0.31/0.48 ( sup_su1301156759ecy_KS
% 0.31/0.48 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_commute
% 0.31/0.48 thf(fact_255_Un__commute,axiom,
% 0.31/0.48 ( sup_su370684444chanID
% 0.31/0.48 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_commute
% 0.31/0.48 thf(fact_256_Un__absorb,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ A @ A )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Un_absorb
% 0.31/0.48 thf(fact_257_Un__absorb,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ A @ A )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % Un_absorb
% 0.31/0.48 thf(fact_258_Un__assoc,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.31/0.48 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 0.31/0.48 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_assoc
% 0.31/0.48 thf(fact_259_Un__assoc,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.31/0.48 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 0.31/0.48 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_assoc
% 0.31/0.48 thf(fact_260_ball__Un,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.31/0.48 ( ( ! [X3: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X3 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.48 => ( P @ X3 ) ) )
% 0.31/0.48 = ( ! [X3: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X3 @ A )
% 0.31/0.48 => ( P @ X3 ) )
% 0.31/0.48 & ! [X3: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X3 @ B )
% 0.31/0.48 => ( P @ X3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ball_Un
% 0.31/0.48 thf(fact_261_ball__Un,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.31/0.48 ( ( ! [X3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X3 @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.48 => ( P @ X3 ) ) )
% 0.31/0.48 = ( ! [X3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X3 @ A )
% 0.31/0.48 => ( P @ X3 ) )
% 0.31/0.48 & ! [X3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X3 @ B )
% 0.31/0.48 => ( P @ X3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ball_Un
% 0.31/0.48 thf(fact_262_bex__Un,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.31/0.48 ( ( ? [X3: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X3 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.48 & ( P @ X3 ) ) )
% 0.31/0.48 = ( ? [X3: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X3 @ A )
% 0.31/0.48 & ( P @ X3 ) )
% 0.31/0.48 | ? [X3: secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ X3 @ B )
% 0.31/0.48 & ( P @ X3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bex_Un
% 0.31/0.48 thf(fact_263_bex__Un,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.31/0.48 ( ( ? [X3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X3 @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.48 & ( P @ X3 ) ) )
% 0.31/0.48 = ( ? [X3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X3 @ A )
% 0.31/0.48 & ( P @ X3 ) )
% 0.31/0.48 | ? [X3: secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ X3 @ B )
% 0.31/0.48 & ( P @ X3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % bex_Un
% 0.31/0.48 thf(fact_264_UnI2,axiom,
% 0.31/0.48 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ C @ B )
% 0.31/0.48 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI2
% 0.31/0.48 thf(fact_265_UnI2,axiom,
% 0.31/0.48 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ C @ B )
% 0.31/0.48 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI2
% 0.31/0.48 thf(fact_266_UnI2,axiom,
% 0.31/0.48 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ C @ B )
% 0.31/0.48 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI2
% 0.31/0.48 thf(fact_267_UnI2,axiom,
% 0.31/0.48 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ C @ B )
% 0.31/0.48 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI2
% 0.31/0.48 thf(fact_268_UnI2,axiom,
% 0.31/0.48 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ C @ B )
% 0.31/0.48 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI2
% 0.31/0.48 thf(fact_269_UnI1,axiom,
% 0.31/0.48 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ C @ A )
% 0.31/0.48 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI1
% 0.31/0.48 thf(fact_270_UnI1,axiom,
% 0.31/0.48 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ C @ A )
% 0.31/0.48 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI1
% 0.31/0.48 thf(fact_271_UnI1,axiom,
% 0.31/0.48 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ C @ A )
% 0.31/0.48 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI1
% 0.31/0.48 thf(fact_272_UnI1,axiom,
% 0.31/0.48 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ C @ A )
% 0.31/0.48 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI1
% 0.31/0.48 thf(fact_273_UnI1,axiom,
% 0.31/0.48 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ C @ A )
% 0.31/0.48 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnI1
% 0.31/0.48 thf(fact_274_UnE,axiom,
% 0.31/0.48 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.31/0.48 => ( ~ ( member740727610specID @ C @ A )
% 0.31/0.48 => ( member740727610specID @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnE
% 0.31/0.48 thf(fact_275_UnE,axiom,
% 0.31/0.48 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.48 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.31/0.48 => ( ~ ( member2138796287ecrets @ C @ A )
% 0.31/0.48 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnE
% 0.31/0.48 thf(fact_276_UnE,axiom,
% 0.31/0.48 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.48 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 0.31/0.48 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnE
% 0.31/0.48 thf(fact_277_UnE,axiom,
% 0.31/0.48 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ C @ A )
% 0.31/0.48 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnE
% 0.31/0.48 thf(fact_278_UnE,axiom,
% 0.31/0.48 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.48 => ( ~ ( member1967978193chanID @ C @ A )
% 0.31/0.48 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % UnE
% 0.31/0.48 thf(fact_279_KS_Oexhaust,axiom,
% 0.31/0.48 ! [Y3: secrecy_KS] :
% 0.31/0.48 ( ! [X12: secrecy_Keys] :
% 0.31/0.48 ( Y3
% 0.31/0.48 != ( secrecy_kKS @ X12 ) )
% 0.31/0.48 => ~ ! [X22: secrecy_Secrets] :
% 0.31/0.48 ( Y3
% 0.31/0.48 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % KS.exhaust
% 0.31/0.48 thf(fact_280_KS_Oinduct,axiom,
% 0.31/0.48 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.31/0.48 ( ! [X4: secrecy_Keys] : ( P @ ( secrecy_kKS @ X4 ) )
% 0.31/0.48 => ( ! [X4: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X4 ) )
% 0.31/0.48 => ( P @ KS ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % KS.induct
% 0.31/0.48 thf(fact_281_KS_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.31/0.48 ( ( secrecy_kKS @ X1 )
% 0.31/0.48 != ( secrecy_sKS @ X2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % KS.distinct(1)
% 0.31/0.48 thf(fact_282_Expression_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.31/0.48 ( ( secrecy_kE @ X1 )
% 0.31/0.48 != ( secrecy_sE @ X2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % Expression.distinct(1)
% 0.31/0.48 thf(fact_283_know_Osimps_I1_J,axiom,
% 0.31/0.48 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.48 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.48 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.31/0.48 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % know.simps(1)
% 0.31/0.48 thf(fact_284_insert__is__Un,axiom,
% 0.31/0.48 ( insert_Secrecy_KS
% 0.31/0.48 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_is_Un
% 0.31/0.48 thf(fact_285_insert__is__Un,axiom,
% 0.31/0.48 ( insert1671894227specID
% 0.31/0.48 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_is_Un
% 0.31/0.48 thf(fact_286_insert__is__Un,axiom,
% 0.31/0.48 ( insert751661162chanID
% 0.31/0.48 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_is_Un
% 0.31/0.48 thf(fact_287_Un__singleton__iff,axiom,
% 0.31/0.48 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 0.31/0.48 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.48 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.48 & ( B = bot_bo1943466239ecy_KS ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_singleton_iff
% 0.31/0.48 thf(fact_288_Un__singleton__iff,axiom,
% 0.31/0.48 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 0.31/0.48 ( ( ( sup_su1712599557specID @ A @ B )
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.48 = ( ( ( A = bot_bo1785112429specID )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.48 & ( B = bot_bo1785112429specID ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_singleton_iff
% 0.31/0.48 thf(fact_289_Un__singleton__iff,axiom,
% 0.31/0.48 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 0.31/0.48 ( ( ( sup_su370684444chanID @ A @ B )
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.48 = ( ( ( A = bot_bo443197316chanID )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.48 & ( B = bot_bo443197316chanID ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Un_singleton_iff
% 0.31/0.48 thf(fact_290_singleton__Un__iff,axiom,
% 0.31/0.48 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.48 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 0.31/0.48 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.48 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.48 & ( B = bot_bo1943466239ecy_KS ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_Un_iff
% 0.31/0.48 thf(fact_291_singleton__Un__iff,axiom,
% 0.31/0.48 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.48 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 0.31/0.48 = ( sup_su1712599557specID @ A @ B ) )
% 0.31/0.48 = ( ( ( A = bot_bo1785112429specID )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.48 & ( B = bot_bo1785112429specID ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_Un_iff
% 0.31/0.48 thf(fact_292_singleton__Un__iff,axiom,
% 0.31/0.48 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.48 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 0.31/0.48 = ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.48 = ( ( ( A = bot_bo443197316chanID )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.48 & ( B = bot_bo443197316chanID ) )
% 0.31/0.48 | ( ( A
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_Un_iff
% 0.31/0.48 thf(fact_293_LocalSecretsComposition__neg__loc__k,axiom,
% 0.31/0.48 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.48 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.31/0.48 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % LocalSecretsComposition_neg_loc_k
% 0.31/0.48 thf(fact_294_LocalSecretsComposition__neg__k,axiom,
% 0.31/0.48 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.48 ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.48 => ( ( correctCompositionKS @ PQ )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.31/0.48 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.31/0.48 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.31/0.48 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.48 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % LocalSecretsComposition_neg_k
% 0.31/0.48 thf(fact_295_know__composition__neg__ine__k,axiom,
% 0.31/0.48 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.48 ( ~ ( knowle945212990e_know @ P @ ( secrecy_kKS @ Key ) )
% 0.31/0.48 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_kKS @ Key ) )
% 0.31/0.48 => ( ( ( subcomponents @ PQ )
% 0.31/0.48 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.48 => ( ( correctCompositionIn @ PQ )
% 0.31/0.48 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % know_composition_neg_ine_k
% 0.31/0.49 thf(fact_296_LocalSecretsComposition__ine1__k,axiom,
% 0.31/0.49 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.49 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.49 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.31/0.49 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % LocalSecretsComposition_ine1_k
% 0.31/0.49 thf(fact_297_LocalSecretsComposition__ine2__k,axiom,
% 0.31/0.49 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.49 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.49 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.31/0.49 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % LocalSecretsComposition_ine2_k
% 0.31/0.49 thf(fact_298_LocalSecretsComposition__neg1__k,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.31/0.49 ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.49 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.31/0.49 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.31/0.49 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % LocalSecretsComposition_neg1_k
% 0.31/0.49 thf(fact_299_LocalSecretsComposition__exprChannel__k,axiom,
% 0.31/0.49 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.49 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.31/0.49 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.31/0.49 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.31/0.49 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.31/0.49 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % LocalSecretsComposition_exprChannel_k
% 0.31/0.49 thf(fact_300_LocalSecretsComposition__neg,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.49 ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.49 => ( ( correctCompositionKS @ PQ )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.31/0.49 => ( ! [M4: secrecy_Keys] :
% 0.31/0.49 ( ( Ks
% 0.31/0.49 = ( secrecy_kKS @ M4 ) )
% 0.31/0.49 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.31/0.49 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.31/0.49 => ( ! [M4: secrecy_Secrets] :
% 0.31/0.49 ( ( Ks
% 0.31/0.49 = ( secrecy_sKS @ M4 ) )
% 0.31/0.49 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.31/0.49 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.49 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % LocalSecretsComposition_neg
% 0.31/0.49 thf(fact_301_LocalSecretsComposition__neg1,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.49 ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.49 => ( ! [M4: secrecy_Keys] :
% 0.31/0.49 ( ( Ks
% 0.31/0.49 = ( secrecy_kKS @ M4 ) )
% 0.31/0.49 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.31/0.49 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.31/0.49 => ( ! [M4: secrecy_Secrets] :
% 0.31/0.49 ( ( Ks
% 0.31/0.49 = ( secrecy_sKS @ M4 ) )
% 0.31/0.49 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.31/0.49 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.31/0.49 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.31/0.49 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % LocalSecretsComposition_neg1
% 0.31/0.49 thf(fact_302_sup__bot__left,axiom,
% 0.31/0.49 ! [X: set_Secrecy_KS] :
% 0.31/0.49 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_left
% 0.31/0.49 thf(fact_303_sup__bot__left,axiom,
% 0.31/0.49 ! [X: set_Secrecy_specID] :
% 0.31/0.49 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_left
% 0.31/0.49 thf(fact_304_sup__bot__left,axiom,
% 0.31/0.49 ! [X: set_Secrecy_chanID] :
% 0.31/0.49 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_left
% 0.31/0.49 thf(fact_305_sup__bot__right,axiom,
% 0.31/0.49 ! [X: set_Secrecy_KS] :
% 0.31/0.49 ( ( sup_su1301156759ecy_KS @ X @ bot_bo1943466239ecy_KS )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_right
% 0.31/0.49 thf(fact_306_sup__bot__right,axiom,
% 0.31/0.49 ! [X: set_Secrecy_specID] :
% 0.31/0.49 ( ( sup_su1712599557specID @ X @ bot_bo1785112429specID )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_right
% 0.31/0.49 thf(fact_307_sup__bot__right,axiom,
% 0.31/0.49 ! [X: set_Secrecy_chanID] :
% 0.31/0.49 ( ( sup_su370684444chanID @ X @ bot_bo443197316chanID )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_right
% 0.31/0.49 thf(fact_308_bot__eq__sup__iff,axiom,
% 0.31/0.49 ! [X: set_Secrecy_KS,Y3: set_Secrecy_KS] :
% 0.31/0.49 ( ( bot_bo1943466239ecy_KS
% 0.31/0.49 = ( sup_su1301156759ecy_KS @ X @ Y3 ) )
% 0.31/0.49 = ( ( X = bot_bo1943466239ecy_KS )
% 0.31/0.49 & ( Y3 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bot_eq_sup_iff
% 0.31/0.49 thf(fact_309_bot__eq__sup__iff,axiom,
% 0.31/0.49 ! [X: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 0.31/0.49 ( ( bot_bo1785112429specID
% 0.31/0.49 = ( sup_su1712599557specID @ X @ Y3 ) )
% 0.31/0.49 = ( ( X = bot_bo1785112429specID )
% 0.31/0.49 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bot_eq_sup_iff
% 0.31/0.49 thf(fact_310_bot__eq__sup__iff,axiom,
% 0.31/0.49 ! [X: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.31/0.49 ( ( bot_bo443197316chanID
% 0.31/0.49 = ( sup_su370684444chanID @ X @ Y3 ) )
% 0.31/0.49 = ( ( X = bot_bo443197316chanID )
% 0.31/0.49 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bot_eq_sup_iff
% 0.31/0.49 thf(fact_311_sup__eq__bot__iff,axiom,
% 0.31/0.49 ! [X: set_Secrecy_KS,Y3: set_Secrecy_KS] :
% 0.31/0.49 ( ( ( sup_su1301156759ecy_KS @ X @ Y3 )
% 0.31/0.49 = bot_bo1943466239ecy_KS )
% 0.31/0.49 = ( ( X = bot_bo1943466239ecy_KS )
% 0.31/0.49 & ( Y3 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_eq_bot_iff
% 0.31/0.49 thf(fact_312_sup__eq__bot__iff,axiom,
% 0.31/0.49 ! [X: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 0.31/0.49 ( ( ( sup_su1712599557specID @ X @ Y3 )
% 0.31/0.49 = bot_bo1785112429specID )
% 0.31/0.49 = ( ( X = bot_bo1785112429specID )
% 0.31/0.49 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_eq_bot_iff
% 0.31/0.49 thf(fact_313_sup__eq__bot__iff,axiom,
% 0.31/0.49 ! [X: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.31/0.49 ( ( ( sup_su370684444chanID @ X @ Y3 )
% 0.31/0.49 = bot_bo443197316chanID )
% 0.31/0.49 = ( ( X = bot_bo443197316chanID )
% 0.31/0.49 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_eq_bot_iff
% 0.31/0.49 thf(fact_314_sup__bot_Oright__neutral,axiom,
% 0.31/0.49 ! [A2: set_Secrecy_specID] :
% 0.31/0.49 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 0.31/0.49 = A2 ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.right_neutral
% 0.31/0.49 thf(fact_315_sup__bot_Oright__neutral,axiom,
% 0.31/0.49 ! [A2: set_Secrecy_chanID] :
% 0.31/0.49 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 0.31/0.49 = A2 ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.right_neutral
% 0.31/0.49 thf(fact_316_ineM__Un1,axiom,
% 0.31/0.49 ! [P: secrecy_specID,A: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 0.31/0.49 ( ( ineM @ P @ A @ E )
% 0.31/0.49 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E ) ) ).
% 0.31/0.49
% 0.31/0.49 % ineM_Un1
% 0.31/0.49 thf(fact_317_notSpecKeysSecretsExpr__def,axiom,
% 0.31/0.49 ( notSpe1586871396tsExpr
% 0.31/0.49 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 0.31/0.49 ( ! [X3: secrecy_Keys] :
% 0.31/0.49 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X3 ) @ E3 )
% 0.31/0.49 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X3 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.31/0.49 & ! [Y5: secrecy_Secrets] :
% 0.31/0.49 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y5 ) @ E3 )
% 0.31/0.49 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y5 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % notSpecKeysSecretsExpr_def
% 0.31/0.49 thf(fact_318_TBtheorem5a__empty,axiom,
% 0.31/0.49 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.49 ( ( ( eout @ P @ E )
% 0.31/0.49 | ( eout @ Q @ E ) )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( ( loc @ PQ )
% 0.31/0.49 = bot_bo443197316chanID )
% 0.31/0.49 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5a_empty
% 0.31/0.49 thf(fact_319_correctCompositionKS__subcomp4,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.31/0.49 ( ( correctCompositionKS @ C3 )
% 0.31/0.49 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.49 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 0.31/0.49 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % correctCompositionKS_subcomp4
% 0.31/0.49 thf(fact_320_TBtheorem2a,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.49 ( ( eout @ PQ @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( eout @ P @ E )
% 0.31/0.49 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem2a
% 0.31/0.49 thf(fact_321_correctCompositionKS__subcomp2,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.31/0.49 ( ( correctCompositionKS @ C3 )
% 0.31/0.49 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.49 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 0.31/0.49 => ? [X4: secrecy_specID] :
% 0.31/0.49 ( ( member740727610specID @ X4 @ ( subcomponents @ C3 ) )
% 0.31/0.49 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X4 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % correctCompositionKS_subcomp2
% 0.31/0.49 thf(fact_322_TBtheorem5a__notP1,axiom,
% 0.31/0.49 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.49 ( ( eout @ P @ E )
% 0.31/0.49 => ( ~ ( eout @ Q @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.49 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.31/0.49 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5a_notP1
% 0.31/0.49 thf(fact_323_TBtheorem5a__notP2,axiom,
% 0.31/0.49 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.49 ( ~ ( eout @ Q @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.49 => ( ! [X4: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.31/0.49 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5a_notP2
% 0.31/0.49 thf(fact_324_TBtheorem5a__notPQ,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.31/0.49 ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.49 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.49 => ( ! [X4: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.31/0.49 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ( ! [X4: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.31/0.49 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5a_notPQ
% 0.31/0.49 thf(fact_325_out__exprChannelSingle__Set,axiom,
% 0.31/0.49 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.49 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.31/0.49 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.31/0.49
% 0.31/0.49 % out_exprChannelSingle_Set
% 0.31/0.49 thf(fact_326_out__exprChannelSet__Single,axiom,
% 0.31/0.49 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.49 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.31/0.49 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.31/0.49
% 0.31/0.49 % out_exprChannelSet_Single
% 0.31/0.49 thf(fact_327_TBtheorem5b__notPQ,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 0.31/0.49 ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.49 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.49 => ( ( M2
% 0.31/0.49 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 0.31/0.49 => ( ! [X4: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.31/0.49 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ( ! [X4: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.31/0.49 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5b_notPQ
% 0.31/0.49 thf(fact_328_eout__know__nonKS__s,axiom,
% 0.31/0.49 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.31/0.49 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.31/0.49 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 0.31/0.49 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.49 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eout_know_nonKS_s
% 0.31/0.49 thf(fact_329_eoutKnowCorrect__L1s,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.49 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.31/0.49 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.31/0.49 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.31/0.49 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eoutKnowCorrect_L1s
% 0.31/0.49 thf(fact_330_eoutM__eout,axiom,
% 0.31/0.49 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.49 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.49 => ( eout @ P @ E ) ) ).
% 0.31/0.49
% 0.31/0.49 % eoutM_eout
% 0.31/0.49 thf(fact_331_not__eout__eoutM,axiom,
% 0.31/0.49 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 0.31/0.49 ( ~ ( eout @ P @ E )
% 0.31/0.49 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 0.31/0.49
% 0.31/0.49 % not_eout_eoutM
% 0.31/0.49 thf(fact_332_TBtheorem2b,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.49 ( ( eoutM @ PQ @ M2 @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( eoutM @ P @ M2 @ E )
% 0.31/0.49 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem2b
% 0.31/0.49 thf(fact_333_TBtheorem5b__notP2,axiom,
% 0.31/0.49 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.49 ( ~ ( eoutM @ Q @ M2 @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.49 => ( ! [X4: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.31/0.49 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5b_notP2
% 0.31/0.49 thf(fact_334_TBtheorem5b__notP1,axiom,
% 0.31/0.49 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.49 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.49 => ( ~ ( eoutM @ Q @ M2 @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.49 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.31/0.49 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.31/0.49 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5b_notP1
% 0.31/0.49 thf(fact_335_eout__know__s,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.49 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.31/0.49 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.31/0.49 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.31/0.49 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eout_know_s
% 0.31/0.49 thf(fact_336_not__know__s__not__eout,axiom,
% 0.31/0.49 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.31/0.49 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.31/0.49 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.49 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.49 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % not_know_s_not_eout
% 0.31/0.49 thf(fact_337_TBtheore54b__P,axiom,
% 0.31/0.49 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.49 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 0.31/0.49 & ( exprChannel @ Ch2 @ E )
% 0.31/0.49 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.31/0.49 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 0.31/0.49 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheore54b_P
% 0.31/0.49 thf(fact_338_TBtheorem5b__PQ,axiom,
% 0.31/0.49 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.49 ( ( ( eoutM @ P @ M2 @ E )
% 0.31/0.49 | ( eoutM @ Q @ M2 @ E ) )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.49 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.31/0.49 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.31/0.49 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.31/0.49 & ( exprChannel @ Ch2 @ E )
% 0.31/0.49 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5b_PQ
% 0.31/0.49 thf(fact_339_TBtheorem45a__P,axiom,
% 0.31/0.49 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.49 ( ( eout @ P @ E )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.31/0.49 & ( exprChannel @ Ch2 @ E )
% 0.31/0.49 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem45a_P
% 0.31/0.49 thf(fact_340_eout__def,axiom,
% 0.31/0.49 ( eout
% 0.31/0.49 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.31/0.49 ? [Ch3: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.31/0.49 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eout_def
% 0.31/0.49 thf(fact_341_eoutM__def,axiom,
% 0.31/0.49 ( eoutM
% 0.31/0.49 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.49 ? [Ch3: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.31/0.49 & ( member1967978193chanID @ Ch3 @ M3 )
% 0.31/0.49 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eoutM_def
% 0.31/0.49 thf(fact_342_out__exprChannelSet__def,axiom,
% 0.31/0.49 ( out_exprChannelSet
% 0.31/0.49 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.49 ( ! [X3: secrecy_chanID] :
% 0.31/0.49 ( ( member1967978193chanID @ X3 @ ChSet2 )
% 0.31/0.49 => ( ( member1967978193chanID @ X3 @ ( out @ SP ) )
% 0.31/0.49 & ( exprChannel @ X3 @ E2 ) ) )
% 0.31/0.49 & ! [X3: secrecy_chanID] :
% 0.31/0.49 ( ( ~ ( member1967978193chanID @ X3 @ ChSet2 )
% 0.31/0.49 & ( member1967978193chanID @ X3 @ ( out @ SP ) ) )
% 0.31/0.49 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % out_exprChannelSet_def
% 0.31/0.49 thf(fact_343_out__exprChannelSingle__def,axiom,
% 0.31/0.49 ( out_ex985543062Single
% 0.31/0.49 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.49 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.31/0.49 & ( exprChannel @ Ch3 @ E2 )
% 0.31/0.49 & ! [X3: secrecy_chanID,T: nat] :
% 0.31/0.49 ( ( ( member1967978193chanID @ X3 @ ( out @ SP ) )
% 0.31/0.49 & ( X3 != Ch3 ) )
% 0.31/0.49 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % out_exprChannelSingle_def
% 0.31/0.49 thf(fact_344_correctCompositionOut__prop1,axiom,
% 0.31/0.49 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.31/0.49 ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 0.31/0.49 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 0.31/0.49 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % correctCompositionOut_prop1
% 0.31/0.49 thf(fact_345_TBtheorem5a__PQ,axiom,
% 0.31/0.49 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.49 ( ( ( eout @ P @ E )
% 0.31/0.49 | ( eout @ Q @ E ) )
% 0.31/0.49 => ( ( ( subcomponents @ PQ )
% 0.31/0.49 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.49 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.49 => ( ? [Ch2: secrecy_chanID] :
% 0.31/0.49 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.31/0.49 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.31/0.49 & ( exprChannel @ Ch2 @ E )
% 0.31/0.49 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.31/0.49 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % TBtheorem5a_PQ
% 0.31/0.49 thf(fact_346_outStream__def,axiom,
% 0.31/0.49 ( outStream
% 0.31/0.49 = ( ^ [X3: secrecy_specID] :
% 0.31/0.49 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.31/0.49 @ ( out @ X3 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % outStream_def
% 0.31/0.49 thf(fact_347_eout__know__k,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.49 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.31/0.49 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.31/0.49 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.31/0.49 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eout_know_k
% 0.31/0.49 thf(fact_348_correctCompositionKS__subcomp1,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.31/0.49 ( ( correctCompositionKS @ C3 )
% 0.31/0.49 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.49 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 0.31/0.49 => ? [X4: secrecy_specID] :
% 0.31/0.49 ( ( member740727610specID @ X4 @ ( subcomponents @ C3 ) )
% 0.31/0.49 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X4 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % correctCompositionKS_subcomp1
% 0.31/0.49 thf(fact_349_correctCompositionKS__subcomp3,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.31/0.49 ( ( correctCompositionKS @ C3 )
% 0.31/0.49 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.49 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.31/0.49 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % correctCompositionKS_subcomp3
% 0.31/0.49 thf(fact_350_eout__know__nonKS__k,axiom,
% 0.31/0.49 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.31/0.49 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.31/0.49 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 0.31/0.49 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.49 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eout_know_nonKS_k
% 0.31/0.49 thf(fact_351_eoutKnowCorrect__L1k,axiom,
% 0.31/0.49 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.49 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.31/0.49 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.31/0.49 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.31/0.49 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eoutKnowCorrect_L1k
% 0.31/0.49 thf(fact_352_not__know__k__not__eout,axiom,
% 0.31/0.49 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.31/0.49 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.31/0.49 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.49 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.49 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % not_know_k_not_eout
% 0.31/0.49 thf(fact_353_adv__not__know2,axiom,
% 0.31/0.49 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.49 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 0.31/0.49 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.49 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % adv_not_know2
% 0.31/0.49 thf(fact_354_adv__not__know1,axiom,
% 0.31/0.49 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.49 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 0.31/0.49 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.49 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % adv_not_know1
% 0.31/0.49
% 0.31/0.49 % Conjectures (1)
% 0.31/0.49 thf(conj_0,conjecture,
% 0.31/0.49 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ) ).
% 0.31/0.49
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 ------------------------
% 2.68/1.65 ---- Embedded in THF ---
% 2.68/1.65 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.68/1.65 %%% Generated on Tue Feb 24 08:26:36 EST 2026
% 2.68/1.65 %%% using '$$dhol' embedding, version 1.3.0.
% 2.68/1.65 %%% Logic specification used:
% 2.68/1.65 %%% thf(spec, logic, $$dhol).
% 2.68/1.65
% 2.68/1.65 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2DTF13473.p
% See solution above
% 2.68/1.65 ------------------------
% 2.68/1.68 ---- Cleaned THF ---
% 2.68/1.68 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.68/1.68 list_S529945141ession: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.68/1.68 set_Secrecy_Secrets: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.68/1.68 set_Secrecy_specID: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.68/1.68 set_Secrecy_chanID: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.68/1.68 set_Secrecy_Keys: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.68/1.68 set_Secrecy_KS: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Secrecy____types__OExpression,type,
% 2.68/1.68 secrecy_Expression: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 2.68/1.68 secrecy_Secrets: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Secrecy____types__OspecID,type,
% 2.68/1.68 secrecy_specID: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Secrecy____types__OchanID,type,
% 2.68/1.68 secrecy_chanID: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Secrecy____types__OKeys,type,
% 2.68/1.68 secrecy_Keys: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Secrecy____types__OKS,type,
% 2.68/1.68 secrecy_KS: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(ty_n_t__Nat__Onat,type,
% 2.68/1.68 nat: $tType ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.68/1.68 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 2.68/1.68 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 2.68/1.68 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.68/1.68 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.68/1.68 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.68/1.68 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.68/1.68 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.68/1.68 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 2.68/1.68 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 2.68/1.68 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 2.68/1.68 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 2.68/1.68 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 2.68/1.68 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 2.68/1.68 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.68/1.68 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.68/1.68 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.68/1.68 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.68/1.68 bot_bo443197316chanID: set_Secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.68/1.68 bot_bo1785112429specID: set_Secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.68/1.68 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 2.68/1.68 correctCompositionKS: secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_Oeout,type,
% 2.68/1.68 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OeoutM,type,
% 2.68/1.68 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OexprChannel,type,
% 2.68/1.68 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_Oine,type,
% 2.68/1.68 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OineM,type,
% 2.68/1.68 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 2.68/1.68 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 2.68/1.68 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 2.68/1.68 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 2.68/1.68 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 2.68/1.68 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OspecKeys,type,
% 2.68/1.68 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 2.68/1.68 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy_OspecSecrets,type,
% 2.68/1.68 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 2.68/1.68 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 2.68/1.68 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 2.68/1.68 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 2.68/1.68 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 2.68/1.68 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 2.68/1.68 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 2.68/1.68 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 2.68/1.68 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 2.68/1.68 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 2.68/1.68 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 2.68/1.68 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 2.68/1.68 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 2.68/1.68 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 2.68/1.68 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 2.68/1.68 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 2.68/1.68 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 2.68/1.68 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 2.68/1.68 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 2.68/1.68 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 2.68/1.68 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 2.68/1.68 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 2.68/1.68 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 2.68/1.68 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 2.68/1.68 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_OcorrectCompositionIn,type,
% 2.68/1.68 correctCompositionIn: secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 2.68/1.68 correc965049635ionLoc: secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_OcorrectCompositionOut,type,
% 2.68/1.68 correc990227761ionOut: secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_OinStream,type,
% 2.68/1.68 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_Oins,type,
% 2.68/1.68 ins: secrecy_specID > set_Secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_Oloc,type,
% 2.68/1.68 loc: secrecy_specID > set_Secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_OlocStream,type,
% 2.68/1.68 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_Oout,type,
% 2.68/1.68 out: secrecy_specID > set_Secrecy_chanID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_OoutStream,type,
% 2.68/1.68 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_inout_Osubcomponents,type,
% 2.68/1.68 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 2.68/1.68 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 2.68/1.68 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 2.68/1.68 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 2.68/1.68 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 2.68/1.68 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 2.68/1.68
% 2.68/1.68 thf(sy_v_P,type,
% 2.68/1.68 p: secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_v_PQ,type,
% 2.68/1.68 pq: secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_v_Q,type,
% 2.68/1.68 q: secrecy_specID ).
% 2.68/1.68
% 2.68/1.68 thf(sy_v_m,type,
% 2.68/1.68 m: secrecy_KS ).
% 2.68/1.68
% 2.68/1.68 thf(sy_v_secret____,type,
% 2.68/1.68 secret: secrecy_Secrets ).
% 2.68/1.68
% 2.68/1.68 thf(fact_0_cCompLoc,axiom,
% 2.68/1.68 correc965049635ionLoc @ pq ).
% 2.68/1.68
% 2.68/1.68 thf(fact_1_sg1a,axiom,
% 2.68/1.68 ~ ( ine @ p @ ( secrecy_sE @ secret ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_2_sg2a,axiom,
% 2.68/1.68 ~ ( ine @ q @ ( secrecy_sE @ secret ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_3_sg1b,axiom,
% 2.68/1.68 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_4_sg2b,axiom,
% 2.68/1.68 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_5_subPQ,axiom,
% 2.68/1.68 ( ( subcomponents @ pq )
% 2.68/1.68 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_6_a2,axiom,
% 2.68/1.68 ( m
% 2.68/1.68 = ( secrecy_sKS @ secret ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_7_cCompI,axiom,
% 2.68/1.68 correctCompositionIn @ pq ).
% 2.68/1.68
% 2.68/1.68 thf(fact_8_sg3,axiom,
% 2.68/1.68 ~ ( ine @ pq @ ( secrecy_sE @ secret ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_9_KS_Oinject_I2_J,axiom,
% 2.68/1.68 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.68/1.68 ( ( ( secrecy_sKS @ X2 )
% 2.68/1.68 = ( secrecy_sKS @ Y2 ) )
% 2.68/1.68 = ( X2 = Y2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_10_sg1,axiom,
% 2.68/1.68 ~ ( knowle945212990e_know @ p @ ( secrecy_sKS @ secret ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_11_sg2,axiom,
% 2.68/1.68 ~ ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_12_know_Osimps_I2_J,axiom,
% 2.68/1.68 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.68/1.68 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.68/1.68 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 2.68/1.68 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_13_LocalSecretsComposition__ine1__s,axiom,
% 2.68/1.68 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.68 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.68/1.68 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_14_LocalSecretsComposition__ine2__s,axiom,
% 2.68/1.68 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.68 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.68/1.68 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_15_LocalSecretsComposition__neg1__s,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.68 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.68/1.68 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.68/1.68 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_16_KS2Expression_Osimps_I2_J,axiom,
% 2.68/1.68 ! [M: secrecy_Secrets] :
% 2.68/1.68 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 2.68/1.68 = ( secrecy_sE @ M ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_17_LocalSecretsComposition1,axiom,
% 2.68/1.68 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_18_not__know__s__not__ine,axiom,
% 2.68/1.68 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.68/1.68 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.68/1.68 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_19_notknowQ,axiom,
% 2.68/1.68 ~ ( knowle945212990e_know @ q @ m ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_20_notknowP,axiom,
% 2.68/1.68 ~ ( knowle945212990e_know @ p @ m ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_21_Expression_Oinject_I2_J,axiom,
% 2.68/1.68 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.68/1.68 ( ( ( secrecy_sE @ X2 )
% 2.68/1.68 = ( secrecy_sE @ Y2 ) )
% 2.68/1.68 = ( X2 = Y2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_22_know__composition__neg__ine__s,axiom,
% 2.68/1.68 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ~ ( knowle945212990e_know @ P @ ( secrecy_sKS @ Secret ) )
% 2.68/1.68 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_23_TBtheorem1a,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( ine @ PQ @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( ine @ P @ E )
% 2.68/1.68 | ( ine @ Q @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_24_TBtheorem3a,axiom,
% 2.68/1.68 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ~ ( ine @ P @ E )
% 2.68/1.68 => ( ~ ( ine @ Q @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_25_singletonI,axiom,
% 2.68/1.68 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_26_singletonI,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_27_singletonI,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_28_singletonI,axiom,
% 2.68/1.68 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_29_singletonI,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_30_insertCI,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 2.68/1.68 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 2.68/1.68 => ( A2 = B2 ) )
% 2.68/1.68 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_31_insertCI,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.68/1.68 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 2.68/1.68 => ( A2 = B2 ) )
% 2.68/1.68 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_32_insertCI,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.68/1.68 ( ( ~ ( member740727610specID @ A2 @ B )
% 2.68/1.68 => ( A2 = B2 ) )
% 2.68/1.68 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_33_insertCI,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 2.68/1.68 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 2.68/1.68 => ( A2 = B2 ) )
% 2.68/1.68 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_34_insertCI,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 2.68/1.68 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 2.68/1.68 => ( A2 = B2 ) )
% 2.68/1.68 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_35_insert__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 2.68/1.68 = ( ( A2 = B2 )
% 2.68/1.68 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_36_insert__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 2.68/1.68 = ( ( A2 = B2 )
% 2.68/1.68 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_37_insert__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 2.68/1.68 = ( ( A2 = B2 )
% 2.68/1.68 | ( member740727610specID @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_38_insert__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 2.68/1.68 = ( ( A2 = B2 )
% 2.68/1.68 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_39_insert__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 2.68/1.68 = ( ( A2 = B2 )
% 2.68/1.68 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_40_insert__absorb2,axiom,
% 2.68/1.68 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A ) )
% 2.68/1.68 = ( insert1671894227specID @ X @ A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_41_insert__absorb2,axiom,
% 2.68/1.68 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A ) )
% 2.68/1.68 = ( insert751661162chanID @ X @ A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_42_empty__iff,axiom,
% 2.68/1.68 ! [C: secrecy_KS] :
% 2.68/1.68 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_43_empty__iff,axiom,
% 2.68/1.68 ! [C: secrecy_Secrets] :
% 2.68/1.68 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_44_empty__iff,axiom,
% 2.68/1.68 ! [C: secrecy_Keys] :
% 2.68/1.68 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_45_empty__iff,axiom,
% 2.68/1.68 ! [C: secrecy_specID] :
% 2.68/1.68 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_46_empty__iff,axiom,
% 2.68/1.68 ! [C: secrecy_chanID] :
% 2.68/1.68 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_47_all__not__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS] :
% 2.68/1.68 ( ( ! [X3: secrecy_KS] :
% 2.68/1.68 ~ ( member_Secrecy_KS @ X3 @ A ) )
% 2.68/1.68 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_48_all__not__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( ! [X3: secrecy_Secrets] :
% 2.68/1.68 ~ ( member2138796287ecrets @ X3 @ A ) )
% 2.68/1.68 = ( A = bot_bo1124690338ecrets ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_49_all__not__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( ! [X3: secrecy_Keys] :
% 2.68/1.68 ~ ( member_Secrecy_Keys @ X3 @ A ) )
% 2.68/1.68 = ( A = bot_bo701486667y_Keys ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_50_all__not__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID] :
% 2.68/1.68 ( ( ! [X3: secrecy_specID] :
% 2.68/1.68 ~ ( member740727610specID @ X3 @ A ) )
% 2.68/1.68 = ( A = bot_bo1785112429specID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_51_all__not__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( ! [X3: secrecy_chanID] :
% 2.68/1.68 ~ ( member1967978193chanID @ X3 @ A ) )
% 2.68/1.68 = ( A = bot_bo443197316chanID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_52_Collect__empty__eq,axiom,
% 2.68/1.68 ! [P: secrecy_specID > $o] :
% 2.68/1.68 ( ( ( collec1545797240specID @ P )
% 2.68/1.68 = bot_bo1785112429specID )
% 2.68/1.68 = ( ! [X3: secrecy_specID] :
% 2.68/1.68 ~ ( P @ X3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_53_Collect__empty__eq,axiom,
% 2.68/1.68 ! [P: secrecy_chanID > $o] :
% 2.68/1.68 ( ( ( collec625564175chanID @ P )
% 2.68/1.68 = bot_bo443197316chanID )
% 2.68/1.68 = ( ! [X3: secrecy_chanID] :
% 2.68/1.68 ~ ( P @ X3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_54_empty__Collect__eq,axiom,
% 2.68/1.68 ! [P: secrecy_specID > $o] :
% 2.68/1.68 ( ( bot_bo1785112429specID
% 2.68/1.68 = ( collec1545797240specID @ P ) )
% 2.68/1.68 = ( ! [X3: secrecy_specID] :
% 2.68/1.68 ~ ( P @ X3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_55_empty__Collect__eq,axiom,
% 2.68/1.68 ! [P: secrecy_chanID > $o] :
% 2.68/1.68 ( ( bot_bo443197316chanID
% 2.68/1.68 = ( collec625564175chanID @ P ) )
% 2.68/1.68 = ( ! [X3: secrecy_chanID] :
% 2.68/1.68 ~ ( P @ X3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_56_ex__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS] :
% 2.68/1.68 ( ( ? [X3: secrecy_KS] : ( member_Secrecy_KS @ X3 @ A ) )
% 2.68/1.68 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_57_ex__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( ? [X3: secrecy_Secrets] : ( member2138796287ecrets @ X3 @ A ) )
% 2.68/1.68 = ( A != bot_bo1124690338ecrets ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_58_ex__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( ? [X3: secrecy_Keys] : ( member_Secrecy_Keys @ X3 @ A ) )
% 2.68/1.68 = ( A != bot_bo701486667y_Keys ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_59_ex__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID] :
% 2.68/1.68 ( ( ? [X3: secrecy_specID] : ( member740727610specID @ X3 @ A ) )
% 2.68/1.68 = ( A != bot_bo1785112429specID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_60_ex__in__conv,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( ? [X3: secrecy_chanID] : ( member1967978193chanID @ X3 @ A ) )
% 2.68/1.68 = ( A != bot_bo443197316chanID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_61_equals0I,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS] :
% 2.68/1.68 ( ! [Y: secrecy_KS] :
% 2.68/1.68 ~ ( member_Secrecy_KS @ Y @ A )
% 2.68/1.68 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_62_equals0I,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ! [Y: secrecy_Secrets] :
% 2.68/1.68 ~ ( member2138796287ecrets @ Y @ A )
% 2.68/1.68 => ( A = bot_bo1124690338ecrets ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_63_equals0I,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Keys] :
% 2.68/1.68 ( ! [Y: secrecy_Keys] :
% 2.68/1.68 ~ ( member_Secrecy_Keys @ Y @ A )
% 2.68/1.68 => ( A = bot_bo701486667y_Keys ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_64_equals0I,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID] :
% 2.68/1.68 ( ! [Y: secrecy_specID] :
% 2.68/1.68 ~ ( member740727610specID @ Y @ A )
% 2.68/1.68 => ( A = bot_bo1785112429specID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_65_equals0I,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ! [Y: secrecy_chanID] :
% 2.68/1.68 ~ ( member1967978193chanID @ Y @ A )
% 2.68/1.68 => ( A = bot_bo443197316chanID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_66_equals0D,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 2.68/1.68 ( ( A = bot_bo1943466239ecy_KS )
% 2.68/1.68 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_67_equals0D,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 2.68/1.68 ( ( A = bot_bo1124690338ecrets )
% 2.68/1.68 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_68_equals0D,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 2.68/1.68 ( ( A = bot_bo701486667y_Keys )
% 2.68/1.68 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_69_equals0D,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 2.68/1.68 ( ( A = bot_bo1785112429specID )
% 2.68/1.68 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_70_equals0D,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 2.68/1.68 ( ( A = bot_bo443197316chanID )
% 2.68/1.68 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_71_emptyE,axiom,
% 2.68/1.68 ! [A2: secrecy_KS] :
% 2.68/1.68 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_72_emptyE,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets] :
% 2.68/1.68 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_73_emptyE,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys] :
% 2.68/1.68 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_74_emptyE,axiom,
% 2.68/1.68 ! [A2: secrecy_specID] :
% 2.68/1.68 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_75_emptyE,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID] :
% 2.68/1.68 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_76_mk__disjoint__insert,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ A2 @ A )
% 2.68/1.68 => ? [B3: set_Secrecy_KS] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 2.68/1.68 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_77_mk__disjoint__insert,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ A2 @ A )
% 2.68/1.68 => ? [B3: set_Secrecy_chanID] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert751661162chanID @ A2 @ B3 ) )
% 2.68/1.68 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_78_mk__disjoint__insert,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ A2 @ A )
% 2.68/1.68 => ? [B3: set_Secrecy_specID] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert1671894227specID @ A2 @ B3 ) )
% 2.68/1.68 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_79_mk__disjoint__insert,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ A2 @ A )
% 2.68/1.68 => ? [B3: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert565337510ecrets @ A2 @ B3 ) )
% 2.68/1.68 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_80_mk__disjoint__insert,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ A2 @ A )
% 2.68/1.68 => ? [B3: set_Secrecy_Keys] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 2.68/1.68 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_81_insert__commute,axiom,
% 2.68/1.68 ! [X: secrecy_specID,Y3: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y3 @ A ) )
% 2.68/1.68 = ( insert1671894227specID @ Y3 @ ( insert1671894227specID @ X @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_82_insert__commute,axiom,
% 2.68/1.68 ! [X: secrecy_chanID,Y3: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y3 @ A ) )
% 2.68/1.68 = ( insert751661162chanID @ Y3 @ ( insert751661162chanID @ X @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_83_insert__eq__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.68 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 2.68/1.68 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 2.68/1.68 = ( insert_Secrecy_KS @ B2 @ B ) )
% 2.68/1.68 = ( ( ( A2 = B2 )
% 2.68/1.68 => ( A = B ) )
% 2.68/1.68 & ( ( A2 != B2 )
% 2.68/1.68 => ? [C2: set_Secrecy_KS] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 2.68/1.68 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 2.68/1.68 & ( B
% 2.68/1.68 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 2.68/1.68 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_84_insert__eq__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.68 ( ~ ( member1967978193chanID @ A2 @ A )
% 2.68/1.68 => ( ~ ( member1967978193chanID @ B2 @ B )
% 2.68/1.68 => ( ( ( insert751661162chanID @ A2 @ A )
% 2.68/1.68 = ( insert751661162chanID @ B2 @ B ) )
% 2.68/1.68 = ( ( ( A2 = B2 )
% 2.68/1.68 => ( A = B ) )
% 2.68/1.68 & ( ( A2 != B2 )
% 2.68/1.68 => ? [C2: set_Secrecy_chanID] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert751661162chanID @ B2 @ C2 ) )
% 2.68/1.68 & ~ ( member1967978193chanID @ B2 @ C2 )
% 2.68/1.68 & ( B
% 2.68/1.68 = ( insert751661162chanID @ A2 @ C2 ) )
% 2.68/1.68 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_85_insert__eq__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.68 ( ~ ( member740727610specID @ A2 @ A )
% 2.68/1.68 => ( ~ ( member740727610specID @ B2 @ B )
% 2.68/1.68 => ( ( ( insert1671894227specID @ A2 @ A )
% 2.68/1.68 = ( insert1671894227specID @ B2 @ B ) )
% 2.68/1.68 = ( ( ( A2 = B2 )
% 2.68/1.68 => ( A = B ) )
% 2.68/1.68 & ( ( A2 != B2 )
% 2.68/1.68 => ? [C2: set_Secrecy_specID] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert1671894227specID @ B2 @ C2 ) )
% 2.68/1.68 & ~ ( member740727610specID @ B2 @ C2 )
% 2.68/1.68 & ( B
% 2.68/1.68 = ( insert1671894227specID @ A2 @ C2 ) )
% 2.68/1.68 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_86_insert__eq__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.68/1.68 ( ~ ( member2138796287ecrets @ A2 @ A )
% 2.68/1.68 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 2.68/1.68 => ( ( ( insert565337510ecrets @ A2 @ A )
% 2.68/1.68 = ( insert565337510ecrets @ B2 @ B ) )
% 2.68/1.68 = ( ( ( A2 = B2 )
% 2.68/1.68 => ( A = B ) )
% 2.68/1.68 & ( ( A2 != B2 )
% 2.68/1.68 => ? [C2: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert565337510ecrets @ B2 @ C2 ) )
% 2.68/1.68 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 2.68/1.68 & ( B
% 2.68/1.68 = ( insert565337510ecrets @ A2 @ C2 ) )
% 2.68/1.68 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_87_insert__eq__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 2.68/1.68 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 2.68/1.68 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 2.68/1.68 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 2.68/1.68 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 2.68/1.68 = ( ( ( A2 = B2 )
% 2.68/1.68 => ( A = B ) )
% 2.68/1.68 & ( ( A2 != B2 )
% 2.68/1.68 => ? [C2: set_Secrecy_Keys] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 2.68/1.68 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 2.68/1.68 & ( B
% 2.68/1.68 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 2.68/1.68 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_88_insert__absorb,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ A2 @ A )
% 2.68/1.68 => ( ( insert_Secrecy_KS @ A2 @ A )
% 2.68/1.68 = A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_89_insert__absorb,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ A2 @ A )
% 2.68/1.68 => ( ( insert751661162chanID @ A2 @ A )
% 2.68/1.68 = A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_90_insert__absorb,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ A2 @ A )
% 2.68/1.68 => ( ( insert1671894227specID @ A2 @ A )
% 2.68/1.68 = A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_91_insert__absorb,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ A2 @ A )
% 2.68/1.68 => ( ( insert565337510ecrets @ A2 @ A )
% 2.68/1.68 = A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_92_insert__absorb,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ A2 @ A )
% 2.68/1.68 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 2.68/1.68 = A ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_93_insert__ident,axiom,
% 2.68/1.68 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.68 ( ~ ( member_Secrecy_KS @ X @ A )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ X @ B )
% 2.68/1.68 => ( ( ( insert_Secrecy_KS @ X @ A )
% 2.68/1.68 = ( insert_Secrecy_KS @ X @ B ) )
% 2.68/1.68 = ( A = B ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_94_insert__ident,axiom,
% 2.68/1.68 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.68 ( ~ ( member1967978193chanID @ X @ A )
% 2.68/1.68 => ( ~ ( member1967978193chanID @ X @ B )
% 2.68/1.68 => ( ( ( insert751661162chanID @ X @ A )
% 2.68/1.68 = ( insert751661162chanID @ X @ B ) )
% 2.68/1.68 = ( A = B ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_95_insert__ident,axiom,
% 2.68/1.68 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.68 ( ~ ( member740727610specID @ X @ A )
% 2.68/1.68 => ( ~ ( member740727610specID @ X @ B )
% 2.68/1.68 => ( ( ( insert1671894227specID @ X @ A )
% 2.68/1.68 = ( insert1671894227specID @ X @ B ) )
% 2.68/1.68 = ( A = B ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_96_insert__ident,axiom,
% 2.68/1.68 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.68/1.68 ( ~ ( member2138796287ecrets @ X @ A )
% 2.68/1.68 => ( ~ ( member2138796287ecrets @ X @ B )
% 2.68/1.68 => ( ( ( insert565337510ecrets @ X @ A )
% 2.68/1.68 = ( insert565337510ecrets @ X @ B ) )
% 2.68/1.68 = ( A = B ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_97_insert__ident,axiom,
% 2.68/1.68 ! [X: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.68/1.68 ( ~ ( member_Secrecy_Keys @ X @ A )
% 2.68/1.68 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 2.68/1.68 => ( ( ( insert_Secrecy_Keys @ X @ A )
% 2.68/1.68 = ( insert_Secrecy_Keys @ X @ B ) )
% 2.68/1.68 = ( A = B ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_98_Set_Oset__insert,axiom,
% 2.68/1.68 ! [X: secrecy_KS,A: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X @ A )
% 2.68/1.68 => ~ ! [B3: set_Secrecy_KS] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert_Secrecy_KS @ X @ B3 ) )
% 2.68/1.68 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_99_Set_Oset__insert,axiom,
% 2.68/1.68 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X @ A )
% 2.68/1.68 => ~ ! [B3: set_Secrecy_chanID] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert751661162chanID @ X @ B3 ) )
% 2.68/1.68 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_100_Set_Oset__insert,axiom,
% 2.68/1.68 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ X @ A )
% 2.68/1.68 => ~ ! [B3: set_Secrecy_specID] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert1671894227specID @ X @ B3 ) )
% 2.68/1.68 => ( member740727610specID @ X @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_101_Set_Oset__insert,axiom,
% 2.68/1.68 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ X @ A )
% 2.68/1.68 => ~ ! [B3: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert565337510ecrets @ X @ B3 ) )
% 2.68/1.68 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_102_Set_Oset__insert,axiom,
% 2.68/1.68 ! [X: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ X @ A )
% 2.68/1.68 => ~ ! [B3: set_Secrecy_Keys] :
% 2.68/1.68 ( ( A
% 2.68/1.68 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 2.68/1.68 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_103_mem__Collect__eq,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 2.68/1.68 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 2.68/1.68 = ( P @ A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_104_mem__Collect__eq,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 2.68/1.68 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 2.68/1.68 = ( P @ A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_105_mem__Collect__eq,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 2.68/1.68 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 2.68/1.68 = ( P @ A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_106_mem__Collect__eq,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 2.68/1.68 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 2.68/1.68 = ( P @ A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_107_mem__Collect__eq,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 2.68/1.68 = ( P @ A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_108_Collect__mem__eq,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS] :
% 2.68/1.68 ( ( collect_Secrecy_KS
% 2.68/1.68 @ ^ [X3: secrecy_KS] : ( member_Secrecy_KS @ X3 @ A ) )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_109_Collect__mem__eq,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( collec625564175chanID
% 2.68/1.68 @ ^ [X3: secrecy_chanID] : ( member1967978193chanID @ X3 @ A ) )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_110_Collect__mem__eq,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID] :
% 2.68/1.68 ( ( collec1545797240specID
% 2.68/1.68 @ ^ [X3: secrecy_specID] : ( member740727610specID @ X3 @ A ) )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_111_Collect__mem__eq,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( collec836099393ecrets
% 2.68/1.68 @ ^ [X3: secrecy_Secrets] : ( member2138796287ecrets @ X3 @ A ) )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_112_Collect__mem__eq,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( collect_Secrecy_Keys
% 2.68/1.68 @ ^ [X3: secrecy_Keys] : ( member_Secrecy_Keys @ X3 @ A ) )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_113_insertI2,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ A2 @ B )
% 2.68/1.68 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_114_insertI2,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ A2 @ B )
% 2.68/1.68 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_115_insertI2,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ A2 @ B )
% 2.68/1.68 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_116_insertI2,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ A2 @ B )
% 2.68/1.68 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_117_insertI2,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ A2 @ B )
% 2.68/1.68 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_118_insertI1,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_119_insertI1,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_120_insertI1,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_121_insertI1,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_122_insertI1,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_123_insertE,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 2.68/1.68 => ( ( A2 != B2 )
% 2.68/1.68 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_124_insertE,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 2.68/1.68 => ( ( A2 != B2 )
% 2.68/1.68 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_125_insertE,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 2.68/1.68 => ( ( A2 != B2 )
% 2.68/1.68 => ( member740727610specID @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_126_insertE,axiom,
% 2.68/1.68 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 2.68/1.68 => ( ( A2 != B2 )
% 2.68/1.68 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_127_insertE,axiom,
% 2.68/1.68 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 2.68/1.68 => ( ( A2 != B2 )
% 2.68/1.68 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_128_singleton__inject,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 2.68/1.68 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 2.68/1.68 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.68/1.68 => ( A2 = B2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_129_singleton__inject,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 2.68/1.68 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 2.68/1.68 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.68/1.68 => ( A2 = B2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_130_insert__not__empty,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( insert1671894227specID @ A2 @ A )
% 2.68/1.68 != bot_bo1785112429specID ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_131_insert__not__empty,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( insert751661162chanID @ A2 @ A )
% 2.68/1.68 != bot_bo443197316chanID ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_132_doubleton__eq__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 2.68/1.68 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.68/1.68 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 2.68/1.68 = ( ( ( A2 = C )
% 2.68/1.68 & ( B2 = D ) )
% 2.68/1.68 | ( ( A2 = D )
% 2.68/1.68 & ( B2 = C ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_133_doubleton__eq__iff,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 2.68/1.68 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.68/1.68 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 2.68/1.68 = ( ( ( A2 = C )
% 2.68/1.68 & ( B2 = D ) )
% 2.68/1.68 | ( ( A2 = D )
% 2.68/1.68 & ( B2 = C ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_134_singleton__iff,axiom,
% 2.68/1.68 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 2.68/1.68 = ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_135_singleton__iff,axiom,
% 2.68/1.68 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 2.68/1.68 = ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_136_singleton__iff,axiom,
% 2.68/1.68 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 2.68/1.68 = ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_137_singleton__iff,axiom,
% 2.68/1.68 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 2.68/1.68 = ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_138_singleton__iff,axiom,
% 2.68/1.68 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 2.68/1.68 = ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_139_singletonD,axiom,
% 2.68/1.68 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 2.68/1.68 => ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_140_singletonD,axiom,
% 2.68/1.68 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 2.68/1.68 => ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_141_singletonD,axiom,
% 2.68/1.68 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 2.68/1.68 => ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_142_singletonD,axiom,
% 2.68/1.68 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 2.68/1.68 => ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_143_singletonD,axiom,
% 2.68/1.68 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 2.68/1.68 => ( B2 = A2 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_144_the__elem__eq,axiom,
% 2.68/1.68 ! [X: secrecy_specID] :
% 2.68/1.68 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.68/1.68 = X ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_145_the__elem__eq,axiom,
% 2.68/1.68 ! [X: secrecy_chanID] :
% 2.68/1.68 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.68/1.68 = X ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_146_is__singletonI,axiom,
% 2.68/1.68 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_147_is__singletonI,axiom,
% 2.68/1.68 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_148_TBtheorem4a__empty,axiom,
% 2.68/1.68 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ( ( ine @ P @ E )
% 2.68/1.68 | ( ine @ Q @ E ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( ( loc @ PQ )
% 2.68/1.68 = bot_bo443197316chanID )
% 2.68/1.68 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_149_TBtheorem3b,axiom,
% 2.68/1.68 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ~ ( ineM @ P @ M2 @ E )
% 2.68/1.68 => ( ~ ( ineM @ Q @ M2 @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_150_TBtheorem1b,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( ineM @ PQ @ M2 @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( ineM @ P @ M2 @ E )
% 2.68/1.68 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_151_Set_Ois__empty__def,axiom,
% 2.68/1.68 ( is_emp1849217361specID
% 2.68/1.68 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_152_Set_Ois__empty__def,axiom,
% 2.68/1.68 ( is_emp928984296chanID
% 2.68/1.68 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_153_correctCompositionIn__prop1,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 2.68/1.68 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_154_correctCompositionIn__L2,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_155_bot__set__def,axiom,
% 2.68/1.68 ( bot_bo1785112429specID
% 2.68/1.68 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_156_bot__set__def,axiom,
% 2.68/1.68 ( bot_bo443197316chanID
% 2.68/1.68 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_157_ineM__ine,axiom,
% 2.68/1.68 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.68 ( ( ineM @ P @ M2 @ E )
% 2.68/1.68 => ( ine @ P @ E ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_158_not__ine__ineM,axiom,
% 2.68/1.68 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 2.68/1.68 ( ~ ( ine @ P @ E )
% 2.68/1.68 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_159_is__singleton__the__elem,axiom,
% 2.68/1.68 ( is_sin1501507247specID
% 2.68/1.68 = ( ^ [A3: set_Secrecy_specID] :
% 2.68/1.68 ( A3
% 2.68/1.68 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_160_is__singleton__the__elem,axiom,
% 2.68/1.68 ( is_sin581274182chanID
% 2.68/1.68 = ( ^ [A3: set_Secrecy_chanID] :
% 2.68/1.68 ( A3
% 2.68/1.68 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_161_correctCompositionIn__L1,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_162_is__singletonI_H,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS] :
% 2.68/1.68 ( ( A != bot_bo1943466239ecy_KS )
% 2.68/1.68 => ( ! [X4: secrecy_KS,Y: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X4 @ A )
% 2.68/1.68 => ( ( member_Secrecy_KS @ Y @ A )
% 2.68/1.68 => ( X4 = Y ) ) )
% 2.68/1.68 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_163_is__singletonI_H,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( A != bot_bo1124690338ecrets )
% 2.68/1.68 => ( ! [X4: secrecy_Secrets,Y: secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ X4 @ A )
% 2.68/1.68 => ( ( member2138796287ecrets @ Y @ A )
% 2.68/1.68 => ( X4 = Y ) ) )
% 2.68/1.68 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_164_is__singletonI_H,axiom,
% 2.68/1.68 ! [A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( A != bot_bo701486667y_Keys )
% 2.68/1.68 => ( ! [X4: secrecy_Keys,Y: secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ X4 @ A )
% 2.68/1.68 => ( ( member_Secrecy_Keys @ Y @ A )
% 2.68/1.68 => ( X4 = Y ) ) )
% 2.68/1.68 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_165_is__singletonI_H,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID] :
% 2.68/1.68 ( ( A != bot_bo1785112429specID )
% 2.68/1.68 => ( ! [X4: secrecy_specID,Y: secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ X4 @ A )
% 2.68/1.68 => ( ( member740727610specID @ Y @ A )
% 2.68/1.68 => ( X4 = Y ) ) )
% 2.68/1.68 => ( is_sin1501507247specID @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_166_is__singletonI_H,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( A != bot_bo443197316chanID )
% 2.68/1.68 => ( ! [X4: secrecy_chanID,Y: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ A )
% 2.68/1.68 => ( ( member1967978193chanID @ Y @ A )
% 2.68/1.68 => ( X4 = Y ) ) )
% 2.68/1.68 => ( is_sin581274182chanID @ A ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_167_is__singletonE,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID] :
% 2.68/1.68 ( ( is_sin1501507247specID @ A )
% 2.68/1.68 => ~ ! [X4: secrecy_specID] :
% 2.68/1.68 ( A
% 2.68/1.68 != ( insert1671894227specID @ X4 @ bot_bo1785112429specID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_168_is__singletonE,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( is_sin581274182chanID @ A )
% 2.68/1.68 => ~ ! [X4: secrecy_chanID] :
% 2.68/1.68 ( A
% 2.68/1.68 != ( insert751661162chanID @ X4 @ bot_bo443197316chanID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_169_is__singleton__def,axiom,
% 2.68/1.68 ( is_sin1501507247specID
% 2.68/1.68 = ( ^ [A3: set_Secrecy_specID] :
% 2.68/1.68 ? [X3: secrecy_specID] :
% 2.68/1.68 ( A3
% 2.68/1.68 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_170_is__singleton__def,axiom,
% 2.68/1.68 ( is_sin581274182chanID
% 2.68/1.68 = ( ^ [A3: set_Secrecy_chanID] :
% 2.68/1.68 ? [X3: secrecy_chanID] :
% 2.68/1.68 ( A3
% 2.68/1.68 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_171_subcomponents__loc,axiom,
% 2.68/1.68 ! [X: secrecy_specID] :
% 2.68/1.68 ( ( correc965049635ionLoc @ X )
% 2.68/1.68 => ( ( ( subcomponents @ X )
% 2.68/1.68 = bot_bo1785112429specID )
% 2.68/1.68 => ( ( loc @ X )
% 2.68/1.68 = bot_bo443197316chanID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_172_TBtheorem4b__notP1,axiom,
% 2.68/1.68 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ( ineM @ P @ M2 @ E )
% 2.68/1.68 => ( ~ ( ineM @ Q @ M2 @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.68 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 2.68/1.68 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.68/1.68 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_173_TBtheorem4a__notP1,axiom,
% 2.68/1.68 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ( ine @ P @ E )
% 2.68/1.68 => ( ~ ( ine @ Q @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.68 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 2.68/1.68 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_174_TBtheorem4b__notP2,axiom,
% 2.68/1.68 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.68/1.68 ( ~ ( ineM @ Q @ M2 @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.68/1.68 => ( ! [X4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.68/1.68 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_175_TBtheorem4b__notPQ,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.68/1.68 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.68/1.68 => ( ! [X4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.68/1.68 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ( ! [X4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.68/1.68 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_176_TBtheorem4a__notP2,axiom,
% 2.68/1.68 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.68/1.68 ( ~ ( ine @ Q @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.68/1.68 => ( ! [X4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.68/1.68 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_177_TBtheorem4a__notPQ,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.68/1.68 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.68/1.68 => ( ! [X4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.68/1.68 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ( ! [X4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.68/1.68 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_178_ine__exprChannelSingle__Set,axiom,
% 2.68/1.68 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.68 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 2.68/1.68 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_179_ine__exprChannelSet__Single,axiom,
% 2.68/1.68 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.68 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 2.68/1.68 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_180_ine__empty__exprChannelSet,axiom,
% 2.68/1.68 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.68 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.68/1.68 => ( ( ChSet = bot_bo443197316chanID )
% 2.68/1.68 => ~ ( ine @ P @ E ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_181_ine__nonempty__exprChannelSet,axiom,
% 2.68/1.68 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.68 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.68/1.68 => ( ( ChSet != bot_bo443197316chanID )
% 2.68/1.68 => ( ine @ P @ E ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_182_locStream__def,axiom,
% 2.68/1.68 ( locStream
% 2.68/1.68 = ( ^ [X3: secrecy_specID] :
% 2.68/1.68 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 2.68/1.68 @ ( loc @ X3 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_183_inStream__def,axiom,
% 2.68/1.68 ( inStream
% 2.68/1.68 = ( ^ [X3: secrecy_specID] :
% 2.68/1.68 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 2.68/1.68 @ ( ins @ X3 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_184_TBtheorem4b__PQ,axiom,
% 2.68/1.68 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ( ( ineM @ P @ M2 @ E )
% 2.68/1.68 | ( ineM @ Q @ M2 @ E ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.68 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.68/1.68 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.68/1.68 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.68/1.68 & ( exprChannel @ Ch2 @ E )
% 2.68/1.68 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_185_TBtheorem4b__P,axiom,
% 2.68/1.68 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( ineM @ P @ M2 @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 2.68/1.68 & ( exprChannel @ Ch2 @ E )
% 2.68/1.68 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.68/1.68 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 2.68/1.68 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_186_TBtheorem4a__PQ,axiom,
% 2.68/1.68 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ( ( ine @ P @ E )
% 2.68/1.68 | ( ine @ Q @ E ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.68 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.68/1.68 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.68/1.68 & ( exprChannel @ Ch2 @ E )
% 2.68/1.68 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_187_TBtheorem4a__P,axiom,
% 2.68/1.68 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( ine @ P @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.68/1.68 & ( exprChannel @ Ch2 @ E )
% 2.68/1.68 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.68 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_188_ine__def,axiom,
% 2.68/1.68 ( ine
% 2.68/1.68 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.68/1.68 ? [Ch3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.68/1.68 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_189_ine__ins__neg1,axiom,
% 2.68/1.68 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 2.68/1.68 ( ~ ( ine @ P @ M )
% 2.68/1.68 => ( ( exprChannel @ X @ M )
% 2.68/1.68 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_190_ineM__def,axiom,
% 2.68/1.68 ( ineM
% 2.68/1.68 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.68/1.68 ? [Ch3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.68/1.68 & ( member1967978193chanID @ Ch3 @ M3 )
% 2.68/1.68 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_191_ineM__L1,axiom,
% 2.68/1.68 ! [Ch: secrecy_chanID,M2: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch @ M2 )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ E )
% 2.68/1.68 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_192_ine__exprChannelSet__def,axiom,
% 2.68/1.68 ( ine_exprChannelSet
% 2.68/1.68 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.68/1.68 ( ! [X3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X3 @ ChSet2 )
% 2.68/1.68 => ( ( member1967978193chanID @ X3 @ ( ins @ SP ) )
% 2.68/1.68 & ( exprChannel @ X3 @ E2 ) ) )
% 2.68/1.68 & ! [X3: secrecy_chanID] :
% 2.68/1.68 ( ( ~ ( member1967978193chanID @ X3 @ ChSet2 )
% 2.68/1.68 & ( member1967978193chanID @ X3 @ ( ins @ SP ) ) )
% 2.68/1.68 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_193_ine__exprChannelSingle__def,axiom,
% 2.68/1.68 ( ine_ex1303305700Single
% 2.68/1.68 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.68/1.68 & ( exprChannel @ Ch3 @ E2 )
% 2.68/1.68 & ! [X3: secrecy_chanID,T: nat] :
% 2.68/1.68 ( ( ( member1967978193chanID @ X3 @ ( ins @ SP ) )
% 2.68/1.68 & ( X3 != Ch3 ) )
% 2.68/1.68 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_194_LocalSecretsComposition__exprChannel__s,axiom,
% 2.68/1.68 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.68 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 2.68/1.68 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 2.68/1.68 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 2.68/1.68 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 2.68/1.68 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_195_correctCompositionInLoc__exprChannel,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ M )
% 2.68/1.68 => ( ! [X4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X4 @ ( ins @ PQ ) )
% 2.68/1.68 => ~ ( exprChannel @ X4 @ M ) )
% 2.68/1.68 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_196_TBlemma3b,axiom,
% 2.68/1.68 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 2.68/1.68 ( ~ ( ineM @ P @ M2 @ E )
% 2.68/1.68 => ( ~ ( ineM @ Q @ M2 @ E )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ M2 )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.68/1.68 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_197_Collect__empty__eq__bot,axiom,
% 2.68/1.68 ! [P: secrecy_specID > $o] :
% 2.68/1.68 ( ( ( collec1545797240specID @ P )
% 2.68/1.68 = bot_bo1785112429specID )
% 2.68/1.68 = ( P = bot_bo1767780696ecID_o ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_198_Collect__empty__eq__bot,axiom,
% 2.68/1.68 ! [P: secrecy_chanID > $o] :
% 2.68/1.68 ( ( ( collec625564175chanID @ P )
% 2.68/1.68 = bot_bo443197316chanID )
% 2.68/1.68 = ( P = bot_bo1012329985anID_o ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_199_bot__empty__eq,axiom,
% 2.68/1.68 ( bot_bot_Secrecy_KS_o
% 2.68/1.68 = ( ^ [X3: secrecy_KS] : ( member_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_200_bot__empty__eq,axiom,
% 2.68/1.68 ( bot_bo1909946299rets_o
% 2.68/1.68 = ( ^ [X3: secrecy_Secrets] : ( member2138796287ecrets @ X3 @ bot_bo1124690338ecrets ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_201_bot__empty__eq,axiom,
% 2.68/1.68 ( bot_bo2072920570Keys_o
% 2.68/1.68 = ( ^ [X3: secrecy_Keys] : ( member_Secrecy_Keys @ X3 @ bot_bo701486667y_Keys ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_202_bot__empty__eq,axiom,
% 2.68/1.68 ( bot_bo1767780696ecID_o
% 2.68/1.68 = ( ^ [X3: secrecy_specID] : ( member740727610specID @ X3 @ bot_bo1785112429specID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_203_bot__empty__eq,axiom,
% 2.68/1.68 ( bot_bo1012329985anID_o
% 2.68/1.68 = ( ^ [X3: secrecy_chanID] : ( member1967978193chanID @ X3 @ bot_bo443197316chanID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_204_LocalSecretsComposition__neg__loc__s,axiom,
% 2.68/1.68 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.68/1.68 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 2.68/1.68 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_205_correctCompositionKS__exprChannel__s__P,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_206_correctCompositionKS__exprChannel__s__Q,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_207_correctCompositionKS__negQ,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_208_correctCompositionKS__negP,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_209_correctCompositionKS__neg1,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.68/1.68 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_210_correctCompositionKS__PQ,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.68/1.68 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_211_know__composition2,axiom,
% 2.68/1.68 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.68/1.68 => ( ( knowle945212990e_know @ Q @ M )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_212_know__composition1,axiom,
% 2.68/1.68 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.68/1.68 => ( ( knowle945212990e_know @ P @ M )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_213_know__composition,axiom,
% 2.68/1.68 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.68 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.68/1.68 => ( ( ( knowle945212990e_know @ P @ M )
% 2.68/1.68 | ( knowle945212990e_know @ Q @ M ) )
% 2.68/1.68 => ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_214_correctCompositionKS__exprChannel__s__Qex,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ? [Ch4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_215_correctCompositionKS__exprChannel__s__Pex,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ? [Ch4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_216_LocalSecretsComposition__neg__s,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.68/1.68 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 2.68/1.68 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.68/1.68 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_217_correctCompositionKS__exprChannel__k__Qex,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ? [Ch4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_218_correctCompositionKS__exprChannel__k__Pex,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ? [Ch4: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_219_correctCompositionKS__exprChannel__k__Q,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_220_correctCompositionKS__exprChannel__k__P,axiom,
% 2.68/1.68 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.68/1.68 ( ( ( subcomponents @ PQ )
% 2.68/1.68 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.68 => ( ( correctCompositionKS @ PQ )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.68/1.68 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.68/1.68 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.68/1.68 => ( ( correctCompositionIn @ PQ )
% 2.68/1.68 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.68/1.68 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_221_Un__iff,axiom,
% 2.68/1.68 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 2.68/1.68 = ( ( member740727610specID @ C @ A )
% 2.68/1.68 | ( member740727610specID @ C @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_222_Un__iff,axiom,
% 2.68/1.68 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 2.68/1.68 = ( ( member2138796287ecrets @ C @ A )
% 2.68/1.68 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_223_Un__iff,axiom,
% 2.68/1.68 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 2.68/1.68 = ( ( member_Secrecy_Keys @ C @ A )
% 2.68/1.68 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_224_Un__iff,axiom,
% 2.68/1.68 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.68/1.68 = ( ( member_Secrecy_KS @ C @ A )
% 2.68/1.68 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_225_Un__iff,axiom,
% 2.68/1.68 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 2.68/1.68 = ( ( member1967978193chanID @ C @ A )
% 2.68/1.68 | ( member1967978193chanID @ C @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_226_UnCI,axiom,
% 2.68/1.68 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( ~ ( member740727610specID @ C @ B )
% 2.68/1.68 => ( member740727610specID @ C @ A ) )
% 2.68/1.68 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_227_UnCI,axiom,
% 2.68/1.68 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( ~ ( member2138796287ecrets @ C @ B )
% 2.68/1.68 => ( member2138796287ecrets @ C @ A ) )
% 2.68/1.68 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_228_UnCI,axiom,
% 2.68/1.68 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 2.68/1.68 => ( member_Secrecy_Keys @ C @ A ) )
% 2.68/1.68 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_229_UnCI,axiom,
% 2.68/1.68 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 2.68/1.68 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 2.68/1.68 => ( member_Secrecy_KS @ C @ A ) )
% 2.68/1.68 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_230_UnCI,axiom,
% 2.68/1.68 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( ~ ( member1967978193chanID @ C @ B )
% 2.68/1.68 => ( member1967978193chanID @ C @ A ) )
% 2.68/1.68 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_231_KS_Oinject_I1_J,axiom,
% 2.68/1.68 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.68/1.68 ( ( ( secrecy_kKS @ X1 )
% 2.68/1.68 = ( secrecy_kKS @ Y1 ) )
% 2.68/1.68 = ( X1 = Y1 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_232_Expression_Oinject_I1_J,axiom,
% 2.68/1.68 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.68/1.68 ( ( ( secrecy_kE @ X1 )
% 2.68/1.68 = ( secrecy_kE @ Y1 ) )
% 2.68/1.68 = ( X1 = Y1 ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_233_Un__empty,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.68 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 2.68/1.68 = bot_bo1943466239ecy_KS )
% 2.68/1.68 = ( ( A = bot_bo1943466239ecy_KS )
% 2.68/1.68 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_234_Un__empty,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.68 ( ( ( sup_su1712599557specID @ A @ B )
% 2.68/1.68 = bot_bo1785112429specID )
% 2.68/1.68 = ( ( A = bot_bo1785112429specID )
% 2.68/1.68 & ( B = bot_bo1785112429specID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_235_Un__empty,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.68 ( ( ( sup_su370684444chanID @ A @ B )
% 2.68/1.68 = bot_bo443197316chanID )
% 2.68/1.68 = ( ( A = bot_bo443197316chanID )
% 2.68/1.68 & ( B = bot_bo443197316chanID ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_236_Un__insert__left,axiom,
% 2.68/1.68 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 2.68/1.68 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 2.68/1.68 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_237_Un__insert__left,axiom,
% 2.68/1.68 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 2.68/1.68 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_238_Un__insert__left,axiom,
% 2.68/1.68 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 2.68/1.68 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_239_Un__insert__right,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.68 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 2.68/1.68 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_240_Un__insert__right,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 2.68/1.68 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_241_Un__insert__right,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 2.68/1.68 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_242_not__know__k__not__ine,axiom,
% 2.68/1.68 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.68/1.68 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.68/1.68 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_243_Un__empty__right,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_244_Un__empty__right,axiom,
% 2.68/1.68 ! [A: set_Secrecy_specID] :
% 2.68/1.68 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_245_Un__empty__right,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_246_Un__empty__left,axiom,
% 2.68/1.68 ! [B: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 2.68/1.68 = B ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_247_Un__empty__left,axiom,
% 2.68/1.68 ! [B: set_Secrecy_specID] :
% 2.68/1.68 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 2.68/1.68 = B ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_248_Un__empty__left,axiom,
% 2.68/1.68 ! [B: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 2.68/1.68 = B ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_249_KS2Expression_Osimps_I1_J,axiom,
% 2.68/1.68 ! [M: secrecy_Keys] :
% 2.68/1.68 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 2.68/1.68 = ( secrecy_kE @ M ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_250_Un__left__commute,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 2.68/1.68 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_251_Un__left__commute,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 2.68/1.68 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_252_Un__left__absorb,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.68/1.68 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_253_Un__left__absorb,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 2.68/1.68 = ( sup_su370684444chanID @ A @ B ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_254_Un__commute,axiom,
% 2.68/1.68 ( sup_su1301156759ecy_KS
% 2.68/1.68 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_255_Un__commute,axiom,
% 2.68/1.68 ( sup_su370684444chanID
% 2.68/1.68 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_256_Un__absorb,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ A @ A )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_257_Un__absorb,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ A @ A )
% 2.68/1.68 = A ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_258_Un__assoc,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.68/1.68 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 2.68/1.68 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_259_Un__assoc,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.68/1.68 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 2.68/1.68 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_260_ball__Un,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 2.68/1.68 ( ( ! [X3: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X3 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.68/1.68 => ( P @ X3 ) ) )
% 2.68/1.68 = ( ! [X3: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X3 @ A )
% 2.68/1.68 => ( P @ X3 ) )
% 2.68/1.68 & ! [X3: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X3 @ B )
% 2.68/1.68 => ( P @ X3 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_261_ball__Un,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.68/1.68 ( ( ! [X3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X3 @ ( sup_su370684444chanID @ A @ B ) )
% 2.68/1.68 => ( P @ X3 ) ) )
% 2.68/1.68 = ( ! [X3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X3 @ A )
% 2.68/1.68 => ( P @ X3 ) )
% 2.68/1.68 & ! [X3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X3 @ B )
% 2.68/1.68 => ( P @ X3 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_262_bex__Un,axiom,
% 2.68/1.68 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 2.68/1.68 ( ( ? [X3: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X3 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.68/1.68 & ( P @ X3 ) ) )
% 2.68/1.68 = ( ? [X3: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X3 @ A )
% 2.68/1.68 & ( P @ X3 ) )
% 2.68/1.68 | ? [X3: secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ X3 @ B )
% 2.68/1.68 & ( P @ X3 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_263_bex__Un,axiom,
% 2.68/1.68 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.68/1.68 ( ( ? [X3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X3 @ ( sup_su370684444chanID @ A @ B ) )
% 2.68/1.68 & ( P @ X3 ) ) )
% 2.68/1.68 = ( ? [X3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X3 @ A )
% 2.68/1.68 & ( P @ X3 ) )
% 2.68/1.68 | ? [X3: secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ X3 @ B )
% 2.68/1.68 & ( P @ X3 ) ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_264_UnI2,axiom,
% 2.68/1.68 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ C @ B )
% 2.68/1.68 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_265_UnI2,axiom,
% 2.68/1.68 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ C @ B )
% 2.68/1.68 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_266_UnI2,axiom,
% 2.68/1.68 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ C @ B )
% 2.68/1.68 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_267_UnI2,axiom,
% 2.68/1.68 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ C @ B )
% 2.68/1.68 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_268_UnI2,axiom,
% 2.68/1.68 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.68/1.68 ( ( member1967978193chanID @ C @ B )
% 2.68/1.68 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_269_UnI1,axiom,
% 2.68/1.68 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.68 ( ( member740727610specID @ C @ A )
% 2.68/1.68 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_270_UnI1,axiom,
% 2.68/1.68 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.68/1.68 ( ( member2138796287ecrets @ C @ A )
% 2.68/1.68 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_271_UnI1,axiom,
% 2.68/1.68 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.68/1.68 ( ( member_Secrecy_Keys @ C @ A )
% 2.68/1.68 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.68/1.68
% 2.68/1.68 thf(fact_272_UnI1,axiom,
% 2.68/1.68 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.68 ( ( member_Secrecy_KS @ C @ A )
% 2.68/1.69 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_273_UnI1,axiom,
% 2.68/1.69 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ C @ A )
% 2.68/1.69 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_274_UnE,axiom,
% 2.68/1.69 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.69 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 2.68/1.69 => ( ~ ( member740727610specID @ C @ A )
% 2.68/1.69 => ( member740727610specID @ C @ B ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_275_UnE,axiom,
% 2.68/1.69 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.68/1.69 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 2.68/1.69 => ( ~ ( member2138796287ecrets @ C @ A )
% 2.68/1.69 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_276_UnE,axiom,
% 2.68/1.69 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.68/1.69 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 2.68/1.69 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_277_UnE,axiom,
% 2.68/1.69 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.69 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ C @ A )
% 2.68/1.69 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_278_UnE,axiom,
% 2.68/1.69 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 2.68/1.69 => ( ~ ( member1967978193chanID @ C @ A )
% 2.68/1.69 => ( member1967978193chanID @ C @ B ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_279_KS_Oexhaust,axiom,
% 2.68/1.69 ! [Y3: secrecy_KS] :
% 2.68/1.69 ( ! [X12: secrecy_Keys] :
% 2.68/1.69 ( Y3
% 2.68/1.69 != ( secrecy_kKS @ X12 ) )
% 2.68/1.69 => ~ ! [X22: secrecy_Secrets] :
% 2.68/1.69 ( Y3
% 2.68/1.69 != ( secrecy_sKS @ X22 ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_280_KS_Oinduct,axiom,
% 2.68/1.69 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 2.68/1.69 ( ! [X4: secrecy_Keys] : ( P @ ( secrecy_kKS @ X4 ) )
% 2.68/1.69 => ( ! [X4: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X4 ) )
% 2.68/1.69 => ( P @ KS ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_281_KS_Odistinct_I1_J,axiom,
% 2.68/1.69 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.68/1.69 ( ( secrecy_kKS @ X1 )
% 2.68/1.69 != ( secrecy_sKS @ X2 ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_282_Expression_Odistinct_I1_J,axiom,
% 2.68/1.69 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.68/1.69 ( ( secrecy_kE @ X1 )
% 2.68/1.69 != ( secrecy_sE @ X2 ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_283_know_Osimps_I1_J,axiom,
% 2.68/1.69 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.68/1.69 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.68/1.69 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 2.68/1.69 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_284_insert__is__Un,axiom,
% 2.68/1.69 ( insert_Secrecy_KS
% 2.68/1.69 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_285_insert__is__Un,axiom,
% 2.68/1.69 ( insert1671894227specID
% 2.68/1.69 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_286_insert__is__Un,axiom,
% 2.68/1.69 ( insert751661162chanID
% 2.68/1.69 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_287_Un__singleton__iff,axiom,
% 2.68/1.69 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 2.68/1.69 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.68/1.69 = ( ( ( A = bot_bo1943466239ecy_KS )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.68/1.69 & ( B = bot_bo1943466239ecy_KS ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_288_Un__singleton__iff,axiom,
% 2.68/1.69 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 2.68/1.69 ( ( ( sup_su1712599557specID @ A @ B )
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.68/1.69 = ( ( ( A = bot_bo1785112429specID )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.68/1.69 & ( B = bot_bo1785112429specID ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_289_Un__singleton__iff,axiom,
% 2.68/1.69 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 2.68/1.69 ( ( ( sup_su370684444chanID @ A @ B )
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.68/1.69 = ( ( ( A = bot_bo443197316chanID )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.68/1.69 & ( B = bot_bo443197316chanID ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_290_singleton__Un__iff,axiom,
% 2.68/1.69 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.68/1.69 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 2.68/1.69 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.68/1.69 = ( ( ( A = bot_bo1943466239ecy_KS )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.68/1.69 & ( B = bot_bo1943466239ecy_KS ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_291_singleton__Un__iff,axiom,
% 2.68/1.69 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.68/1.69 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 2.68/1.69 = ( sup_su1712599557specID @ A @ B ) )
% 2.68/1.69 = ( ( ( A = bot_bo1785112429specID )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.68/1.69 & ( B = bot_bo1785112429specID ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_292_singleton__Un__iff,axiom,
% 2.68/1.69 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.68/1.69 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 2.68/1.69 = ( sup_su370684444chanID @ A @ B ) )
% 2.68/1.69 = ( ( ( A = bot_bo443197316chanID )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.68/1.69 & ( B = bot_bo443197316chanID ) )
% 2.68/1.69 | ( ( A
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.68/1.69 & ( B
% 2.68/1.69 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_293_LocalSecretsComposition__neg__loc__k,axiom,
% 2.68/1.69 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.68/1.69 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 2.68/1.69 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 2.68/1.69 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_294_LocalSecretsComposition__neg__k,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 2.68/1.69 ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.69 => ( ( correctCompositionKS @ PQ )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 2.68/1.69 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.68/1.69 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_295_know__composition__neg__ine__k,axiom,
% 2.68/1.69 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.69 ( ~ ( knowle945212990e_know @ P @ ( secrecy_kKS @ Key ) )
% 2.68/1.69 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_kKS @ Key ) )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correctCompositionIn @ PQ )
% 2.68/1.69 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_296_LocalSecretsComposition__ine1__k,axiom,
% 2.68/1.69 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.69 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.69 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.68/1.69 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_297_LocalSecretsComposition__ine2__k,axiom,
% 2.68/1.69 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.69 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.68/1.69 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_298_LocalSecretsComposition__neg1__k,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 2.68/1.69 ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.68/1.69 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 2.68/1.69 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_299_LocalSecretsComposition__exprChannel__k,axiom,
% 2.68/1.69 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.69 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.68/1.69 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.68/1.69 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 2.68/1.69 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_300_LocalSecretsComposition__neg,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.68/1.69 ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.69 => ( ( correctCompositionKS @ PQ )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.68/1.69 => ( ! [M4: secrecy_Keys] :
% 2.68/1.69 ( ( Ks
% 2.68/1.69 = ( secrecy_kKS @ M4 ) )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 2.68/1.69 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 2.68/1.69 => ( ! [M4: secrecy_Secrets] :
% 2.68/1.69 ( ( Ks
% 2.68/1.69 = ( secrecy_sKS @ M4 ) )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 2.68/1.69 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.68/1.69 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_301_LocalSecretsComposition__neg1,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.68/1.69 ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc965049635ionLoc @ PQ )
% 2.68/1.69 => ( ! [M4: secrecy_Keys] :
% 2.68/1.69 ( ( Ks
% 2.68/1.69 = ( secrecy_kKS @ M4 ) )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 2.68/1.69 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 2.68/1.69 => ( ! [M4: secrecy_Secrets] :
% 2.68/1.69 ( ( Ks
% 2.68/1.69 = ( secrecy_sKS @ M4 ) )
% 2.68/1.69 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 2.68/1.69 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 2.68/1.69 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 2.68/1.69 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_302_sup__bot__left,axiom,
% 2.68/1.69 ! [X: set_Secrecy_KS] :
% 2.68/1.69 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X )
% 2.68/1.69 = X ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_303_sup__bot__left,axiom,
% 2.68/1.69 ! [X: set_Secrecy_specID] :
% 2.68/1.69 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X )
% 2.68/1.69 = X ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_304_sup__bot__left,axiom,
% 2.68/1.69 ! [X: set_Secrecy_chanID] :
% 2.68/1.69 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X )
% 2.68/1.69 = X ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_305_sup__bot__right,axiom,
% 2.68/1.69 ! [X: set_Secrecy_KS] :
% 2.68/1.69 ( ( sup_su1301156759ecy_KS @ X @ bot_bo1943466239ecy_KS )
% 2.68/1.69 = X ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_306_sup__bot__right,axiom,
% 2.68/1.69 ! [X: set_Secrecy_specID] :
% 2.68/1.69 ( ( sup_su1712599557specID @ X @ bot_bo1785112429specID )
% 2.68/1.69 = X ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_307_sup__bot__right,axiom,
% 2.68/1.69 ! [X: set_Secrecy_chanID] :
% 2.68/1.69 ( ( sup_su370684444chanID @ X @ bot_bo443197316chanID )
% 2.68/1.69 = X ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_308_bot__eq__sup__iff,axiom,
% 2.68/1.69 ! [X: set_Secrecy_KS,Y3: set_Secrecy_KS] :
% 2.68/1.69 ( ( bot_bo1943466239ecy_KS
% 2.68/1.69 = ( sup_su1301156759ecy_KS @ X @ Y3 ) )
% 2.68/1.69 = ( ( X = bot_bo1943466239ecy_KS )
% 2.68/1.69 & ( Y3 = bot_bo1943466239ecy_KS ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_309_bot__eq__sup__iff,axiom,
% 2.68/1.69 ! [X: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 2.68/1.69 ( ( bot_bo1785112429specID
% 2.68/1.69 = ( sup_su1712599557specID @ X @ Y3 ) )
% 2.68/1.69 = ( ( X = bot_bo1785112429specID )
% 2.68/1.69 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_310_bot__eq__sup__iff,axiom,
% 2.68/1.69 ! [X: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.68/1.69 ( ( bot_bo443197316chanID
% 2.68/1.69 = ( sup_su370684444chanID @ X @ Y3 ) )
% 2.68/1.69 = ( ( X = bot_bo443197316chanID )
% 2.68/1.69 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_311_sup__eq__bot__iff,axiom,
% 2.68/1.69 ! [X: set_Secrecy_KS,Y3: set_Secrecy_KS] :
% 2.68/1.69 ( ( ( sup_su1301156759ecy_KS @ X @ Y3 )
% 2.68/1.69 = bot_bo1943466239ecy_KS )
% 2.68/1.69 = ( ( X = bot_bo1943466239ecy_KS )
% 2.68/1.69 & ( Y3 = bot_bo1943466239ecy_KS ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_312_sup__eq__bot__iff,axiom,
% 2.68/1.69 ! [X: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 2.68/1.69 ( ( ( sup_su1712599557specID @ X @ Y3 )
% 2.68/1.69 = bot_bo1785112429specID )
% 2.68/1.69 = ( ( X = bot_bo1785112429specID )
% 2.68/1.69 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_313_sup__eq__bot__iff,axiom,
% 2.68/1.69 ! [X: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.68/1.69 ( ( ( sup_su370684444chanID @ X @ Y3 )
% 2.68/1.69 = bot_bo443197316chanID )
% 2.68/1.69 = ( ( X = bot_bo443197316chanID )
% 2.68/1.69 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_314_sup__bot_Oright__neutral,axiom,
% 2.68/1.69 ! [A2: set_Secrecy_specID] :
% 2.68/1.69 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 2.68/1.69 = A2 ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_315_sup__bot_Oright__neutral,axiom,
% 2.68/1.69 ! [A2: set_Secrecy_chanID] :
% 2.68/1.69 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 2.68/1.69 = A2 ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_316_ineM__Un1,axiom,
% 2.68/1.69 ! [P: secrecy_specID,A: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 2.68/1.69 ( ( ineM @ P @ A @ E )
% 2.68/1.69 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_317_notSpecKeysSecretsExpr__def,axiom,
% 2.68/1.69 ( notSpe1586871396tsExpr
% 2.68/1.69 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 2.68/1.69 ( ! [X3: secrecy_Keys] :
% 2.68/1.69 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X3 ) @ E3 )
% 2.68/1.69 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X3 ) @ ( specKeysSecrets @ P2 ) ) )
% 2.68/1.69 & ! [Y5: secrecy_Secrets] :
% 2.68/1.69 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y5 ) @ E3 )
% 2.68/1.69 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y5 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_318_TBtheorem5a__empty,axiom,
% 2.68/1.69 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.69 ( ( ( eout @ P @ E )
% 2.68/1.69 | ( eout @ Q @ E ) )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( ( loc @ PQ )
% 2.68/1.69 = bot_bo443197316chanID )
% 2.68/1.69 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_319_correctCompositionKS__subcomp4,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 2.68/1.69 ( ( correctCompositionKS @ C3 )
% 2.68/1.69 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.68/1.69 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 2.68/1.69 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_320_TBtheorem2a,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.69 ( ( eout @ PQ @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( eout @ P @ E )
% 2.68/1.69 | ( eout @ Q @ E ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_321_correctCompositionKS__subcomp2,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 2.68/1.69 ( ( correctCompositionKS @ C3 )
% 2.68/1.69 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.68/1.69 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 2.68/1.69 => ? [X4: secrecy_specID] :
% 2.68/1.69 ( ( member740727610specID @ X4 @ ( subcomponents @ C3 ) )
% 2.68/1.69 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X4 ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_322_TBtheorem5a__notP1,axiom,
% 2.68/1.69 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.69 ( ( eout @ P @ E )
% 2.68/1.69 => ( ~ ( eout @ Q @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.69 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 2.68/1.69 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_323_TBtheorem5a__notP2,axiom,
% 2.68/1.69 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.68/1.69 ( ~ ( eout @ Q @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.68/1.69 => ( ! [X4: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.68/1.69 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_324_TBtheorem5a__notPQ,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.68/1.69 ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.68/1.69 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.68/1.69 => ( ! [X4: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.68/1.69 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ( ! [X4: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.68/1.69 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_325_out__exprChannelSingle__Set,axiom,
% 2.68/1.69 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.69 ( ( out_ex985543062Single @ P @ Ch @ E )
% 2.68/1.69 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_326_out__exprChannelSet__Single,axiom,
% 2.68/1.69 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.69 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 2.68/1.69 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_327_TBtheorem5b__notPQ,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 2.68/1.69 ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.68/1.69 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.68/1.69 => ( ( M2
% 2.68/1.69 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 2.68/1.69 => ( ! [X4: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.68/1.69 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ( ! [X4: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.68/1.69 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_328_eout__know__nonKS__s,axiom,
% 2.68/1.69 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 2.68/1.69 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 2.68/1.69 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 2.68/1.69 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 2.68/1.69 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_329_eoutKnowCorrect__L1s,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 2.68/1.69 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 2.68/1.69 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 2.68/1.69 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 2.68/1.69 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_330_eoutM__eout,axiom,
% 2.68/1.69 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.68/1.69 ( ( eoutM @ P @ M2 @ E )
% 2.68/1.69 => ( eout @ P @ E ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_331_not__eout__eoutM,axiom,
% 2.68/1.69 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 2.68/1.69 ( ~ ( eout @ P @ E )
% 2.68/1.69 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_332_TBtheorem2b,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.69 ( ( eoutM @ PQ @ M2 @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( eoutM @ P @ M2 @ E )
% 2.68/1.69 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_333_TBtheorem5b__notP2,axiom,
% 2.68/1.69 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.68/1.69 ( ~ ( eoutM @ Q @ M2 @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.68/1.69 => ( ! [X4: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.68/1.69 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_334_TBtheorem5b__notP1,axiom,
% 2.68/1.69 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.69 ( ( eoutM @ P @ M2 @ E )
% 2.68/1.69 => ( ~ ( eoutM @ Q @ M2 @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.69 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 2.68/1.69 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.68/1.69 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_335_eout__know__s,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 2.68/1.69 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 2.68/1.69 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 2.68/1.69 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 2.68/1.69 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_336_not__know__s__not__eout,axiom,
% 2.68/1.69 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 2.68/1.69 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 2.68/1.69 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.68/1.69 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 2.68/1.69 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_337_TBtheore54b__P,axiom,
% 2.68/1.69 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.69 ( ( eoutM @ P @ M2 @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 2.68/1.69 & ( exprChannel @ Ch2 @ E )
% 2.68/1.69 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.68/1.69 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 2.68/1.69 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_338_TBtheorem5b__PQ,axiom,
% 2.68/1.69 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.69 ( ( ( eoutM @ P @ M2 @ E )
% 2.68/1.69 | ( eoutM @ Q @ M2 @ E ) )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.69 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.68/1.69 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.68/1.69 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.68/1.69 & ( exprChannel @ Ch2 @ E )
% 2.68/1.69 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_339_TBtheorem45a__P,axiom,
% 2.68/1.69 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.68/1.69 ( ( eout @ P @ E )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.68/1.69 & ( exprChannel @ Ch2 @ E )
% 2.68/1.69 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_340_eout__def,axiom,
% 2.68/1.69 ( eout
% 2.68/1.69 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.68/1.69 ? [Ch3: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.68/1.69 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_341_eoutM__def,axiom,
% 2.68/1.69 ( eoutM
% 2.68/1.69 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.68/1.69 ? [Ch3: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.68/1.69 & ( member1967978193chanID @ Ch3 @ M3 )
% 2.68/1.69 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_342_out__exprChannelSet__def,axiom,
% 2.68/1.69 ( out_exprChannelSet
% 2.68/1.69 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.68/1.69 ( ! [X3: secrecy_chanID] :
% 2.68/1.69 ( ( member1967978193chanID @ X3 @ ChSet2 )
% 2.68/1.69 => ( ( member1967978193chanID @ X3 @ ( out @ SP ) )
% 2.68/1.69 & ( exprChannel @ X3 @ E2 ) ) )
% 2.68/1.69 & ! [X3: secrecy_chanID] :
% 2.68/1.69 ( ( ~ ( member1967978193chanID @ X3 @ ChSet2 )
% 2.68/1.69 & ( member1967978193chanID @ X3 @ ( out @ SP ) ) )
% 2.68/1.69 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_343_out__exprChannelSingle__def,axiom,
% 2.68/1.69 ( out_ex985543062Single
% 2.68/1.69 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 2.68/1.69 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.68/1.69 & ( exprChannel @ Ch3 @ E2 )
% 2.68/1.69 & ! [X3: secrecy_chanID,T: nat] :
% 2.68/1.69 ( ( ( member1967978193chanID @ X3 @ ( out @ SP ) )
% 2.68/1.69 & ( X3 != Ch3 ) )
% 2.68/1.69 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_344_correctCompositionOut__prop1,axiom,
% 2.68/1.69 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 2.68/1.69 ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 2.68/1.69 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 2.68/1.69 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_345_TBtheorem5a__PQ,axiom,
% 2.68/1.69 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.68/1.69 ( ( ( eout @ P @ E )
% 2.68/1.69 | ( eout @ Q @ E ) )
% 2.68/1.69 => ( ( ( subcomponents @ PQ )
% 2.68/1.69 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.68/1.69 => ( ( correc990227761ionOut @ PQ )
% 2.68/1.69 => ( ? [Ch2: secrecy_chanID] :
% 2.68/1.69 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.68/1.69 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.68/1.69 & ( exprChannel @ Ch2 @ E )
% 2.68/1.69 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.68/1.69 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_346_outStream__def,axiom,
% 2.68/1.69 ( outStream
% 2.68/1.69 = ( ^ [X3: secrecy_specID] :
% 2.68/1.69 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 2.68/1.69 @ ( out @ X3 ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_347_eout__know__k,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 2.68/1.69 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 2.68/1.69 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 2.68/1.69 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 2.68/1.69 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_348_correctCompositionKS__subcomp1,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 2.68/1.69 ( ( correctCompositionKS @ C3 )
% 2.68/1.69 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.68/1.69 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 2.68/1.69 => ? [X4: secrecy_specID] :
% 2.68/1.69 ( ( member740727610specID @ X4 @ ( subcomponents @ C3 ) )
% 2.68/1.69 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X4 ) ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_349_correctCompositionKS__subcomp3,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 2.68/1.69 ( ( correctCompositionKS @ C3 )
% 2.68/1.69 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.68/1.69 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 2.68/1.69 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_350_eout__know__nonKS__k,axiom,
% 2.68/1.69 ! [M: secrecy_Keys,A: secrecy_specID] :
% 2.68/1.69 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 2.68/1.69 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 2.68/1.69 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 2.68/1.69 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_351_eoutKnowCorrect__L1k,axiom,
% 2.68/1.69 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 2.68/1.69 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 2.68/1.69 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 2.68/1.69 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 2.68/1.69 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_352_not__know__k__not__eout,axiom,
% 2.68/1.69 ! [M: secrecy_Keys,A: secrecy_specID] :
% 2.68/1.69 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 2.68/1.69 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.68/1.69 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 2.68/1.69 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_353_adv__not__know2,axiom,
% 2.68/1.69 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 2.68/1.69 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 2.68/1.69 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.68/1.69 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(fact_354_adv__not__know1,axiom,
% 2.68/1.69 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Keys] :
% 2.68/1.69 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 2.68/1.69 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.68/1.69 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 2.68/1.69
% 2.68/1.69 thf(conj_0,conjecture,
% 2.68/1.69 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ) ).
% 2.68/1.69 ------------------------
% 2.81/1.72 % (13720)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/183Mi)
% 2.81/1.72 % (13726)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/18Mi)
% 2.81/1.73 % (13724)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_13473 for (2999ds/2Mi)
% 2.81/1.73 % (13723)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/2Mi)
% 2.81/1.73 % (13724)Instruction limit reached!
% 2.81/1.73 % (13724)------------------------------
% 2.81/1.73 % (13724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.73 % (13724)Termination reason: Unknown
% 2.81/1.73 % (13724)Termination phase: shuffling
% 2.81/1.73
% 2.81/1.73 % (13724)Memory used [KB]: 1407
% 2.81/1.73 % (13724)Time elapsed: 0.003 s
% 2.81/1.73 % (13724)Instructions burned: 5 (million)
% 2.81/1.73 % (13724)------------------------------
% 2.81/1.73 % (13724)------------------------------
% 2.81/1.73 % (13723)Instruction limit reached!
% 2.81/1.73 % (13723)------------------------------
% 2.81/1.73 % (13723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.73 % (13723)Termination reason: Unknown
% 2.81/1.73 % (13723)Termination phase: shuffling
% 2.81/1.73
% 2.81/1.73 % (13723)Memory used [KB]: 1407
% 2.81/1.73 % (13723)Time elapsed: 0.003 s
% 2.81/1.73 % (13723)Instructions burned: 2 (million)
% 2.81/1.73 % (13723)------------------------------
% 2.81/1.73 % (13723)------------------------------
% 2.81/1.73 % (13726)Instruction limit reached!
% 2.81/1.73 % (13726)------------------------------
% 2.81/1.73 % (13726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.73 % (13726)Termination reason: Unknown
% 2.81/1.73 % (13726)Termination phase: shuffling
% 2.81/1.73
% 2.81/1.73 % (13726)Memory used [KB]: 1791
% 2.81/1.73 % (13726)Time elapsed: 0.008 s
% 2.81/1.73 % (13726)Instructions burned: 20 (million)
% 2.81/1.73 % (13726)------------------------------
% 2.81/1.73 % (13726)------------------------------
% 2.81/1.73 % (13721)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_13473 for (2999ds/4Mi)
% 2.81/1.73 % (13722)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_13473 for (2999ds/27Mi)
% 2.81/1.73 % (13725)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_13473 for (2999ds/275Mi)
% 2.81/1.74 % (13721)Instruction limit reached!
% 2.81/1.74 % (13721)------------------------------
% 2.81/1.74 % (13721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.74 % (13721)Termination reason: Unknown
% 2.81/1.74 % (13721)Termination phase: shuffling
% 2.81/1.74
% 2.81/1.74 % (13721)Memory used [KB]: 1407
% 2.81/1.74 % (13721)Time elapsed: 0.005 s
% 2.81/1.74 % (13721)Instructions burned: 5 (million)
% 2.81/1.74 % (13721)------------------------------
% 2.81/1.74 % (13721)------------------------------
% 2.81/1.74 % (13731)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/3Mi)
% 2.81/1.74 % (13731)Instruction limit reached!
% 2.81/1.74 % (13731)------------------------------
% 2.81/1.74 % (13731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.74 % (13731)Termination reason: Unknown
% 2.81/1.74 % (13731)Termination phase: shuffling
% 2.81/1.74
% 2.81/1.74 % (13731)Memory used [KB]: 1407
% 2.81/1.74 % (13731)Time elapsed: 0.003 s
% 2.81/1.74 % (13731)Instructions burned: 3 (million)
% 2.81/1.74 % (13731)------------------------------
% 2.81/1.74 % (13731)------------------------------
% 2.81/1.74 % (13734)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_13473 for (2999ds/15Mi)
% 2.81/1.74 % (13733)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_13473 for (2999ds/37Mi)
% 2.81/1.75 % (13734)Instruction limit reached!
% 2.81/1.75 % (13734)------------------------------
% 2.81/1.75 % (13734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.75 % (13734)Termination reason: Unknown
% 2.81/1.75 % (13734)Termination phase: shuffling
% 2.81/1.75
% 2.81/1.75 % (13734)Memory used [KB]: 1663
% 2.81/1.75 % (13734)Time elapsed: 0.006 s
% 2.81/1.75 % (13734)Instructions burned: 15 (million)
% 2.81/1.75 % (13734)------------------------------
% 2.81/1.75 % (13734)------------------------------
% 2.81/1.75 % (13722)Instruction limit reached!
% 2.81/1.75 % (13722)------------------------------
% 2.81/1.75 % (13722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.75 % (13722)Termination reason: Unknown
% 2.81/1.75 % (13722)Termination phase: shuffling
% 2.81/1.75
% 2.81/1.75 % (13722)Memory used [KB]: 1918
% 2.81/1.75 % (13722)Time elapsed: 0.019 s
% 2.81/1.75 % (13722)Instructions burned: 28 (million)
% 2.81/1.75 % (13722)------------------------------
% 2.81/1.75 % (13722)------------------------------
% 2.81/1.75 % (13738)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_13473 for (2999ds/1041Mi)
% 2.81/1.75 % (13736)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_13473 for (2999ds/3Mi)
% 2.81/1.75 % (13736)Instruction limit reached!
% 2.81/1.75 % (13736)------------------------------
% 2.81/1.75 % (13736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.75 % (13736)Termination reason: Unknown
% 2.81/1.75 % (13736)Termination phase: shuffling
% 2.81/1.75
% 2.81/1.75 % (13736)Memory used [KB]: 1407
% 2.81/1.75 % (13736)Time elapsed: 0.004 s
% 2.81/1.75 % (13736)Instructions burned: 3 (million)
% 2.81/1.75 % (13736)------------------------------
% 2.81/1.75 % (13736)------------------------------
% 2.81/1.75 % (13733)Instruction limit reached!
% 2.81/1.75 % (13733)------------------------------
% 2.81/1.75 % (13733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.75 % (13733)Termination reason: Unknown
% 2.81/1.75 % (13733)Termination phase: shuffling
% 2.81/1.75
% 2.81/1.75 % (13733)Memory used [KB]: 2174
% 2.81/1.75 % (13733)Time elapsed: 0.012 s
% 2.81/1.75 % (13733)Instructions burned: 37 (million)
% 2.81/1.75 % (13733)------------------------------
% 2.81/1.75 % (13733)------------------------------
% 2.81/1.76 % (13739)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/7Mi)
% 2.81/1.76 % (13739)Instruction limit reached!
% 2.81/1.76 % (13739)------------------------------
% 2.81/1.76 % (13739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.76 % (13739)Termination reason: Unknown
% 2.81/1.76 % (13739)Termination phase: shuffling
% 2.81/1.76
% 2.81/1.76 % (13739)Memory used [KB]: 1535
% 2.81/1.76 % (13739)Time elapsed: 0.004 s
% 2.81/1.76 % (13739)Instructions burned: 9 (million)
% 2.81/1.76 % (13739)------------------------------
% 2.81/1.76 % (13739)------------------------------
% 2.81/1.76 % (13745)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_13473 for (2999ds/3Mi)
% 2.81/1.77 % (13745)Instruction limit reached!
% 2.81/1.77 % (13745)------------------------------
% 2.81/1.77 % (13745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.77 % (13745)Termination reason: Unknown
% 2.81/1.77 % (13745)Termination phase: shuffling
% 2.81/1.77
% 2.81/1.77 % (13745)Memory used [KB]: 1407
% 2.81/1.77 % (13745)Time elapsed: 0.002 s
% 2.81/1.77 % (13745)Instructions burned: 3 (million)
% 2.81/1.77 % (13745)------------------------------
% 2.81/1.77 % (13745)------------------------------
% 2.81/1.77 % (13741)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/16Mi)
% 2.81/1.77 % (13747)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/7Mi)
% 2.81/1.77 % (13747)Instruction limit reached!
% 2.81/1.77 % (13747)------------------------------
% 2.81/1.77 % (13747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.77 % (13747)Termination reason: Unknown
% 2.81/1.77 % (13747)Termination phase: shuffling
% 2.81/1.77
% 2.81/1.77 % (13747)Memory used [KB]: 1535
% 2.81/1.77 % (13747)Time elapsed: 0.004 s
% 2.81/1.77 % (13747)Instructions burned: 9 (million)
% 2.81/1.77 % (13747)------------------------------
% 2.81/1.77 % (13747)------------------------------
% 2.81/1.77 % (13744)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_13473 for (2999ds/3Mi)
% 2.81/1.77 % (13741)Instruction limit reached!
% 2.81/1.77 % (13741)------------------------------
% 2.81/1.77 % (13741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.77 % (13741)Termination reason: Unknown
% 2.81/1.77 % (13725)Refutation not found, incomplete strategy
% 2.81/1.77 % (13725)------------------------------
% 2.81/1.77 % (13725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.77 % (13741)Termination phase: shuffling
% 2.81/1.77
% 2.81/1.77 % (13741)Memory used [KB]: 1791
% 2.81/1.77 % (13725)Termination reason: Refutation not found, incomplete strategy
% 2.81/1.77
% 2.81/1.77 % (13741)Time elapsed: 0.009 s
% 2.81/1.77
% 2.81/1.77 % (13741)Instructions burned: 17 (million)
% 2.81/1.77 % (13741)------------------------------
% 2.81/1.77 % (13741)------------------------------
% 2.81/1.77 % (13725)Memory used [KB]: 6652
% 2.81/1.77 % (13725)Time elapsed: 0.043 s
% 2.81/1.77 % (13725)Instructions burned: 68 (million)
% 2.81/1.77 % (13725)------------------------------
% 2.81/1.77 % (13725)------------------------------
% 2.81/1.77 % (13744)Instruction limit reached!
% 2.81/1.77 % (13744)------------------------------
% 2.81/1.77 % (13744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.77 % (13744)Termination reason: Unknown
% 2.81/1.77 % (13744)Termination phase: shuffling
% 2.81/1.77
% 2.81/1.77 % (13744)Memory used [KB]: 1407
% 2.81/1.77 % (13744)Time elapsed: 0.004 s
% 2.81/1.77 % (13744)Instructions burned: 3 (million)
% 2.81/1.77 % (13744)------------------------------
% 2.81/1.77 % (13744)------------------------------
% 2.81/1.77 % (13750)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/3Mi)
% 2.81/1.77 % (13720)Instruction limit reached!
% 2.81/1.77 % (13720)------------------------------
% 2.81/1.77 % (13720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.77 % (13720)Termination reason: Unknown
% 2.81/1.77 % (13720)Termination phase: Saturation
% 2.81/1.77
% 2.81/1.77 % (13720)Memory used [KB]: 7419
% 2.81/1.77 % (13720)Time elapsed: 0.052 s
% 2.81/1.77 % (13720)Instructions burned: 184 (million)
% 2.81/1.77 % (13720)------------------------------
% 2.81/1.77 % (13720)------------------------------
% 2.81/1.78 % (13750)Instruction limit reached!
% 2.81/1.78 % (13750)------------------------------
% 2.81/1.78 % (13750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.78 % (13750)Termination reason: Unknown
% 2.81/1.78 % (13750)Termination phase: shuffling
% 2.81/1.78
% 2.81/1.78 % (13750)Memory used [KB]: 1535
% 2.81/1.78 % (13750)Time elapsed: 0.003 s
% 2.81/1.78 % (13750)Instructions burned: 6 (million)
% 2.81/1.78 % (13750)------------------------------
% 2.81/1.78 % (13750)------------------------------
% 2.81/1.78 % (13751)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/4Mi)
% 2.81/1.78 % (13751)Instruction limit reached!
% 2.81/1.78 % (13751)------------------------------
% 2.81/1.78 % (13751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.78 % (13751)Termination reason: Unknown
% 2.81/1.78 % (13751)Termination phase: shuffling
% 2.81/1.78
% 2.81/1.78 % (13751)Memory used [KB]: 1535
% 2.81/1.78 % (13751)Time elapsed: 0.003 s
% 2.81/1.78 % (13751)Instructions burned: 6 (million)
% 2.81/1.78 % (13751)------------------------------
% 2.81/1.78 % (13751)------------------------------
% 2.81/1.78 % (13757)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_13473 for (2999ds/902Mi)
% 2.81/1.79 % (13759)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_13473 for (2999ds/21Mi)
% 2.81/1.79 % (13755)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/710Mi)
% 2.81/1.79 % (13762)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/5Mi)
% 2.81/1.79 % (13754)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/18Mi)
% 2.81/1.79 % (13756)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/6Mi)
% 2.81/1.79 % (13759)Instruction limit reached!
% 2.81/1.79 % (13759)------------------------------
% 2.81/1.79 % (13759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.79 % (13759)Termination reason: Unknown
% 2.81/1.79 % (13759)Termination phase: shuffling
% 2.81/1.79
% 2.81/1.79 % (13759)Memory used [KB]: 1791
% 2.81/1.79 % (13759)Time elapsed: 0.008 s
% 2.81/1.79 % (13759)Instructions burned: 21 (million)
% 2.81/1.79 % (13759)------------------------------
% 2.81/1.79 % (13759)------------------------------
% 2.81/1.79 % (13762)Instruction limit reached!
% 2.81/1.79 % (13762)------------------------------
% 2.81/1.79 % (13762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.79 % (13762)Termination reason: Unknown
% 2.81/1.79 % (13762)Termination phase: shuffling
% 2.81/1.79
% 2.81/1.79 % (13762)Memory used [KB]: 1535
% 2.81/1.79 % (13762)Time elapsed: 0.003 s
% 2.81/1.79 % (13762)Instructions burned: 6 (million)
% 2.81/1.79 % (13762)------------------------------
% 2.81/1.79 % (13762)------------------------------
% 2.81/1.80 % (13756)Instruction limit reached!
% 2.81/1.80 % (13756)------------------------------
% 2.81/1.80 % (13756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.80 % (13756)Termination reason: Unknown
% 2.81/1.80 % (13756)Termination phase: shuffling
% 2.81/1.80
% 2.81/1.80 % (13756)Memory used [KB]: 1535
% 2.81/1.80 % (13756)Time elapsed: 0.006 s
% 2.81/1.80 % (13756)Instructions burned: 6 (million)
% 2.81/1.80 % (13756)------------------------------
% 2.81/1.80 % (13756)------------------------------
% 2.81/1.80 % (13766)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_13473 for (2999ds/6Mi)
% 2.81/1.80 % (13767)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13473 for (2999ds/377Mi)
% 2.81/1.80 % (13754)Instruction limit reached!
% 2.81/1.80 % (13754)------------------------------
% 2.81/1.80 % (13754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.80 % (13754)Termination reason: Unknown
% 2.81/1.80 % (13754)Termination phase: shuffling
% 2.81/1.80
% 2.81/1.80 % (13754)Memory used [KB]: 1791
% 2.81/1.80 % (13754)Time elapsed: 0.013 s
% 2.81/1.80 % (13754)Instructions burned: 18 (million)
% 2.81/1.80 % (13754)------------------------------
% 2.81/1.80 % (13754)------------------------------
% 2.81/1.80 % (13766)Instruction limit reached!
% 2.81/1.80 % (13766)------------------------------
% 2.81/1.80 % (13766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.80 % (13766)Termination reason: Unknown
% 2.81/1.80 % (13766)Termination phase: shuffling
% 2.81/1.80
% 2.81/1.80 % (13766)Memory used [KB]: 1535
% 2.81/1.80 % (13766)Time elapsed: 0.003 s
% 2.81/1.80 % (13766)Instructions burned: 7 (million)
% 2.81/1.80 % (13766)------------------------------
% 2.81/1.80 % (13766)------------------------------
% 2.81/1.81 % (13769)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_13473 for (2999ds/779Mi)
% 2.81/1.81 % (13774)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13473 for (2998ds/879Mi)
% 2.81/1.82 % (13755)Refutation not found, incomplete strategy
% 2.81/1.82 % (13755)------------------------------
% 2.81/1.82 % (13755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.82 % (13755)Termination reason: Refutation not found, incomplete strategy
% 2.81/1.82
% 2.81/1.82
% 2.81/1.82 % (13755)Memory used [KB]: 6524
% 2.81/1.82 % (13755)Time elapsed: 0.025 s
% 2.81/1.82 % (13755)Instructions burned: 57 (million)
% 2.81/1.82 % (13755)------------------------------
% 2.81/1.82 % (13755)------------------------------
% 2.81/1.82 % (13773)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_13473 for (2998ds/19Mi)
% 2.81/1.83 % (13776)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13473 for (2998ds/17Mi)
% 2.81/1.83 % (13773)Instruction limit reached!
% 2.81/1.83 % (13773)------------------------------
% 2.81/1.83 % (13773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.83 % (13773)Termination reason: Unknown
% 2.81/1.83 % (13773)Termination phase: shuffling
% 2.81/1.83
% 2.81/1.83 % (13773)Memory used [KB]: 1791
% 2.81/1.83 % (13773)Time elapsed: 0.010 s
% 2.81/1.83 % (13773)Instructions burned: 20 (million)
% 2.81/1.83 % (13773)------------------------------
% 2.81/1.83 % (13773)------------------------------
% 2.81/1.83 % (13776)Instruction limit reached!
% 2.81/1.83 % (13776)------------------------------
% 2.81/1.83 % (13776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.83 % (13776)Termination reason: Unknown
% 2.81/1.83 % (13776)Termination phase: shuffling
% 2.81/1.83
% 2.81/1.83 % (13776)Memory used [KB]: 1791
% 2.81/1.83 % (13776)Time elapsed: 0.008 s
% 2.81/1.83 % (13776)Instructions burned: 18 (million)
% 2.81/1.83 % (13776)------------------------------
% 2.81/1.83 % (13776)------------------------------
% 2.81/1.84 % (13757)Refutation not found, incomplete strategy
% 2.81/1.84 % (13757)------------------------------
% 2.81/1.84 % (13757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.84 % (13757)Termination reason: Refutation not found, incomplete strategy
% 2.81/1.84
% 2.81/1.84
% 2.81/1.84 % (13757)Memory used [KB]: 7803
% 2.81/1.84 % (13757)Time elapsed: 0.052 s
% 2.81/1.84 % (13757)Instructions burned: 176 (million)
% 2.81/1.84 % (13757)------------------------------
% 2.81/1.84 % (13757)------------------------------
% 2.81/1.84 % (13778)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13473 for (2998ds/3Mi)
% 2.81/1.84 % (13778)Instruction limit reached!
% 2.81/1.84 % (13778)------------------------------
% 2.81/1.84 % (13778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.84 % (13778)Termination reason: Unknown
% 2.81/1.84 % (13778)Termination phase: shuffling
% 2.81/1.84
% 2.81/1.84 % (13778)Memory used [KB]: 1407
% 2.81/1.84 % (13778)Time elapsed: 0.003 s
% 2.81/1.84 % (13778)Instructions burned: 4 (million)
% 2.81/1.84 % (13778)------------------------------
% 2.81/1.84 % (13778)------------------------------
% 2.81/1.84 % (13780)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13473 for (2998ds/30Mi)
% 2.81/1.85 % (13782)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13473 for (2998ds/127Mi)
% 2.81/1.85 % (13784)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13473 for (2998ds/100Mi)
% 2.81/1.85 % (13780)Instruction limit reached!
% 2.81/1.85 % (13780)------------------------------
% 2.81/1.85 % (13780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.85 % (13780)Termination reason: Unknown
% 2.81/1.85 % (13780)Termination phase: shuffling
% 2.81/1.85
% 2.81/1.85 % (13780)Memory used [KB]: 1918
% 2.81/1.85 % (13780)Time elapsed: 0.012 s
% 2.81/1.85 % (13780)Instructions burned: 30 (million)
% 2.81/1.85 % (13780)------------------------------
% 2.81/1.85 % (13780)------------------------------
% 2.81/1.86 % (13788)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_13473 for (2998ds/3Mi)
% 2.81/1.86 % (13788)Instruction limit reached!
% 2.81/1.86 % (13788)------------------------------
% 2.81/1.86 % (13788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.86 % (13788)Termination reason: Unknown
% 2.81/1.86 % (13788)Termination phase: shuffling
% 2.81/1.86
% 2.81/1.86 % (13788)Memory used [KB]: 1407
% 2.81/1.86 % (13788)Time elapsed: 0.003 s
% 2.81/1.86 % (13788)Instructions burned: 3 (million)
% 2.81/1.86 % (13788)------------------------------
% 2.81/1.86 % (13788)------------------------------
% 2.81/1.87 % (13789)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_13473 for (2998ds/20Mi)
% 2.81/1.88 % (13784)Instruction limit reached!
% 2.81/1.88 % (13784)------------------------------
% 2.81/1.88 % (13784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.88 % (13784)Termination reason: Unknown
% 2.81/1.88 % (13784)Termination phase: Preprocessing 3
% 2.81/1.88
% 2.81/1.88 % (13784)Memory used [KB]: 2686
% 2.81/1.88 % (13784)Time elapsed: 0.028 s
% 2.81/1.88 % (13784)Instructions burned: 102 (million)
% 2.81/1.88 % (13784)------------------------------
% 2.81/1.88 % (13784)------------------------------
% 2.81/1.88 % (13789)Instruction limit reached!
% 2.81/1.88 % (13789)------------------------------
% 2.81/1.88 % (13789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.88 % (13789)Termination reason: Unknown
% 2.81/1.88 % (13789)Termination phase: shuffling
% 2.81/1.88
% 2.81/1.88 % (13789)Memory used [KB]: 1791
% 2.81/1.88 % (13789)Time elapsed: 0.008 s
% 2.81/1.88 % (13789)Instructions burned: 20 (million)
% 2.81/1.88 % (13789)------------------------------
% 2.81/1.88 % (13789)------------------------------
% 2.81/1.88 % (13782)Instruction limit reached!
% 2.81/1.88 % (13782)------------------------------
% 2.81/1.88 % (13782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.88 % (13782)Termination reason: Unknown
% 2.81/1.88 % (13782)Termination phase: Property scanning
% 2.81/1.88
% 2.81/1.88 % (13782)Memory used [KB]: 2558
% 2.81/1.88 % (13782)Time elapsed: 0.037 s
% 2.81/1.88 % (13782)Instructions burned: 129 (million)
% 2.81/1.88 % (13782)------------------------------
% 2.81/1.88 % (13782)------------------------------
% 2.81/1.89 % (13793)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_13473 for (2998ds/86Mi)
% 2.81/1.89 % (13796)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_13473 for (2997ds/39Mi)
% 2.81/1.89 % (13795)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_13473 for (2997ds/107Mi)
% 2.81/1.90 % (13796)Instruction limit reached!
% 2.81/1.90 % (13796)------------------------------
% 2.81/1.90 % (13796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.90 % (13796)Termination reason: Unknown
% 2.81/1.90 % (13796)Termination phase: shuffling
% 2.81/1.90
% 2.81/1.90 % (13796)Memory used [KB]: 2174
% 2.81/1.90 % (13796)Time elapsed: 0.012 s
% 2.81/1.90 % (13796)Instructions burned: 40 (million)
% 2.81/1.90 % (13796)------------------------------
% 2.81/1.90 % (13796)------------------------------
% 2.81/1.91 % (13767)Instruction limit reached!
% 2.81/1.91 % (13767)------------------------------
% 2.81/1.91 % (13767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.91 % (13767)Termination reason: Unknown
% 2.81/1.91 % (13767)Termination phase: Saturation
% 2.81/1.91
% 2.81/1.91 % (13767)Memory used [KB]: 8315
% 2.81/1.91 % (13767)Time elapsed: 0.105 s
% 2.81/1.91 % (13767)Instructions burned: 377 (million)
% 2.81/1.91 % (13767)------------------------------
% 2.81/1.91 % (13767)------------------------------
% 2.81/1.91 % (13801)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_13473 for (2997ds/448Mi)
% 2.81/1.91 % (13793)Instruction limit reached!
% 2.81/1.91 % (13793)------------------------------
% 2.81/1.91 % (13793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.91 % (13793)Termination reason: Unknown
% 2.81/1.91 % (13793)Termination phase: Property scanning
% 2.81/1.91
% 2.81/1.91 % (13793)Memory used [KB]: 2430
% 2.81/1.91 % (13793)Time elapsed: 0.026 s
% 2.81/1.91 % (13793)Instructions burned: 87 (million)
% 2.81/1.91 % (13793)------------------------------
% 2.81/1.91 % (13793)------------------------------
% 2.81/1.92 % (13802)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_13473 for (2997ds/46Mi)
% 2.81/1.92 % (13803)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_13473 for (2997ds/98Mi)
% 2.81/1.92 % (13795)Instruction limit reached!
% 2.81/1.92 % (13795)------------------------------
% 2.81/1.92 % (13795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.92 % (13795)Termination reason: Unknown
% 2.81/1.92 % (13795)Termination phase: Property scanning
% 2.81/1.92
% 2.81/1.92 % (13795)Memory used [KB]: 2430
% 2.81/1.92 % (13795)Time elapsed: 0.035 s
% 2.81/1.92 % (13795)Instructions burned: 108 (million)
% 2.81/1.92 % (13795)------------------------------
% 2.81/1.92 % (13795)------------------------------
% 2.81/1.93 % (13802)Instruction limit reached!
% 2.81/1.93 % (13802)------------------------------
% 2.81/1.93 % (13802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.93 % (13802)Termination reason: Unknown
% 2.81/1.93 % (13802)Termination phase: Property scanning
% 2.81/1.93
% 2.81/1.93 % (13802)Memory used [KB]: 2046
% 2.81/1.93 % (13802)Time elapsed: 0.015 s
% 2.81/1.93 % (13802)Instructions burned: 46 (million)
% 2.81/1.93 % (13802)------------------------------
% 2.81/1.93 % (13802)------------------------------
% 2.81/1.93 % (13809)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_13473 for (2997ds/507Mi)
% 2.81/1.94 % (13811)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_13473 for (2997ds/149Mi)
% 2.81/1.95 % (13803)Instruction limit reached!
% 2.81/1.95 % (13803)------------------------------
% 2.81/1.95 % (13803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.95 % (13803)Termination reason: Unknown
% 2.81/1.95 % (13803)Termination phase: Property scanning
% 2.81/1.95
% 2.81/1.95 % (13803)Memory used [KB]: 2686
% 2.81/1.95 % (13803)Time elapsed: 0.027 s
% 2.81/1.95 % (13803)Instructions burned: 99 (million)
% 2.81/1.95 % (13803)------------------------------
% 2.81/1.95 % (13803)------------------------------
% 2.81/1.95 % (13774)First to succeed.
% 2.81/1.95 % (13774)Refutation found. Thanks to Tanya!
% 2.81/1.95 % SZS status Theorem for DTF2THF_13473
% 2.81/1.95 % SZS output start Proof for DTF2THF_13473
% 2.81/1.95 thf(type_def_5, type, secrecy_specID: $tType).
% 2.81/1.95 thf(type_def_6, type, set_Secrecy_KS: $tType).
% 2.81/1.95 thf(type_def_8, type, secrecy_KS: $tType).
% 2.81/1.95 thf(type_def_9, type, set_Secrecy_Keys: $tType).
% 2.81/1.95 thf(type_def_10, type, set_Secrecy_Secrets: $tType).
% 2.81/1.95 thf(type_def_11, type, set_Secrecy_chanID: $tType).
% 2.81/1.95 thf(type_def_12, type, set_Secrecy_specID: $tType).
% 2.81/1.95 thf(type_def_13, type, secrecy_Expression: $tType).
% 2.81/1.95 thf(type_def_14, type, list_S529945141ession: $tType).
% 2.81/1.95 thf(type_def_15, type, secrecy_Keys: $tType).
% 2.81/1.95 thf(type_def_16, type, secrecy_Secrets: $tType).
% 2.81/1.95 thf(type_def_17, type, secrecy_chanID: $tType).
% 2.81/1.95 thf(type_def_18, type, nat: $tType).
% 2.81/1.95 thf(func_def_0, type, list_S529945141ession: $tType).
% 2.81/1.95 thf(func_def_1, type, set_Secrecy_Secrets: $tType).
% 2.81/1.95 thf(func_def_2, type, set_Secrecy_specID: $tType).
% 2.81/1.95 thf(func_def_3, type, set_Secrecy_chanID: $tType).
% 2.81/1.95 thf(func_def_4, type, set_Secrecy_Keys: $tType).
% 2.81/1.95 thf(func_def_5, type, set_Secrecy_KS: $tType).
% 2.81/1.95 thf(func_def_6, type, secrecy_Expression: $tType).
% 2.81/1.95 thf(func_def_7, type, secrecy_Secrets: $tType).
% 2.81/1.95 thf(func_def_8, type, secrecy_specID: $tType).
% 2.81/1.95 thf(func_def_9, type, secrecy_chanID: $tType).
% 2.81/1.95 thf(func_def_10, type, secrecy_Keys: $tType).
% 2.81/1.95 thf(func_def_11, type, secrecy_KS: $tType).
% 2.81/1.95 thf(func_def_12, type, nat: $tType).
% 2.81/1.95 thf(func_def_13, type, localSecrets: secrecy_specID > set_Secrecy_KS).
% 2.81/1.95 thf(func_def_14, type, knowle233900195orrect: secrecy_specID > secrecy_KS > $o).
% 2.81/1.95 thf(func_def_15, type, knowle945212990e_know: secrecy_specID > secrecy_KS > $o).
% 2.81/1.95 thf(func_def_16, type, sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 2.81/1.95 thf(func_def_17, type, sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 2.81/1.95 thf(func_def_18, type, sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 2.81/1.95 thf(func_def_19, type, sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 2.81/1.95 thf(func_def_20, type, sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 2.81/1.95 thf(func_def_21, type, mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o).
% 2.81/1.95 thf(func_def_22, type, bot_bot_Secrecy_KS_o: secrecy_KS > $o).
% 2.81/1.95 thf(func_def_23, type, bot_bo2072920570Keys_o: secrecy_Keys > $o).
% 2.81/1.95 thf(func_def_24, type, bot_bo1909946299rets_o: secrecy_Secrets > $o).
% 2.81/1.95 thf(func_def_25, type, bot_bo1012329985anID_o: secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_26, type, bot_bo1767780696ecID_o: secrecy_specID > $o).
% 2.81/1.95 thf(func_def_27, type, bot_bo1943466239ecy_KS: set_Secrecy_KS).
% 2.81/1.95 thf(func_def_28, type, bot_bo701486667y_Keys: set_Secrecy_Keys).
% 2.81/1.95 thf(func_def_29, type, bot_bo1124690338ecrets: set_Secrecy_Secrets).
% 2.81/1.95 thf(func_def_30, type, bot_bo443197316chanID: set_Secrecy_chanID).
% 2.81/1.95 thf(func_def_31, type, bot_bo1785112429specID: set_Secrecy_specID).
% 2.81/1.95 thf(func_def_32, type, ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_33, type, correctCompositionKS: secrecy_specID > $o).
% 2.81/1.95 thf(func_def_34, type, eout: secrecy_specID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_35, type, eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_36, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_37, type, ine: secrecy_specID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_38, type, ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_39, type, ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_40, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_41, type, notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o).
% 2.81/1.95 thf(func_def_42, type, out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_43, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 2.81/1.95 thf(func_def_44, type, specKeys: secrecy_specID > set_Secrecy_Keys).
% 2.81/1.95 thf(func_def_45, type, specKeysSecrets: secrecy_specID > set_Secrecy_KS).
% 2.81/1.95 thf(func_def_46, type, specSecrets: secrecy_specID > set_Secrecy_Secrets).
% 2.81/1.95 thf(func_def_47, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 2.81/1.95 thf(func_def_48, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 2.81/1.95 thf(func_def_49, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 2.81/1.95 thf(func_def_50, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 2.81/1.95 thf(func_def_51, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 2.81/1.95 thf(func_def_52, type, collect_Secrecy_KS: (secrecy_KS > $o) > set_Secrecy_KS).
% 2.81/1.95 thf(func_def_53, type, collect_Secrecy_Keys: (secrecy_Keys > $o) > set_Secrecy_Keys).
% 2.81/1.95 thf(func_def_54, type, collec836099393ecrets: (secrecy_Secrets > $o) > set_Secrecy_Secrets).
% 2.81/1.95 thf(func_def_55, type, collec625564175chanID: (secrecy_chanID > $o) > set_Secrecy_chanID).
% 2.81/1.95 thf(func_def_56, type, collec1545797240specID: (secrecy_specID > $o) > set_Secrecy_specID).
% 2.81/1.95 thf(func_def_57, type, insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 2.81/1.95 thf(func_def_58, type, insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 2.81/1.95 thf(func_def_59, type, insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 2.81/1.95 thf(func_def_60, type, insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 2.81/1.95 thf(func_def_61, type, insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 2.81/1.95 thf(func_def_62, type, is_emp928984296chanID: set_Secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_63, type, is_emp1849217361specID: set_Secrecy_specID > $o).
% 2.81/1.95 thf(func_def_64, type, is_sin1442426433ecy_KS: set_Secrecy_KS > $o).
% 2.81/1.95 thf(func_def_65, type, is_sin1096471309y_Keys: set_Secrecy_Keys > $o).
% 2.81/1.95 thf(func_def_66, type, is_sin1002224330ecrets: set_Secrecy_Secrets > $o).
% 2.81/1.95 thf(func_def_67, type, is_sin581274182chanID: set_Secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_68, type, is_sin1501507247specID: set_Secrecy_specID > $o).
% 2.81/1.95 thf(func_def_69, type, the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID).
% 2.81/1.95 thf(func_def_70, type, the_el827131246specID: set_Secrecy_specID > secrecy_specID).
% 2.81/1.95 thf(func_def_71, type, correctCompositionIn: secrecy_specID > $o).
% 2.81/1.95 thf(func_def_72, type, correc965049635ionLoc: secrecy_specID > $o).
% 2.81/1.95 thf(func_def_73, type, correc990227761ionOut: secrecy_specID > $o).
% 2.81/1.95 thf(func_def_74, type, inStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_75, type, ins: secrecy_specID > set_Secrecy_chanID).
% 2.81/1.95 thf(func_def_76, type, loc: secrecy_specID > set_Secrecy_chanID).
% 2.81/1.95 thf(func_def_77, type, locStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_78, type, out: secrecy_specID > set_Secrecy_chanID).
% 2.81/1.95 thf(func_def_79, type, outStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_80, type, subcomponents: secrecy_specID > set_Secrecy_specID).
% 2.81/1.95 thf(func_def_81, type, member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o).
% 2.81/1.95 thf(func_def_82, type, member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o).
% 2.81/1.95 thf(func_def_83, type, member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o).
% 2.81/1.95 thf(func_def_84, type, member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o).
% 2.81/1.95 thf(func_def_85, type, member740727610specID: secrecy_specID > set_Secrecy_specID > $o).
% 2.81/1.95 thf(func_def_86, type, p: secrecy_specID).
% 2.81/1.95 thf(func_def_87, type, pq: secrecy_specID).
% 2.81/1.95 thf(func_def_88, type, q: secrecy_specID).
% 2.81/1.95 thf(func_def_89, type, m: secrecy_KS).
% 2.81/1.95 thf(func_def_90, type, secret: secrecy_Secrets).
% 2.81/1.95 thf(func_def_106, type, sK0: (secrecy_KS > $o) > secrecy_Keys).
% 2.81/1.95 thf(func_def_107, type, sK1: (secrecy_KS > $o) > secrecy_Secrets).
% 2.81/1.95 thf(func_def_108, type, sK2: secrecy_specID > secrecy_Keys > secrecy_chanID).
% 2.81/1.95 thf(func_def_109, type, sK3: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 2.81/1.95 thf(func_def_110, type, sK4: secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Keys).
% 2.81/1.95 thf(func_def_111, type, sK5: secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Secrets).
% 2.81/1.95 thf(func_def_112, type, sK6: secrecy_KS > secrecy_Keys).
% 2.81/1.95 thf(func_def_113, type, sK7: secrecy_KS > secrecy_Secrets).
% 2.81/1.95 thf(func_def_114, type, sK8: secrecy_specID > secrecy_Secrets > secrecy_chanID).
% 2.81/1.95 thf(func_def_115, type, sK9: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets).
% 2.81/1.95 thf(func_def_116, type, sK10: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys).
% 2.81/1.95 thf(func_def_117, type, sK11: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 2.81/1.95 thf(func_def_119, type, ph13: !>[X0: $tType]:(X0)).
% 2.81/1.95 thf(f1737,plain,(
% 2.81/1.95 $false),
% 2.81/1.95 inference(subsumption_resolution,[status(thm)],[f1736,f1136])).
% 2.81/1.95 thf(f1136,plain,(
% 2.81/1.95 ((correc965049635ionLoc @ pq) = $true)),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f382])).
% 2.81/1.95 thf(f382,plain,(
% 2.81/1.95 ((correc965049635ionLoc @ pq) = $true)),
% 2.81/1.95 inference(fool_elimination,[status(thm)],[f381])).
% 2.81/1.95 thf(f381,plain,(
% 2.81/1.95 (correc965049635ionLoc @ pq)),
% 2.81/1.95 inference(rectify,[status(thm)],[f1])).
% 2.81/1.95 thf(f1,axiom,(
% 2.81/1.95 (correc965049635ionLoc @ pq)),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_0_cCompLoc)).
% 2.81/1.95 thf(f1736,plain,(
% 2.81/1.95 ((correc965049635ionLoc @ pq) != $true)),
% 2.81/1.95 inference(subsumption_resolution,[status(thm)],[f1735,f1113])).
% 2.81/1.95 thf(f1113,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) != $true)),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f985])).
% 2.81/1.95 thf(f985,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) != $true)),
% 2.81/1.95 inference(flattening,[status(thm)],[f454])).
% 2.81/1.95 thf(f454,plain,(
% 2.81/1.95 ~((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 2.81/1.95 inference(fool_elimination,[status(thm)],[f453])).
% 2.81/1.95 thf(f453,plain,(
% 2.81/1.95 ~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q))),
% 2.81/1.95 inference(rectify,[status(thm)],[f5])).
% 2.81/1.95 thf(f5,axiom,(
% 2.81/1.95 ~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q))),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_4_sg2b)).
% 2.81/1.95 thf(f1735,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true) | ((correc965049635ionLoc @ pq) != $true)),
% 2.81/1.95 inference(subsumption_resolution,[status(thm)],[f1734,f1130])).
% 2.81/1.95 thf(f1130,plain,(
% 2.81/1.95 ((ine @ q @ (secrecy_sE @ secret)) != $true)),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f999])).
% 2.81/1.95 thf(f999,plain,(
% 2.81/1.95 ((ine @ q @ (secrecy_sE @ secret)) != $true)),
% 2.81/1.95 inference(flattening,[status(thm)],[f870])).
% 2.81/1.95 thf(f870,plain,(
% 2.81/1.95 ~((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 2.81/1.95 inference(fool_elimination,[status(thm)],[f869])).
% 2.81/1.95 thf(f869,plain,(
% 2.81/1.95 ~(ine @ q @ (secrecy_sE @ secret))),
% 2.81/1.95 inference(rectify,[status(thm)],[f3])).
% 2.81/1.95 thf(f3,axiom,(
% 2.81/1.95 ~(ine @ q @ (secrecy_sE @ secret))),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_2_sg2a)).
% 2.81/1.95 thf(f1734,plain,(
% 2.81/1.95 ((ine @ q @ (secrecy_sE @ secret)) = $true) | ((correc965049635ionLoc @ pq) != $true) | ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 2.81/1.95 inference(subsumption_resolution,[status(thm)],[f1733,f1086])).
% 2.81/1.95 thf(f1086,plain,(
% 2.81/1.95 ((ine @ p @ (secrecy_sE @ secret)) != $true)),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f1000])).
% 2.81/1.95 thf(f1000,plain,(
% 2.81/1.95 ((ine @ p @ (secrecy_sE @ secret)) != $true)),
% 2.81/1.95 inference(flattening,[status(thm)],[f856])).
% 2.81/1.95 thf(f856,plain,(
% 2.81/1.95 ~((ine @ p @ (secrecy_sE @ secret)) = $true)),
% 2.81/1.95 inference(fool_elimination,[status(thm)],[f855])).
% 2.81/1.95 thf(f855,plain,(
% 2.81/1.95 ~(ine @ p @ (secrecy_sE @ secret))),
% 2.81/1.95 inference(rectify,[status(thm)],[f2])).
% 2.81/1.95 thf(f2,axiom,(
% 2.81/1.95 ~(ine @ p @ (secrecy_sE @ secret))),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_1_sg1a)).
% 2.81/1.95 thf(f1733,plain,(
% 2.81/1.95 ((ine @ p @ (secrecy_sE @ secret)) = $true) | ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true) | ((correc965049635ionLoc @ pq) != $true) | ((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 2.81/1.95 inference(subsumption_resolution,[status(thm)],[f1732,f1085])).
% 2.81/1.95 thf(f1085,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) != $true)),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f984])).
% 2.81/1.95 thf(f984,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) != $true)),
% 2.81/1.95 inference(flattening,[status(thm)],[f497])).
% 2.81/1.95 thf(f497,plain,(
% 2.81/1.95 ~((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) = $true)),
% 2.81/1.95 inference(fool_elimination,[status(thm)],[f496])).
% 2.81/1.95 thf(f496,plain,(
% 2.81/1.95 ~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p))),
% 2.81/1.95 inference(rectify,[status(thm)],[f4])).
% 2.81/1.95 thf(f4,axiom,(
% 2.81/1.95 ~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p))),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_3_sg1b)).
% 2.81/1.95 thf(f1732,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) = $true) | ((ine @ p @ (secrecy_sE @ secret)) = $true) | ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true) | ((correc965049635ionLoc @ pq) != $true) | ((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 2.81/1.95 inference(trivial_inequality_removal,[status(thm)],[f1731])).
% 2.81/1.95 thf(f1731,plain,(
% 2.81/1.95 ((ine @ q @ (secrecy_sE @ secret)) = $true) | ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true) | ($true != $true) | ((ine @ p @ (secrecy_sE @ secret)) = $true) | ((subcomponents @ pq) != (subcomponents @ pq)) | ((correc965049635ionLoc @ pq) != $true) | ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) = $true)),
% 2.81/1.95 inference(superposition,[status(thm)],[f1255,f1084])).
% 2.81/1.95 thf(f1084,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq)) = $true)),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f965])).
% 2.81/1.95 thf(f965,plain,(
% 2.81/1.95 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq)) = $true)),
% 2.81/1.95 inference(flattening,[status(thm)],[f648])).
% 2.81/1.95 thf(f648,plain,(
% 2.81/1.95 ~~((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq)) = $true)),
% 2.81/1.95 inference(fool_elimination,[status(thm)],[f647])).
% 2.81/1.95 thf(f647,plain,(
% 2.81/1.95 ~~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq))),
% 2.81/1.95 inference(rectify,[status(thm)],[f357])).
% 2.81/1.95 thf(f357,negated_conjecture,(
% 2.81/1.95 ~~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq))),
% 2.81/1.95 inference(negated_conjecture,[status(cth)],[f356])).
% 2.81/1.95 thf(f356,conjecture,(
% 2.81/1.95 ~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq))),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',conj_0)).
% 2.81/1.95 thf(f1255,plain,(
% 2.81/1.95 ( ! [X0 : secrecy_specID,X1 : secrecy_Secrets] : (($true != (member_Secrecy_KS @ (secrecy_sKS @ X1) @ (localSecrets @ X0))) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X1) @ (localSecrets @ q))) | ((correc965049635ionLoc @ X0) != $true) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X1) @ (localSecrets @ p))) | ($true = (ine @ q @ (secrecy_sE @ X1))) | ($true = (ine @ p @ (secrecy_sE @ X1)))) )),
% 2.81/1.95 inference(superposition,[status(thm)],[f1101,f1135])).
% 2.81/1.95 thf(f1135,plain,(
% 2.81/1.95 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f6])).
% 2.81/1.95 thf(f6,axiom,(
% 2.81/1.95 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_5_subPQ)).
% 2.81/1.95 thf(f1101,plain,(
% 2.81/1.95 ( ! [X2 : secrecy_specID,X3 : secrecy_specID,X0 : secrecy_Secrets,X1 : secrecy_specID] : (((subcomponents @ X2) != (insert1671894227specID @ X1 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))) | ((correc965049635ionLoc @ X2) != $true) | ((ine @ X3 @ (secrecy_sE @ X0)) = $true) | ($true != (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X2))) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X3))) | ($true = (ine @ X1 @ (secrecy_sE @ X0)))) )),
% 2.81/1.95 inference(cnf_transformation,[status(thm)],[f1004])).
% 2.81/1.95 thf(f1004,plain,(
% 2.81/1.95 ! [X0 : secrecy_Secrets,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID] : (((ine @ X3 @ (secrecy_sE @ X0)) = $true) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))) | ($true != (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X2))) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X3))) | ($true = (ine @ X1 @ (secrecy_sE @ X0))) | ((correc965049635ionLoc @ X2) != $true) | ((subcomponents @ X2) != (insert1671894227specID @ X1 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))))),
% 2.81/1.95 inference(flattening,[status(thm)],[f1003])).
% 2.81/1.95 thf(f1003,plain,(
% 2.81/1.95 ! [X0 : secrecy_Secrets,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID] : ((((((($true = (ine @ X1 @ (secrecy_sE @ X0))) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X3)))) | ($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1)))) | ((ine @ X3 @ (secrecy_sE @ X0)) = $true)) | ((correc965049635ionLoc @ X2) != $true)) | ((subcomponents @ X2) != (insert1671894227specID @ X1 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID)))) | ($true != (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X2))))),
% 2.81/1.95 inference(ennf_transformation,[status(thm)],[f979])).
% 2.81/1.95 thf(f979,plain,(
% 2.81/1.95 ! [X0 : secrecy_Secrets,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID] : (($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X2))) => (((subcomponents @ X2) = (insert1671894227specID @ X1 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) => (((correc965049635ionLoc @ X2) = $true) => (((ine @ X3 @ (secrecy_sE @ X0)) != $true) => (($true != (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))) => (($true != (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X3))) => ($true = (ine @ X1 @ (secrecy_sE @ X0)))))))))),
% 2.81/1.95 inference(flattening,[status(thm)],[f630])).
% 2.81/1.95 thf(f630,plain,(
% 2.81/1.95 ! [X0 : secrecy_Secrets,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID] : (($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X2))) => (((subcomponents @ X2) = (insert1671894227specID @ X1 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) => (((correc965049635ionLoc @ X2) = $true) => (~((ine @ X3 @ (secrecy_sE @ X0)) = $true) => (~($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))) => (~($true = (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X3))) => ($true = (ine @ X1 @ (secrecy_sE @ X0)))))))))),
% 2.81/1.95 inference(fool_elimination,[status(thm)],[f629])).
% 2.81/1.95 thf(f629,plain,(
% 2.81/1.95 ! [X0 : secrecy_Secrets,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID] : ((member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X2)) => (((subcomponents @ X2) = (insert1671894227specID @ X1 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) => ((correc965049635ionLoc @ X2) => (~(ine @ X3 @ (secrecy_sE @ X0)) => (~(member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1)) => (~(member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X3)) => (ine @ X1 @ (secrecy_sE @ X0))))))))),
% 2.81/1.95 inference(rectify,[status(thm)],[f14])).
% 2.81/1.95 thf(f14,axiom,(
% 2.81/1.95 ! [X4 : secrecy_Secrets,X6 : secrecy_specID,X5 : secrecy_specID,X7 : secrecy_specID] : ((member_Secrecy_KS @ (secrecy_sKS @ X4) @ (localSecrets @ X5)) => (((subcomponents @ X5) = (insert1671894227specID @ X6 @ (insert1671894227specID @ X7 @ bot_bo1785112429specID))) => ((correc965049635ionLoc @ X5) => (~(ine @ X7 @ (secrecy_sE @ X4)) => (~(member_Secrecy_KS @ (secrecy_sKS @ X4) @ (localSecrets @ X6)) => (~(member_Secrecy_KS @ (secrecy_sKS @ X4) @ (localSecrets @ X7)) => (ine @ X6 @ (secrecy_sE @ X4))))))))),
% 2.81/1.95 file('/export/starexec/sandbox/tmp/tmp.jEeFmEA2B4/DTF2THF_13473.p',fact_13_LocalSecretsComposition__ine1__s)).
% 2.81/1.95 % SZS output end Proof for DTF2THF_13473
% 2.81/1.95 % (13774)------------------------------
% 2.81/1.95 % (13774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.95 % (13774)Termination reason: Refutation
% 2.81/1.95
% 2.81/1.95 % (13774)Memory used [KB]: 7164
% 2.81/1.95 % (13774)Time elapsed: 0.161 s
% 2.81/1.95 % (13774)Instructions burned: 442 (million)
% 2.81/1.95 % (13774)------------------------------
% 2.81/1.95 % (13774)------------------------------
% 2.81/1.95 % (13709)Success in time 0.272 s
%------------------------------------------------------------------------------